Daily Papers

The extrapolation capability of Large Language Models (LLMs) based on Rotary Position Embedding is currently a topic of considerable interest. The mainstream approach to addressing extrapolation with LLMs involves modifying RoPE by replacing 10000, the rotary base of theta_n={10000}^{-2n/d} in the original RoPE, with a larger value and providing longer fine-tuning text. In this work, we first observe that fine-tuning a RoPE-based LLM with either a smaller or larger base in pre-training context length could significantly enhance its extrapolation performance. After that, we propose \textit{Scaling Laws of RoPE-based Extrapolation}, a unified framework from the periodic perspective, to describe the relationship between the extrapolation performance and base value as well as tuning context length. In this process, we also explain the origin of the RoPE-based extrapolation issue by \textit{critical dimension for extrapolation}. Besides these observations and analyses, we achieve extrapolation up to 1 million context length within only 16K training length on LLaMA2 7B and 13B.

Extrapolation remains a grand challenge in deep neural networks across all application domains. We propose an operator learning method to solve time-dependent partial differential equations (PDEs) continuously and with extrapolation in time without any temporal discretization. The proposed method, named Diffusion-inspired Temporal Transformer Operator (DiTTO), is inspired by latent diffusion models and their conditioning mechanism, which we use to incorporate the temporal evolution of the PDE, in combination with elements from the transformer architecture to improve its capabilities. Upon training, DiTTO can make inferences in real-time. We demonstrate its extrapolation capability on a climate problem by estimating the temperature around the globe for several years, and also in modeling hypersonic flows around a double-cone. We propose different training strategies involving temporal-bundling and sub-sampling and demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals as well as zero-shot super-resolution in time.

Large Language Models (LLMs) often struggle to process and generate coherent context when the number of input tokens exceeds the pre-trained length. Recent advancements in long-context extension have significantly expanded the context window of LLMs but require expensive overhead to train the large-scale models with longer context. In this work, we propose Dimension-Wise Positional Embeddings Manipulation (DPE), a training-free framework to extrapolate the context window of LLMs by diving into RoPE's different hidden dimensions. Instead of manipulating all dimensions equally, DPE detects the effective length for every dimension and finds the key dimensions for context extension. We reuse the original position indices with their embeddings from the pre-trained model and manipulate the key dimensions' position indices to their most effective lengths. In this way, DPE adjusts the pre-trained models with minimal modifications while ensuring that each dimension reaches its optimal state for extrapolation. DPE significantly surpasses well-known baselines such as YaRN and Self-Extend. DPE enables Llama3-8k 8B to support context windows of 128k tokens without continual training and integrates seamlessly with Flash Attention 2. In addition to its impressive extrapolation capability, DPE also dramatically improves the models' performance within training length, such as Llama3.1 70B, by over 18 points on popular long-context benchmarks RULER. When compared with commercial models, Llama 3.1 70B with DPE even achieves better performance than GPT-4-128K.

Linear position interpolation helps pre-trained models using rotary position embeddings (RoPE) to extrapolate to longer sequence lengths. We propose using linear position interpolation to extend the extrapolation range of models using Attention with Linear Biases (ALiBi). We find position interpolation significantly improves extrapolation capability on upstream language modelling and downstream summarization and retrieval tasks.

Recent image diffusion transformers achieve high-fidelity generation, but struggle to generate images beyond these scales, suffering from content repetition and quality degradation. In this work, we present UltraImage, a principled framework that addresses both issues. Through frequency-wise analysis of positional embeddings, we identify that repetition arises from the periodicity of the dominant frequency, whose period aligns with the training resolution. We introduce a recursive dominant frequency correction to constrain it within a single period after extrapolation. Furthermore, we find that quality degradation stems from diluted attention and thus propose entropy-guided adaptive attention concentration, which assigns higher focus factors to sharpen local attention for fine detail and lower ones to global attention patterns to preserve structural consistency. Experiments show that UltraImage consistently outperforms prior methods on Qwen-Image and Flux (around 4K) across three generation scenarios, reducing repetition and improving visual fidelity. Moreover, UltraImage can generate images up to 6K*6K without low-resolution guidance from a training resolution of 1328p, demonstrating its extreme extrapolation capability. Project page is available at https://thu-ml.github.io/ultraimage.github.io/{https://thu-ml.github.io/ultraimage.github.io/}.

The ability of Large Language Models (LLMs) to process and generate coherent text is markedly weakened when the number of input tokens exceeds their pretraining length. Given the expensive overhead of finetuning large-scale models with longer sequences, we propose Dual Chunk Attention (DCA), which enables Llama2 70B to support context windows of more than 100k tokens without continual training. By decomposing the attention computation for long sequences into chunk-based modules, DCA manages to effectively capture the relative positional information of tokens within the same chunk (Intra-Chunk) and across distinct chunks (Inter-Chunk), as well as integrates seamlessly with Flash Attention. In addition to its impressive extrapolation capability, DCA achieves performance on practical long-context tasks that is comparable to or even better than that of finetuned models. When compared with proprietary models, our training-free 70B model attains 94% of the performance of gpt-3.5-16k, indicating it is a viable open-source alternative. All code and data used in this work are released at https://github.com/HKUNLP/ChunkLlama.

Transformer and its variants are fundamental neural architectures in deep learning. Recent works show that learning attention in the Fourier space can improve the long sequence learning capability of Transformers. We argue that wavelet transform shall be a better choice because it captures both position and frequency information with linear time complexity. Therefore, in this paper, we systematically study the synergy between wavelet transform and Transformers. We propose Wavelet Space Attention (WavSpA) that facilitates attention learning in a learnable wavelet coefficient space which replaces the attention in Transformers by (1) applying forward wavelet transform to project the input sequences to multi-resolution bases, (2) conducting attention learning in the wavelet coefficient space, and (3) reconstructing the representation in input space via backward wavelet transform. Extensive experiments on the Long Range Arena demonstrate that learning attention in the wavelet space using either fixed or adaptive wavelets can consistently improve Transformer's performance and also significantly outperform learning in Fourier space. We further show our method can enhance Transformer's reasoning extrapolation capability over distance on the LEGO chain-of-reasoning task.

To tackle long-context reasoning tasks without the quadratic complexity of standard attention mechanisms, approaches based on agent memory have emerged, which typically maintain a dynamically updated memory when linearly processing document chunks. To mitigate the potential loss of latent evidence in this memorize-while-reading paradigm, recent works have integrated retrieval modules that allow agents to recall information previously discarded during memory overwriting. However, retrieval-based recall suffers from both evidence loss during memory formation and interference induced by invalid queries. To overcome these limitations, we propose MemReread. Built upon streaming reading, MemReread circumvents intermediate retrieval. It triggers question decomposition and rereading when the final memory is insufficient, enabling the recovery of indirect facts that were prematurely discarded. This design supports non-linear reasoning while preserving the inherent logical flow of document comprehension. To further enhance practicality, we introduce a reinforcement learning framework that enhances length extrapolation capability while dynamically determining the number of rereading passes based on task complexity, thereby flexibly controlling computational overhead. Extensive experiments demonstrate that MemReread consistently outperforms baseline frameworks on long-context reasoning tasks, while maintaining linear time complexity with respect to context length.

The tradeoff between precision and performance in molecular simulations can nowadays be addressed by machine-learned force fields (MLFF), which combine ab initio accuracy with force field numerical efficiency. Different from conventional force fields however, incorporating relevant electronic degrees of freedom into MLFFs becomes important. Here, we implement an equivariant transformer that embeds molecular net charge and spin state without additional neural network parameters. The model trained on a singlet/triplet non-correlated CH2 dataset can identify different spin states and shows state-of-the-art extrapolation capability. Therein, self-attention sensibly captures non-local effects, which, as we show, can be finely tuned over the network hyper-parameters. We indeed found that Softmax activation functions utilised in the self-attention mechanism of graph networks outperformed ReLU-like functions in prediction accuracy. Increasing the attention temperature from τ= d to 2d further improved the extrapolation capability, indicating a weighty role of nonlocality. Additionally, a weight initialisation method was purposed that sensibly accelerated the training process.

Self-supervised training of language models (LMs) has seen great success for protein sequences in learning meaningful representations and for generative drug design. Most protein LMs are based on the Transformer architecture trained on individual proteins with short context lengths. Such protein LMs cannot extrapolate to longer proteins and protein complexes well. They also fail to account for the underlying biological mechanisms carried out by biomolecular interactions and dynamics i.e., proteins often interact with other proteins, molecules, and pathways in complex biological systems. In this work, we propose LC-PLM based on an alternative protein LM architecture, BiMamba-S, built off selective structured state-space models, to learn high-quality universal protein representations at the amino acid token level using masked language modeling. We also introduce its graph-contextual variant, LC-PLM-G, which contextualizes protein-protein interaction (PPI) graphs for a second stage of training. LC-PLM demonstrates favorable neural scaling laws, better length extrapolation capability, and a 7% to 34% improvement on protein downstream tasks than Transformer-based ESM-2. LC-PLM-G further trained within the context of PPI graphs shows promising results on protein structure and function prediction tasks. Our study demonstrates the benefit of increasing the context size with computationally efficient LM architecture (e.g. structured state space models) in learning universal protein representations and incorporating molecular interaction context contained in biological graphs.

The quadratic complexity of full attention limits efficient long-context processing in large language models (LLMs). Sparse attention mitigates this cost by restricting each query to attend to a subset of previous tokens; however, training-free approaches often lead to severe performance degradation. Native sparse-attention methods (e.g., NSA, MoBA) alleviate this issue, yet exhibit a critical paradox: they produce lower attention sparsity than full-attention models, despite aiming to approximate full attention, which may constrain their effectiveness. We attribute this paradox to gradient update deficiency: low-ranked key-value pairs excluded during sparse training receive neither forward contribution nor backward gradients, and thus never learn proper suppression. To overcome this limitation, we propose SSA (Sparse Sparse Attention), a unified training framework that considers both sparse and full attention and enforces bidirectional alignment at every layer. This design preserves gradient flow to all tokens while explicitly encouraging sparse-attention outputs to align with their full-attention counterparts, thereby promoting stronger sparsity. As a result, SSA achieves state-of-the-art performance under both sparse and full attention inference across multiple commonsense benchmarks. Furthermore, SSA enables models to adapt smoothly to varying sparsity budgets; performance improves consistently as more tokens are allowed to attend, supporting flexible compute-performance trade-offs at inference time. Finally, we show that native sparse-attention training surprisingly improves long-context extrapolation by mitigating the over-allocation of attention values in sink areas, with SSA demonstrating the strongest extrapolation capability.

An ideal length-extrapolatable Transformer language model can handle sequences longer than the training length without any fine-tuning. Such long-context utilization capability relies heavily on a flexible positional embedding design. Upon investigating the flexibility of existing large pre-trained Transformer language models, we find that the T5 family deserves a closer look, as its positional embeddings capture rich and flexible attention patterns. However, T5 suffers from the dispersed attention issue: the longer the input sequence, the flatter the attention distribution. To alleviate the issue, we propose two attention alignment strategies via temperature scaling. Our findings show improvement on the long-context utilization capability of T5 on language modeling, retrieval, multi-document question answering, and code completion tasks without any fine-tuning. This suggests that a flexible positional embedding design and attention alignment can go a long way toward Transformer length extrapolation.

With the development of large language models (LLMs), the ability to handle longer contexts has become a key capability for Web applications such as cross-document understanding and LLM-powered search systems. However, this progress faces two major challenges: performance degradation due to sequence lengths out-of-distribution, and excessively long inference times caused by the quadratic computational complexity of attention. These issues hinder the application of LLMs in long-context scenarios. In this paper, we propose Dynamic Token-Level KV Cache Selection (TokenSelect), a model-agnostic, training-free method for efficient and accurate long-context inference. TokenSelect builds upon the observation of non-contiguous attention sparsity, using Query-Key dot products to measure per-head KV Cache criticality at token-level. By per-head soft voting mechanism, TokenSelect selectively involves a small number of critical KV cache tokens in the attention calculation without sacrificing accuracy. To further accelerate TokenSelect, we designed the Selection Cache based on observations of consecutive Query similarity and implemented efficient dot product kernel, significantly reducing the overhead of token selection. A comprehensive evaluation of TokenSelect demonstrates up to 23.84x speedup in attention computation and up to 2.28x acceleration in end-to-end latency, while providing superior performance compared to state-of-the-art long-context inference methods.

Sora unveils the potential of scaling Diffusion Transformer for generating photorealistic images and videos at arbitrary resolutions, aspect ratios, and durations, yet it still lacks sufficient implementation details. In this technical report, we introduce the Lumina-T2X family - a series of Flow-based Large Diffusion Transformers (Flag-DiT) equipped with zero-initialized attention, as a unified framework designed to transform noise into images, videos, multi-view 3D objects, and audio clips conditioned on text instructions. By tokenizing the latent spatial-temporal space and incorporating learnable placeholders such as [nextline] and [nextframe] tokens, Lumina-T2X seamlessly unifies the representations of different modalities across various spatial-temporal resolutions. This unified approach enables training within a single framework for different modalities and allows for flexible generation of multimodal data at any resolution, aspect ratio, and length during inference. Advanced techniques like RoPE, RMSNorm, and flow matching enhance the stability, flexibility, and scalability of Flag-DiT, enabling models of Lumina-T2X to scale up to 7 billion parameters and extend the context window to 128K tokens. This is particularly beneficial for creating ultra-high-definition images with our Lumina-T2I model and long 720p videos with our Lumina-T2V model. Remarkably, Lumina-T2I, powered by a 5-billion-parameter Flag-DiT, requires only 35% of the training computational costs of a 600-million-parameter naive DiT. Our further comprehensive analysis underscores Lumina-T2X's preliminary capability in resolution extrapolation, high-resolution editing, generating consistent 3D views, and synthesizing videos with seamless transitions. We expect that the open-sourcing of Lumina-T2X will further foster creativity, transparency, and diversity in the generative AI community.

In this paper, we investigate the length-extension of state-space models (SSMs) in language modeling. Length extension involves training models on short sequences and testing them on longer ones. We show that state-space models trained with zero hidden states initialization have difficulty doing length extension. We explain this difficulty by pointing out the length extension is equivalent to polynomial extrapolation. Based on the theory, we propose a simple yet effective method - changing the hidden states initialization scheme - to improve the length extension. Moreover, our method shows that using long training sequence length is beneficial but not necessary to length extension. Changing the hidden state initialization enables the efficient training of long-memory model with a smaller training context length.

Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to interpolation between data points in their training corpora. In this paper, we consider the challenge of learning representations that support extrapolation. We introduce a novel visual analogy benchmark that allows the graded evaluation of extrapolation as a function of distance from the convex ___domain defined by the training data. We also introduce a simple technique, temporal context normalization, that encourages representations that emphasize the relations between objects. We find that this technique enables a significant improvement in the ability to extrapolate, considerably outperforming a number of competitive techniques.

In this work, we leverage the intrinsic segmentation of language sequences and design a new positional encoding method called Bilevel Positional Encoding (BiPE). For each position, our BiPE blends an intra-segment encoding and an inter-segment encoding. The intra-segment encoding identifies the locations within a segment and helps the model capture the semantic information therein via absolute positional encoding. The inter-segment encoding specifies the segment index, models the relationships between segments, and aims to improve extrapolation capabilities via relative positional encoding. Theoretical analysis shows this disentanglement of positional information makes learning more effective. The empirical results also show that our BiPE has superior length extrapolation capabilities across a wide range of tasks in diverse text modalities.

Modern large language models (LLMs) that rely on attention mechanisms are typically trained with fixed context lengths which enforce upper limits on the length of input sequences that they can handle at evaluation time. To use these models on sequences longer than the train-time context length, one might employ techniques from the growing family of context length extrapolation methods -- most of which focus on modifying the system of positional encodings used in the attention mechanism to indicate where tokens or activations are located in the input sequence. We conduct a wide survey of existing methods of context length extrapolation on a base LLaMA or LLaMA 2 model, and introduce some of our own design as well -- in particular, a new truncation strategy for modifying the basis for the position encoding. We test these methods using three new evaluation tasks (FreeFormQA, AlteredNumericQA, and LongChat-Lines) as well as perplexity, which we find to be less fine-grained as a measure of long context performance of LLMs. We release the three tasks publicly as datasets on HuggingFace. We discover that linear scaling is the best method for extending context length, and show that further gains can be achieved by using longer scales at evaluation time. We also discover promising extrapolation capabilities in the truncated basis. To support further research in this area, we release three new 13B parameter long-context models which we call Giraffe: 4k and 16k context models trained from base LLaMA-13B, and a 32k context model trained from base LLaMA2-13B. We also release the code to replicate our results.

Recent advances in video generative models have promoted rapid progress in controllable world models. However, maintaining fine-grained spatio-temporal consistency under long-horizon reasoning remains a key challenge. In this work, we move beyond explicit 3D memory and coarse frame-level implicit modeling, and propose a fine-grained, learnable, and scalable memory for consistent world generation. We first identify two fundamental limitations of naïve learnable memory architectures in long-horizon extrapolation, namely computational inefficiency and attention dispersion. Through a systematic analysis of attention dispersion, we propose DecMem, a decoupled memory architecture that employs Sparse Global Memory for efficient fine-grained access to global history and Anchored Local Memory for stable and high-quality extrapolation. Extensive experiments demonstrate that DecMem significantly outperforms current state-of-the-art methods. By ensuring precise and efficient long-term memory and achieving superior extrapolation capabilities, DecMem enables minute-level controllable long video generation with high fidelity and consistency.

The attention mechanism in a Transformer architecture matches key to query based on both content -- the what -- and position in a sequence -- the where. We present an analysis indicating that what and where are entangled in the popular RoPE rotary position embedding. This entanglement can impair performance particularly when decisions require independent matches on these two factors. We propose an improvement to RoPE, which we call Polar Coordinate Position Embeddings or PoPE, that eliminates the what-where confound. PoPE is far superior on a diagnostic task requiring indexing solely by position or by content. On autoregressive sequence modeling in music, genomic, and natural language domains, Transformers using PoPE as the positional encoding scheme outperform baselines using RoPE with respect to evaluation loss (perplexity) and downstream task performance. On language modeling, these gains persist across model scale, from 124M to 774M parameters. Crucially, PoPE shows strong zero-shot length extrapolation capabilities compared not only to RoPE but even a method designed for extrapolation, YaRN, which requires additional fine tuning and frequency interpolation.

Arbitrary-resolution image generation still remains a challenging task in AIGC, as it requires handling varying resolutions and aspect ratios while maintaining high visual quality. Existing transformer-based diffusion methods suffer from quadratic computation cost and limited resolution extrapolation capabilities, making them less effective for this task. In this paper, we propose FlowDCN, a purely convolution-based generative model with linear time and memory complexity, that can efficiently generate high-quality images at arbitrary resolutions. Equipped with a new design of learnable group-wise deformable convolution block, our FlowDCN yields higher flexibility and capability to handle different resolutions with a single model. FlowDCN achieves the state-of-the-art 4.30 sFID on 256times256 ImageNet Benchmark and comparable resolution extrapolation results, surpassing transformer-based counterparts in terms of convergence speed (only 1{5} images), visual quality, parameters (8% reduction) and FLOPs (20% reduction). We believe FlowDCN offers a promising solution to scalable and flexible image synthesis.

Since self-attention layers in Transformers are permutation invariant by design, positional encodings must be explicitly incorporated to enable spatial understanding. However, fixed-size lookup tables used in traditional learnable position embeddings (PEs) limit extrapolation capabilities beyond pre-trained sequence lengths. Expert-designed methods such as ALiBi and RoPE, mitigate this limitation but demand extensive modifications for adapting to new modalities, underscoring fundamental challenges in adaptability and scalability. In this work, we present SeqPE, a unified and fully learnable position encoding framework that represents each n-dimensional position index as a symbolic sequence and employs a lightweight sequential position encoder to learn their embeddings in an end-to-end manner. To regularize SeqPE's embedding space, we introduce two complementary objectives: a contrastive objective that aligns embedding distances with a predefined position-distance function, and a knowledge distillation loss that anchors out-of-distribution position embeddings to in-distribution teacher representations, further enhancing extrapolation performance. Experiments across language modeling, long-context question answering, and 2D image classification demonstrate that SeqPE not only surpasses strong baselines in perplexity, exact match (EM), and accuracy--particularly under context length extrapolation--but also enables seamless generalization to multi-dimensional inputs without requiring manual architectural redesign. We release our code, data, and checkpoints at https://github.com/ghrua/seqpe.

Sea ice is governed by highly complex, scale-invariant, and anisotropic processes that are challenging to represent in Earth system models. While advanced numerical models have improved our understanding of the sea-ice dynamics, their computational costs often limit their application in ensemble forecasting and climate simulations. Here, we introduce GenSIM, the first generative AI-based pan-Arctic model that predicts the evolution of all relevant key properties, including concentration, thickness, and drift, in a 12-hour window with improved accuracy over deterministic predictions and high computational efficiency, while remaining physically consistent. Trained on a long simulation from a state-of-the-art sea-ice--ocean system, GenSIM robustly reproduces statistics as observed in numerical models and observations, exhibiting brittle-like short-term dynamics while also depicting the long-term sea-ice decline. Driven solely by atmospheric forcings, we attribute GenSIM's emergent extrapolation capabilities to patterns that reflect the long-term impact of the ocean: it seemingly has learned an internal ocean emulator. This ability to infer slowly evolving climate-relevant dynamics from short-term predictions underlines the large potential of generative models to generalise for unseen climates and to encode hidden physics.

Talking head generation intends to produce vivid and realistic talking head videos from a single portrait and speech audio clip. Although significant progress has been made in diffusion-based talking head generation, almost all methods rely on autoregressive strategies, which suffer from limited context utilization beyond the current generation step, error accumulation, and slower generation speed. To address these challenges, we present DAWN (Dynamic frame Avatar With Non-autoregressive diffusion), a framework that enables all-at-once generation of dynamic-length video sequences. Specifically, it consists of two main components: (1) audio-driven holistic facial dynamics generation in the latent motion space, and (2) audio-driven head pose and blink generation. Extensive experiments demonstrate that our method generates authentic and vivid videos with precise lip motions, and natural pose/blink movements. Additionally, with a high generation speed, DAWN possesses strong extrapolation capabilities, ensuring the stable production of high-quality long videos. These results highlight the considerable promise and potential impact of DAWN in the field of talking head video generation. Furthermore, we hope that DAWN sparks further exploration of non-autoregressive approaches in diffusion models. Our code will be publicly at https://github.com/Hanbo-Cheng/DAWN-pytorch.

Training Large Language Models (LLMs) is prohibitively expensive, creating a critical scaling gap where insights from small-scale experiments often fail to transfer to resource-intensive production systems, thereby hindering efficient innovation. To bridge this, we introduce Farseer, a novel and refined scaling law offering enhanced predictive accuracy across scales. By systematically constructing a model loss surface L(N,D), Farseer achieves a significantly better fit to empirical data than prior laws (e.g., Chinchilla's law). Our methodology yields accurate, robust, and highly generalizable predictions, demonstrating excellent extrapolation capabilities, improving upon Chinchilla's law by reducing extrapolation error by 433\%. This allows for the reliable evaluation of competing training strategies across all (N,D) settings, enabling conclusions from small-scale ablation studies to be confidently extrapolated to predict large-scale performance. Furthermore, Farseer provides new insights into optimal compute allocation, better reflecting the nuanced demands of modern LLM training. To validate our approach, we trained an extensive suite of approximately 1,000 LLMs across diverse scales and configurations, consuming roughly 3 million NVIDIA H100 GPU hours. We are comprehensively open-sourcing all models, data, results, and logs at https://github.com/Farseer-Scaling-Law/Farseer to foster further research.

In the realm of large-scale language models, a significant challenge arises when extrapolating sequences beyond the maximum allowable length. This is because the model's position embedding mechanisms are limited to positions encountered during training, thus preventing effective representation of positions in longer sequences. We analyzed conventional position encoding methods for long contexts and found the following characteristics. (1) When the representation dimension is regarded as the time axis, Rotary Position Embedding (RoPE) can be interpreted as a restricted wavelet transform using Haar-like wavelets. However, because it uses only a fixed scale parameter, it does not fully exploit the advantages of wavelet transforms, which capture the fine movements of non-stationary signals using multiple scales (window sizes). This limitation could explain why RoPE performs poorly in extrapolation. (2) Previous research as well as our own analysis indicates that Attention with Linear Biases (ALiBi) functions similarly to windowed attention, using windows of varying sizes. However, it has limitations in capturing deep dependencies because it restricts the receptive field of the model. From these insights, we propose a new position representation method that captures multiple scales (i.e., window sizes) by leveraging wavelet transforms without limiting the model's attention field. Experimental results show that this new method improves the performance of the model in both short and long contexts. In particular, our method allows extrapolation of position information without limiting the model's attention field.

End-to-end reinforcement learning on images showed significant progress in the recent years. Data-based approach leverage data augmentation and ___domain randomization while representation learning methods use auxiliary losses to learn task-relevant features. Yet, reinforcement still struggles in visually diverse environments full of distractions and spurious noise. In this work, we tackle the problem of robust visual control at its core and present VIBR (View-Invariant Bellman Residuals), a method that combines multi-view training and invariant prediction to reduce out-of-distribution (OOD) generalization gap for RL based visuomotor control. Our model-free approach improve baselines performances without the need of additional representation learning objectives and with limited additional computational cost. We show that VIBR outperforms existing methods on complex visuo-motor control environment with high visual perturbation. Our approach achieves state-of the-art results on the Distracting Control Suite benchmark, a challenging benchmark still not solved by current methods, where we evaluate the robustness to a number of visual perturbators, as well as OOD generalization and extrapolation capabilities.

Nucleotide sequences constitute the fundamental genetic basis of biological systems, rendering viral genomic analysis critical for biomedical advancement. Despite progress in biological foundation models, specifically nucleotide foundation models (NFMs), the field lacks a unified standard for viral genomics to facilitate community development and enforce biosecurity constraints. To address this, we introduce ViroBench, the first comprehensive and large-scale benchmark specifically designed for NFMs in viral settings. ViroBench evaluates models across two critical dimensions: biological understanding and latent biosecurity risk, covering 18 diverse scenarios within 4 task types. Extensive evaluation of 66 NFMs across diverse architectures yields three critical conclusions. Firstly, NFMs exhibit a performance degradation in biological understanding under phylogenetic and temporal shifts, indicating weak extrapolation capabilities. Secondly, generation tasks reveal a decoupling between statistical likelihood and biological functional validity, posing latent biosecurity risks. Thirdly, controlled ablation studies reveal that taxonomic diversity in pretraining data outweighs parameter scale. Specifically, a lightweight baseline trained on diverse data achieves a 67.5% performance gain over its original model. Overall, ViroBench provides interpretable, diagnostic evaluations and a reproducible measurement framework for future research on viral nucleotide foundation models. The datasets and code are publicly available at https://github.com/QIANJINYDX/ViroBench.

Linear Recurrent Neural Networks (linear RNNs) have emerged as competitive alternatives to Transformers for sequence modeling, offering efficient training and linear-time inference. However, existing architectures face a fundamental trade-off between expressivity and efficiency, dictated by the structure of their state-transition matrices. Diagonal matrices, used in models such as Mamba, GLA, or mLSTM, yield fast runtime but have limited expressivity. To address this, recent architectures such as DeltaNet and RWKV-7 adopted a diagonal plus rank-1 structure, which allows simultaneous token and channel mixing, improving associative recall and, as recently shown, state-tracking when allowing negative eigenvalues in the state-transition matrices. Building on the interpretation of DeltaNet's recurrence as performing one step of online gradient descent per token on an associative recall loss, we introduce DeltaProduct, which instead takes multiple (n_h) steps per token. This naturally leads to diagonal plus rank-n_h state-transition matrices, formed as products of n_h generalized Householder transformations, providing a tunable mechanism to balance expressivity and efficiency. We provide a detailed theoretical characterization of the state-tracking capability of DeltaProduct in finite precision, showing how it improves by increasing n_h. Our extensive experiments demonstrate that DeltaProduct outperforms DeltaNet in both state-tracking and language modeling, while also showing significantly improved length extrapolation capabilities.

Lumina-T2X is a nascent family of Flow-based Large Diffusion Transformers that establishes a unified framework for transforming noise into various modalities, such as images and videos, conditioned on text instructions. Despite its promising capabilities, Lumina-T2X still encounters challenges including training instability, slow inference, and extrapolation artifacts. In this paper, we present Lumina-Next, an improved version of Lumina-T2X, showcasing stronger generation performance with increased training and inference efficiency. We begin with a comprehensive analysis of the Flag-DiT architecture and identify several suboptimal components, which we address by introducing the Next-DiT architecture with 3D RoPE and sandwich normalizations. To enable better resolution extrapolation, we thoroughly compare different context extrapolation methods applied to text-to-image generation with 3D RoPE, and propose Frequency- and Time-Aware Scaled RoPE tailored for diffusion transformers. Additionally, we introduced a sigmoid time discretization schedule to reduce sampling steps in solving the Flow ODE and the Context Drop method to merge redundant visual tokens for faster network evaluation, effectively boosting the overall sampling speed. Thanks to these improvements, Lumina-Next not only improves the quality and efficiency of basic text-to-image generation but also demonstrates superior resolution extrapolation capabilities and multilingual generation using decoder-based LLMs as the text encoder, all in a zero-shot manner. To further validate Lumina-Next as a versatile generative framework, we instantiate it on diverse tasks including visual recognition, multi-view, audio, music, and point cloud generation, showcasing strong performance across these domains. By releasing all codes and model weights, we aim to advance the development of next-generation generative AI capable of universal modeling.

Standard Neural Networks can learn mathematical operations, but they do not extrapolate. Extrapolation means that the model can apply to larger numbers, well beyond those observed during training. Recent architectures tackle arithmetic operations and can extrapolate; however, the equally important problem of quantitative reasoning remains unaddressed. In this work, we propose a novel architectural element, the Neural Status Register (NSR), for quantitative reasoning over numbers. Our NSR relaxes the discrete bit logic of physical status registers to continuous numbers and allows end-to-end learning with gradient descent. Experiments show that the NSR achieves solutions that extrapolate to numbers many orders of magnitude larger than those in the training set. We successfully train the NSR on number comparisons, piecewise discontinuous functions, counting in sequences, recurrently finding minimums, finding shortest paths in graphs, and comparing digits in images.

Since the introduction of the transformer model by Vaswani et al. (2017), a fundamental question has yet to be answered: how does a model achieve extrapolation at inference time for sequences that are longer than it saw during training? We first show that extrapolation can be enabled by simply changing the position representation method, though we find that current methods do not allow for efficient extrapolation. We therefore introduce a simpler and more efficient position method, Attention with Linear Biases (ALiBi). ALiBi does not add positional embeddings to word embeddings; instead, it biases query-key attention scores with a penalty that is proportional to their distance. We show that this method trains a 1.3 billion parameter model on input sequences of length 1024 that extrapolates to input sequences of length 2048, achieving the same perplexity as a sinusoidal position embedding model trained on inputs of length 2048 but training 11% faster and using 11% less memory. ALiBi's inductive bias towards recency also leads it to outperform multiple strong position methods on the WikiText-103 benchmark.

The notion of interpolation and extrapolation is fundamental in various fields from deep learning to function approximation. Interpolation occurs for a sample x whenever this sample falls inside or on the boundary of the given dataset's convex hull. Extrapolation occurs when x falls outside of that convex hull. One fundamental (mis)conception is that state-of-the-art algorithms work so well because of their ability to correctly interpolate training data. A second (mis)conception is that interpolation happens throughout tasks and datasets, in fact, many intuitions and theories rely on that assumption. We empirically and theoretically argue against those two points and demonstrate that on any high-dimensional (>100) dataset, interpolation almost surely never happens. Those results challenge the validity of our current interpolation/extrapolation definition as an indicator of generalization performances.

Large Language Models (LLMs) that can continually improve beyond their training budgets are able to solve increasingly difficult problems by adapting at test time, a property we refer to as extrapolation. However, standard reinforcement learning (RL) operates over fixed problem distributions and training budgets, which limits extrapolation amidst distribution shift at test time. To address this, we introduce RC, an iterative decoding algorithm that replaces standard autoregressive decoding during both training and inference. RC exploits an asymmetry between the response generation and summarization capabilities of LLMs to construct reasoning chains that consistently improve across iterations. Models trained to use RC can extrapolate and continually improve over reasoning horizons more than an order of magnitude longer than those seen during training. Empirically, training a 4B model with RC using a 16k-token training budget improves performance on HMMT 2025 from 40% to nearly 70% with 0.5m tokens at test time, outperforming both comparably sized models and many larger reasoning LLMs. Finally, we also show that models trained with RC can more effectively leverage existing scaffolds to further scale test-time performance, due to the improved summary-conditioned generation abilities learned through training.

The largest experiments in machine learning now require resources far beyond the budget of all but a few institutions. Fortunately, it has recently been shown that the results of these huge experiments can often be extrapolated from the results of a sequence of far smaller, cheaper experiments. In this work, we show that not only can the extrapolation be done based on the size of the model, but on the size of the problem as well. By conducting a sequence of experiments using AlphaZero and Hex, we show that the performance achievable with a fixed amount of compute degrades predictably as the game gets larger and harder. Along with our main result, we further show that the test-time and train-time compute available to an agent can be traded off while maintaining performance.

Learning curve extrapolation aims to predict model performance in later epochs of training, based on the performance in earlier epochs. In this work, we argue that, while the inherent uncertainty in the extrapolation of learning curves warrants a Bayesian approach, existing methods are (i) overly restrictive, and/or (ii) computationally expensive. We describe the first application of prior-data fitted neural networks (PFNs) in this context. A PFN is a transformer, pre-trained on data generated from a prior, to perform approximate Bayesian inference in a single forward pass. We propose LC-PFN, a PFN trained to extrapolate 10 million artificial right-censored learning curves generated from a parametric prior proposed in prior art using MCMC. We demonstrate that LC-PFN can approximate the posterior predictive distribution more accurately than MCMC, while being over 10 000 times faster. We also show that the same LC-PFN achieves competitive performance extrapolating a total of 20 000 real learning curves from four learning curve benchmarks (LCBench, NAS-Bench-201, Taskset, and PD1) that stem from training a wide range of model architectures (MLPs, CNNs, RNNs, and Transformers) on 53 different datasets with varying input modalities (tabular, image, text, and protein data). Finally, we investigate its potential in the context of model selection and find that a simple LC-PFN based predictive early stopping criterion obtains 2 - 6x speed-ups on 45 of these datasets, at virtually no overhead.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

Position modeling plays a critical role in Transformers. In this paper, we focus on length extrapolation, i.e., training on short texts while evaluating longer sequences. We define attention resolution as an indicator of extrapolation. Then we propose two designs to improve the above metric of Transformers. Specifically, we introduce a relative position embedding to explicitly maximize attention resolution. Moreover, we use blockwise causal attention during inference for better resolution. We evaluate different Transformer variants with language modeling. Experimental results show that our model achieves strong performance in both interpolation and extrapolation settings. The code will be available at https://aka.ms/LeX-Transformer.

We propose ExtraNeRF, a novel method for extrapolating the range of views handled by a Neural Radiance Field (NeRF). Our main idea is to leverage NeRFs to model scene-specific, fine-grained details, while capitalizing on diffusion models to extrapolate beyond our observed data. A key ingredient is to track visibility to determine what portions of the scene have not been observed, and focus on reconstructing those regions consistently with diffusion models. Our primary contributions include a visibility-aware diffusion-based inpainting module that is fine-tuned on the input imagery, yielding an initial NeRF with moderate quality (often blurry) inpainted regions, followed by a second diffusion model trained on the input imagery to consistently enhance, notably sharpen, the inpainted imagery from the first pass. We demonstrate high-quality results, extrapolating beyond a small number of (typically six or fewer) input views, effectively outpainting the NeRF as well as inpainting newly disoccluded regions inside the original viewing volume. We compare with related work both quantitatively and qualitatively and show significant gains over prior art.

Length extrapolation has attracted considerable attention recently since it allows transformers to be tested on longer sequences than those used in training. Previous research has shown that this property can be attained by using carefully designed Relative Positional Encodings (RPEs). While these methods perform well on a variety of corpora, the conditions for length extrapolation have yet to be investigated. This paper attempts to determine what types of RPEs allow for length extrapolation through a thorough mathematical and empirical analysis. We discover that a transformer is certain to possess this property as long as the series that corresponds to the RPE's exponential converges. Two practices are derived from the conditions and examined in language modeling tasks on a variety of corpora. As a bonus from the conditions, we derive a new Theoretical Receptive Field (TRF) to measure the receptive field of RPEs without taking any training steps. Extensive experiments are conducted on the Wikitext-103, Books, Github, and WikiBook datasets to demonstrate the viability of our discovered conditions. We also compare TRF to Empirical Receptive Field (ERF) across different models, showing consistently matched trends on the aforementioned datasets. The code is available at https://github.com/OpenNLPLab/Rpe.

We study the degree of reliability of extrapolation of complex electromagnetic permittivity functions based on their analyticity properties. Given two analytic functions, representing extrapolants of the same experimental data, we examine how much they can differ at an extrapolation point outside of the experimentally accessible frequency band. We give a sharp upper bound on the worst case extrapolation error, in terms of a solution of an integral equation of Fredholm type. We conjecture and give numerical evidence that this bound exhibits a power law precision deterioration as one moves further away from the frequency band containing measurement data.

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

Reinforcement learning with verifiable rewards (RLVR) has become a central component of large language model (LLM) post-training. Unlike supervised fine-tuning (SFT), RLVR lets an LLM generate multiple candidate solutions and reinforces those that lead to a verifiably correct final answer. However, in practice, RLVR often requires thousands of training steps to reach strong performance, incurring substantial computation largely attributed to prolonged exploration. In this work, we make a surprising observation: during RLVR, LLMs evolve in a strongly linear manner. Specifically, both model weights and model output log-probabilities exhibit strong linear correlations with RL training steps. This suggests that RLVR predominantly amplifies trends that emerge early in training, rather than continuously discovering new behaviors throughout the entire optimization trajectory. Motivated by this linearity, we investigate whether future model states can be predicted from intermediate checkpoints via extrapolation, avoiding continued expensive training. We show that Weight Extrapolation produces models with performance comparable to standard RL training while requiring significantly less computation. Moreover, Logits Extrapolation consistently outperforms continued RL training on all four benchmarks by extrapolating beyond the step range where RL training remains stable.

Assessing the capabilities and risks of frontier AI systems is a critical area of research, and recent work has shown that repeated sampling from models can dramatically increase both. For instance, repeated sampling has been shown to increase their capabilities, such as solving difficult math and coding problems, but it has also been shown to increase their potential for harm, such as being jailbroken. Such results raise a crucial question for both capability and safety forecasting: how can one accurately predict a model's behavior when scaled to a massive number of attempts, given a vastly smaller sampling budget? This question is directly relevant to model providers, who serve hundreds of millions of users daily, and to governmental regulators, who seek to prevent harms. To answer this questions, we make three contributions. First, we find that standard methods for fitting these laws suffer from statistical shortcomings that hinder predictive accuracy, especially in data-limited scenarios. Second, we remedy these shortcomings by introducing a robust estimation framework, which uses a beta-binomial distribution to generate more accurate predictions from limited data. Third, we propose a dynamic sampling strategy that allocates a greater budget to harder problems. Combined, these innovations enable more reliable prediction of rare risks and capabilities at a fraction of the computational cost.

The poor performance of transformers on arithmetic tasks seems to stem in large part from their inability to keep track of the exact position of each digit inside of a large span of digits. We mend this problem by adding an embedding to each digit that encodes its position relative to the start of the number. In addition to the boost these embeddings provide on their own, we show that this fix enables architectural modifications such as input injection and recurrent layers to improve performance even further. With positions resolved, we can study the logical extrapolation ability of transformers. Can they solve arithmetic problems that are larger and more complex than those in their training data? We find that training on only 20 digit numbers with a single GPU for one day, we can reach state-of-the-art performance, achieving up to 99% accuracy on 100 digit addition problems. Finally, we show that these gains in numeracy also unlock improvements on other multi-step reasoning tasks including sorting and multiplication.

We study the problem of extrapolative controlled generation, i.e., generating sequences with attribute values beyond the range seen in training. This task is of significant importance in automated design, especially drug discovery, where the goal is to design novel proteins that are better (e.g., more stable) than existing sequences. Thus, by definition, the target sequences and their attribute values are out of the training distribution, posing challenges to existing methods that aim to directly generate the target sequence. Instead, in this work, we propose Iterative Controlled Extrapolation (ICE) which iteratively makes local edits to a sequence to enable extrapolation. We train the model on synthetically generated sequence pairs that demonstrate small improvement in the attribute value. Results on one natural language task (sentiment analysis) and two protein engineering tasks (ACE2 stability and AAV fitness) show that ICE considerably outperforms state-of-the-art approaches despite its simplicity. Our code and models are available at: https://github.com/vishakhpk/iter-extrapolation.

Despite advances, video diffusion transformers still struggle to generalize beyond their training length, a challenge we term video length extrapolation. We identify two failure modes: model-specific periodic content repetition and a universal quality degradation. Prior works attempt to solve repetition via positional encodings, overlooking quality degradation and achieving only limited extrapolation. In this paper, we revisit this challenge from a more fundamental view: attention maps, which directly govern how context influences outputs. We identify that both failure modes arise from a unified cause: attention dispersion, where tokens beyond the training window dilute learned attention patterns. This leads to quality degradation and repetition emerges as a special case when this dispersion becomes structured into periodic attention patterns, induced by harmonic properties of positional encodings. Building on this insight, we propose UltraViCo, a training-free, plug-and-play method that suppresses attention for tokens beyond the training window via a constant decay factor. By jointly addressing both failure modes, we outperform a broad set of baselines largely across models and extrapolation ratios, pushing the extrapolation limit from 2x to 4x. Remarkably, it improves Dynamic Degree and Imaging Quality by 233% and 40.5% over the previous best method at 4x extrapolation. Furthermore, our method generalizes seamlessly to downstream tasks such as controllable video synthesis and editing.

The relationship between memorization and generalization in large language models (LLMs) remains an open area of research, with growing evidence that the two are deeply intertwined. In this work, we investigate this relationship by pre-training a series of capacity-limited Transformer models from scratch on two synthetic character-level tasks designed to separately probe generalization (via arithmetic extrapolation) and memorization (via factual recall). We observe a consistent trade-off: small models extrapolate to unseen arithmetic cases but fail to memorize facts, while larger models memorize but fail to extrapolate. An intermediate-capacity model exhibits a similar shift toward memorization. When trained on both tasks jointly, no model (regardless of size) succeeds at extrapolation. These findings suggest that pre-training may intrinsically favor one learning mode over the other. By isolating these dynamics in a controlled setting, our study offers insight into how model capacity shapes learning behavior and offers broader implications for the design and deployment of small language models.

Rectified Flow Transformers (RFTs) offer superior training and inference efficiency, making them likely the most viable direction for scaling up diffusion models. However, progress in generation resolution has been relatively slow due to data quality and training costs. Tuning-free resolution extrapolation presents an alternative, but current methods often reduce generative stability, limiting practical application. In this paper, we review existing resolution extrapolation methods and introduce the I-Max framework to maximize the resolution potential of Text-to-Image RFTs. I-Max features: (i) a novel Projected Flow strategy for stable extrapolation and (ii) an advanced inference toolkit for generalizing model knowledge to higher resolutions. Experiments with Lumina-Next-2K and Flux.1-dev demonstrate I-Max's ability to enhance stability in resolution extrapolation and show that it can bring image detail emergence and artifact correction, confirming the practical value of tuning-free resolution extrapolation.

For improving image composition and aesthetic quality, most existing methods modulate the captured images by striking out redundant content near the image borders. However, such image cropping methods are limited in the range of image views. Some methods have been suggested to extrapolate the images and predict cropping boxes from the extrapolated image. Nonetheless, the synthesized extrapolated regions may be included in the cropped image, making the image composition result not real and potentially with degraded image quality. In this paper, we circumvent this issue by presenting a joint framework for both unbounded recommendation of camera view and image composition (i.e., UNIC). In this way, the cropped image is a sub-image of the image acquired by the predicted camera view, and thus can be guaranteed to be real and consistent in image quality. Specifically, our framework takes the current camera preview frame as input and provides a recommendation for view adjustment, which contains operations unlimited by the image borders, such as zooming in or out and camera movement. To improve the prediction accuracy of view adjustment prediction, we further extend the field of view by feature extrapolation. After one or several times of view adjustments, our method converges and results in both a camera view and a bounding box showing the image composition recommendation. Extensive experiments are conducted on the datasets constructed upon existing image cropping datasets, showing the effectiveness of our UNIC in unbounded recommendation of camera view and image composition. The source code, dataset, and pretrained models is available at https://github.com/liuxiaoyu1104/UNIC.

We present Position Interpolation (PI) that extends the context window sizes of RoPE-based pretrained LLMs such as LLaMA models to up to 32768 with minimal fine-tuning (within 1000 steps), while demonstrating strong empirical results on various tasks that require long context, including passkey retrieval, language modeling, and long document summarization from LLaMA 7B to 65B. Meanwhile, the extended model by Position Interpolation preserve quality relatively well on tasks within its original context window. To achieve this goal, Position Interpolation linearly down-scales the input position indices to match the original context window size, rather than extrapolating beyond the trained context length which may lead to catastrophically high attention scores that completely ruin the self-attention mechanism. Our theoretical study shows that the upper bound of interpolation is at least sim 600 times smaller than that of extrapolation, further demonstrating its stability. Models extended via Position Interpolation retain its original architecture and can reuse most pre-existing optimization and infrastructure.

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These include theorem proving, solving quantitative mathematics problems, and reading/summarizing novels. In this paper, we run careful empirical studies exploring the length generalization capabilities of transformer-based language models. We first establish that naively finetuning transformers on length generalization tasks shows significant generalization deficiencies independent of model scale. We then show that combining pretrained large language models' in-context learning abilities with scratchpad prompting (asking the model to output solution steps before producing an answer) results in a dramatic improvement in length generalization. We run careful failure analyses on each of the learning modalities and identify common sources of mistakes that highlight opportunities in equipping language models with the ability to generalize to longer problems.

Photorealistic simulators are essential for the training and evaluation of vision-centric autonomous vehicles (AVs). At their core is Novel View Synthesis (NVS), a crucial capability that generates diverse unseen viewpoints to accommodate the broad and continuous pose distribution of AVs. Recent advances in radiance fields, such as 3D Gaussian Splatting, achieve photorealistic rendering at real-time speeds and have been widely used in modeling large-scale driving scenes. However, their performance is commonly evaluated using an interpolated setup with highly correlated training and test views. In contrast, extrapolation, where test views largely deviate from training views, remains underexplored, limiting progress in generalizable simulation technology. To address this gap, we leverage publicly available AV datasets with multiple traversals, multiple vehicles, and multiple cameras to build the first Extrapolated Urban View Synthesis (EUVS) benchmark. Meanwhile, we conduct quantitative and qualitative evaluations of state-of-the-art Gaussian Splatting methods across different difficulty levels. Our results show that Gaussian Splatting is prone to overfitting to training views. Besides, incorporating diffusion priors and improving geometry cannot fundamentally improve NVS under large view changes, highlighting the need for more robust approaches and large-scale training. We have released our data to help advance self-driving and urban robotics simulation technology.

Scene extrapolation -- the idea of generating novel views by flying into a given image -- is a promising, yet challenging task. For each predicted frame, a joint inpainting and 3D refinement problem has to be solved, which is ill posed and includes a high level of ambiguity. Moreover, training data for long-range scenes is difficult to obtain and usually lacks sufficient views to infer accurate camera poses. We introduce DiffDreamer, an unsupervised framework capable of synthesizing novel views depicting a long camera trajectory while training solely on internet-collected images of nature scenes. Utilizing the stochastic nature of the guided denoising steps, we train the diffusion models to refine projected RGBD images but condition the denoising steps on multiple past and future frames for inference. We demonstrate that image-conditioned diffusion models can effectively perform long-range scene extrapolation while preserving consistency significantly better than prior GAN-based methods. DiffDreamer is a powerful and efficient solution for scene extrapolation, producing impressive results despite limited supervision. Project page: https://primecai.github.io/diffdreamer.

Transformers' ability to generalize to longer sequences than they have been trained on, known as length extrapolation, degrades as sequence length increases. Most of Relative Positional Encoding (RPE) methods address this problem by either adding constant linear biases or learning general biases, lacking the ability to specialize for different sequences. In this work, inspired by ALiBi, we propose Context-aware Biases for Length Extrapolation (Cable), that learns token-specific biases for each head in decoder-based transformers. Cable learns adaptive, context-aware biases, overcoming the limitations of fixed patterns by adding dynamic biases specific to each token in the sequence. Results show that when tested on a sequence length of 1024, a GPT-3 Medium (334M parameters) with our positional encoding, trained on a sequence length of 512, achieves better perplexity (-0.65) than a similar network with sinusoidal positional encoding trained on a sequence length of 1024. This is achieved with 48% lower memory usage, and only 3.5% higher training time. Furthermore, our method notably improves the extrapolation ability of existing RPE methods on the Edu-FineWeb10B and WikiText-103 datasets. Code is available at: https://github.com/axiomlab/Cable

Large language models are moving from static text generators toward real-world decision-support systems, where forecasting is a composite capability that links information gathering, evidence integration, situational judgment, and action-oriented decision making. This capability is in broad demand across finance, policy, industry, and scientific research, yet its evaluation remains difficult: live benchmarks evaluate forecasts before answers exist, making them the cleanest way to measure forecasting ability, but they expire once events resolve; retrospective benchmarks are reproducible, but they cannot reliably distinguish genuine forecasting from facts a model may have already learned during pretraining. Prompting models to "pretend not to know" cannot replace a genuine knowledge boundary. We propose OracleProto, a reproducible framework for evaluating LLM native forecasting capability. OracleProto reconstructs resolved events into time-bounded forecasting samples by combining model-cutoff-aligned sample admission, tool-level temporal masking, content-level leakage detection, discrete answer normalization, and hierarchical scoring. Instantiated on a FutureX-Past-derived dataset with six contemporary LLMs, OracleProto distinguishes forecasting quality, sampling stability, and cost efficiency under controlled information boundaries, while reducing residual leakage to the 1% level, an order of magnitude below tool-only temporal filtering. OracleProto turns LLM forecasting from one-off evaluation into an auditable, reusable, and trainable dataset-level capability, providing a unified interface for fair cross-model comparison and a controlled signal source for downstream SFT and RL. Code and data are available at https://github.com/MaYiding/OracleProto and https://huggingface.co/datasets/MaYiding/OracleProto.

Recent advancements in differentiable rendering and 3D reasoning have driven exciting results in novel view synthesis from a single image. Despite realistic results, methods are limited to relatively small view change. In order to synthesize immersive scenes, models must also be able to extrapolate. We present an approach that fuses 3D reasoning with autoregressive modeling to outpaint large view changes in a 3D-consistent manner, enabling scene synthesis. We demonstrate considerable improvement in single image large-angle view synthesis results compared to a variety of methods and possible variants across simulated and real datasets. In addition, we show increased 3D consistency compared to alternative accumulation methods. Project website: https://crockwell.github.io/pixelsynth/

This paper shows that two commonly used evaluation metrics for generative models, the Fr\'echet Inception Distance (FID) and the Inception Score (IS), are biased -- the expected value of the score computed for a finite sample set is not the true value of the score. Worse, the paper shows that the bias term depends on the particular model being evaluated, so model A may get a better score than model B simply because model A's bias term is smaller. This effect cannot be fixed by evaluating at a fixed number of samples. This means all comparisons using FID or IS as currently computed are unreliable. We then show how to extrapolate the score to obtain an effectively bias-free estimate of scores computed with an infinite number of samples, which we term textrm{FID}_infty and textrm{IS}_infty. In turn, this effectively bias-free estimate requires good estimates of scores with a finite number of samples. We show that using Quasi-Monte Carlo integration notably improves estimates of FID and IS for finite sample sets. Our extrapolated scores are simple, drop-in replacements for the finite sample scores. Additionally, we show that using low discrepancy sequence in GAN training offers small improvements in the resulting generator.

Although the capabilities of large language models (LLMs) ideally scale up with increasing data and compute, they are inevitably constrained by limited resources in reality. Suppose we have a moderately trained LLM (e.g., trained to align with human preference) in hand, can we further exploit its potential and cheaply acquire a stronger model? In this paper, we propose a simple method called ExPO to boost LLMs' alignment with human preference. ExPO assumes that a medium-aligned model can be interpolated between a less-aligned (weaker) model, e.g., the initial SFT model, and a better-aligned (stronger) one, thereby directly obtaining this stronger model by extrapolating from the weights of the former two relatively weaker models. On the AlpacaEval 2.0 benchmark, we show that ExPO pushes models trained with less preference data (e.g., 10% or 20%) to reach and even surpass the fully-trained one, without any additional training. Furthermore, ExPO also significantly improves off-the-shelf DPO/RLHF models and exhibits decent scalability across model sizes from 7B to 70B. Our work demonstrates the efficacy of model extrapolation in exploiting LLMs' capabilities, suggesting a promising direction that deserves future exploration.

The field of novel view synthesis has made significant strides thanks to the development of radiance field methods. However, most radiance field techniques are far better at novel view interpolation than novel view extrapolation where the synthesis novel views are far beyond the observed training views. We design ViewExtrapolator, a novel view synthesis approach that leverages the generative priors of Stable Video Diffusion (SVD) for realistic novel view extrapolation. By redesigning the SVD denoising process, ViewExtrapolator refines the artifact-prone views rendered by radiance fields, greatly enhancing the clarity and realism of the synthesized novel views. ViewExtrapolator is a generic novel view extrapolator that can work with different types of 3D rendering such as views rendered from point clouds when only a single view or monocular video is available. Additionally, ViewExtrapolator requires no fine-tuning of SVD, making it both data-efficient and computation-efficient. Extensive experiments demonstrate the superiority of ViewExtrapolator in novel view extrapolation. Project page: https://kunhao-liu.github.io/ViewExtrapolator/.

Large Language Diffusion Models, or diffusion LLMs, have emerged as a significant focus in NLP research, with substantial effort directed toward understanding their scalability and downstream task performance. However, their long-context capabilities remain unexplored, lacking systematic analysis or methods for context extension. In this work, we present the first systematic investigation comparing the long-context performance of diffusion LLMs and traditional auto-regressive LLMs. We first identify a unique characteristic of diffusion LLMs, unlike auto-regressive LLMs, they maintain remarkably \textit{stable perplexity} during direct context extrapolation. Furthermore, where auto-regressive models fail outright during the Needle-In-A-Haystack task with context exceeding their pretrained length, we discover diffusion LLMs exhibit a distinct \textit{local perception} phenomenon, enabling successful retrieval from recent context segments. We explain both phenomena through the lens of Rotary Position Embedding (RoPE) scaling theory. Building on these observations, we propose LongLLaDA, a training-free method that integrates LLaDA with the NTK-based RoPE extrapolation. Our results validate that established extrapolation scaling laws remain effective for extending the context windows of diffusion LLMs. Furthermore, we identify long-context tasks where diffusion LLMs outperform auto-regressive LLMs and others where they fall short. Consequently, this study establishes the first context extrapolation method for diffusion LLMs while providing essential theoretical insights and empirical benchmarks critical for advancing future research on long-context diffusion LLMs.

Long-range sequence processing poses a significant challenge for Transformers due to their quadratic complexity in input length. A promising alternative is Mamba, which demonstrates high performance and achieves Transformer-level capabilities while requiring substantially fewer computational resources. In this paper we explore the length-generalization capabilities of Mamba, which we find to be relatively limited. Through a series of visualizations and analyses we identify that the limitations arise from a restricted effective receptive field, dictated by the sequence length used during training. To address this constraint, we introduce DeciMamba, a context-extension method specifically designed for Mamba. This mechanism, built on top of a hidden filtering mechanism embedded within the S6 layer, enables the trained model to extrapolate well even without additional training. Empirical experiments over real-world long-range NLP tasks show that DeciMamba can extrapolate to context lengths that are 25x times longer than the ones seen during training, and does so without utilizing additional computational resources. We will release our code and models.

Addressing the limitation of context length in large language models for code-related tasks is the primary focus of this paper. Existing LLMs are constrained by their pre-trained context lengths, leading to performance issues in handling long complex code sequences. Inspired by how human programmers navigate code, we introduce Hierarchical Rotary Position Embedding (HiRoPE), a novel approach that enhances the traditional rotary position embedding into a hierarchical format based on the hierarchical structure of source code. HiRoPE offers easy integration into existing LLMs without extra training costs. Our method is extensively evaluated with various LLMs, demonstrating stable performance in tasks such as language modeling and long code completion. We also introduce a new long code understanding task with real-world code projects, in hopes of promoting further development in this code-related field. Theoretically and experimentally, we find that HiRoPE also addresses the out-of-distribution issue in position encoding. Our HiRoPE significantly expands the context length capabilities of LLMs, enabling inference at lengths exponentially greater than the training length.

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving reasoning in large language models (LLMs), yet the underlying geometry of the resulting parameter trajectories remains underexplored. In this work, we demonstrate that RLVR weight trajectories are extremely low-rank and highly predictable. Specifically, we find that the majority of downstream performance gains are captured by a rank-1 approximation of the parameter deltas, where the magnitude of this projection evolves near-linearly with training steps. Motivated by this, we propose a simple and compute-efficient method RELEX (REinforcement Learning EXtrapolation), which estimates the rank-1 subspace from a short observation window and extrapolates future checkpoints via linear regression, with no learned model required. Across three models (i.e., Qwen2.5-Math-1.5B, Qwen3-4B-Base, and Qwen3-8B-Base), RELEX produces checkpoints that match or exceed RLVR performance on both in-___domain and out-of-___domain benchmarks, requiring as few as 15% steps of full RLVR training. Remarkably, RELEX is able to extrapolate far beyond the observation window at no training cost, predicting checkpoints up to 10-20times beyond the observed prefix with continued improvement (e.g., observe only the first 50 steps and extrapolate to 1000 steps). Our ablation analysis confirms the minimalist sufficiency of RELEX: neither increasing the subspace rank nor employing non-linear modeling yields further gains in extrapolation. Finally, we show that RELEX's success stems from a "denoising" effect: by projecting updates onto the rank-1 subspace, the model discards stochastic optimization noise that would otherwise degrade performance during extrapolation. Our code is available at https://github.com/weizhepei/RELEX.

Transformers excel at in-context retrieval but suffer from quadratic complexity with sequence length, while State Space Models (SSMs) offer efficient linear-time processing but have limited retrieval capabilities. We investigate whether hybrid architectures combining Transformers and SSMs can achieve the best of both worlds on two synthetic in-context retrieval tasks. The first task, n-gram retrieval, requires the model to identify and reproduce an n-gram that succeeds the query within the input sequence. The second task, position retrieval, presents the model with a single query token and requires it to perform a two-hop associative lookup: first locating the corresponding element in the sequence, and then outputting its positional index. Under controlled experimental conditions, we assess data efficiency, length generalization, robustness to out of ___domain training examples, and learned representations across Transformers, SSMs, and hybrid architectures. We find that hybrid models outperform SSMs and match or exceed Transformers in data efficiency and extrapolation for information-dense context retrieval. However, Transformers maintain superiority in position retrieval tasks. Through representation analysis, we discover that SSM-based models develop locality-aware embeddings where tokens representing adjacent positions become neighbors in embedding space, forming interpretable structures. This emergent property, absent in Transformers, explains both the strengths and limitations of SSMs and hybrids for different retrieval tasks. Our findings provide principled guidance for architecture selection based on task requirements and reveal fundamental differences in how Transformers and SSMs, and hybrid models learn positional associations.

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search benchmarks, we still know little about how they perform in terms of interpolation and extrapolation. In this paper, we demonstrate the importance of separately evaluating the two capabilities of neural retrieval models. Firstly, we examine existing ad-hoc search benchmarks from the two perspectives. We investigate the distribution of training and test data and find a considerable overlap in query entities, query intent, and relevance labels. This finding implies that the evaluation on these test sets is biased toward interpolation and cannot accurately reflect the extrapolation capacity. Secondly, we propose a novel evaluation protocol to separately evaluate the interpolation and extrapolation performance on existing benchmark datasets. It resamples the training and test data based on query similarity and utilizes the resampled dataset for training and evaluation. Finally, we leverage the proposed evaluation protocol to comprehensively revisit a number of widely-adopted neural retrieval models. Results show models perform differently when moving from interpolation to extrapolation. For example, representation-based retrieval models perform almost as well as interaction-based retrieval models in terms of interpolation but not extrapolation. Therefore, it is necessary to separately evaluate both interpolation and extrapolation performance and the proposed resampling method serves as a simple yet effective evaluation tool for future IR studies.

There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as 3 arctan 2 + ln 9 + 1, that closely approximate the float. Examples include AskConstants, Inverse Symbolic Calculator, the Maple identify function, MESearch, OEIS, RIES, and WolframAlpha. Usefully often such a result is the exact limit as the float is computed with increasing precision. Therefore these program results are candidates for proving an exact result that you could not otherwise compute or conjecture without the program. Moreover, candidates that are not the exact limit can be provable bounds, or convey qualitative insight, or suggest series that they truncate, or provide sufficiently close efficient approximations for subsequent computation. This article describes some of these programs, how they work, and how best to use each of them. Almost everyone who uses or should use mathematical software can benefit from acquaintance with several such programs, because these programs differ in the sets of constants that they can return.

Forecasting has become a natural benchmark for reasoning under uncertainty. Yet existing evaluations of large language models remain limited to judgmental tasks in simple formats, such as binary or multiple-choice questions. In practice, however, forecasting spans a far broader scope. Across domains such as economics, public health, and social demographics, decisions hinge on numerical estimates over continuous quantities, a capability that current benchmarks do not capture. Evaluating such estimates requires a format that makes uncertainty explicit and testable. We propose prediction intervals as a natural and rigorous interface for this purpose. They demand scale awareness, internal consistency across confidence levels, and calibration over a continuum of outcomes, making them a more suitable evaluation format than point estimates for numerical forecasting. To assess this capability, we introduce a new benchmark QuantSightBench, and evaluate frontier models under multiple settings, assessing both empirical coverage and interval sharpness. Our results show that none of the 11 evaluated frontier and open-weight models achieves the 90\% coverage target, with the top performers Gemini 3.1 Pro (79.1\%), Grok 4 (76.4\%), and GPT-5.4 (75.3\%) all falling at least 10 percentage points short. Calibration degrades sharply at extreme magnitudes, revealing systematic overconfidence across all evaluated models.

Transformer-based Large Language Models (LLMs) are pioneering advances in many natural language processing tasks, however, their exceptional capabilities are restricted within the preset context window of Transformer. Position Embedding (PE) scaling methods, while effective in extending the context window to a specific length, demonstrate either notable limitations in their extrapolation abilities or sacrificing partial performance within the context window. Length extrapolation methods, although theoretically capable of extending the context window beyond the training sequence length, often underperform in practical long-context applications. To address these challenges, we propose Continuous Length EXtrapolation (CLEX) for LLMs. We generalise the PE scaling approaches to model the continuous dynamics by ordinary differential equations over the length scaling factor, thereby overcoming the constraints of current PE scaling methods designed for specific lengths. Moreover, by extending the dynamics to desired context lengths beyond the training sequence length, CLEX facilitates the length extrapolation with impressive performance in practical tasks. We demonstrate that CLEX can be seamlessly incorporated into LLMs equipped with Rotary Position Embedding, such as LLaMA and GPT-NeoX, with negligible impact on training and inference latency. Experimental results reveal that CLEX can effectively extend the context window to over 4x or almost 8x training length, with no deterioration in performance. Furthermore, when evaluated on the practical LongBench benchmark, our model trained on a 4k length exhibits competitive performance against state-of-the-art open-source models trained on context lengths up to 32k.

Large Language Models (LLMs) exhibit impressive capabilities, but remain susceptible to a growing spectrum of safety risks, including jailbreaks, toxic content, hallucinations, and bias. Existing defenses often address only a single threat type or resort to rigid outright rejection, sacrificing user experience and failing to generalize across diverse and novel attacks. This paper introduces Adversarial Scenario Extrapolation (ASE), a novel inference-time computation framework that leverages Chain-of-Thought (CoT) reasoning to simultaneously enhance LLM robustness and seamlessness. ASE guides the LLM through a self-generative process of contemplating potential adversarial scenarios and formulating defensive strategies before generating a response to the user query. Comprehensive evaluation on four adversarial benchmarks with four latest LLMs shows that ASE achieves near-zero jailbreak attack success rates and minimal toxicity, while slashing outright rejections to <4%. ASE outperforms six state-of-the-art defenses in robustness-seamlessness trade-offs, with 92-99% accuracy on adversarial Q&A and 4-10x lower bias scores. By transforming adversarial perception into an intrinsic cognitive process, ASE sets a new paradigm for secure and natural human-AI interaction.

Large Language Models (LLMs) have shown excellent performance in language understanding, text generation, code synthesis, and many other tasks, while they still struggle in complex multi-step reasoning problems, such as mathematical reasoning. In this paper, through a newly proposed arithmetical puzzle problem, we show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that not only the model can reach a zero-shot pass@1 at 0.44 on the in-___domain dataset, it also demonstrates certain generalization capabilities on the out-of-___domain datasets. Specifically, this paper has designed two out-of-___domain datasets in the form of extending the numerical range and the composing components of the arithmetical puzzle problem separately. The fine-tuned models have shown encouraging performance on these two far more difficult tasks with the zero-shot pass@1 at 0.33 and 0.35, respectively.

Scaling up language models has been shown to predictably improve performance and sample efficiency on a wide range of downstream tasks. This paper instead discusses an unpredictable phenomenon that we refer to as emergent abilities of large language models. We consider an ability to be emergent if it is not present in smaller models but is present in larger models. Thus, emergent abilities cannot be predicted simply by extrapolating the performance of smaller models. The existence of such emergence implies that additional scaling could further expand the range of capabilities of language models.

Transformer models, notably large language models (LLMs), have the remarkable ability to perform in-context learning (ICL) -- to perform new tasks when prompted with unseen input-output examples without any explicit model training. In this work, we study how effectively transformers can bridge between their pretraining data mixture, comprised of multiple distinct task families, to identify and learn new tasks in-context which are both inside and outside the pretraining distribution. Building on previous work, we investigate this question in a controlled setting, where we study transformer models trained on sequences of (x, f(x)) pairs rather than natural language. Our empirical results show transformers demonstrate near-optimal unsupervised model selection capabilities, in their ability to first in-context identify different task families and in-context learn within them when the task families are well-represented in their pretraining data. However when presented with tasks or functions which are out-of-___domain of their pretraining data, we demonstrate various failure modes of transformers and degradation of their generalization for even simple extrapolation tasks. Together our results highlight that the impressive ICL abilities of high-capacity sequence models may be more closely tied to the coverage of their pretraining data mixtures than inductive biases that create fundamental generalization capabilities.

We introduce Leap+Verify, a framework that applies speculative execution -- predicting future model weights and validating predictions before acceptance -- to accelerate neural network training. Inspired by speculative decoding in language model inference and by the Automatically Scalable Computation (ASC) architecture for program execution, Leap+Verify decomposes training into three dynamically detected regimes (chaotic, transition, stable) using activation-space cosine similarity as a real-time Lyapunov proxy signal. Within each regime, analytic weight predictors (momentum, linear, quadratic extrapolation) attempt to forecast model parameters K training steps ahead; predictions are accepted only when validated against a held-out loss criterion. We evaluate Leap+Verify on GPT-2 124M and Qwen 2.5-1.5B trained on WikiText-103 across five random seeds, sweeping prediction depth K in {5, 10, 25, 50, 75, 100}. Momentum-based prediction (Adam moment extrapolation) fails catastrophically at both scales, with predicted losses exceeding actuals by 100-10,000x -- a universal norm explosion in optimizer-state extrapolation. Finite-difference predictors (linear, quadratic) succeed where momentum fails: at 124M, they achieve 24% strict acceptance at K=5 in stable regimes; at 1.5B, they achieve 37% strict acceptance in transition regimes. The scale-dependent finding is in regime distribution: GPT-2 124M spends 34% of training in stable regime, while Qwen 1.5B spends 64% in chaotic regime and reaches stable in only 0-2 of 40 checkpoints. Larger models are more predictable when predictable, but less often predictable -- the practical bottleneck shifts from predictor accuracy to regime availability. Cross-seed results are highly consistent (less than 1% validation loss variance), and the three-regime framework produces identical phase boundaries (plus or minus 50 steps) across seeds.

Recent advancements in video generation have enabled models to synthesize high-quality, minute-long videos. However, generating even longer videos with temporal coherence remains a major challenge, and existing length extrapolation methods lead to temporal repetition or motion deceleration. In this work, we systematically analyze the role of frequency components in positional embeddings and identify an intrinsic frequency that primarily governs extrapolation behavior. Based on this insight, we propose RIFLEx, a minimal yet effective approach that reduces the intrinsic frequency to suppress repetition while preserving motion consistency, without requiring any additional modifications. RIFLEx offers a true free lunch--achieving high-quality 2times extrapolation on state-of-the-art video diffusion transformers in a completely training-free manner. Moreover, it enhances quality and enables 3times extrapolation by minimal fine-tuning without long videos. Project page and codes: https://riflex-video.github.io/{https://riflex-video.github.io/.}

On-policy distillation (OPD) is widely used for LLM post-training. When pushed with a reward-extrapolation coefficient lambda > 1, the student can lift past the teacher in ___domain, but past a threshold lambda* the same step violates the output contract on structured-output tasks. In a single-position Bernoulli reduction, we derive a closed-form base-relative clip-safety threshold lambda*(p,b,c) determined by three measurable quantities: the teacher modal probability, the warm-start mass, and the importance-sampling clip strength. Above lambda*, the extrapolated fixed point exits the clip-safe region, changing training from format-preserving to format-collapsing. We extend the rule to calibrated K-ary listwise JSON tasks where a single binding equivalence class dominates the output contract and SFT retains parse headroom. On Amazon Fashion, three pre-registered tests--a fine-grid cliff interval, a budget-extension test, and a small-clip cross-prediction--fall within their locked prediction windows, with the small-clip value matching the closed-form prediction below grid resolution. Operating just below lambda*, ListOPD brings a 1.7B Qwen3 student to in-___domain parity with an 8B-SFT baseline at one-fifth the parameters. The gain is driven primarily by format adherence: NDCG@1 on parsed outputs remains flat across lambda, while parse validity sharply changes at the predicted boundary. The cliff diagnostic is rubric-independent, whereas the parity claim uses a Gemini-graded rubric and inherits that evaluator's exposure.

Machine-learning-based parameterizations (i.e. representation of sub-grid processes) of global climate models or turbulent simulations have recently been proposed as a powerful alternative to physical, but empirical, representations, offering a lower computational cost and higher accuracy. Yet, those approaches still suffer from a lack of generalization and extrapolation beyond the training data, which is however critical to projecting climate change or unobserved regimes of turbulence. Here we show that a multi-fidelity approach, which integrates datasets of different accuracy and abundance, can provide the best of both worlds: the capacity to extrapolate leveraging the physically-based parameterization and a higher accuracy using the machine-learning-based parameterizations. In an application to climate modeling, the multi-fidelity framework yields more accurate climate projections without requiring major increase in computational resources. Our multi-fidelity randomized prior networks (MF-RPNs) combine physical parameterization data as low-fidelity and storm-resolving historical run's data as high-fidelity. To extrapolate beyond the training data, the MF-RPNs are tested on high-fidelity warming scenarios, +4K, data. We show the MF-RPN's capacity to return much more skillful predictions compared to either low- or high-fidelity (historical data) simulations trained only on one regime while providing trustworthy uncertainty quantification across a wide range of scenarios. Our approach paves the way for the use of machine-learning based methods that can optimally leverage historical observations or high-fidelity simulations and extrapolate to unseen regimes such as climate change.

Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position embedding for extrapolation by kernelizing positional differences. We achieve this goal using conditionally positive definite (CPD) kernels, a class of functions known for generalizing distance metrics. To maintain the inner product interpretation of self-attention, we show that a CPD kernel can be transformed into a PD kernel by adding a constant offset. This offset is implicitly absorbed in the Softmax normalization during self-attention. The diversity of CPD kernels allows us to derive various RPEs that enable length extrapolation in a principled way. Experiments demonstrate that the logarithmic variant achieves excellent extrapolation performance on three large language modeling datasets. Our implementation and pretrained checkpoints are released at https://github.com/chijames/KERPLE.git.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

Transformers, central to the successes in modern Natural Language Processing, often falter on arithmetic tasks despite their vast capabilities --which paradoxically include remarkable coding abilities. We observe that a crucial challenge is their naive reliance on positional information to solve arithmetic problems with a small number of digits, leading to poor performance on larger numbers. Herein, we delve deeper into the role of positional encoding, and propose several ways to fix the issue, either by modifying the positional encoding directly, or by modifying the representation of the arithmetic task to leverage standard positional encoding differently. We investigate the value of these modifications for three tasks: (i) classical multiplication, (ii) length extrapolation in addition, and (iii) addition in natural language context. For (i) we train a small model on a small dataset (100M parameters and 300k samples) with remarkable aptitude in (direct, no scratchpad) 15 digits multiplication and essentially perfect up to 12 digits, while usual training in this context would give a model failing at 4 digits multiplication. In the experiments on addition, we use a mere 120k samples to demonstrate: for (ii) extrapolation from 10 digits to testing on 12 digits numbers while usual training would have no extrapolation, and for (iii) almost perfect accuracy up to 5 digits while usual training would be correct only up to 3 digits (which is essentially memorization with a training set of 120k samples).

Out-of-distribution (OOD) generalization is a favorable yet challenging property for deep neural networks. The core challenges lie in the limited availability of source domains that help models learn an invariant representation from the spurious features. Various ___domain augmentation have been proposed but largely rely on interpolating existing domains and frequently face difficulties in creating truly "novel" domains. Humans, on the other hand, can easily extrapolate novel domains, thus, an intriguing question arises: How can neural networks extrapolate like humans and achieve OOD generalization? We introduce a novel approach to ___domain extrapolation that leverages reasoning ability and the extensive knowledge encapsulated within large language models (LLMs) to synthesize entirely new domains. Starting with the class of interest, we query the LLMs to extract relevant knowledge for these novel domains. We then bridge the gap between the text-centric knowledge derived from LLMs and the pixel input space of the model using text-to-image generation techniques. By augmenting the training set of ___domain generalization datasets with high-fidelity, photo-realistic images of these new domains, we achieve significant improvements over all existing methods, as demonstrated in both single and multi-___domain generalization across various benchmarks. With the ability to extrapolate any domains for any class, our method has the potential to learn a generalized model for any task without any data. To illustrate, we put forth a much more difficult setting termed, data-free ___domain generalization, that aims to learn a generalized model in the absence of any collected data. Our empirical findings support the above argument and our methods exhibit commendable performance in this setting, even surpassing the supervised setting by approximately 1-2\% on datasets such as VLCS.

This technical report introduces VibeThinker-3B, a compact dense model with 3B parameters developed to investigate how far verifiable reasoning can be pushed within a strictly small-model regime. Building upon the Spectrum-to-Signal post-training paradigm, we systematically enhance the model through an optimized pipeline that includes curriculum-based supervised fine-tuning, multi-___domain reinforcement learning, and offline self-distillation. Experimental evaluations demonstrate that VibeThinker-3B achieves frontier-level performance on highly demanding verifiable tasks. Specifically, it attains a score of 94.3 on AIME26 (improving to 97.1 with claim-level test-time scaling), an 80.2 Pass@1 on LiveCodeBench v6, and exhibits strong out-of-distribution generalization with a 96.1\% acceptance rate on recent unseen LeetCode contests. This effectively places it in the performance band of first-tier reasoning systems, matching or exceeding flagship models that are orders of magnitude larger, such as DeepSeek V3.2, GLM-5, and Gemini 3 Pro. Furthermore, a score of 93.4 on IFEval confirms that this extreme reasoning enhancement does not compromise strict instruction controllability. Extending our previous 1.5B work, these findings motivate the Parametric Compression-Coverage Hypothesis, which views verifiable reasoning as compressible into compact reasoning cores, while open-___domain knowledge and general-purpose competence require broad parameter coverage over facts, concepts, and long-tail scenarios. This perspective suggests that compact models are not merely deployment-efficient substitutes, but a complementary path toward frontier-level performance in parameter-dense capability regimes.

We propose Parabolic Position Encoding (PaPE), a parabola-based position encoding for vision modalities in attention-based architectures. Given a set of vision tokens-such as images, point clouds, videos, or event camera streams-our objective is to encode their positions while accounting for the characteristics of vision modalities. Prior works have largely extended position encodings from 1D-sequences in language to nD-structures in vision, but only with partial account of vision characteristics. We address this gap by designing PaPE from principles distilled from prior work: translation invariance, rotation invariance (PaPE-RI), distance decay, directionality, and context awareness. We evaluate PaPE on 8 datasets that span 4 modalities. We find that either PaPE or PaPE-RI achieves the top performance on 7 out of 8 datasets. Extrapolation experiments on ImageNet-1K show that PaPE extrapolates remarkably well, improving in absolute terms by up to 10.5% over the next-best position encoding. Code is available at https://github.com/DTU-PAS/parabolic-position-encoding.

Transformer has taken the field of natural language processing (NLP) by storm since its birth. Further, Large language models (LLMs) built upon it have captured worldwide attention due to its superior abilities. Nevertheless, all Transformer-based models including these powerful LLMs suffer from a preset length limit and can hardly generalize from short training sequences to longer inference ones, namely, they can not perform length extrapolation. Hence, a plethora of methods have been proposed to enhance length extrapolation of Transformer, in which the positional encoding (PE) is recognized as the major factor. In this survey, we present these advances towards length extrapolation in a unified notation from the perspective of PE. Specifically, we first introduce extrapolatable PEs, including absolute and relative PEs. Then, we dive into extrapolation methods based on them, covering position interpolation and randomized position methods. Finally, several challenges and future directions in this area are highlighted. Through this survey, We aim to enable the reader to gain a deep understanding of existing methods and provide stimuli for future research.

Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the specific sources and mechanisms underlying these reasoning capabilities remain insufficiently understood. Optimization reasoning, i.e. finding extrema under constraints, represents a fundamental abstraction that underpins critical applications in planning, control, resource allocation, and prompt search. To systematically evaluate this capability, we introduce ExtremBench, a benchmark dataset for solving mathematical extremal problems, curated from inequality exercises used for Chinese Mathematical Olympiad and transformed into 93 standardized extrema-finding problems. We conduct extensive evaluations across various state-of-the-art open-source model families, including the Qwen3, GPT-OSS, and DeepSeek. Our results reveal that LLMs' extremal-solving reasoning capabilities do not always align with those of current mathematical benchmarks such as AIME25 and MATH-500, with some models showing strong general mathematical reasoning but poor extremal-solving skills, and vice versa. This discrepancy highlights a critical gap in current evaluation practices and suggests that existing benchmarks may not comprehensively capture the full spectrum of mathematical reasoning abilities.

Reinforcement learning with offline data suffers from Q-value extrapolation errors. To address this issue, we first demonstrate that linear extrapolation of the Q-function beyond the data range is particularly problematic. To mitigate this, we propose guiding the gradual decrease of Q-values outside the data range, which is achieved through reward scaling with layer normalization (RS-LN) and a penalization mechanism for infeasible actions (PA). By combining RS-LN and PA, we develop a new algorithm called PARS. We evaluate PARS across a range of tasks, demonstrating superior performance compared to state-of-the-art algorithms in both offline training and online fine-tuning on the D4RL benchmark, with notable success in the challenging AntMaze Ultra task.

Chain-of-Thought (CoT) reasoning successfully enhances the reasoning capabilities of Large Language Models (LLMs), yet it incurs substantial computational overhead for inference. Existing CoT compression methods often suffer from a critical loss of logical fidelity at high compression ratios, resulting in significant performance degradation. To achieve high-fidelity, fast reasoning, we propose a novel EXTreme-RAtio Chain-of-Thought Compression framework, termed Extra-CoT, which aggressively reduces the token budget while preserving answer accuracy. To generate reliable, high-fidelity supervision, we first train a dedicated semantically-preserved compressor on mathematical CoT data with fine-grained annotations. An LLM is then fine-tuned on these compressed pairs via a mixed-ratio supervised fine-tuning (SFT), teaching it to follow a spectrum of compression budgets and providing a stable initialization for reinforcement learning (RL). We further propose Constrained and Hierarchical Ratio Policy Optimization (CHRPO) to explicitly incentivize question-solving ability under lower budgets by a hierarchical reward. Experiments on three mathematical reasoning benchmarks show the superiority of Extra-CoT. For example, on MATH-500 using Qwen3-1.7B, Extra-CoT achieves over 73\% token reduction with an accuracy improvement of 0.6\%, significantly outperforming state-of-the-art (SOTA) methods. Our source codes have been released at https://github.com/Mwie1024/Extra-CoT.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the magnitude of these updates, largely overlooking their direction. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference Δlog p between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that Δlog p more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a test-time extrapolation method that amplifies the policy along the learned Δlog p direction to improve reasoning accuracy without further training; (2) a training-time reweighting method that focuses learning on low-probability (corresponding to higher Δlog p) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

We present EBench, a simulation benchmark that diagnoses generalist mobile manipulation policies beyond a single success-rate scalar. EBench comprises 26 diverse and challenging manipulation tasks annotated along 5 capability dimensions and 4 generalization dimensions. We evaluate state-of-the-art generalist manipulation models including π_0, π_{0.5}, XVLA, and InternVLA-A1, and reveal that models with near success rates exhibit strikingly different capability profiles: π_{0.5} achieves the highest test success rate and the best train--test retention, whereas InternVLA-A1 dominates mobile manipulation but collapses on dexterous tasks, and XVLA exhibits strengths on a disjoint set of atomic skills compared to other policies. Beyond capability profiling, EBench analyzes the generalization ability from 4 representative perspectives, identifying the impact of different distribution shift factors. The results reveal strengths and weaknesses of models behind an overall score. We hope this benchmark offers a broad set of diagnostic signals to guide iteration on generalist manipulation models.

Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal robust model will probably behave similarly to the oracle (e.g., the human users), thus a good evaluation protocol is probably to evaluate the models' behaviors in comparison to the oracle. In this paper, we introduce a new robustness measurement that directly measures the image classification model's performance compared with a surrogate oracle (i.e., a foundation model). Besides, we design a simple method that can accomplish the evaluation beyond the scope of the benchmarks. Our method extends the image datasets with new samples that are sufficiently perturbed to be distinct from the ones in the original sets, but are still bounded within the same image-label structure the original test image represents, constrained by a foundation model pretrained with a large amount of samples. As a result, our new method will offer us a new way to evaluate the models' robustness performance, free of limitations of fixed benchmarks or constrained perturbations, although scoped by the power of the oracle. In addition to the evaluation results, we also leverage our generated data to understand the behaviors of the model and our new evaluation strategies.

High-resolution images offer more information about scenes that can improve model accuracy. However, the dominant model architecture in computer vision, the vision transformer (ViT), cannot effectively leverage larger images without finetuning -- ViTs poorly extrapolate to more patches at test time, although transformers offer sequence length flexibility. We attribute this shortcoming to the current patch position encoding methods, which create a distribution shift when extrapolating. We propose a drop-in replacement for the position encoding of plain ViTs that restricts attention heads to fixed fields of view, pointed in different directions, using 2D attention masks. Our novel method, called LookHere, provides translation-equivariance, ensures attention head diversity, and limits the distribution shift that attention heads face when extrapolating. We demonstrate that LookHere improves performance on classification (avg. 1.6%), against adversarial attack (avg. 5.4%), and decreases calibration error (avg. 1.5%) -- on ImageNet without extrapolation. With extrapolation, LookHere outperforms the current SoTA position encoding method, 2D-RoPE, by 21.7% on ImageNet when trained at 224^2 px and tested at 1024^2 px. Additionally, we release a high-resolution test set to improve the evaluation of high-resolution image classifiers, called ImageNet-HR.

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

LLM-based software engineering agents are increasingly used in real-world development tasks, often with access to sensitive data or security-critical codebases. Such agents could intentionally sabotage these codebases if they were misaligned. We investigate asynchronous monitoring, in which a monitoring system reviews agent actions after the fact. Unlike synchronous monitoring, this approach does not impose runtime latency, while still attempting to disrupt attacks before irreversible harm occurs. We treat monitor development as an adversarial game between a blue team (who design monitors) and a red team (who create sabotaging agents). We attempt to set the game rules such that they upper bound the sabotage potential of an agent based on Claude 4.1 Opus. To ground this game in a realistic, high-stakes deployment scenario, we develop a suite of 5 diverse software engineering environments that simulate tasks that an agent might perform within an AI developer's internal infrastructure. Over the course of the game, we develop an ensemble monitor that achieves a 6% false negative rate at 1% false positive rate on a held out test environment. Then, we estimate risk of sabotage at deployment time by extrapolating from our monitor's false negative rate. We describe one simple model for this extrapolation, present a sensitivity analysis, and describe situations in which the model would be invalid. Code is available at: https://github.com/UKGovernmentBEIS/async-control.

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

As the rapid progression of practical applications based on Large Language Models continues, the importance of extrapolating performance has grown exponentially in the research ___domain. In our study, we identified an anomalous behavior in Transformer models that had been previously overlooked, leading to a chaos around closest tokens which carried the most important information. We've coined this discovery the "headache of Transformers". To address this at its core, we introduced a novel self-attention structure named Collinear Constrained Attention (CoCA). This structure can be seamlessly integrated with existing extrapolation, interpolation methods, and other optimization strategies designed for traditional Transformer models. We have achieved excellent extrapolating performance even for 16 times to 24 times of sequence lengths during inference without any fine-tuning on our model. We have also enhanced CoCA's computational and spatial efficiency to ensure its practicality. We plan to open-source CoCA shortly. In the meantime, we've made our code available in the appendix for reappearing experiments.

Recently, scaling reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs) has emerged as an effective training paradigm for significantly improving model capabilities, which requires guiding the model to perform extensive exploration and learning, leading to substantial computational overhead and becoming a key challenge. To reduce the number of training steps, Prior work performs linear extrapolation of model parameters. However, the dynamics of model parameter updates during RLVR training remain insufficiently understood. To further investigate the evolution of LLMs during RLVR training, we conduct empirical experiments and find that the rank-1 subspace of the model does not evolve linearly, and its dominance over the original parameters is further amplified during LoRA training. Based on the above insights, we propose the Nonlinear Extrapolation of low-rank trajectories (NExt), a novel framework that models and extrapolates low-rank parameter trajectories in a nonlinear manner. Concretely, we first train the model using LoRA and extract the rank-1 subspace of parameter differences at multiple training steps, which is then used for the subsequent nonlinear extrapolation. Afterward, we utilized the extracted rank-1 subspace to train a predictor, which can model the trajectory of parameter updates during RLVR, and then perform the predict-extend process to extrapolate model parameters, achieving the acceleration of RLVR. To further study and understand NExt, we conduct comprehensive experiments that demonstrate the effectiveness and robustness of the method. Our method reduces computational overhead by approximately 37.5\% while remaining compatible with a wide range of RLVR algorithms and tasks. We release our code in https://github.com/RUCAIBox/NExt.

Reinforcement Learning (RL) is notoriously data-inefficient, which makes training on a real robot difficult. While model-based RL algorithms (world models) improve data-efficiency to some extent, they still require hours or days of interaction to learn skills. Recently, offline RL has been proposed as a framework for training RL policies on pre-existing datasets without any online interaction. However, constraining an algorithm to a fixed dataset induces a state-action distribution shift between training and inference, and limits its applicability to new tasks. In this work, we seek to get the best of both worlds: we consider the problem of pretraining a world model with offline data collected on a real robot, and then finetuning the model on online data collected by planning with the learned model. To mitigate extrapolation errors during online interaction, we propose to regularize the planner at test-time by balancing estimated returns and (epistemic) model uncertainty. We evaluate our method on a variety of visuo-motor control tasks in simulation and on a real robot, and find that our method enables few-shot finetuning to seen and unseen tasks even when offline data is limited. Videos, code, and data are available at https://yunhaifeng.com/FOWM .

Modern recurrent architectures, such as xLSTM and Mamba, have recently challenged the Transformer in language modeling. However, their structure constrains their applicability to sequences only or requires processing multi-dimensional data structures, such as images or molecular graphs, in a pre-defined sequential order. In contrast, Multi-Dimensional RNNs (MDRNNs) are well suited for data with a higher level structure, like 2D grids, trees, and directed acyclic graphs (DAGs). In this work, we extend the notion of multi-dimensionality to linear RNNs. We introduce parallelizable Linear Source Transition Mark networks (pLSTMs) using Source, Transition, and Mark gates that act on the line graph of a general DAG. This enables parallelization in analogy to parallel associative scans and the chunkwise-recurrent form of sequential linear RNNs, but for DAGs. For regular grids (1D and 2D), like images, this scheme can be efficiently implemented using einsum operations, concatenations, and padding in logarithmic time. pLSTMs tackle the vanishing/exploding activation/gradient problem for long distances in DAGs via two distinct modes: a directed propagation mode (P-mode) and a diffusive distribution mode (D-mode). To showcase the long-range capabilities of pLSTM, we introduce arrow-pointing extrapolation as a synthetic computer vision task that contains long-distance directional information. We demonstrate that pLSTMs generalize well to larger image sizes, whereas Transformers struggle to extrapolate. On established molecular graph and computer vision benchmarks, pLSTMs also show strong performance. Code and Datasets are available at: https://github.com/ml-jku/plstm_experiments.

We present BlockFusion, a diffusion-based model that generates 3D scenes as unit blocks and seamlessly incorporates new blocks to extend the scene. BlockFusion is trained using datasets of 3D blocks that are randomly cropped from complete 3D scene meshes. Through per-block fitting, all training blocks are converted into the hybrid neural fields: with a tri-plane containing the geometry features, followed by a Multi-layer Perceptron (MLP) for decoding the signed distance values. A variational auto-encoder is employed to compress the tri-planes into the latent tri-plane space, on which the denoising diffusion process is performed. Diffusion applied to the latent representations allows for high-quality and diverse 3D scene generation. To expand a scene during generation, one needs only to append empty blocks to overlap with the current scene and extrapolate existing latent tri-planes to populate new blocks. The extrapolation is done by conditioning the generation process with the feature samples from the overlapping tri-planes during the denoising iterations. Latent tri-plane extrapolation produces semantically and geometrically meaningful transitions that harmoniously blend with the existing scene. A 2D layout conditioning mechanism is used to control the placement and arrangement of scene elements. Experimental results indicate that BlockFusion is capable of generating diverse, geometrically consistent and unbounded large 3D scenes with unprecedented high-quality shapes in both indoor and outdoor scenarios.

Minimax problems are notoriously challenging to optimize. However, we demonstrate that the two-timescale extragradient can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under a mild condition. This work surpasses all previous results as we eliminate a crucial assumption that the Hessian, with respect to the maximization variable, is nondegenerate.

Because of the diversity in lighting environments, existing illumination estimation techniques have been designed explicitly on indoor or outdoor environments. Methods have focused specifically on capturing accurate energy (e.g., through parametric lighting models), which emphasizes shading and strong cast shadows; or producing plausible texture (e.g., with GANs), which prioritizes plausible reflections. Approaches which provide editable lighting capabilities have been proposed, but these tend to be with simplified lighting models, offering limited realism. In this work, we propose to bridge the gap between these recent trends in the literature, and propose a method which combines a parametric light model with 360{\deg} panoramas, ready to use as HDRI in rendering engines. We leverage recent advances in GAN-based LDR panorama extrapolation from a regular image, which we extend to HDR using parametric spherical gaussians. To achieve this, we introduce a novel lighting co-modulation method that injects lighting-related features throughout the generator, tightly coupling the original or edited scene illumination within the panorama generation process. In our representation, users can easily edit light direction, intensity, number, etc. to impact shading while providing rich, complex reflections while seamlessly blending with the edits. Furthermore, our method encompasses indoor and outdoor environments, demonstrating state-of-the-art results even when compared to ___domain-specific methods.

Can we build continuous generative models which generalize across scales, can be evaluated at any coordinate, admit calculation of exact derivatives, and are conceptually simple? Existing MLP-based architectures generate worse samples than the grid-based generators with favorable convolutional inductive biases. Models that focus on generating images at different scales do better, but employ complex architectures not designed for continuous evaluation of images and derivatives. We take a signal-processing perspective and treat continuous image generation as interpolation from samples. Indeed, correctly sampled discrete images contain all information about the low spatial frequencies. The question is then how to extrapolate the spectrum in a data-driven way while meeting the above design criteria. Our answer is FunkNN -- a new convolutional network which learns how to reconstruct continuous images at arbitrary coordinates and can be applied to any image dataset. Combined with a discrete generative model it becomes a functional generator which can act as a prior in continuous ill-posed inverse problems. We show that FunkNN generates high-quality continuous images and exhibits strong out-of-distribution performance thanks to its patch-based design. We further showcase its performance in several stylized inverse problems with exact spatial derivatives.

Recent advances in multimodal time series learning underscore a paradigm shift from analytics centered on basic patterns toward advanced time series understanding and reasoning. However, existing multimodal time series datasets mostly remain at the level of surface alignment and question answering, without reaching the depth of genuine reasoning. The absence of well-defined tasks that genuinely require time series reasoning, along with the scarcity of high-quality data, has limited progress in building practical time series reasoning models (TSRMs). To this end, we introduce Time Series Reasoning Suite (TSR-Suite), which formalizes four atomic tasks that span three fundamental capabilities for reasoning with time series: (1) perception, acquired through scenario understanding and causality discovery; (2) extrapolation, realized via event-aware forecasting; and (3) decision-making, developed through deliberation over perception and extrapolation. TSR-Suite is the first comprehensive time series reasoning suite that supports not only thorough evaluation but also the data pipeline and training of TSRMs. It contains more than 23K samples, of which 2.3K are carefully curated through a human-guided hierarchical annotation process. Building on this foundation, we introduce TimeOmni-1, the first unified reasoning model designed to address diverse real-world problems demanding time series reasoning. The model is trained in multiple stages, integrating a mixture of task scenarios, novel reward functions, and tailored optimizations. Experiments show that TimeOmni-1 delivers strong out-of-distribution generalization across all tasks and achieves a high rate of valid responses. It significantly improves causality discovery accuracy (64.0% vs. 35.9% with GPT-4.1) and raises the valid response rate by over 6% compared to GPT-4.1 on the event-aware forecasting task.

The diversity in length constitutes a significant characteristic of text. Due to the long-tail distribution of text lengths, most existing methods for scene text recognition (STR) only work well on short or seen-length text, lacking the capability of recognizing longer text or performing length extrapolation. This is a crucial issue, since the lengths of the text to be recognized are usually not given in advance in real-world applications, but it has not been adequately investigated in previous works. Therefore, we propose in this paper a method called Length-Insensitive Scene TExt Recognizer (LISTER), which remedies the limitation regarding the robustness to various text lengths. Specifically, a Neighbor Decoder is proposed to obtain accurate character attention maps with the assistance of a novel neighbor matrix regardless of the text lengths. Besides, a Feature Enhancement Module is devised to model the long-range dependency with low computation cost, which is able to perform iterations with the neighbor decoder to enhance the feature map progressively. To the best of our knowledge, we are the first to achieve effective length-insensitive scene text recognition. Extensive experiments demonstrate that the proposed LISTER algorithm exhibits obvious superiority on long text recognition and the ability for length extrapolation, while comparing favourably with the previous state-of-the-art methods on standard benchmarks for STR (mainly short text).

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we propose an architecture that represents numerical quantities as linear activations which are manipulated using primitive arithmetic operators, controlled by learned gates. We call this module a neural arithmetic logic unit (NALU), by analogy to the arithmetic logic unit in traditional processors. Experiments show that NALU-enhanced neural networks can learn to track time, perform arithmetic over images of numbers, translate numerical language into real-valued scalars, execute computer code, and count objects in images. In contrast to conventional architectures, we obtain substantially better generalization both inside and outside of the range of numerical values encountered during training, often extrapolating orders of magnitude beyond trained numerical ranges.

Deep sequence models typically degrade in accuracy when test sequences significantly exceed their training lengths, yet many critical tasks--such as algorithmic reasoning, multi-step arithmetic, and compositional generalization--require robust length extrapolation. We introduce PRISM, a Probabilistic Relative-position Implicit Superposition Model, a novel positional encoding mechanism that enables Transformers to extrapolate accurately up to 10x beyond their training length. PRISM learns continuous relative positions through a differentiable histogram-filter update, preserving position uncertainty via a probabilistic superposition rather than conventional deterministic embeddings. Empirically, PRISM achieves state-of-the-art length extrapolation, successfully generalizing to previously intractable sequence lengths across algorithmic benchmarks--including arithmetic (addition, multiplication), SCAN compositionality tasks, and complex copy variants derived from DeepMind's recent datasets. Our analysis demonstrates that PRISM's stochastic positional encoding maintains sharp and interpretable internal states, providing a theoretical basis for reliable length generalization. These results advance the goal of neural sequence models that remain algorithmically robust at lengths far exceeding their training horizon.

A well-calibrated model should express confidence that matches its actual accuracy -- when it claims 80\% confidence, it should be correct 80\% of the time. While large language models (LLMs) have achieved remarkable performance across diverse tasks, their epistemic calibration remains poorly understood. We introduce KalshiBench, a benchmark of 300 prediction market questions from Kalshi, a CFTC-regulated exchange, with verifiable real-world outcomes occurring after model training cutoffs. Unlike traditional benchmarks measuring accuracy on static knowledge, KalshiBench evaluates whether models can appropriately quantify uncertainty about genuinely unknown future events. We evaluate five frontier models -- Claude Opus 4.5, GPT-5.2, DeepSeek-V3.2, Qwen3-235B, and Kimi-K2 -- and find systematic overconfidence across all models. Even the best-calibrated model (Claude Opus 4.5, ECE=0.120) shows substantial calibration errors, while reasoning-enhanced models like GPT-5.2-XHigh exhibit worse calibration (ECE=0.395) despite comparable accuracy. Critically, only one model achieves a positive Brier Skill Score, indicating most models perform worse than simply predicting base rates. Our findings suggest that scaling and enhanced reasoning do not automatically confer calibration benefits, highlighting epistemic calibration as a distinct capability requiring targeted development.

Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having limited diversity of symbols and rules, coupled with closed-ended answers. This paper proposes a method to leverage these shortcomings as useful features to a construct dynamic, counterfactual benchmark, which can be used to both reveal overfitting and measure true reasoning. We demonstrate this via MatheMagic, which generates math test instances with the interpretations of numbers and operators altered, yet has automatically verifiable answers. Test instances are randomly seeded and constructed at test time to evaluate a model's induction or deduction capability, offering stability, extensibility, comparability, and robustness to overfitting. Our experiments find that models solve deduction more easily than induction, but they revert to standard math. Further analysis reveals that math-adapted models fail to exhibit a general "skill" of reasoning, and fine-tuning on induction tasks generalizes poorly.

Scaling laws are used to plan multi-million-dollar training runs, but fitting those laws can itself cost millions. In modern large-scale workflows, assembling a sufficiently informative set of pilot experiments is already a major budget-allocation problem rather than a routine preprocessing step. We formulate scaling-law fitting as budget-aware sequential experimental design: given a finite pool of runnable experiments with heterogeneous costs, choose which runs to execute so as to maximize extrapolation accuracy in a high-cost target region. We then propose an uncertainty-aware method for sequentially allocating experimental budget toward the runs most useful for target-region extrapolation. Across a diverse benchmark of scaling-law tasks, our method consistently outperforms classical design-based baselines, and often approaches the performance of fitting on the full experimental set while using only about 10% of the total training budget. Our code is available at https://github.com/PlanarG/active-sl.

City-scale 3D reconstruction from satellite imagery presents the challenge of extreme viewpoint extrapolation, where our goal is to synthesize ground-level novel views from sparse orbital images with minimal parallax. This requires inferring nearly 90^circ viewpoint gaps from image sources with severely foreshortened facades and flawed textures, causing state-of-the-art reconstruction engines such as NeRF and 3DGS to fail. To address this problem, we propose two design choices tailored for city structures and satellite inputs. First, we model city geometry as a 2.5D height map, implemented as a Z-monotonic signed distance field (SDF) that matches urban building layouts from top-down viewpoints. This stabilizes geometry optimization under sparse, off-nadir satellite views and yields a watertight mesh with crisp roofs and clean, vertically extruded facades. Second, we paint the mesh appearance from satellite images via differentiable rendering techniques. While the satellite inputs may contain long-range, blurry captures, we further train a generative texture restoration network to enhance the appearance, recovering high-frequency, plausible texture details from degraded inputs. Our method's scalability and robustness are demonstrated through extensive experiments on large-scale urban reconstruction. For example, in our teaser figure, we reconstruct a 4,km^2 real-world region from only a few satellite images, achieving state-of-the-art performance in synthesizing photorealistic ground views. The resulting models are not only visually compelling but also serve as high-fidelity, application-ready assets for downstream tasks like urban planning and simulation. Project page can be found at https://pku-vcl-geometry.github.io/Orbit2Ground/.

Contrastive decoding (CD) (Li et al., 2023) improves the next-token distribution of a large expert language model (LM) using a small amateur LM. Although CD is applied to various LMs and domains to enhance open-ended text generation, it is still unclear why CD often works well, when it could fail, and how we can make it better. To deepen our understanding of CD, we first theoretically prove that CD could be viewed as linearly extrapolating the next-token logits from a huge and hypothetical LM. We also highlight that the linear extrapolation could make CD unable to output the most obvious answers that have already been assigned high probabilities by the amateur LM. To overcome CD's limitation, we propose a new unsupervised decoding method called Asymptotic Probability Decoding (APD). APD explicitly extrapolates the probability curves from the LMs of different sizes to infer the asymptotic probabilities from an infinitely large LM without inducing more inference costs than CD. In FactualityPrompts, an open-ended text generation benchmark, sampling using APD significantly boosts factuality in comparison to the CD sampling and its variants, and achieves state-of-the-art results for Pythia 6.9B and OPT 6.7B. Furthermore, in five commonsense QA datasets, APD is often significantly better than CD and achieves a similar effect of using a larger LLM. For example, the perplexity of APD on top of Pythia 6.9B is even lower than the perplexity of Pythia 12B in CommonsenseQA and LAMBADA.

The Neural Arithmetic Logic Unit (NALU) is a neural network layer that can learn exact arithmetic operations between the elements of a hidden state. The goal of NALU is to learn perfect extrapolation, which requires learning the exact underlying logic of an unknown arithmetic problem. Evaluating the performance of the NALU is non-trivial as one arithmetic problem might have many solutions. As a consequence, single-instance MSE has been used to evaluate and compare performance between models. However, it can be hard to interpret what magnitude of MSE represents a correct solution and models sensitivity to initialization. We propose using a success-criterion to measure if and when a model converges. Using a success-criterion we can summarize success-rate over many initialization seeds and calculate confidence intervals. We contribute a generalized version of the previous arithmetic benchmark to measure models sensitivity under different conditions. This is, to our knowledge, the first extensive evaluation with respect to convergence of the NALU and its sub-units. Using a success-criterion to summarize 4800 experiments we find that consistently learning arithmetic extrapolation is challenging, in particular for multiplication.

What makes a good Large Language Model (LLM)? That it performs well on the relevant benchmarks -- which hopefully measure, with some validity, the presence of capabilities that are also challenged in real application. But what makes the model perform well? What gives a model its abilities? We take a recently introduced type of benchmark that is meant to challenge capabilities in a goal-directed, agentive context through self-play of conversational games, and analyse how performance develops as a function of model characteristics like number of parameters, or type of training. We find that while there is a clear relationship between number of parameters and performance, there is still a wide spread of performance points within a given size bracket, which is to be accounted for by training parameters such as fine-tuning data quality and method. From a more practical angle, we also find a certain degree of unpredictability about performance across access methods, possible due to unexposed sampling parameters, and a, very welcome, performance stability against at least moderate weight quantisation during inference.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Recent reinforcement learning (RL) techniques have yielded impressive reasoning improvements in language models, yet it remains unclear whether post-training truly extends a model's reasoning ability beyond what it acquires during pre-training. A central challenge is the lack of control in modern training pipelines: large-scale pre-training corpora are opaque, mid-training is often underexamined, and RL objectives interact with unknown prior knowledge in complex ways. To resolve this ambiguity, we develop a fully controlled experimental framework that isolates the causal contributions of pre-training, mid-training, and RL-based post-training. Our approach employs synthetic reasoning tasks with explicit atomic operations, parseable step-by-step reasoning traces, and systematic manipulation of training distributions. We evaluate models along two axes: extrapolative generalization to more complex compositions and contextual generalization across surface contexts. Using this framework, we reconcile competing views on RL's effectiveness. We show that: 1) RL produces true capability gains (pass@128) only when pre-training leaves sufficient headroom and when RL data target the model's edge of competence, tasks at the boundary that are difficult but not yet out of reach. 2) Contextual generalization requires minimal yet sufficient pre-training exposure, after which RL can reliably transfer. 3) Mid-training significantly enhances performance under fixed compute compared with RL only, demonstrating its central but underexplored role in training pipelines. 4) Process-level rewards reduce reward hacking and improve reasoning fidelity. Together, these results clarify the interplay between pre-training, mid-training, and RL, offering a foundation for understanding and improving reasoning LM training strategies.

The view synthesis problem--generating novel views of a scene from known imagery--has garnered recent attention due in part to compelling applications in virtual and augmented reality. In this paper, we explore an intriguing scenario for view synthesis: extrapolating views from imagery captured by narrow-baseline stereo cameras, including VR cameras and now-widespread dual-lens camera phones. We call this problem stereo magnification, and propose a learning framework that leverages a new layered representation that we call multiplane images (MPIs). Our method also uses a massive new data source for learning view extrapolation: online videos on YouTube. Using data mined from such videos, we train a deep network that predicts an MPI from an input stereo image pair. This inferred MPI can then be used to synthesize a range of novel views of the scene, including views that extrapolate significantly beyond the input baseline. We show that our method compares favorably with several recent view synthesis methods, and demonstrate applications in magnifying narrow-baseline stereo images.

We apply augmentations to our dataset to enhance the quality of our predictions and make our final models more resilient to noisy data and ___domain drifts. Yet the question remains, how are these augmentations going to perform with different hyper-parameters? In this study we evaluate the sensitivity of augmentations with regards to the model's hyper parameters along with their consistency and influence by performing a Local Surrogate (LIME) interpretation on the impact of hyper-parameters when different augmentations are applied to a machine learning model. We have utilized Linear regression coefficients for weighing each augmentation. Our research has proved that there are some augmentations which are highly sensitive to hyper-parameters and others which are more resilient and reliable.

Recent advances in reinforcement learning (RL) have led to substantial improvements in the mathematical reasoning abilities of LLMs, as measured by standard benchmarks. Yet these gains often persist even when models are trained with flawed signals, such as random or inverted rewards. This raises a fundamental question: do such improvements reflect genuine reasoning, or are they merely artifacts of overfitting to benchmark-specific patterns? To answer this question, we adopt an evaluation-centric perspective and highlight two critical shortcomings in existing protocols. First, benchmark contamination arises because test problems are publicly available, thereby increasing the risk of data leakage. Second, evaluation fragility results from reliance on single-instance assessments, which are sensitive to stochastic outputs and fail to capture reasoning consistency. These limitations suggest the need for a new evaluation paradigm that can probe reasoning ability beyond memorization and one-off success. As response, we propose VAR-MATH, a symbolic evaluation framework that converts fixed numerical problems into parameterized templates and requires models to solve multiple instantiations of each. This design enforces consistency across structurally equivalent variants, mitigates contamination, and enhances robustness through bootstrapped metrics. We apply VAR-MATH to transform three popular benchmarks, AMC23, AIME24, and AIME25, into their symbolic counterparts, VAR-AMC23, VAR-AIME24, and VAR-AIME25. Experimental results show substantial performance drops for RL-trained models on these variabilized benchmarks, especially for smaller models, with average declines of 47.9\% on AMC23, 58.8\% on AIME24, and 72.9\% on AIME25. These findings indicate that some existing RL methods rely on superficial heuristics and fail to generalize beyond specific numerical forms.

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine learning algorithms to fit an imprecise regression model to data that consist of intervals rather than point values. The method is based on a single-layer interval neural network which can be trained to produce an interval prediction. It seeks parameters for the optimal model that minimizes the mean squared error between the actual and predicted interval values of the dependent variable using a first-order gradient-based optimization and interval analysis computations to model the measurement imprecision of the data. An additional extension to a multi-layer neural network is also presented. We consider the explanatory variables to be precise point values, but the measured dependent values are characterized by interval bounds without any probabilistic information. The proposed iterative method estimates the lower and upper bounds of the expectation region, which is an envelope of all possible precise regression lines obtained by ordinary regression analysis based on any configuration of real-valued points from the respective y-intervals and their x-values.

This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods with auxiliary training objectives can improve performance and reduce the number of convergence steps. However, they typically incur significant computational overhead due to the additional losses from auxiliary objectives. To simultaneously achieve the enhanced capabilities of auxiliary training with the simplicity of standard SFT, we decouple the two objectives of auxiliary-objective SFT within the parameter space, namely, enhancing general capabilities and fitting task-specific action distributions. To deliver the goal, we only need to train the model to converge on a small-scale task set using two distinct training strategies, resulting in two finetuned models. The parameters' difference between the two models can then be interpreted as capability vectors provided by auxiliary objectives. These vectors are then merged with pretrained parameters to form a capability-enhanced meta model. Moreover, when standard SFT is augmented with a lightweight orthogonal regularization loss, the merged model attains performance comparable to auxiliary finetuned baselines with reduced computational overhead. Internal and external experiments demonstrate that our capability vectors (1) are effective and versatile across diverse models, (2) can generalize to novel environments and embodiments out of the box.