Daily Papers

We provide a full characterisation of all of the possible alternating group (A_n) equivariant neural networks whose layers are some tensor power of R^{n}. In particular, we find a basis of matrices for the learnable, linear, A_n-equivariant layer functions between such tensor power spaces in the standard basis of R^{n}. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

Recent investigations on the set of commutators between the elements of a finite group having relatively prime orders have prompt us to propose a variant of the Ore conjecture: For every finite non-abelian simple group and for every gin G, there exist x,yin G with g=[y,x] and with the order of x relatively prime to the order of y. In this note we present some evidence towards the veracity of this conjecture by proving it for alternating groups and some sporadic simple groups.

This paper introduces a novel approach to enhance the capabilities of Large Language Models (LLMs) in processing and understanding extensive text sequences, a critical aspect in applications requiring deep comprehension and synthesis of large volumes of information. Recognizing the inherent challenges in extending the context window for LLMs, primarily built on Transformer architecture, we propose a new model architecture, referred to as Zebra. This architecture efficiently manages the quadratic time and memory complexity issues associated with full attention in the Transformer by employing grouped local-global attention layers. Our model, akin to a zebra's alternating stripes, balances local and global attention layers, significantly reducing computational requirements and memory consumption. Comprehensive experiments, including pretraining from scratch, continuation of long context adaptation training, and long instruction tuning, are conducted to evaluate the Zebra's performance. The results show that Zebra achieves comparable or superior performance on both short and long sequence benchmarks, while also enhancing training and inference efficiency.

LLMs are used predominantly in synchronous communication, where a human user and a model communicate in alternating turns. In contrast, many real-world settings are inherently asynchronous. For example, in group chats, online team meetings, or social games, there is no inherent notion of turns; therefore, the decision of when to speak forms a crucial part of the participant's decision making. In this work, we develop an adaptive asynchronous LLM-agent which, in addition to determining what to say, also decides when to say it. To evaluate our agent, we collect a unique dataset of online Mafia games, including both human participants, as well as our asynchronous agent. Overall, our agent performs on par with human players, both in game performance, as well as in its ability to blend in with the other human players. Our analysis shows that the agent's behavior in deciding when to speak closely mirrors human patterns, although differences emerge in message content. We release all our data and code to support and encourage further research for more realistic asynchronous communication between LLM agents. This work paves the way for integration of LLMs into realistic human group settings, from assistance in team discussions to educational and professional environments where complex social dynamics must be navigated.

In this work, we conduct a systematic analysis of Native Sparse Attention (NSA) and propose targeted improvements that enhance long-context modeling. A key insight is that alternating between local (sliding-window) and global (compression, selective) attention across layers, rather than using fixed patterns, enables more effective propagation of long-range dependencies and substantially boosts performance on long-sequence tasks. Meanwhile, we further refine NSA's branches with Latent Attention that the sliding-window branch is enhanced with Multi-head Latent Attention (MLA) while compression and selective branches adopt Group-head Latent Attention (GLA). These changes reduce KV-cache memory by 50\% versus NSA while improving the model's common-sense reasoning and long-text understanding capabilities. Experiments on models from 340M to 1.3B parameters (trained on 15B and 100B tokens) show our method matches or exceeds full attention and native sparse attention in both common-sense reasoning and long-context understanding tasks.

Semi-supervised learning has become a compelling approach for 3D tooth segmentation from CBCT scans, where labeled data is minimal. However, existing methods still face two persistent challenges: limited corrective supervision in structurally ambiguous or mislabeled regions during supervised training and performance degradation caused by unreliable pseudo-labels on unlabeled data. To address these problems, we propose Region-Aware Instructive Learning (RAIL), a dual-group dual-student, semi-supervised framework. Each group contains two student models guided by a shared teacher network. By alternating training between the two groups, RAIL promotes intergroup knowledge transfer and collaborative region-aware instruction while reducing overfitting to the characteristics of any single model. Specifically, RAIL introduces two instructive mechanisms. Disagreement-Focused Supervision (DFS) Controller improves supervised learning by instructing predictions only within areas where student outputs diverge from both ground truth and the best student, thereby concentrating supervision on structurally ambiguous or mislabeled areas. In the unsupervised phase, Confidence-Aware Learning (CAL) Modulator reinforces agreement in regions with high model certainty while reducing the effect of low-confidence predictions during training. This helps prevent our model from learning unstable patterns and improves the overall reliability of pseudo-labels. Extensive experiments on four CBCT tooth segmentation datasets show that RAIL surpasses state-of-the-art methods under limited annotation. Our code will be available at https://github.com/Tournesol-Saturday/RAIL.

Livestock methane emissions represent 32% of human-caused methane production, making automated monitoring critical for climate mitigation strategies. We introduce GasTwinFormer, a hybrid vision transformer for real-time methane emission segmentation and dietary classification in optical gas imaging through a novel Mix Twin encoder alternating between spatially-reduced global attention and locally-grouped attention mechanisms. Our architecture incorporates a lightweight LR-ASPP decoder for multi-scale feature aggregation and enables simultaneous methane segmentation and dietary classification in a unified framework. We contribute the first comprehensive beef cattle methane emission dataset using OGI, containing 11,694 annotated frames across three dietary treatments. GasTwinFormer achieves 74.47% mIoU and 83.63% mF1 for segmentation while maintaining exceptional efficiency with only 3.348M parameters, 3.428G FLOPs, and 114.9 FPS inference speed. Additionally, our method achieves perfect dietary classification accuracy (100%), demonstrating the effectiveness of leveraging diet-emission correlations. Extensive ablation studies validate each architectural component, establishing GasTwinFormer as a practical solution for real-time livestock emission monitoring. Please see our project page at gastwinformer.github.io.

Let F be a field, and n geq r>0 be integers, with r even. Denote by A_n(F) the space of all n-by-n alternating matrices with entries in F. We consider the problem of determining the greatest possible dimension for an affine subspace of A_n(F) in which every matrix has rank equal to r (or rank at least r). Recently Rubei has solved this problem over the field of real numbers. We extend her result to all fields with large enough cardinality. Provided that n geq r+3 and |F|geq minbigl(r-1,r{2}+2bigr), we also determine the affine subspaces of rank r matrices in A_n(F) that have the greatest possible dimension, and we point to difficulties for the corresponding problem in the case nleq r+2.