Eye gaze offers valuable cues about attention, short-term intent, and future actions, making it a powerful signal for modeling egocentric behavior. In this work, we propose a gaze-regularized framework that enhances VLMs for two key egocentric understanding tasks: fine-grained future event prediction and current activity understanding. Unlike prior approaches that rely solely on visual inputs or use gaze as an auxiliary input signal, our method uses gaze only during training. We introduce a gaze-regularized attention mechanism that aligns model focus with human visual gaze. This design is flexible and modular, allowing it to generalize across multiple VLM architectures that utilize attention. Experimental results show that our approach improves semantic prediction scores by up to 11% for future event prediction and around 7% for current activity understanding, compared to the corresponding baseline models trained without gaze regularization.

Attention mechanisms have achieved significant empirical success in multiple fields, but their underlying optimization objectives remain unclear yet. Moreover, the quadratic complexity of self-attention has become increasingly prohibitive. Although interpretability and efficiency are two mutually reinforcing pursuits, prior work typically investigates them separately. In this paper, we propose a unified optimization objective that derives inherently interpretable and efficient attention mechanisms through algorithm unrolling. Precisely, we construct a gradient step of the proposed objective with a set of forward-pass operations of our Contractand-Broadcast Self-Attention (CBSA), which compresses input tokens towards low-dimensional structures by contracting a few representatives of them. This novel mechanism can not only scale linearly by fixing the number of representatives, but also covers the instantiations of varied attention mechanisms when using different sets of representatives. We conduct extensive experiments to demonstrate comparable performance and superior advantages over black-box attention mechanisms on visual tasks.

The quadratic complexity of self-attention prevents transformers from scaling effectively to long input sequences. On the other hand, modern GPUs and other specialized hardware accelerators are well-optimized for processing small input sequences in transformers during both training and inference. A natural question arises: can we take advantage of the efficiency of small transformers to deal with long input sequences? In this paper, we show that transformers with long input sequences (large transformers) can be efficiently simulated by transformers that can only take short input sequences (small transformers). Specifically, we prove that any transformer with input length N can be efficiently simulated by only O((N/M)2) transformers with input length M N, and that this cannot be improved in the worst case. However, we then prove that in various natural scenarios including average-case inputs, sliding window masking and attention sinks, the optimal number O(N/M) of small transformers suffice.

Transformers have driven remarkable breakthroughs in natural language processing 2and computer vision, yet their standard attention mechanism still imposes O(N) complexity, hindering scalability to longer sequences. We introduce Circularconvolutional ATtention (CAT), a Fourier-based approach that efficiently applies circular power. CA con T volutions achieves to O reduce (N log comple N) computations, xity without requires sacrificing fewer representational learnable parameters by streamlining fully connected layers, and introduces no additional heavy operations, resulting in consistent accuracy improvements and about a 10% speedup in naive PyTorch implementations. Based on the Engineering-Isomorphic Transformers (EITs) framework, CAT's design not only offers practical efficiency and ease of implementation, but also provides insights to guide the development of

We investigate the universal approximation property (UAP) of transformer-type architectures, providing a unified theoretical framework that extends prior results on residual networks to models incorporating attention mechanisms. Our work identifies token distinguishability as a fundamental requirement for UAP and introduces a general sufficient condition that applies to a broad class of architectures. Leveraging an analyticity assumption on the attention layer, we can significantly simplify the verification of this condition, providing a non-constructive approach in establishing UAP for such architectures. We demonstrate the applicability of our framework by proving UAP for transformers with various attention mechanisms, including kernel-based and sparse ones. The corollaries of our results either generalize prior works or establish UAP for architectures not previously covered. Furthermore, our framework offers a principled foundation for designing novel transformer architectures with inherent UAP guarantees, including those with specific functional symmetries. We propose examples to illustrate these insights.

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with RoPE and any possible position encoding mechanisms, TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducTATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines, including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at the decoding stage enable processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models.

Heterogeneous temporal graphs (HTGs) are ubiquitous data structures in the real world. Recently, to enhance representation learning on HTGs, numerous attentionbased neural networks have been proposed. Despite these successes, existing methods rely on a decoupled temporal and spatial learning paradigm, which weakens interactions of spatio-temporal information and leads to a high model complexity. To bridge this gap, we propose a novel learning paradigm for HTGs called Simple and Efficient Heterogeneous Temporal Graph Neural Network (SE-HTGNN). Specifically, we innovatively integrate temporal modeling into spatial learning via a novel dynamic attention mechanism, which substantially reduces model complexity while enhancing discriminative representation learning on HTGs. Additionally, to comprehensively and adaptively understand HTGs, we leverage large language models to prompt SE-HTGNN, enabling the model to capture the implicit properties of node types as prior knowledge. Extensive experiments demonstrate that SE-HTGNN achieves up to 10 speed-up over the state-of-the-art and latest baseline while maintaining the best forecasting accuracy.

Can algebraic geometry enhance the sharpness, robustness, and interpretability of modern neural reasoning models by equipping them with a mathematically grounded inductive bias? To answer this, we introduce Tropical Attention, an attention mechanism grounded in tropical geometry that lifts the attention kernel into tropical projective space, where reasoning is piecewise-linear and 1-Lipschitz, thus preserving the polyhedral decision structure inherent to combinatorial reasoning. We prove that Multi-Head Tropical Attention (MHTA) stacks universally approximate tropical circuits and realize tropical transitive closure through composition, achieving polynomial resource bounds without invoking recurrent mechanisms. These guarantees explain why the induced polyhedral decision boundaries remain sharp and scale-invariant, rather than smoothed by Softmax. Empirically, we show that Tropical Attention delivers stronger out-of-distribution generalization in both length and value, with high robustness against perturbative noise, and substantially faster inference with fewer parameters compared to Softmax-based and recurrent attention baselines, respectively. For the first time, we push the domain of neural algorithmic reasoning beyond PTIME problems to NP-hard/complete problems, paving the way toward sharper and more expressive Large Reasoning Models (LRMs) capable of tackling complex combinatorial challenges in Phylogenetics, Cryptography, Particle Physics, and Mathematical Discovery.

A key advantage of Recurrent Neural Networks (RNNs) over Transformers is their linear computational and space complexity enables faster training and inference for long sequences. However, RNNs are fundamentally unable to randomly access historical context, and simply integrating attention mechanisms may undermine their efficiency advantages. To overcome this limitation, we propose Hierarchical Sparse Attention (HSA), a novel attention mechanism that enhances RNNs with long-range random access flexibility while preserving their merits in efficiency and length generalization. HSA divides inputs into chunks, selects the top-k chunks and hierarchically aggregates information. The core innovation lies in learning token-to-chunk relevance based on fine-grained token-level information inside each chunk. This approach enhances the precision of chunk selection across both in-domain and out-of-domain context lengths. To make HSA efficient, we further introduce a hardware-aligned kernel design. By combining HSA with Mamba, we introduce RAMba, which achieves perfect accuracy in passkey retrieval across 64 million contexts despite pre-training on only 4K-length contexts, and significant improvements on various downstream tasks, with nearly constant memory footprint. These results show RAMba's huge potential in long-context modeling.

Recent advances in Large Language Models (LLMs) have highlighted the critical importance of extending context length, yet the quadratic complexity of attention mechanisms poses significant challenges for efficient long-context modeling. KV cache compression has emerged as a key approach to address this challenge. Through extensive empirical analysis, we reveal a fundamental yet previously overlooked asymmetry in KV caches: while adjacent keys receive similar attention weights (local homogeneity), adjacent values demonstrate distinct heterogeneous distributions. This key-value asymmetry reveals a critical limitation in existing compression methods that treat keys and values uniformly. To address the limitation, we propose a training-free compression framework (AsymKV) that combines homogeneity-based key merging with a mathematically proven lossless value compression. Extensive experiments demonstrate that AsymKV consistently outperforms existing long-context methods across various tasks and base models.