Local Attention

Large language models (LLMs) have achieved remarkable breakthroughs across various applications. However, their architectures remain inefficient in pretraining due to two main limitations: (i) self-attention lacks an explicit inductive bias for locality, leading to redundant modeling of sequence-internal local information; (ii) mixture-of-experts (MoE) implicitly couples knowledge storage with computational pathways, hindering flexible access to sequence-external global knowledge. To overcome these limitations, we propose LoKiFormer, a novel LLM architecture that augments the standard decoder with two dedicated modules: 1) Local Fusion Attention (LFA), which incorporates a convolutional fusion to attention, explicitly capturing local patterns and allowing the attention to operate on more informative representations; 2) Knowledge Memory Module (KMM), which introduces a parametric key-value memory that explicitly stores global knowledge in addressable slots, decoupling storage from computation and enabling direct knowledge retrieval. Together, these modules enable LoKiFormer to achieve more efficient and effective integration of information at both levels. Experimental results show that LoKiFormer converges 1.33x faster in pre-training than baseline models, underscoring its superiority over existing LLM architectures.

Spiking Transformers provide a promising paradigm for efficient visual processing with spike-driven computation, yet their Softmax-free Spiking Self-Attention (SSA) struggles to establish spatially localized token interactions. Although existing locality-enhanced SSA methods improve accuracy, it remains unclear whether they consistently induce spatial locality across layers and different Spiking Transformer architectures. Through Mean Attention Distance (MAD) analysis, we reveal that computational locality does not necessarily translate into spatial locality and show that uniformly applying the same locality enhancement overlooks architecture-dependent deployment requirements. Motivated by these observations, we propose Spatially Contiguous Local Attention with Boundary Continuity Pathway (SCLA-BCP). SCLA computes attention within non-overlapping regions of spatially adjacent tokens, while BCP facilitates cross-boundary information exchange through a lightweight convolutional pathway. Furthermore, we develop a hierarchical locality deployment strategy to effectively apply SCLA-BCP across the two major Spiking Transformer architectures. Extensive experiments on seven static and neuromorphic datasets covering classification, detection, and segmentation demonstrate consistent improvements with limited parameter and energy overhead. Notably, our approach improves mAP@50 by up to 9.50% on COCO 2017 and mIoU by up to 3.42% on ADE20K. Visualizations, MAD analysis, and ablation studies further validate its effectiveness.

Can a strictly local, iterated, weight-shared computation primitive support language modelling, and which of those three properties actually drives the model's behaviour? We define \textsc{TextNCA}, a 1D causal windowed-attention realisation of the Neural Cellular Automaton primitive, and study a hierarchical variant that cascades three stages with windows $w \in \{8, 32, 128\}$ and $T_s$ shared-weight iterations per stage, all on WikiText-103 at roughly 30M parameters and 60k training steps. The model does not match a parameter-matched Transformer at this scale (Hier-TextNCA $60.3$ vs.\ Transformer-6L $52.8$ and Transformer-12L $44.7$ PPL), so we treat it as an analytical probe rather than a proposed alternative. The behaviour we observe is largely explained by the staged narrow-to-wide schedule: a non-iterating sliding-window Transformer that reuses the same schedule comes within $+4.1$ PPL of the iterated model, while reversing, flattening, or breaking the monotonic ordering of the schedule costs between $+16.7$ and $+70.8$ PPL. Iteration adds a smaller bounded benefit on top of the schedule, with a clear optimum at $T_s{=}4$ and a U-shaped degradation beyond it. The GRU gate and learned per-step embeddings are required for that benefit to appear, and training with random $T_s$ yields an inference-time iteration-count knob at the cost of substantially higher absolute PPL. We position the work as a controlled reading of which parts of NCA-style computation carry the weight in language modelling.

A striking feature of the human visual system is that it ingests visual information through a series of local foveated glimpses, rather than a single global computation. This makes human vision distinctly different from most popular computer vision models in use today, which input images globally and in a single shot. A natural question therefore is whether local, sequential vision models may provide any fundamental computational benefits in addition to being biologically more plausible than global models. In this work, we investigate this question from the perspective of visual state tracking and length generalization. Inspired by recent studies of length generalization in language models, we study the behavior of vision models trained on simple vision tasks that require the aggregation of local information across an image. Our experiments reveal that, similar to language models, vision models can learn to exploit global shortcuts and thereby fail to generalize over task length or complexity. We also show that recurrent vision policies based on strictly local perception can mitigate these failures, thereby allowing models to generalize on these tasks. Our results show that local attention may be an essential overlooked requirement for robust compositional generalization.

Autoregressive (AR) streaming models have emerged as a powerful paradigm for long video generation. However, the linearly growing Key-Value (KV) cache poses a significant bottleneck, leading to memory overload and degraded inference throughput. A common compression method is to drop redundant KV tokens, which often breaks long-range dependencies, resulting in temporal flickering and identity loss. In this paper, we propose Instance-Specific Parametric Absorption (ISPA), a novel framework that shifts the KV cache compression from discarding to distilling. The core idea is to transit a subset of layers from Full-Attention (F-Layers) to memory-efficient Local-Attention (L-Layers) by "absorbing" historical context into the model's weights. Specifically, during a brief warmup phase, ISPA monitors the output discrepancy between global and local attention. At the transition point, we solve a closed-form least-squares problem to compute an instance-specific weight modulation that compensates for the missing history. Experiments across architectures (1.3B to 14B) demonstrate that ISPA can remove up to 50% of the KV cache with near-lossless visual quality. We hope this perspective encourages future work to explore parametric memory consolidation beyond external token-level cache management for streaming generative models.

Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries. However, existing approaches implicitly assume a fixed domain size, which limits their ability to generalize at inference. In this work, we investigate domain extension, namely zero-shot inference on spatial domains that are significantly larger than those encountered during training. We argue that this setting fundamentally requires spatial locality and translation equivariance. We propose to implement this locality via a decomposable bias in the attention logits computation, enabling finely controllable locality while remaining fully decomposable into query-key inner products and directly compatible with optimized attention kernels. Combined with rotary positional embeddings, it enables expressive embeddings with controllable spatial support without altering the transformer architecture. We empirically show that our approach substantially improves zero-shot generalization to larger domains across two PDE benchmarks and a 3D industrial atmospheric flow application. Our code and datasets are available at https://github.com/cerea-daml/domain-extension.

Hybrid Transformers reduce the cost of long-context modeling by combining local attention with periodic full-attention layers. When global communication is already available, however, the best use of local computation remains unclear. We introduce Post-Boundary Bridge (PBB), which preserves causal attention within blocks and adds direct connections across their boundaries. Rather than extending the range of information relayed through successive local layers, PBB prioritizes within-block modeling and nearby exchange, leaving long-range communication to full-attention layers. Across dense and mixture-of-experts models with 205 million to 2.07 billion stored parameters, PBB hybrids retain near-Full perplexity and competitive performance on standard downstream benchmarks while improving controlled source retrieval. At 205 million parameters, PBB also matches a hybrid using sliding-window attention (SWA) in perplexity and achieves higher source-retrieval accuracy. The same boundary-aligned structure enables Flash-PBB, an exact decoding implementation that updates its key-value cache without relocating retained entries. Compared with Flash-SWA, Flash-PBB delivers 1.82x decode attention-core throughput with half the allocated local key-value cache. These results show that targeted boundary exchange can preserve model quality while enabling faster, more memory-efficient local attention between global layers.

Transformer-based Spiking Neural Networks (SNNs) integrate SNNs with global self-attention and have demonstrated impressive performance. However, existing Transformer-based SNNs suffer from two fundamental limitations. First, they typically employ max pooling layers to reduce the size of feature maps, but the max pooling captures only the strongest response and fails to comprehensively preserve representative regional features. Second, the global self-attention involves all global feature interactions, resulting in computational redundancy and quadratic computational complexity, thus conflicting with the sparse and energy-efficient characteristics of SNNs. To address these challenges, we develop Local Structure-Aware Spiking Transformer (LSFormer), a novel Transformer-based Spiking Neural Network that incorporates Spiking Response Pooling (SPooling) and Local Structure-Aware Spiking Self-Attention (LS-SSA). For the first time, our LSFormer leverages a local dilated window mechanism to capture both local details and long-range dependencies. Experimental results demonstrate that our LSFormer achieves state-of-the-art performance compared to existing advanced Transformer-based SNNs. Notably, on the more challenging static dataset Tiny-ImageNet and neuromorphic dataset N-CALTECH101, LSFormer substantially outperforms state-of-the-art baselines by 4.3% and 8.6% in top-1 classification accuracy, respectively. These results highlight the potential of LSFormer to advance energy-efficient spiking models toward practical deployment in large-scale vision applications.

The transformer is the most popular neural architecture for language modeling. The cornerstone of the transformer is its global attention mechanism, which lets the model aggregate information from all preceding tokens before generating the next token. One common variant of attention is called local attention, which restricts each token to aggregating information from a bounded window of predecessors, reducing the quadratic cost of global attention to linear. Although this restriction is usually motivated by efficiency, it has also been found to improve model quality, a phenomenon that has so far lacked a satisfactory explanation. We provide a formal account of this phenomenon in terms of recognizer expressivity. It has been shown that fixed-precision transformers with global attention correspond to a fragment of linear temporal logic containing a single past operator. We additionally prove that adding local attention introduces a second temporal operator, strictly enlarging the class of recognizable regular languages. Moreover, global and local attention are expressively complementary: neither subsumes the other, and combining them yields the richest fragment. Experiments on formal language recognition and natural language modeling corroborate the theory, showing that hybrid global--local transformers outperform their global-only counterparts.