Transformer is a transformative framework for deep learning which models sequential data and has achieved remarkable performance on a wide range of tasks, but with high computational and energy cost. To improve its efficiency, a popular choice is to compress the models via binarization which constrains the floating-point values into binary ones to save resource consumption owing to cheap bitwise operations significantly. However, existing binarization methods only aim at minimizing the information loss for the input distribution statistically, while ignoring the pairwise similarity modeling at the core of the attention mechanism. To this end, we propose a new binarization paradigm customized to high-dimensional softmax attention via kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. The kernelized hash functions are learned to match the ground-truth similarity relations extracted from the attention map in a self-supervised way. Based on the equivalence between the inner product of binary codes and the Hamming distance as well as the associative property of matrix multiplication, we can approximate the attention in linear complexity by expressing it as a dot-product of binary codes. Moreover, the compact binary representations of queries and keys in EcoFormer enable us to replace most of the expensive multiply-accumulate operations in attention with simple accumulations to save considerable on-chip energy footprint on edge devices. Extensive experiments on both vision and language tasks show that EcoFormer consistently achieves comparable performance with standard attentions while consuming much fewer resources. For example, based on PVTv2-B0 and ImageNet-1K, EcoFormer achieves a 73% reduction in on-chip energy footprint with only a slight performance drop of 0.33% compared to the standard attention.

Complex-valued signals encode both amplitude and phase, yet most deep models treat attention as real-valued correlation, overlooking interference effects. We introduce the Holographic Transformer, a physics-inspired architecture that incorporates wave interference principles into self-attention. Holographic attention modulates interactions by relative phase and coherently superimposes values, ensuring consistency between amplitude and phase. A dual-headed decoder simultaneously reconstructs the input and predicts task outputs, preventing phase collapse when losses prioritize magnitude over phase. We demonstrate that holographic attention implements a discrete interference operator and maintains phase consistency under linear mixing. Experiments on PolSAR image classification and wireless channel prediction show strong performance, achieving high classification accuracy and F1 scores, low regression error, and increased robustness to phase perturbations. These results highlight that enforcing physical consistency in attention leads to generalizable improvements in complex-valued learning and provides a unified, physics-based framework for coherent signal modeling. The code is available at https://github.com/EonHao/Holographic-Transformers.

The success of Transformer language models is widely credited to their dot-product attention mechanism, which interweaves a set of key design principles: mixing information across positions (enabling multi-token interactions), sequence-dependent activations (where attention weights adapt to each input), a specific mathematical form (dot-product similarities plus softmax weighting), and coupling of queries and keys to evolving hidden states (grounding attention in the current layer). However, the necessity of each of these principles remains largely untested. In this work, we systematically deconstruct attention by designing controlled variants that selectively relax these principles, applied both uniformly across all layers and in hybrid architectures where only some layers retain standard attention. Our empirical analysis reveals that mechanisms for mixing tokens are indispensable, as their absence collapses models to near-random behavior, while the exact mathematical form and sequence dependency can be substantially relaxed, especially when preserved in just a subset of layers. Surprisingly, even variants that fail in isolation can achieve robust performance when interleaved with standard attention, highlighting a cooperative effect. These findings deepen our understanding of what truly underpins attention's effectiveness and open new avenues for simplifying language models without sacrificing performance.

Differential Attention (DA) has been proposed as a refinement to standard attention, suppressing redundant or noisy context through a subtractive structure and thereby reducing contextual hallucination. While this design sharpens task-relevant focus, we show that it also introduces a structural fragility under adversarial perturbations. Our theoretical analysis identifies negative gradient alignment-a configuration encouraged by DA's subtraction-as the key driver of sensitivity amplification, leading to increased gradient norms and elevated local Lipschitz constants. We empirically validate this Fragile Principle through systematic experiments on ViT/DiffViT and evaluations of pretrained CLIP/DiffCLIP, spanning five datasets in total. These results demonstrate higher attack success rates, frequent gradient opposition, and stronger local sensitivity compared to standard attention. Furthermore, depth-dependent experiments reveal a robustness crossover: stacking DA layers attenuates small perturbations via depth-dependent noise cancellation, though this protection fades under larger attack budgets. Overall, our findings uncover a fundamental trade-off: DA improves discriminative focus on clean inputs but increases adversarial vulnerability, underscoring the need to jointly design for selectivity and robustness in future attention mechanisms.

Standard attention mechanisms in transformers employ static token representations that remain unchanged across all pair-wise computations in each layer. This limits their representational alignment with the potentially diverse relational dynamics of each token-pair interaction. While they excel in domains with relatively homogeneous relationships, standard attention's static relational learning struggles to capture the diverse, heterogeneous inter-channel dependencies of multivariate time series (MTS) data--where different channel-pair interactions within a single system may be governed by entirely different physical laws or temporal dynamics. To better align the attention mechanism for such domain phenomena, we propose attention with dynamic relational priming (prime attention). Unlike standard attention where each token presents an identical representation across all of its pair-wise interactions, prime attention tailors each token dynamically (or per interaction) through learnable modulations to best capture the unique relational dynamics of each token pair, optimizing each pair-wise interaction for that specific relationship. This representational plasticity of prime attention enables effective extraction of relationship-specific information in MTS while maintaining the same asymptotic computational complexity as standard attention. Our results demonstrate that prime attention consistently outperforms standard attention across benchmarks, achieving up to 6.5% improvement in forecasting accuracy. In addition, we find that prime attention achieves comparable or superior performance using up to 40% less sequence length compared to standard attention, further demonstrating its superior relational modeling capabilities. An important challenge in applying transformers to multivariate time series (MTS) stems from domain mismatch. In language modeling, token relationships are predominantly semantic in nature, enabling most critical patterns to be captured by simple weighted sums of token representations. Similarly, in computer vision, spatial relationships dominate, enabling attention mechanisms to focus on regions of interest through uniform spatial reasoning. Learning on graphs exhibits comparable homogeneity, where node relationships are fundamentally structural and connectivity-based, allowing standard attention to model interactions through meaningful topological patterns (that are sometimes separated by relationship type (Schlichtkrull et al., 2018; Hu et al., 2020; Wang et al., 2019)). By static, we mean that token representations in each layer are fixed relative to all other tokens throughout pair-wise modeling. We classify this property of standard attention mechanisms as static relational learning.

The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimensional inputs. Additionally, attention uses the same scoring function for all input pairs, without imposing a distance-dependent compute bias for neighboring tokens in the sequence. In this work, we address these shortcomings by proposing new scoring functions based on computationally efficient structured matrices with high ranks, including Block Tensor-Train (BTT) and Multi-Level Low Rank (MLR) matrices. On in-context regression tasks with high-dimensional inputs, our proposed scoring functions outperform standard attention for any fixed compute budget. On language modeling, a task that exhibits locality patterns, our MLR-based attention method achieves improved scaling laws compared to both standard attention and variants of sliding window attention. Additionally, we show that both BTT and MLR fall under a broader family of efficient structured matrices capable of encoding either full-rank or distance-dependent compute biases, thereby addressing significant shortcomings of standard attention. Finally, we show that MLR attention has promising results for long-range time-series forecasting.

Pre-trained transformer models with extended context windows are notoriously expensive to run at scale, often limiting real-world deployment due to their high computational and memory requirements. In this paper, we introduce Hamming Attention Distillation (HAD), a novel framework that binarizes keys and queries in the attention mechanism to achieve significant efficiency gains. By converting keys and queries into {-1, +1} vectors and replacing dot-product operations with efficient Hamming distance computations, our method drastically reduces computational overhead. Additionally, we incorporate attention matrix sparsification to prune low-impact activations, which further reduces the cost of processing long-context sequences. \par Despite these aggressive compression strategies, our distilled approach preserves a high degree of representational power, leading to substantially improved accuracy compared to prior transformer binarization methods. We evaluate HAD on a range of tasks and models, including the GLUE benchmark, ImageNet, and QuALITY, demonstrating state-of-the-art performance among binarized Transformers while drastically reducing the computational costs of long-context inference. \par We implement HAD in custom hardware simulations, demonstrating superior performance characteristics compared to a custom hardware implementation of standard attention. HAD achieves just $\mathbf{1.78}\%$ performance losses on GLUE compared to $9.08\%$ in state-of-the-art binarization work, and $\mathbf{2.5}\%$ performance losses on ImageNet compared to $12.14\%$, all while targeting custom hardware with a $\mathbf{79}\%$ area reduction and $\mathbf{87}\%$ power reduction compared to its standard attention counterpart.

Transformers have had tremendous impact for several sequence related tasks, largely due to their ability to retrieve from any part of the sequence via softmax based dot-product attention. This mechanism plays a crucial role in Transformer's performance. We analyze the gradients backpropagated through the softmax operation in the attention mechanism and observe that these gradients can often be small. This poor gradient signal backpropagation can lead to inefficient learning of parameters preceeding the attention operations. To this end, we introduce a new attention mechanism called LASER, which we analytically show to admit a larger gradient signal. We show that LASER Attention can be implemented by making small modifications to existing attention implementations. We conduct experiments on autoregressive large language models (LLMs) with upto 2.2 billion parameters where we show upto 3.38% and an average of ~1% improvement over standard attention on downstream evaluations. Using LASER gives the following relative improvements in generalization performance across a variety of tasks (vision, text and speech): 4.67% accuracy in Vision Transformer (ViT) on Imagenet, 2.25% error rate in Conformer on the Librispeech speech-to-text and 0.93% fraction of incorrect predictions in BERT with 2.2 billion parameters.

Transformer is a transformative framework for deep learning which models sequential data and has achieved remarkable performance on a wide range of tasks, but with high computational and energy cost. To improve its efficiency, a popular choice is to compress the models via binarization which constrains the floating-point values into binary ones to save resource consumption owing to cheap bitwise operations significantly. However, existing binarization methods only aim at minimizing the information loss for the input distribution statistically, while ignoring the pairwise similarity modeling at the core of the attention mechanism. To this end, we propose a new binarization paradigm customized to high-dimensional softmax attention via kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. The kernelized hash functions are learned to match the ground-truth similarity relations extracted from the attention map in a self-supervised way.