The paper introduces Cubit, a Transformer‑style architecture that replaces the standard attention mechanism with Kernel Ridge Regression (KRR). By interpreting attention as Nadaraya‑Watson regression, Cubit incorporates the closed‑form KRR solution, combining kernel‑based value aggregation with normalization via the inverse kernel matrix. The authors also propose a Limited‑Range Rescale (LRR) to stabilize training and report that Cubit shows improved long‑sequence modeling, with gains increasing as training sequence length grows.
arXiv:2606. 29256v1 Announce Type: cross Abstract: In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep learning.
arXiv:2605. 18848v3 Announce Type: replace Abstract: This paper introduces Exact Linear Attention (ELA), a mechanism that achieves linear computational complexity for Transformer attention by exploiting the exact decomposition property of kernel functions, thereby eliminating approximation error.
arXiv:2606. 27748v1 Announce Type: cross Abstract: Transformer models rely on attention mechanism to capture long-range dependencies but suffer from quadratic complexity, limiting their scalability to long sequences.
arXiv:2605. 08475v3 Announce Type: replace-cross Abstract: In this paper, we study in-context kernel ridge regression (KRR) with Gaussian kernels and show, both theoretically and empirically, that a standard softmax-attention transformer can approximate the KRR predictor during its forward pass.
The paper introduces Data-Adaptive Mahalanobis Cross-Head Attention (DAMCHA), a new attention mechanism that extends Multi-Head Attention by learning a full cross-head metric matrix, thereby capturing inter-head interactions beyond the block-diagonal structure of standard MHA. DAMCHA parameterizes this metric as an input-dependent function, allowing the attention geometry to adapt dynamically to the data’s intrinsic manifold structure. The authors also propose regularization techniques, such as stack-wise parameter sharing, to maintain computational efficiency and stable optimization, and demonstrate that DAMCHA-equipped Transformers outperform existing baselines on multiple benchmark tasks.
The paper introduces Data-Adaptive Mahalanobis Cross-Head Attention (DAMCHA), a new attention mechanism that extends Multi-Head Attention by learning a full cross-head metric matrix and adapting it to input data. DAMCHA captures inter-head interactions beyond the block-diagonal structure of standard MHA and uses input-dependent parameterization for dynamic attention geometry. The authors provide regularization techniques, such as stack-wise parameter sharing, to maintain efficiency and stability, and report that DAMCHA-based Transformers outperform baselines on several benchmarks.
arXiv:2610.20337v1 Announce Type: new Abstract: The success of transformers is attributed to several factors, including their capacity to express formal languages over variable-length inputs, and abi...
arXiv:2607. 00479v1 Announce Type: new Abstract: Transformer-based large models have demonstrated remarkable generalization abilities across different tasks by leveraging a context-aware attention module for in-context learning.
arXiv:2607. 18759v1 Announce Type: new Abstract: Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not.
arXiv:2607. 20214v1 Announce Type: cross Abstract: The quadratic $N\times N$ attention score matrix remains a central obstacle to extending Transformers to longer input lengths.
The paper examines how to allocate attention heads and head dimensions across Transformer layers to balance expressivity and efficiency. It provides a mathematical analysis of early layers’ role in information extraction and characterizes the trade‑off between head count and dimension under a fixed parameter budget. The authors prove a saturation effect of softmax activations, showing that increasing head dimensions yields diminishing returns, especially for long sequences, and propose strategies for efficient parameter allocation across layers.
arXiv:2609.07086v1 Announce Type: new Abstract: Transformers are a dominant architecture in modern machine learning, powering applications across vision, language, and beyond. At the core of their su...