arXiv Machine Learning
Aug 11
Training-Free Universal Approximation by Prompting Random Transformers
arXiv:2608. 09558v1 Announce Type: new Abstract: How expressive is prompting a transformer?
Transformers Can Implement Preconditioned Richardson Iteration for In-Context Gaussian Kernel Regression
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.
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arXiv Machine Learning
Aug 27
Cubit: Token Mixer with Kernel Ridge Regression
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 Machine Learning
Jul 2
Ghost in the Kernel: In-Context Learning with Efficient Transformers via Domain Generalization
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 Machine Learning
Jul 22
Relative Positions Generalize, Absolute Positions Memorize: An Implicit-Bias Account of Length Generalization in Attention
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 Machine Learning
Jun 17
Softmax as Linear Attention in the Large-Prompt Regime: a Measure-based Perspective
arXiv:2512. 11784v2 Announce Type: replace Abstract: Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis.
arXiv Machine Learning
Jun 5
Exact Linear Attention
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 Machine Learning
Jul 28
The Entropic Bound for Transformers: Why Static Rank Fails and Attention-Native Rank Recovers
arXiv:2607. 23050v1 Announce Type: new Abstract: Neural scaling laws describe how loss decreases as models, data, and compute grow, but they do not answer a prior question: for a fixed task, what is the minimum model capacity required to solve it?
arXiv Machine Learning
1d ago
Predictive Geometry of Hidden Trajectories in Transformers
arXiv:2609.37717v1 Announce Type: new Abstract: Decoder-only transformers are trained only through a terminal next-token prediction loss, yet this loss constrains every intermediate hidden state thro...
arXiv AI
Jul 23
ELSAA: Efficient Low-Rank and Sparse Attention Approximation for Training Transformers
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.
arXiv Machine Learning
6d ago
Transformers as Cross-Task Learners: Shared Structure Drives Sample Efficiency in In-Context Learning
Transformers can learn broad families of tasks during pretraining and adapt to unseen tasks from a short prompt, but a rigorous understanding of this capability is limited. This paper studies how shared cross‑task structure influences the sample complexity of in‑context learning (ICL) by characterizing task‑space complexity through covering numbers, yielding a set of anchor functions that localize unseen tasks and predict responses. The authors construct a Transformer with Softmax attention to approximate this procedure and derive an error bound that separates the effects of pretraining tasks and prompt length, showing that once enough tasks are available the dependence on prompt length becomes dimension‑free.
arXiv Machine Learning
Jun 15
Zeta: Dual Whitening for Matrix Optimization via Coordinate-Adaptive Preconditioning
arXiv:2606. 14187v1 Announce Type: new Abstract: Large-scale neural network training increasingly relies on matrix-aware optimizers that exploit the structure of weight parameters beyond element-wise adaptation.
arXiv Machine Learning
Sep 2
Performance-Efficiency Tradeoffs in Transformers: An Approximation Theory Perspective
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.