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?
Attention Kernels for Learning Maps Between Heavy-Tailed Measures
The paper introduces attention kernels that replace the exponential function in transformer softmax to better handle operator learning on probability measures with heavy-tailed (polynomial) distributions. Two new benchmarks with closed‑form targets are constructed to evaluate how different kernel growth rates and data preprocessing affect performance. The study finds that slower‑growing kernels prevent ensemble collapse on heavy‑tailed tasks, while softmax with symlog preprocessing only succeeds on a subset of problems, and that all kernels perform similarly on Gaussian data.
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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 AI
6d ago
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.
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
Sep 4
Entropy-Generated Attention Beyond Softmax and Entmax: Kaniadakis and Reciprocal-Symmetric Abe Operators
The paper introduces two novel attention operators derived from generalized statistical entropies. The Kaniadakis entropy yields a full-support normalization with algebraically decaying weights, while the Abe entropy produces an implicit reciprocal-symmetric operator. The authors analyze these operators through a Fisher-metric Lagrangian framework, compare them to Softmax and entmax, and provide a tangent-gradient test to distinguish changes in attention profiles from mere scaling effects.
arXiv AI
Jun 29
Flexformer: Flexible Linear Transformer with Learnable Attention Kernel
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 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 AI
Jun 18
Beyond Similarity: Temporal Operator Attention for Time Series Analysis
arXiv:2605. 11287v2 Announce Type: replace-cross Abstract: A persistent paradox in time-series forecasting is that structurally simple MLP and linear models often outperform high-capacity Transformers.
arXiv Machine Learning
Jun 4
DiScoFormer: Plug-In Density and Score Estimation with Transformers
arXiv:2511. 05924v4 Announce Type: replace Abstract: Estimating probability density and its score from samples remains a core problem in generative modeling, Bayesian inference, and kinetic theory.
arXiv Machine Learning
Aug 10
Pay Attention to Attention Distribution: A New Local Lipschitz Bound for Transformers
arXiv:2507. 07814v2 Announce Type: replace Abstract: We introduce a novel upper bound on the local Lipschitz constant of the dot-product self-attention block showing its dependence on the attention map distributions.
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.
arXiv Machine Learning
Jul 27
Class-Balanced Softmax: A Bayes Theory-Based Method for Long-Tailed Recognition
arXiv:2607. 22258v1 Announce Type: new Abstract: Deep learning models using traditional softmax classifiers have achieved remarkable success in various classification tasks.