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?
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?
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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
Aug 27
How Much Rank Does LoRA Need? Rank-Error Bounds for Transformer Attention
arXiv:2608. 26052v1 Announce Type: new Abstract: Choosing the rank of a low-rank adaptation (LoRA) update is usually an empirical task.
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
1d ago
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.
arXiv AI
Aug 18
Exact Attention Sensitivity and the Geometry of Transformer Stability
arXiv:2602. 18849v2 Announce Type: replace-cross Abstract: We develop a sensitivity analysis for transformer attention in a geometry aligned with tokenwise computation.
arXiv Computation and Language
Sep 14
SAS: Simple Attention Sparsification via End-to-End Optimization of Context Ranking
arXiv:2609.13141v1 Announce Type: new Abstract: Post-training attention sparsification reduces the quadratic cumulative attention cost of pretrained Transformers by selecting a small set of context u...
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
Sep 21
What Must Survive? Exact Task-Information--State Frontiers for Resource-Sufficient Learning
arXiv:2609.21523v1 Announce Type: new Abstract: A system may be compressed before its downstream task is fully known. We ask how much retained state is then necessary and how much can be saved by lim...
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
Sep 10
Convergent Stochastic Training of Multi-Headed Attention and Understanding LoRA
The paper establishes rigorous trainability results for multi-headed attention layers and Low Rank Adaptation (LoRA) models under stochastic training methods. By proving that the empirical regression loss induces a Poincaré inequality with constants independent of data dimension for LoRA and independent of head dimensions for multi-head attention, the authors show that a stochastic differential equation mimicking SGD converges to the loss minima. These results hold without assumptions on data or model size, providing the first theoretical guarantees for training such architectures.
arXiv Machine Learning
Aug 20
L\'evy Attention: Single-Pass Predictive Uncertainty for Continuous-Time Attention
arXiv:2608. 19171v1 Announce Type: new Abstract: Deep models for irregularly-sampled time series answer queries at arbitrary continuous timestamps, yet report nothing about how far each answer should be trusted.