arXiv:2608. 09558v1 Announce Type: new Abstract: How expressive is prompting a transformer?
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: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. 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: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 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: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: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...
arXiv:2605. 18079v2 Announce Type: replace Abstract: Existing expressivity results for transformers typically rely on hardmax attention, high precision, and other architectural modifications that disconnect them from the models used in practice.
The paper proves that deep residual self‑attention networks can universally interpolate between any two collections of sequences using only two fixed single‑head attention blocks with Gaussian‑initialized projections. The interpolation is achieved by varying the order, signs, and durations of these blocks, independent of the specific input and output sequences. The result holds for both continuous and finite depth, and the authors also extend the analysis to causal‑masked settings.
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.
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.
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.