Jacob Zavatone-Veth | Searcharxiv

arXiv2026

Sequential Correlations Change In-Context Learning: Effective Context Length and Architectural Mismatch

Modern sequence models have a striking capacity for in-context learning (ICL); they can perform new tasks based only on examples given in the prompt. Understanding how this ability emerges requires theory that captures important properties of natural data. Linear regression has served as a useful sandbox for ICL theory, but existing work has largely focused on prompts with independent examples. In this work, we extend this setting to sequentially correlated data, a basic feature of real sequences. We present a solvable model based on linear attention and test our predictions on realistic transformer architectures. We identify two distinct effects: First, when the query token is independent of the context, within-context correlations induce an effective context length: correlated prompts behave like shorter i.i.d. prompts. Second, when the query is also correlated with its context, test error is reduced, particularly for softmax attention when compared to linear attention. These results suggest that correlated prompts alter not only the effective sample size of in-context learning, but also which attention architectures are best matched to the task.

stat.ML↗

arXiv2026

A Random Matrix Theory Perspective on the Consistency of Diffusion Models

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation $\sigma^2 \mapsto \kappa(\sigma^2)$, explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: \textit{anisotropy} across eigenmodes, \textit{inhomogeneity} across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.

cs.LG↗