Weapplythisnovelformulation of inference as controlto the canonical problem of inferring the hidden scalar state of a linear dynamical system with Gaussian variability.

Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG), quantifying the unavoidable discrepancy between a model's empirical fit and the population benchmark. Recovering the true population $R^2$, therefore, requires correcting observed predictive performance by this bound. Using a broad set of variables, including excess returns, yields, credit spreads, and valuation ratios, we find that the implied LLGs are large. This indicates that standard ML approaches can substantially understate true predictability in financial data. We also derive LLG-based refinements to the classic Hansen and Jagannathan (1991) bounds, analyze implications for parameter learning in general-equilibrium settings, and show that the LLG provides a natural mechanism for generating excess volatility.

Recent studies suggest that the representations learned by large language models (LLMs) are partially aligned to those of the human brain. However, whether and why this alignment score arises from a similar sequence of computations remains elusive. In this study, we explore this question by examining temporally-resolved brain signals of participants listening to 10 hours of an audiobook. We study these neural dynamics jointly with a benchmark encompassing 22 LLMs varying in size and architecture type. Our analyses confirm that LLMs and the brain generate representations in a similar order: specifically, activations in the initial layers of LLMs tend to best align with early brain responses, while the deeper layers of LLMs tend to best align with later brain responses. This brain-LLM alignment is consistent across transformers and recurrent architectures. However, its emergence depends on both model size and context length. Overall, this study sheds light on the sequential nature of computations and the factors underlying the partial convergence between biological and artificial neural networks.

Furthermore, using internal plans proves more robust to model quality compared to simulation-based approaches when predicting actions, while the results for event prediction are more mixed.

Contextual predictability shapes both the form and choice of words in online language production. The effects of the predictability of a word given its previous context are generally well-understood in both production and comprehension, but studies of naturalistic production have also revealed a poorly-understood backward predictability effect of a word given its future context, which may be related to future planning. Here, in two studies of naturalistic speech corpora, we investigate backward predictability effects using improved measures and more powerful language models, introducing a new principled and conceptually motivated information-theoretic predictability measure that integrates predictability from both the future and the past context. Our first study revisits classic predictability effects on word duration. Our second study investigates substitution errors within a generative framework that independently models the effects of lexical, contextual, and communicative factors on word choice, while predicting the actual words that surface as speech errors. We find that our proposed conceptually-motivated alternative to backward predictability yields qualitatively similar effects across both studies. Through a fine-grained analysis of substitution errors, we further show that different kinds of errors are suggestive of how speakers prioritize form, meaning, and context-based information during lexical planning. Together, these findings illuminate the functional roles of past and future context in how speakers encode and choose words, offering a bridge between contextual predictability effects and the mechanisms of sentence planning.

Speculative decoding (SD) has emerged as an effective technique to accelerate large language model (LLM) inference without compromising output quality. However, the achievable speedup largely depends on the effectiveness of the drafting model. While model-based methods like EAGLE-2 are accurate but costly, retrieval-enhanced methods like SAM-Decoding rely on heuristic switching strategies that often trigger unnecessary retrievals. To address this, we propose ReSpec (\textbf{Re}trieval-enhanced \textbf{Spe}culative Decoding), a novel framework that transforms heuristic drafter switching into adaptive decision-making. ReSpec features three core innovations: 1) An \textbf{entropy-guided adaptive trigger} quantifies contextual predictability to initiate retrieval only when uncertainty is low, avoiding costly low-quality speculations. 2) A \textbf{feedback-driven candidate selection} leverages historical feedback to organize multiple high-quality candidates for parallel verification, maximizing retrieval utility. 3) A source-aware \textbf{relaxed verification strategy} applies strict checks to model-generated drafts while using a relaxed verification for retrieved drafts, achieving a better balance between accuracy and efficiency. Extensive experiments on Spec-Bench demonstrate that ReSpec achieves state-of-the-art acceleration,outperforming EAGLE-2 and SAM-Decoding by over $33\%$ and $25\%$, respectively, while maintaining output quality.