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Transformers have demonstrated remarkable in-context learning (ICL) capabilities, adapting to new tasks by simply conditioning on demonstrations without parameter updates. Compelling empirical and theoretical evidence suggests that ICL, as…

As search depth increases in autonomous reasoning and embodied planning, candidate action spaces expand exponentially, often exhausting computational budgets. While heuristic pruning is a critical countermeasure, existing approaches lack…

Structured claim decomposition is often proposed as a solution for verifying complex, multi-faceted claims, yet empirical results have been inconsistent. We argue that these inconsistencies stem from two overlooked bottlenecks: evidence…

Reinforcement learning with function approximation has recently achieved tremendous results in applications with large state spaces. This empirical success has motivated a growing body of theoretical work proposing necessary and sufficient…

Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the…

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how…

Despite their widespread use in fact-checking, moderation, and high-stakes decision-making, large language models (LLMs) remain poorly understood as judges of truth. This study presents the largest evaluation to date of LLMs' veracity…

Large language models (LLMs) excel at explicit reasoning, but their implicit computational strategies remain underexplored. Decades of psychophysics research show that humans intuitively process and integrate noisy signals using…

Laplacian-P-splines (LPS) associate the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. Gaussian Markov field priors imposed on penalized latent variables…

Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As…

Model selection based on classical information criteria, such as BIC, is generally computationally demanding, but its properties are well studied. On the other hand, model selection based on parameter shrinkage by $\ell_1$-type penalties is…

The minimum description length (MDL) principle in supervised learning is studied. One of the most important theories for the MDL principle is Barron and Cover's theory (BC theory), which gives a mathematical justification of the MDL…

Determining how to appropriately select the tuning parameter is essential in penalized likelihood methods for high-dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear…

The performance of Large Language Models (LLMs) on natural language tasks can be improved through both supervised fine-tuning (SFT) and in-context learning (ICL), which operate via distinct mechanisms. Supervised fine-tuning updates the…

The effectiveness of model-based versus model-free methods is a long-standing question in reinforcement learning (RL). Motivated by recent empirical success of RL on continuous control tasks, we study the sample complexity of popular…

This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…

Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value…

Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost…

Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the…

The expansion of the low-altitude economy has underscored the significance of Low-Altitude Network Coverage (LANC) prediction for designing aerial corridors. While accurate LANC forecasting hinges on the antenna beam patterns of Base…