Related papers: On Optimal Testing of Linearity

Offline policy evaluation is a fundamental statistical problem in reinforcement learning that involves estimating the value function of some decision-making policy given data collected by a potentially different policy. In order to tackle…

Over the last three decades, function testing has been extensively studied over Boolean, finite fields, and discrete settings. However, to encode the real-world applications more succinctly, function testing over the reals (where the domain…

In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…

We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…

Prior work proposed simple test-time scaling, a method for replicating this scaling behavior with models distilled from o1-like models by manually controlling test-time compute: either scaling down by enforcing a maximum length or scaling…

Recently, there has been significant work studying distribution testing under the Conditional Sampling model. In this model, a query specifies a subset $S$ of the domain, and the output received is a sample drawn from the distribution…

A central issue of many statistical learning problems is to select an appropriate model from a set of candidate models. Large models tend to inflate the variance (or overfitting), while small models tend to cause biases (or underfitting)…

Evaluating large language models (LLMs) typically requires thousands of benchmark items, making the process expensive, slow, and increasingly impractical at scale. Existing evaluation protocols rely on average accuracy over fixed item sets,…

We propose and analyze a reinforcement learning principle that approximates the Bellman equations by enforcing their validity only along an user-defined space of test functions. Focusing on applications to model-free offline RL with…

Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies…

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large…

Representation multi-task learning (MTL) has achieved tremendous success in practice. However, the theoretical understanding of these methods is still lacking. Most existing theoretical works focus on cases where all tasks share the same…

Set functions with convenient properties (such as submodularity) appear in application areas of current interest, such as algorithmic game theory, and allow for improved optimization algorithms. It is natural to ask (e.g., in the context of…

In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The…

Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference of these two properties also testable? We initiate a systematic study of these basic set-theoretic…

Test-time scaling (TTS) has emerged as a new frontier for scaling the performance of Large Language Models. In test-time scaling, by using more computational resources during inference, LLMs can improve their reasoning process and task…

Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…

Deep neural network training often involves stochastic optimization, meaning each run will produce a different model. This implies that hyperparameters of the training process, such as the random seed itself, can potentially have…

Best-of-N selection is a key technique for improving the reasoning performance of Large Language Models (LLMs) through increased test-time computation. Current state-of-the-art methods often employ computationally intensive reward models…

As enthusiasm for scaling computation (data and parameters) in the pretraining era gradually diminished, test-time scaling (TTS), also referred to as ``test-time computing'' has emerged as a prominent research focus. Recent studies…