Related papers: Step-by-Step Reasoning for Math Problems via Twist…

Process supervision, using a trained verifier to evaluate the intermediate steps generated by a reasoner, has demonstrated significant improvements in multi-step problem solving. In this paper, to avoid the expensive effort of human…

In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…

Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…

Inference-time methods that aggregate and prune multiple samples have emerged as a powerful paradigm for steering large language models, yet we lack any principled understanding of their accuracy-cost tradeoffs. In this paper, we introduce…

Enhancing large language models by simply scaling up datasets has begun to yield diminishing returns, shifting the spotlight to data quality. Monte Carlo Tree Search (MCTS) has emerged as a powerful technique for generating high-quality…

Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…

Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…

In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although…

Multi-sample, importance-weighted variational autoencoders (IWAE) give tighter bounds and more accurate uncertainty estimates than variational autoencoders (VAE) trained with a standard single-sample objective. However, IWAEs scale poorly:…

Verifying multi-step reasoning in large language models is difficult due to imprecise error localization and high token costs. Existing methods either assess entire reasoning chains, suffering attention dilution, or rely on expensive…

Logical reasoning is a pivotal component in the field of artificial intelligence. Proof planning, particularly in contexts requiring the validation of explanation accuracy, continues to present challenges. The recent advancement of large…

Recently a new class of Monte Carlo methods, called Time Relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes have been introduced. A generalized Wild sum expansion of the solution is at…

Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling. PRMs require step-level supervision, making them expensive to train. This work aims to build data-efficient PRMs as…

We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all…

Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that…

Large language models (LLMs) have demonstrated remarkable capabilities across diverse tasks. However, the truthfulness of their outputs is not guaranteed, and their tendency toward overconfidence further limits reliability. Uncertainty…

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…