Related papers: The Biggest Five of Reverse Mathematics
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
The Process Reward Model (PRM) plays a crucial role in mathematical reasoning tasks, requiring high-quality supervised process data. However, we observe that reasoning steps generated by Large Language Models (LLMs) often fail to exhibit…
Reverse Monte Carlo (RMC) is an algorithm that incorporates stochastic modification of the action as part of the process that updates the fields in a Monte Carlo simulation. Such update moves have the potential of lowering or eliminating…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
Recent advances in applying reinforcement learning (RL) to large language models (LLMs) have led to substantial progress. In particular, a series of remarkable yet often counterintuitive phenomena have been reported in LLMs, exhibiting…
Large Reasoning Models (LRMs) have demonstrated remarkable problem-solving abilities in mathematics, as evaluated by existing benchmarks exclusively on well-defined problems. However, such evaluation setup constitutes a critical gap, since…
Large Multimodal Models (LMMs) have achieved remarkable success in vision-language tasks, yet their vast parameter counts are often underutilized during both training and inference. In this work, we embrace the idea of looping back to move…
The availability of large pre-trained models is changing the landscape of Machine Learning research and practice, moving from a training-from-scratch to a fine-tuning paradigm. While in some applications the goal is to "nudge" the…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
This paper describes a generalization of Clark's completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to…
The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
In machine learning, it is common to obtain multiple equally performing models for the same prediction task, e.g., when training neural networks with different random seeds. Model multiplicity (MM) is the situation which arises when these…
We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focussing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form.…
Reward machines (RMs) inform reinforcement learning agents about the reward structure of the environment. This is particularly advantageous for complex non-Markovian tasks because agents with access to RMs can learn more efficiently from…