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Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we…

Reinforcement learning (RL) in continuous state-action spaces remains challenging in scientific computing due to poor sample efficiency and lack of pathwise physical consistency. We introduce Differential Reinforcement Learning…

Aligning large-scale vision-language models (VLMs) for complex reasoning via reinforcement learning is often hampered by the limitations of existing policy optimization algorithms, such as static training schedules and the rigid, uniform…

Group Relative Policy Optimization (GRPO) has significantly advanced the reasoning ability of large language models (LLMs), particularly by boosting their mathematical performance. However, GRPO and related entropy-regularization methods…

Milner's bigraphs are a general framework for reasoning about distributed and concurrent programming languages. Notably, it has been designed to encompass both the pi-calculus and the Ambient calculus. This paper is only concerned with…

Compositional knowledge representations in reinforcement learning (RL) facilitate modular, interpretable, and safe task specifications. However, generating compositional models requires the characterization of minimal assumptions for the…

Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…

In this paper we present an application of a simple technique of local recompression, previously developed by the author in the context of compressed membership problems and compressed pattern matching, to word equations. The technique is…

This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…

By reformulating a learning process of a set system L as a game between Teacher (presenter of data) and Learner (updater of the abstract independent set), we define the order type dim L of L to be the order type of the game tree. The theory…

A significant portion of recent research on Large Language Model (LLM) alignment focuses on developing new policy optimization methods based on Group Relative Policy Optimization (GRPO). Two prominent directions have emerged: (i) a shift…

In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in…

We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…

We propose Q-learning with Adjoint Matching (QAM), a novel TD-based reinforcement learning (RL) algorithm that tackles a long-standing challenge in continuous-action RL: efficient optimization of an expressive diffusion or flow-matching…

In reinforcement learning, conducting task composition by forming cohesive, executable sequences from multiple tasks remains challenging. However, the ability to (de)compose tasks is a linchpin in developing robotic systems capable of…

Direct Preference Optimization (DPO) is an effective approach for aligning protein language models with experimental design goals. However, DPO faces a scalability bottleneck: the number of possible training pairs grows quadratically with…

Existing studies on constrained reinforcement learning (RL) may obtain a well-performing policy in the training environment. However, when deployed in a real environment, it may easily violate constraints that were originally satisfied…

Direct Preference Optimization (DPO) has emerged as a predominant alignment method for diffusion models, facilitating off-policy training without explicit reward modeling. However, its reliance on large-scale, high-quality human preference…

This paper delivers a new perspective of thinking and utilizing syntactic n-grams (sn-grams). Sn-grams are a type of non-linear n-grams which have been playing a critical role in many NLP tasks. Introducing sn-grams to comparing document…

In this paper, we prove a crucial theorem called Mirroring Theorem which affirms that given a collection of samples with enough information in it such that it can be classified into classes and subclasses then (i) There exists a mapping…