Related papers: The computability path ordering
Direct Preference Optimization (DPO) has proven effective in complex reasoning tasks like math word problems and code generation. However, when applied to Text-to-SQL datasets, it often fails to improve performance and can even degrade it.…
Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse…
Test-time scaling has proven effective in further enhancing the performance of pretrained Large Language Models (LLMs). However, mainstream post-training methods (i.e., reinforcement learning (RL) with chain-of-thought (CoT) reasoning)…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
We provide a sound and relatively complete Hoare-like proof system for reasoning about partial correctness of recursive procedures in presence of local variables and the call-by-value parameter mechanism, and in which the correctness proofs…
Large language model reasoning is often treated as a monolithic capability, relying on binary preference supervision that fails to capture partial progress or fine-grained reasoning quality. We introduce Continuous Utility Direct Preference…
This paper is concerned with the automated complexity analysis of term rewrite systems (TRSs for short) and the ramification of these in implicit computational complexity theory (ICC for short). We introduce a novel path order with multiset…
For many applications of reinforcement learning it can be more convenient to specify both a reward function and constraints, rather than trying to design behavior through the reward function. For example, systems that physically interact…
Higher-order constructs enable more expressive and concise code by allowing procedures to be parameterized by other procedures. Assertions allow expressing partial program specifications, which can be verified either at compile time…
This dissertation explores the roles of polarities and focussing in various aspects of Computational Logic. These concepts play a key role in the the interpretation of proofs as programs, a.k.a. the Curry-Howard correspondence, in the…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
Within the domain of large language models, reinforcement fine-tuning algorithms necessitate the generation of a complete reasoning trajectory beginning from the input query, which incurs significant computational overhead during the…
In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by…
This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main…
Reinforcement learning with verifiable rewards has become the standard recipe for improving LLM reasoning, but the dominant algorithm GRPO assigns a single trajectory-level advantage to every token, diluting the signal at pivotal reasoning…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
The static dependency pair method is a method for proving the termination of higher-order rewrite systems a la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability…
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic…