Related papers: Automated Theorem Proving in Intuitionistic Propos…
Mathematical reasoning is one of the crucial abilities of general artificial intelligence, which requires machines to master mathematical logic and knowledge from solving problems. However, existing approaches are not transparent (thus not…
Explainable reinforcement learning allows artificial agents to explain their behavior in a human-like manner aiming at non-expert end-users. An efficient alternative of creating explanations is to use an introspection-based method that…
Reinforcement learning (RL) has emerged as a key paradigm for aligning and optimizing large language models (LLMs). Standard approaches treat the LLM as the policy and apply RL directly over the full vocabulary space. However, this…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
Reinforcement Learning (RL) traditionally relies on scalar reward signals, limiting its ability to leverage the rich semantic knowledge often available in real-world tasks. In contrast, humans learn efficiently by combining numerical…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
Polynomial inequality proving is fundamental to many mathematical disciplines and finds wide applications in diverse fields. Current traditional algebraic methods are based on searching for a polynomial positive definite representation over…
Resource limitations make it hard to provide all students with one of the most effective educational interventions: personalized instruction. Reinforcement learning could be a key tool to reduce the development cost and improve the…
Recent work by Clark et al. (2020) shows that transformers can act as 'soft theorem provers' by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
The policy represented by the deep neural network can overfit the spurious features in observations, which hamper a reinforcement learning agent from learning effective policy. This issue becomes severe in high-dimensional state, where the…
Chain-of-Thought (CoT) prompting methods have enabled large language models (LLMs) to generate reasoning paths and solve math word problems (MWPs). However, they are sensitive to mistakes in the paths, as any mistake can result in an…
Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…
Automated Text Scoring (ATS) provides a cost-effective and consistent alternative to human marking. However, in order to achieve good performance, the predictive features of the system need to be manually engineered by human experts. We…
Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover…
This paper introduces a simple and scalable approach to improve the data efficiency of large language model (LLM) training by augmenting existing text data with thinking trajectories. The compute for pre-training LLMs has been growing at an…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
General reasoning represents a long-standing and formidable challenge in artificial intelligence. Recent breakthroughs, exemplified by large language models (LLMs) and chain-of-thought prompting, have achieved considerable success on…
We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong…
Natural language explanations play a fundamental role in Natural Language Inference (NLI) by revealing how premises logically entail hypotheses. Recent work has shown that the interaction of large language models (LLMs) with theorem provers…