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We introduce LADDER (Learning through Autonomous Difficulty-Driven Example Recursion), a framework which enables Large Language Models to autonomously improve their problem-solving capabilities through self-guided learning by recursively…
Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for…
Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
Recent advances in large language models (LLMs) have shown promise in formal theorem proving, yet evaluating semantic correctness remains challenging. Existing evaluations rely on indirect proxies such as lexical overlap with…
The performance of a constraint model can often be improved by converting a subproblem into a single table constraint (referred to as tabulation). Finding subproblems to tabulate is traditionally a manual and time-intensive process, even…
The use of autonomous vehicles in real-world applications is often precluded by the difficulty of providing safety guarantees for their complex controllers. The simulation-based testing of these controllers cannot deliver sufficient safety…
This paper investigates the logical reasoning capabilities of large language models (LLMs). For a precisely defined yet tractable formulation, we choose the conceptually simple but technically complex task of constructing proofs in Boolean…
Inductive reasoning enables humans to infer abstract rules from limited examples and apply them to novel situations. In this work, we compare an LLM-based hypothesis search framework with direct program generation approaches on few-shot…
The objective of this paper is to propose a method that will generate a causal explanation of observed events in an uncertain world and then make decisions based on that explanation. Feedback can cause the explanation and decisions to be…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning…
We present a novel approach to automated proof generation for the TLA+ Proof System (TLAPS) using Large Language Models (LLMs). Our method combines two key components: a sub-proof obligation generation phase that breaks down complex proof…
Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…
Running LLMs with extended reasoning on every problem is expensive, but determining which inputs actually require additional compute remains challenging. We investigate whether their own likelihood of success is recoverable from their…
Prompt engineering is crucial for achieving reliable and effective outputs from large language models (LLMs), but its design requires specialized knowledge of prompting techniques and a deep understanding of target tasks. To address this…
Answering complex questions that require making latent decisions is a challenging task, especially when limited supervision is available. Recent works leverage the capabilities of large language models (LMs) to perform complex question…