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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…
In this work, we address question answering (QA) over a hybrid of tabular and textual data that are very common content on the Web (e.g. SEC filings), where discrete reasoning capabilities are often required. Recently, large language models…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
Machine Learning (ML) has become an integral part of our society, commonly used in critical domains such as finance, healthcare, and transportation. Therefore, it is crucial to evaluate not only whether ML models make correct predictions…
Automated machine learning (AutoML) has received increasing attention in the recent past. While the main tools for AutoML, such as Auto-WEKA, TPOT, and auto-sklearn, mainly deal with single-label classification and regression, there is very…
As large language models (LLMs) continue to advance rapidly, reliable governance tools have become critical. Publicly verifiable watermarking is particularly essential for fostering a trustworthy AI ecosystem. A central challenge persists:…
Relational programming enables program synthesis through a verifier-to-solver approach. An earlier paper introduced a functional conversion that mitigated some of the inherent performance overhead. However, the conversion was inelegant: it…
This work offers a broad perspective on probabilistic modeling and inference in light of recent advances in probabilistic programming, in which models are formally expressed in Turing-complete programming languages. We consider a typical…
Evaluation of large language models (LLMs) has raised great concerns in the community due to the issue of data contamination. Existing work designed evaluation protocols using well-defined algorithms for specific tasks, which cannot be…
Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by…
Interactive theorem proving software is typically designed around a trusted proof-checking kernel, the sole system component capable of authenticating theorems. Untrusted automation procedures reside outside of the kernel, and drive it to…
Large language models (LLMs) have taken the world by storm by making many previously difficult uses of AI feasible. LLMs are controlled via highly expressive textual prompts and return textual answers. Unfortunately, this unstructured text…
Hofmann (1999) introduced the functional programming language LFPL to characterize the functions computable in polynomial time using an affine type system. LFPL enables a natural programming style, including nested recursion, and has…
Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel…
Probabilistic programming and the formal analysis of probabilistic algorithms are active areas of research, driven by the widespread use of randomness to improve performance. While functional correctness has seen substantial progress,…
Modern separation logics allow one to prove rich properties of intricate code, e.g. functional correctness and linearizability of non-blocking concurrent code. However, this expressiveness leads to a complexity that makes these logics…
We introduce a theorem proving approach to the specification and generation of temporal logical constraints for training neural networks. We formalise a deep embedding of linear temporal logic over finite traces (LTL$_f$) and an associated…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
Liquid Haskell's refinement-reflection feature augments the Haskell language with theorem proving capabilities, allowing programmers to retrofit their existing code with proofs. But many of these proofs require routine, boilerplate code…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…