Related papers: Goedel Machines: Self-Referential Universal Proble…
In many model-based diagnosis applications it is impossible to provide such a set of observations and/or measurements that allow to identify the real cause of a fault. Therefore, diagnosis systems often return many possible candidates,…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
Code Language Models have been trained to generate accurate solutions, typically with no regard for runtime. On the other hand, previous works that explored execution optimisation have observed corresponding drops in functional correctness.…
While language models have shown remarkable performance across diverse tasks, they still encounter challenges in complex reasoning scenarios. Recent research suggests that language models trained on linearized search traces toward…
Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models. However, existing methods rely solely on outcome rewards, without explicitly optimizing verification or leveraging…
In this article, we tackle the math word problem, namely, automatically answering a mathematical problem according to its textual description. Although recent methods have demonstrated their promising results, most of these methods are…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
Many modern high-performing machine learning models such as GPT-3 primarily rely on scaling up models, e.g., transformer networks. Simultaneously, a parallel line of work aims to improve the model performance by augmenting an input instance…
Software developers frequently issue generic natural language queries for code search while using code search engines (e.g., GitHub native search, Krugle). Such queries often do not lead to any relevant results due to vocabulary mismatch…
Recently, researchers have been working toward the development of practical general-purpose protocols for verifiable computation. These protocols enable a computationally weak verifier to offload computations to a powerful but untrusted…
Reconstructing a method's change history efficiently and accurately is critical for many software engineering tasks, including maintenance, refactoring, and comprehension. Despite the availability of method history generation tools such as…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text…
For the generalized eigenvalue problem, a quotient function is devised for estimating eigenvalues in terms of an approximate eigenvector. This gives rise to an infinite family of quotients, all entirely arguable to be used in estimation.…
Through reinforcement learning (RL) with outcome correctness rewards, large reasoning models (LRMs) with scaled inference computation have demonstrated substantial success on complex reasoning tasks. However, the one-sided reward, focused…
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature,…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
Heavy supervised fine-tuning on a target domain can strongly suppress capabilities that were present in the base model. We study this phenomenon in formal mathematics using Goedel-Prover-V2, an open-source model heavily trained on 1.8…
Inspired by Leivant's work on absolute predicativism, Bellantoni and Cook in 1992 introduced a structurally restricted form of recursion called predicative recursion. Using this recursion scheme on the inductive structures of natural…
As the demand for computational power grows, optimizing code through compilers becomes increasingly crucial. In this context, we focus on fully automatic code optimization techniques that automate the process of selecting and applying code…