Related papers: Correctness is Demanding, Performance is Frustrati…

Sequence generation and prediction form a cornerstone of modern machine learning, with applications spanning natural language processing, program synthesis, and time-series forecasting. These tasks are typically modeled in an autoregressive…

We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…

Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…

We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach. Unlike in the first ENIGMA implementation where fast linear classifier is trained and used together with…

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

Agda is a dependently-typed functional programming language, based on an extension of intuitionistic Martin-L\"of type theory. We implement first order natural deduction in Agda. We use Agda's type checker to verify the correctness of…

We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive…

This paper suggests an approach to the development of software testing and debugging automation tools based on precise program behavior models. The program behavior model is defined as a set of events (event trace) with two basic binary…

We consider two high-order tuners that have been shown to have accelerated performance, one based on Polyak's heavy ball method and another based on Nesterov's acceleration method. We show that parameter estimates are bounded and converge…

Retrieval-augmented generation (RAG) frameworks enable large language models (LLMs) to retrieve relevant information from a knowledge base and incorporate it into the context for generating responses. This mitigates hallucinations and…

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

Assertion-Based Verification (ABV) is critical for ensuring functional correctness in modern hardware systems. However, manually writing high-quality SVAs remains labor-intensive and error-prone. To bridge this gap, we propose AssertCoder,…

Unit testing represents the foundational basis of the software testing pyramid, beneath integration and end-to-end testing. Automated software testing researchers have proposed a variety of techniques to assist developers in this…

High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with…

An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…

In order to design and implement tracers, one must decide what exactly to trace and how to produce this trace. On the one hand, trace designs are too often guided by implementation concerns and are not as useful as they should be. On the…

We present a method for learning to satisfy uncertain constraints from demonstrations. Our method uses robust optimization to obtain a belief over the potentially infinite set of possible constraints consistent with the demonstrations, and…

We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…

This paper presents a new approach to the problem of correcting speech recognition errors by means of post-editing. It consists of using a neural sequence tagger that learns how to correct an ASR (Automatic Speech Recognition) hypothesis…

Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of…