Related papers: Beyond Theorem Proving: Formulation, Framework and…
We introduce DafnyBench, the largest benchmark of its kind for training and evaluating machine learning systems for formal software verification. We test the ability of LLMs such as GPT-4 and Claude 3 to auto-generate enough hints for the…
Enhancing the mathematical reasoning capabilities of LLMs has garnered significant attention in both the mathematical and computer science communities. Recent works have made substantial progress in both Natural Language (NL) reasoning and…
Effective problem-solving in physics extends beyond the mere application of mathematical formulas; it necessitates an understanding of how mathematical concepts connect to and reflect the physical world. A strong epistemological framework…
Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem…
The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…
Large Reasoning Models (LRMs) exhibit strong performance, yet often produce rationales that sound plausible but fail to reflect their true decision process, undermining reliability and trust. We introduce a formal framework for reasoning…
The fixed parameter tractable (FPT) approach is a powerful tool in tackling computationally hard problems. In this paper, we link FPT results to classic artificial intelligence (AI) techniques to show how they complement each other.…
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…
Large language models (LLMs) have achieved strong performance on reasoning benchmarks, yet their ability to solve real-world problems requiring end-to-end workflows remains unclear. Mathematical modeling competitions provide a stringent…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
Parameter-Efficient Fine-Tuning (PEFT) methods achieve performance comparable to Full Fine-Tuning (FFT) while requiring significantly fewer computing resources, making it the go-to choice for researchers. We find that although PEFT can…
Formal verification guarantees proof validity but not formalization faithfulness. For natural-language logical reasoning, where models construct axiom systems from scratch without library constraints, this gap between valid proofs and…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
Formal verification of floating-point arithmetic remains challenging due to non-linear arithmetic behavior and the tight coupling between control and datapath logic. Existing approaches often rely on high-level C models for equivalence…
LLMs excel at reasoning, but validating their steps remains challenging. Formal verification offers a solution through mechanically checkable proofs. Interactive theorem provers (ITPs) dominate mathematical reasoning but require detailed…
Verification-aware programming languages such as Dafny and F* provide means to formally specify and prove properties of a program. Although the problem of checking an implementation against a specification can be defined mechanically, there…
As machine learning becomes more widespread and is used in more critical applications, it's important to provide explanations for these models, to prevent unintended behavior. Unfortunately, many current interpretability methods struggle…
Autoformalization aims to produce formal statements that compile and faithfully preserve the intended meaning of informal mathematics. Yet standard single-output evaluation protocols collapse a many-to-many problem into a single-output…
Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on…
Large language models (LLMs) are increasingly deployed for tabular question answering, yet calibration on structured data is largely unstudied. This paper presents the first systematic comparison of five confidence estimation methods across…