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We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…

The ongoing development of Lean 4's Mathlib has produced a macroscopic structural complexity that interweaves logical, mathematical, and infrastructural dependencies. We present a network analysis of this library, extracting its dependency…

We present cryptogram solving as an ideal testbed for studying neural network reasoning and generalization; models must decrypt text encoded with substitution ciphers, choosing from 26! possible mappings without explicit access to the…

Tokenization is a central component of natural language processing in current large language models (LLMs), enabling models to convert raw text into processable units. Although learned tokenizers are widely adopted, they exhibit notable…

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…

We present a method for systematically evaluating the correctness and robustness of instruction-tuned large language models (LLMs) for code generation via a new benchmark, Turbulence. Turbulence consists of a large set of natural language…

Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…

Early-stage specifications of safety-critical systems are typically expressed in natural language, making it difficult to derive formal properties suitable for verification and needed to guarantee safety. While recent Large Language Model…

Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…

This paper investigates whether recent advances in Large Language Models (LLMs) can assist in translating human explanations into a format that can robustly support learning Linear Temporal Logic (LTL) from demonstrations. Both LLMs and…

Autoformalization addresses the scarcity of data for Automated Theorem Proving (ATP) by translating mathematical problems from natural language into formal statements. Efforts in recent work shift from directly prompting large language…

Keyphrase extraction for morphologically rich, low-resource languages remains understudied, largely due to the scarcity of suitable evaluation datasets. We address this gap for Slovak by constructing a dataset of 227,432 scientific…

Predicting problem-difficulty in large language models (LLMs) refers to estimating how difficult a task is according to the model itself, typically by training linear probes on its internal representations. In this work, we study the…

Over the years a number of topologies for the set of laws of stochastic processes have been proposed. Building on the weak topology they all aim to capture more accurately the temporal structure of the processes. In a parallel paper we show…

Large language models (LLMs) in research and development toolchains produce output that triggers attribution of agency and understanding -- a cognitive illusion that degrades verification behavior and trust calibration. No existing…

Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…

Large language models (LLMs) have shown great potential in automating significant aspects of coding by producing natural code from informal natural language (NL) intent. However, given NL is informal, it does not lend easily to checking…

This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…

Large Language Models (LLMs) have achieved excellent performances in various tasks. However, fine-tuning an LLM requires extensive supervision. Human, on the other hand, may improve their reasoning abilities by self-thinking without…

Incorporating natural language rationales in the prompt and In-Context Learning (ICL) have led to a significant improvement of Large Language Models (LLMs) performance. However, generating high-quality rationales require human-annotation or…