LANTERN: Illuminating Hidden Mathematical Knowledge in Language Models

2026-09-26

AI Summary

This study addresses the challenge of efficiently mining implicit mathematical knowledge from the internal representations of large language models. We propose LANTERN, a pipeline that establishes a low-cost, activation-based knowledge discovery paradigm. Specifically, the method extracts activation features from pretrained models, employs classifier ranking and staged filtering to identify candidate relationships, and rigorously verifies them via executable code. Experiments on 10,000 sequences from the OEIS dataset yield 62 valid relationships, ultimately confirming four previously undocumented mathematical patterns within a total runtime of under eight hours. This work demonstrates the feasibility of automating theorem discovery through model-internal representations, offering an efficient new pathway for mathematical knowledge extraction.

Abstract

Language models can now prove theorems, but people still decide which problems to pursue. We ask whether a model's internal representations can help identify promising mathematical connections. We develop LANTERN, a fast, cost-efficient pipeline that uses a classifier over pretrained-model activations to rank candidate relations, followed by staged filtering, hypothesis generation, executable verification, and analytical checking. Applied to the On-Line Encyclopedia of Integer Sequences (OEIS), LANTERN ranked 50 million pairs among 10,000 frequently referenced sequences and produced 62 verified relations between pairs without an existing OEIS cross-reference. A content screen retained 13 relations worth presenting; nine of these are informative or insightful, including four which are entirely novel to the best of our knowledge: none appears in the OEIS or in our targeted literature search. The entire end-to-end process including classifier training, candidate ranking, filtering and verification took under 8 hours.

Problem

• Language Models
• Mathematical Discovery
• Internal Representations
• Integer Sequences
• Hidden Knowledge

Innovation

• Language Models
• Mechanistic Interpretability
• Automated Mathematical Discovery
• Internal Representations
• Pipeline Verification