# LANTERN: Illuminating Hidden Mathematical Knowledge in Language Models

arXiv: https://arxiv.org/abs/2609.32264 · HTML: https://mlsanity.com/paper/2609.32264/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 95 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [Learning Formal Mathematics From Intrinsic Motivation](https://mlsanity.com/paper/2407.00695/) (2024)
- [Predicting the Future of AI with AI: High-quality link prediction in an exponentially growing knowledge network](https://mlsanity.com/paper/2210.00881/) (2022)
- [Predicting New Research Directions in Materials Science using Large Language Models and Concept Graphs](https://mlsanity.com/paper/2506.16824/) (2025)
- [LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving](https://mlsanity.com/paper/2506.22005/) (2025)
- [FACT: Learning Governing Abstractions Behind Integer Sequences](https://mlsanity.com/paper/2209.09543/) (2022)
- [Discovering emergent connections in quantum physics research via dynamic word embeddings](https://mlsanity.com/paper/2411.06577/) (2024)
- [Probing Materials Knowledge in LLMs: From Latent Embeddings to Reliable Predictions](https://mlsanity.com/paper/2603.01834/) (2026)
- [OEIS Open: How many conjectures can language models turn into theorems?](https://mlsanity.com/paper/2608.11941/) (2026)
- [The Problem Is the Problem: Towards Scalable Mathematical Discovery](https://mlsanity.com/paper/2608.16977/) (2026)
- [On the Cryptomorphism between Davis' Subset Lattices, Atomic Lattices, and Closure Systems under T1 Separation Axiom](https://mlsanity.com/paper/2209.12256/) (2022)
- [MECA: A Mechanism-Centered Agent for Constructing Well-Specified and Valuable Mathematical Conjectures](https://mlsanity.com/paper/2607.27709/) (2026)
- [LLM Framework for Discovering Major Mathematical Conjectures: AI's Quest for the Next Riemann Hypothesis](https://mlsanity.com/paper/2607.28632/) (2026)

## Abstract (arXiv)

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.