LANTERN: Illuminating Hidden Mathematical Knowledge in Language Models
Summary
LANTERN is a fast pipeline that uses a classifier over pretrained language model activations to rank candidate mathematical relations, then filters, generates, and verifies hypotheses. Applied to OEIS, it found 62 verified relations, 9 informative ones, and 4 entirely novel mathematical connections, completing the whole process in under 8 hours.
View Cached Full Text
Cached at: 10/01/26, 08:22 AM
Paper page - LANTERN: Illuminating Hidden Mathematical Knowledge in Language Models
Source: https://huggingface.co/papers/2609.32264
Abstract
Languagemodelscannowprovetheorems,butpeoplestilldecidewhichproblemstopursue.Weaskwhetheramodel’sinternalrepresentationscanhelpidentifypromisingmathematicalconnections.WedevelopLANTERN,afast,cost-efficientpipelinethatusesaclassifieroverpretrained-modelactivationstorankcandidaterelations,followedbystagedfiltering,hypothesisgeneration,executableverification,andanalyticalchecking.AppliedtotheOn-LineEncyclopediaofIntegerSequences(OEIS),LANTERNranked50millionpairsamong10,000frequentlyreferencedsequencesandproduced62verifiedrelationsbetweenpairswithoutanexistingOEIScross-reference.Acontentscreenretained13relationsworthpresenting;nineoftheseareinformativeorinsightful,includingfourwhichareentirelynoveltothebestofourknowledge:noneappearsintheOEISorinourtargetedliteraturesearch.Theentireend-to-endprocessincludingclassifiertraining,candidateranking,filteringandverificationtookunder8hours.
View arXiv pageView PDFAdd to collection
Get this paper in your agent:
hf papers read 2609\.32264
Don’t have the latest CLI?curl \-LsSf https://hf\.co/cli/install\.sh \| bash
Models citing this paper0
No model linking this paper
Cite arxiv.org/abs/2609.32264 in a model README.md to link it from this page.
Datasets citing this paper0
No dataset linking this paper
Cite arxiv.org/abs/2609.32264 in a dataset README.md to link it from this page.
Spaces citing this paper0
No Space linking this paper
Cite arxiv.org/abs/2609.32264 in a Space README.md to link it from this page.
Collections including this paper0
No Collection including this paper
Add this paper to acollectionto link it from this page.
Similar Articles
Recent OpenAI research has demonstrated the ability of LLMs to solve frontier problems in mathematics (1 minute read)
OpenAI research shows LLMs can solve nine open math problems from COLT, FOCS, commutative algebra, and Erdős problems using a simple pipeline with GPT-5.5 Pro and Claude Opus 4.8, with Lean formalizations.
Disentangling Mathematical Reasoning in LLMs: A Methodological Investigation of Internal Mechanisms
This paper investigates how large language models perform arithmetic operations by analyzing internal mechanisms through early decoding, revealing that proficient models exhibit a clear division of labor between attention and MLP modules in reasoning tasks.
Learning to Discover Interesting Mathematics
This paper introduces a framework for LLMs to discover and prove interesting mathematical theorems by optimizing for a metric based on proof difficulty, leading to more novel and useful mathematical knowledge with reduced overlap with existing libraries.
Interpreting Language Model Hidden States at Scale
OmniLens is a scalable lens method for interpreting LLM hidden states, using low-rank translators and Subset-KL to reduce parameters and memory, enabling a dense ensemble of 482 lenses on LLaMA-3.3-70B at substantially lower cost.
TabularMath: Understanding Math Reasoning over Tables with Large Language Models
TabularMath introduces a benchmark and AutoT2T framework for evaluating LLMs' mathematical reasoning over tabular data, revealing that table complexity, data quality, and modality significantly impact model performance. The study addresses a gap in LLM evaluation by systematically assessing robustness to incomplete or inconsistent table information in real-world scenarios.