Automated Proving of Shannon-Type Entropy Inequalities via Fine-Tuned Language Models and Guided Tree Search
arXiv:2606.05729v1 Announce Type: cross Abstract: Proving Shannon-type entropy inequalities is a fundamental task in information theory that often requires constructing non-trivial linear combinations of known constraints, which is a combinatorial search problem that scales poorly with the number of random variables. We investigate whether small-scale large language models (0.6B--1.7B parameters), fine-tuned on atomic proof steps and combined with guided beam search, can automate this process. On a held-out test set of 60 inequalities spanning n=10 to 15 variables, our 0.6B fine-tuned model ac
The rapid advancement of large language models and their fine-tuning capabilities is enabling them to tackle increasingly complex symbolic reasoning tasks, beyond their initial generative applications.
Automating complex mathematical proofs, especially in information theory, represents a significant step towards more autonomous scientific discovery and could unlock breakthroughs previously hindered by human combinatorial limits.
The ability to automate proving Shannon-type inequalities suggests a new paradigm for mathematical discovery and optimization in fields relying on information theory, potentially accelerating innovation in areas like AI and communications.
- · AI researchers
- · Information theorists
- · Communication technology developers
- · Software engineers using LLMs
- · Tasks requiring manual, combinatorial proof methods
- · Traditional symbolic AI approaches
Increased efficiency in information theory research and development as proof generation becomes automated.
New breakthroughs in data compression, error correction, and AI algorithms thanks to accelerated discovery of optimal information relationships.
The development of 'AI mathematicians' capable of autonomously generating and verifying novel mathematical theories, fundamentally altering scientific progress.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG