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Research

Research
September 2026Blackdrome AI Labs · PKBoost AI Labs · Preprint

LEMMA: Learned Guidance for Evidence-Carrying Long-Horizon Symbolic Rewriting

Atul Saxena, Pushp Kharat

In plain terms

Instead of a model producing an answer you have to trust, LEMMA produces the derivation: every rewrite is a named rule, every intermediate state is checked, and the verification status is explicit — checked, heuristic, unverified, or unsupported are four different outcomes, not one.

//Abstract

LEMMA is a neuro-symbolic system for long-horizon symbolic mathematical rewriting. It combines a rule engine, guardrail-filtered action generation, evidence-typed verification and learned policy guidance to transform a starting expression into a target through individually validated steps. Six search and decoding methods are evaluated on a frozen 120-problem benchmark.

//What it found

  • On the 89 problems that contain genuine branching decisions, learned local action ranking measurably improves search efficiency under a fixed budget.
  • Evidence typing matters: distinguishing "checked" from "heuristic" from "unsupported" prevents the system from overstating what it has actually proven.
  • The released implementation carries 572 transformation rules with replayable before/after traces.

//Methods

  • Rule engine
  • Beam search
  • MCTS
  • Learned policy guidance
  • Evidence-typed verification

//Keywords

  • neuro-symbolic AI
  • symbolic reasoning
  • mathematical reasoning
  • long-horizon planning
  • Monte Carlo tree search