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ai-for-math

formal theorem proving with RL

AlphaProof, DeepSeek-Prover

SystemTechniques · 16Primitives · 44 ai-for-math Congruence closurecompilers · medium: Union-find over terms with congruence propagation; decides equality with uninterpreted functionsDependent type theorycompilers · medium: Pi and Sigma types, universes, inductive families, definitional equality: core of Lean and CoqNormalization by evaluationcompilers · medium: Normalize lambda terms by evaluating into a semantic domain and reading back; used for type equalityTactic proof searchcompilers · medium: Tactic frameworks: goals, metavariables, backtracking, simp-style rewriting and automationMonte Carlo tree searchgame-ai · medium: Grows a search tree one simulation at a time, picking visits by a bandit rule (UCT or PUCT) and backing up averages; the search behind AlphaZero.›AlphaZero self-playmachine-learning · medium: A policy-value net guides PUCT search; search visit counts and game results become its training targets, so it learns from its own improved play.›Benchmark contamination detectionmachine-learning · medium: Detect test-set leakage into training data via n-gram overlap, perplexity and canary checksUnificationcompilers · low: First-order unification with union-find and occurs check; basis of type inference and logic programmingToken samplingml-training · low: Turn a vector of scores into one chosen item with temperature, top-k, top-p, min-p, repetition penalties and a seed.›Pass at kmachine-learning · low: Unbiased pass@k estimator from n samples with c correct, for code and agent benchmarksE graphscompilers · low: Equality saturation: e-graphs compactly hold many equivalent programs, then extract the cheapestA* searchgraphs · low: Dijkstra ordered by cost-so-far plus an admissible estimate of the remaining cost; optimal paths while exploring far fewer nodes toward the goal.›Back translationmachine-learning · low: Data augmentation for translation: translate monolingual target text back to source to make synthetic parallel pairsLora adaptersml-training · low: Low-rank adapter matrices for fine-tuning; QLoRA; serving many adapters on one base modelRejection samplingml-training · low: Best-of-n and filtered sampling: generate many candidates, keep those passing a verifier or reward thresholdTransformer blockml-training · low: The decoder-only pre-norm block (attention plus MLP on a residual stream) behind every modern LLM, with exact shapes, parameter, FLOP and KV-cache counts.›Hash consingdata-structures · low: Intern structurally equal immutable terms so equality is pointer comparison and sharing is maximalUnion-findgraphs · low: Disjoint-set forest with union by size and path compression; merges sets and answers same-set queries in effectively constant time.›De bruijn indicescompilers · low: Nameless variable representation for binders: shifting, substitution, de Bruijn levelsClosures and upvaluescompilers · low: How interpreters and compilers let a function keep using its enclosing variables after they return: flat closures, open and closed upvalues, closure conversion, capture by value or reference.›Transposition tablegame-ai · low: A fixed-size, lossy hash table of search results keyed by a state hash; gives ordering and cutoffs for repeated states, shared lock-free between threads.›PRNGs (PCG, xoshiro)numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.›Experience replaymachine-learning · low: Ring-buffer replay memory with uniform or prioritized sampling for off-policy and self-play training+ 9 more techniques+ 28 more primitives

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