--- name: abductive-monte-carlo-ba8fecab8f9f description: "Retroductive hypothesis sampling via MCMC: given observations, importance-sample explanations weighted by P(observation|hypothesis) using Gay.jl colored particles as hypothesis candidates." version: 0.1.0 metadata: trit: -1 color: "#C77DEB" --- # Abductive Monte Carlo > *"Abduction is not exhaustive search; it is well-directed wandering in hypothesis space."* **Trit**: -1 (MINUS — retroductive: from effects back to causes) ## GF(3) Triad ``` abductive-monte-carlo (-1) ⊗ abductive-repl (0) ⊗ gay-monte-carlo (+1) = 0 ✓ ``` | Trit | Skill | Role | |------|-------|------| | +1 | gay-monte-carlo | Generative: colored particle distributions as priors | | 0 | abductive-repl | Coordinator: REPL test/refine loop | | -1 | **abductive-monte-carlo** | Retroductive: MCMC sampling back to causes | ## Core Idea Classical abduction: given rule `A → E` and evidence `E`, hypothesize `A`. Abductive Monte Carlo extends this to noisy, high-dimensional settings: ``` P(H | E) ∝ P(E | H) · P(H) ───────────────── likelihood × prior ``` Instead of enumerating hypotheses, we **sample** them. Gay.jl provides: - Deterministic colored particles as hypothesis identities - SplitMix64 seed evolution for reproducible chains - Gamut-aware weighting (hypotheses far from sRGB boundary penalized) ## Algorithm ### Metropolis-Hastings on Hypothesis Space ```python def abductive_mcmc(observation, n_samples=10_000, seed=0xcd0a0fde6e0a8820): """ Sample hypotheses H from P(H|E) ∝ P(E|H) · P(H) using Gay.jl particle coloring for deterministic identity. """ current = initial_hypothesis(seed) samples = [] for i in range(n_samples): # Propose: step in Gay.jl color space proposal = gay_next_color(current.seed) # Likelihood: P(observation | hypothesis) log_like_curr = log_likelihood(observation, current) log_like_prop = log_likelihood(observation, proposal) # Prior: gamut penalty log_prior_curr = log_prior(current) log_prior_prop = log_prior(proposal) # Accept/reject (log-space) log_ratio = (log_like_prop + log_prior_prop) - (log_like_curr + log_prior_curr) if log(uniform()) < log_ratio: current = proposal samples.append(current) return samples ``` ### Importance Sampling Variant (for color abduction) ```julia using Gay, MonteCarloMeasurements function abduce_mcmc(obs_rgb::RGB, seed::UInt64; n=2000) # Prior: uniform over Gay.jl color space candidates = [gay_color_at(seed, i) for i in 1:n] # Likelihood: Gaussian in CIELAB distance weights = [exp(-ciede2000(obs_rgb, c)^2 / 2σ²) for c in candidates] weights ./= sum(weights) # Weighted sample → ranked hypotheses ranked = sortperm(weights, rev=true) [(candidates[i], weights[i]) for i in ranked[1:10]] end ``` ## State Representation Each hypothesis is a **Gay particle** — a colored point in hypothesis space: ``` H = (seed: UInt64, color: RGB, index: Int, log_weight: Float64) Seed evolution: seed_{n+1} = splitmix64(seed_n XOR observation_hash) ``` ## Proof-State Abduction (causal integration) In the `causal/proofgeneral` context, abductive-monte-carlo can retroductively infer which lemmas/tactics led to a given proof state: ```elisp (defun abductive-mcmc-infer-proof-history (goal-state n-samples) "Given a GOAL-STATE (Γ ⊢ G), sample likely proof histories via MCMC." (let* ((obs-hash (sxhash goal-state)) (tactic-vocab (self-walker--discover-tactics)) (chains (abductive-mcmc-sample obs-hash tactic-vocab n-samples))) ;; Return ranked proof history hypotheses (abductive-mcmc-rank chains))) ``` ## Output Format ``` Observation: ⊢ n + 0 = n Top-5 Abduced Proof Paths (MCMC, n=10000, seed=0xcd0a0fde6e0a8820): [1] intro n; simp weight=0.412 color=RGB(200, 120, 180) [2] intro n; ring weight=0.301 color=RGB(198, 118, 177) [3] intro n; omega weight=0.187 color=RGB(203, 123, 182) [4] intro n; exact rfl weight=0.074 color=RGB(196, 116, 175) [5] norm_num weight=0.026 color=RGB(205, 125, 184) GF(3) walk hash: 0x9F3A (Möbius product of tactic trits) Chain acceptance rate: 0.31 (healthy MH range) ``` ## Protocol ### 1. Encode observation ```python obs_hash = sxhash(observation_string) ^ 0x9E3779B97F4A7C15 ``` ### 2. Initialize chain ```python h0 = gay_color_at(seed, obs_hash % 1_000_000) # start in color space ``` ### 3. Run MCMC Metropolis-Hastings with Gay.jl next-color proposals, 10k steps default. ### 4. Extract MAP hypothesis ```python map_hypothesis = max(samples, key=lambda h: h.log_weight) ``` ### 5. Roundtrip verify ```python prediction = forward_simulate(map_hypothesis) assert ciede2000(prediction, observation) < threshold ``` ## Integration Points - **self-walker** (causal): feed terminal proof state as observation → abduce proof history - **gay-monte-carlo**: particle distributions → hypothesis priors - **abductive-repl**: REPL-test the top MCMC hypothesis - **causal-catcolab**: export MAP hypothesis as CatColab olog ## Configuration ```yaml abductive-monte-carlo: n_samples: 10_000 burn_in: 1_000 seed: 0xcd0a0fde6e0a8820 likelihood: metric: ciede2000 # color distance sigma: 5.0 prior: gamut_penalty: true boundary_sigma: 10.0 output: top_k: 10 show_chain: false ``` ## Justfile ```makefile abduce-mcmc obs="0 120 180": julia -e 'using AbductiveMC; abduce_mcmc(RGB($(obs)))' abduce-proof goal: emacs --batch -l causal-catcolab \ --eval "(abductive-mcmc-infer-proof-history \"$(goal)\" 5000)" abduce-test n="1000": julia -e 'using AbductiveMC; roundtrip_accuracy(n=$(n))' ``` ## Related Skills - `abductive-repl` (0): interactive hypothesis-test loop - `gay-monte-carlo` (+1): colored particle distributions, gamut-aware sampling - `self-walker` (0): proof-state walker that generates observations to abduce - `lean-proof-walk` (+1): proof state chains — can be observed for retroduction - `fokker-planck-analyzer` (-1): equilibrium distribution of Markov chain --- Source attribution: plurigrid Original project: https://github.com/plurigrid/asi/blob/293ce9f76e3abcd5ba18db284688bc0d9ac6691d/skills/abductive-monte-carlo/SKILL.md License: MIT License information: https://opensource.org/license/mit Original upstream instructions; downloaded from Mega AI Hub. ## Upstream license notice MIT License Copyright (c) 2025 SkillCreator.ai Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. 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IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. # Mega AI Hub resource metadata Creator / publisher: plurigrid Original project: https://github.com/plurigrid/asi/blob/293ce9f76e3abcd5ba18db284688bc0d9ac6691d/skills/abductive-monte-carlo/SKILL.md Attribution basis: Source repository record Fields of work: Data & Analytics, Development & Engineering Roles: Data Analyst, Data Scientist, ML / AI Engineer Specialties: API Tools: Gay.Jl Country applicability: Country not specified Classification basis: Source catalog labels Instruction SHA-256: 4bca286abaa532d6f6ac921b6486655ec358f9ee9c8ab3ac01cddd91c74da8d4