monad-bayes x ASI Interleave

Bridge connecting tweag/monad-bayes (probabilistic inference as monad transformer stacks) to the ASI skill graph.

Monad Transformer Stack Anatomy

WeightedT m a           <- innermost: accumulates likelihood (MonadFactor)
  |
PopulationT m a         <- = WeightedT (ListT m) a; manages particle populations
  |
SequentialT m a         <- sequential time steps; works with PopulationT
  |
TracedT m a             <- records execution trace for MH proposals
  |-- Static.TracedT:   model :: WeightedT (DensityT m) a
  |-- Basic.TracedT:    model :: WeightedT (DensityT Identity) a
  +-- Dynamic.TracedT:  m (WeightedT (DensityT m) a, Trace a)

DensityT (free monad)   <- categorical structure: computes joint density of traces

Algorithm Compositions

ASI Integration Points

1. abductive-monte-carlo -> monad-bayes SMC Backend

Swap in monad-bayes as the backend for hypothesis sampling:

data Hypothesis = H { content :: Text, trit :: Int }

hypothesisPrior :: MonadInfer m => Text -> m Hypothesis
hypothesisPrior query = do
  t <- categorical (V.fromList [1/3, 1/3, 1/3])
  let tritVal = [-1, 0, 1] !! t
  score <- liftIO $ geminiLikelihood query tritVal
  factor (Exp score)
  return $ H { content = query, trit = tritVal }

sampleHypotheses :: IO [Hypothesis]
sampleHypotheses = do
  let config = SMCConfig { resampler = systematic, numSteps = 10, numParticles = 1000 }
  smc config $ hypothesisPrior "Is this attractor chaotic?"

2. lolita Physics Emulation -> PMMH Parameter Inference

Use PMMH to infer latent parameters from observables (NeurIPS 2025, arxiv:2507.02608):

lolitaPMMH
  :: (MonadSample m, MonadInfer m)
  => [[Double]]  -- observed trajectory (downsampled)
  -> m ([Double], [[Double]])  -- (parameters, inferred latents)
lolitaPMMH obs = do
  params <- do
    reynoldsNum <- gamma 2.0 0.5
    rayleighNum <- gamma 10.0 0.1
    return [reynoldsNum, rayleighNum]
  latents <- forM (zip obs [0..]) $ \(obsT, t) -> do
    latent <- multivariate params t
    mapM_ (\(o, l) -> score $ Normal l 0.1 `logProb` o) (zip obsT latent)
    return latent
  return (params, latents)

3. bayesian-breathing -> RMSMC Sequential State Estimation

RMSMC adds MCMC rejuvenation to respiratory-rate estimation:

breathingRMSMC :: MonadInfer m => [Double] -> m Double
breathingRMSMC observations = do
  let model = foldM (\rate obs -> do
        rate' <- normal rate 0.05
        factor $ Exp (normalLogProb obs (sin (2*pi*rate')) 0.1)
        return rate') 12.0 observations
  rmsmc (RMSMCConfig { numParticles = 200, numMCMCSteps = 5 }) model

4. DensityT -> Categorical Composition

DensityT provides the categorical structure that makes traces composable:

traceToSkillPath :: Trace a -> [SkillInvocation]
traceToSkillPath trace = map toSkillInv (randomVariables trace)
  where
    toSkillInv rv = SkillInvocation
      { skillId  = hashToSkill (rvName rv)
      , logProb  = probDensity rv
      }

Concrete Wiring: Haskell <-> ASI (via babashka/JSON-RPC)

;; babashka: call monad-bayes SMC from Clojure
(require '[babashka.process :as p])

(defn run-smc [model-name n-particles observations]
  (let [proc (p/process {:in :pipe :out :string}
               "cabal" "run" "asi-inference-server")]
    (spit (:in proc)
          (str (pr-str {:method "smc"
                        :params {:model model-name
                                 :particles n-particles
                                 :observations observations}})
               "\n"))
    (-> proc :out deref (json/parse-string true))))

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