Logic and Probabilistic Circuits 2
summary
Probabilistic circuits use decomposability and smoothness to push integrals down to leaves and compute marginals by dynamic programming in linear time, with leaf likelihoods (Gaussians, Bernoulli) providing the base. Compiling Bayesian nets or discrete probabilistic programs into decomposable deterministic circuits yields weighted model counting equivalence; determinism lets sums become maxes so MAP reduces to max‑product DP, otherwise MAP is intractable. A practical system distills a transformer into a tractable circuit, applies marginal inference to enforce CNF constraints on generation, and produces MNIST completions and constrained text with 100% constraint satisfaction and competitive bits‑per‑pixel.
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chapters (14)
- 0:00Understanding circuit basics
- 3:03Performing marginal inference
- 5:50Efficient query processing
- 9:10Conditional probability queries
- 10:22Controlling generative models
- 12:12Language modeling applications
- 15:16Benchmarks and distillation
- 19:38Map inference techniques
- 24:01Circuit learning performance
- 29:45Introduction to logical circuits
- 32:34Circuit properties for queries
- 37:31Model counting with circuits
- 44:20Probabilistic to logical reduction
- 52:15Compilation and applications
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