Logic and Probabilistic Circuits 4
summary
Computing a log of a probabilistic circuit requires log requires determinism because otherwise output loses determinism and the problem becomes NP‑hard; the paper lists exact input/output conditions for operators (product, quotient, power, log) and shows which properties preserve through a pipeline. The method enforces constraints by taking a product of logical+probabilistic circuits at the last layer and training end‑to‑end, computes expectations by product+integration, and handles causal backdoor queries by requiring marginal‑determinism. To capture distributions like DPPs the talk introduces probabilistic generating circuits, uses determinant algorithms (Samuelson‑Berkowitz) to build polynomial‑size representations, and gives polynomial‑time marginal extraction via polynomial interpolation.
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chapters (9)
- 0:00Circuit operations and logarithm
- 2:16Operator properties for composition
- 7:54Neurosymbolic learning with constraints
- 14:18Expectation with partial observations
- 17:37Fairness and causal estimation
- 28:38Tractable distributions and circuits
- 31:47Determinantal point process limits
- 40:46Probabilistic generating circuits
- 54:43Summary and open problems
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