Bit-Blasting Probabilistic Programs
summary
HyBit converts continuous variables into a discrete bitblasted representation by encoding each real as independent Bernoulli bits, then runs exact inference using discrete PPL backends. It proves convergence as the bit-width increases and replaces exponential enumeration with linear piece-wise distributions that require only O(pieces) values. Empirically it reconstructs Gaussians visually indistinguishable at 7 bits with 32 pieces, scales to 32-bit fixed-point (2^32 values represented with 32 flips), and beats generic samplers on several hybrid benchmarks.
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