On the Reparameterisation Gradient for Non-Differentiable but Continuous Models
summary
Claim: the reparameterisation gradient is unbiased for continuous but possibly non-differentiable probabilistic programs. Proof uses a categorical denotational approach with a denotational weight semantics and a generalisation of quasi-Borel/space constructions to interpret smooth conditionals at higher order. Continuity for branching is established by reducing to analytic primitives and checking agreement on the boundary by sampling, and for practical decidable checks the method restricts to affine guards where a linear arithmetic solver verifies consistency.
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