ReverseDiff extension

EpiAwareADToolsReverseDiffExt loads when ReverseDiff is loaded alongside EpiAwareADTools. ReverseDiff depends on ChainRulesCore, so loading it also loads the ChainRulesCore extension, whose rrules this extension lifts onto the tape.

What it registers

A tape-strip method:

primal(x::TrackedReal) = primal(ReverseDiff.value(x))

Reading .value off a tape entry records no operation, so a value stripped this way stays a constant. That is the behaviour a non-differentiable hyperparameter wants. fixed_draw delegates to primal and so inherits it.

Twenty-one @grad_from_chainrules registrations: seven each for _gamma_cdf, _gamma_logccdf and _beta_cdf, one for every non-trivial subset of tracked and untracked arguments, for example

@grad_from_chainrules _gamma_cdf(k::TrackedReal, θ::Real, x::Real)

The full seven per primitive are needed because @grad_from_chainrules is signature-specific rather than abstract, so a mixed call that no registration matches falls through.

What fails without it

The lifted rules are what put the analytic partials on the tape. Without them ReverseDiff either falls back to forward mode through gamma_inc or beta_inc, which have no TrackedReal method and so error, or, depending on the call site, traces the function body instead. Tracing is slower than calling the analytic rrule directly even in the cases where it does produce a number, and it still cannot supply the shape partial SpecialFunctions leaves @not_implemented.

Without the primal(::TrackedReal) method, primal is the identity on a tracked value. The value stays on the tape, and a quantity the caller intended as a constant keeps contributing a gradient.

Upstream target

SpecialFunctions.jl carrying complete ChainRules for gamma_inc (issue #531) and beta_inc, at which point the primitives and their lifts are all deleted. The primal(::TrackedReal) method goes with the rest of the tape-strip once a shared cross-backend stop-gradient primitive exists.