Streaming log-sum-exp: logsumexp_stream

The problem

The package's other shared primitives (the tape-strip pair and the AD-safe evaluation hooks) all target continuous quadrature over a distribution's CDF/PDF. There is no shared primitive for the other recurring shape: an infinite sum in log space over an unbounded discrete support. Every consumer that needs one currently writes its own stopping rule, and the easy mistake is stopping at the first negligible term — which silently truncates a heavy tail that dips low for a term or two and then recovers, biasing the result with no visible signal.

The fix

logsumexp_stream(log_term) computes log(Σ_{k≥0} exp(log_term(k))) without materialising the full term sequence. It accumulates with the classic running maximum/rescale log-sum-exp identity, updated incrementally as each log_term(k) arrives, and stops only once the running total has been unchanged within atol for min_stable_terms CONSECUTIVE further terms — not at the first negligible one:

using EpiAwareADTools

# Σ_{k≥0} exp(-k), a geometric series with ratio exp(-1); the exact closed
# form is 1 / (1 - exp(-1)), so log of that is the reference value.
result = logsumexp_stream(k -> -Float64(k))
result.value ≈ log(1 / (1 - exp(-1))), result.converged

(true, true)

It returns (value, terms_used, converged). When max_terms is reached without stabilising, the default (strict = true) raises a descriptive error rather than silently returning a partial sum; strict = false instead returns the partial result with converged = false.

The accumulator is plain generic Julia control flow — comparisons, exp, log, +, * — over whatever real (or AD-wrapped) values log_term returns, calling no non-differentiable primitive anywhere in the body. Every supported AD backend (ForwardDiff, ReverseDiff, Enzyme, Mooncake, ChainRulesCore) differentiates straight through value with no bespoke per-backend rule needed, the same way a plain sum(logpdf.(...)) loop does. The full docstring, including the numerical trap the three-way step branch guards against, lives on the Public API page.

Upstream target

There is no single upstream owner for a differentiable, convergence-checked streaming log-sum-exp over an unbounded support. LogExpFunctions.jl hosts the ecosystem's logsumexp, but only over an already-materialised, finite collection — not a term generator with a run-based stopping rule. This entry is deleted once LogExpFunctions.jl (or an equivalent shared numerics package) gains a differentiable streaming accumulator with the same convergence guarantee.