GenomeCoder: Neural-Guided Inference of Executable Biological Programs

Many latent quantities in biology are short, executable procedures: an immune receptor records which gene segments were joined and trimmed, an expressed gene is a set of transcript isoforms, a genealogy is a sequence of local trees linked by recombination. Mechanistic models assign probabilities to such programs, while the candidate space grows combinatorially, so exact inference is affordable only in a narrow band. We present **GenomeCoder**, which trains a recognition model to construct a compact support of executable latent programs, scores that support under the mechanistic model, and, when generative parameters are unknown, learns them from observations without latent labels. Where the exact posterior is enumerable, GenomeCoder reaches the *Bayes-optimal recovery rate* in V(D)J recombination, against $0.605$ of it for beam search, and reaches $0.981$ of the splicing ceiling in $37$ exact evaluations. For a fixed mechanistic model, the restricted posterior's error is exactly the posterior mass the support omits, measured exactly in V(D)J and splicing: at $7,000$ evaluations GenomeCoder retains $0.953$ of the splicing posterior against $0.906$ for beam search. The same marginal likelihood selects how much generative-parameter updating the reads support, halving the distance to the generating parameters at matched compute. On the published IGoR benchmark, GenomeCoder matches IGoR in complete-scenario recovery at mean rate $0.1330$. Under the same learned generative model, its retained support matches full enumeration recovery while scoring orders of magnitude fewer programs per read.