BURST: Generator-First Spike-Count Generation with Adaptive Dispersion for Cross-Day Neuroprosthesis Calibration

Intracortical speech decoders degrade across recording days, requiring repeated collection of labeled target-day trials for recalibration. We ask whether generated phoneme-conditioned target-day spike counts can substitute for part of this collection. From an observation-process perspective, we find that attempted-speech counts exhibit rate-dependent sub-Poisson variability and a Fano-rate relationship that changes across sessions beyond estimation noise. We introduce Birth–Death Under-Dispersed Rates for Spike-Train Synthesis (BURST), a generator-first count bridge whose state-dependent jump rates define the conditional path and provide explicit dispersion control. Finite-state propagators evaluate analytic reverse-rate targets for simulation-free bridge matching. A historical Fano-rate profile sets the base schedule; a few-shot day code jointly adapts cross-channel tuning and a bounded profile displacement, and an alignment-free phoneme conditioner supports variable-length sequences from sequence-level labels. Across two transfer horizons on an intracortical speech dataset, equal mixtures of real and generated sentences consistently outperform real-only calibration at the same recording budget and approach calibration with twice as many real sentences. Generated counts reproduce the empirical high-rate sub-Poisson regime. BURST therefore provides a data-efficient route to cross-day neuroprosthesis calibration.