★ SlotFlow: Amortized Trans-Dimensional Inference towards LISA ★

About

Gravitational-wave observations from future space-borne detectors will present a fundamentally new inference challenge: not only we estimate the parameters of each source, but we must simultaneously determine how many sources are present. This is the trans-dimensional Bayesian inference problem, and classical approaches such as Reversible Jump MCMC can take hours to days per analysis.

We present *SlotFlow*, a deep-learning architecture for amortized trans-dimensional inference. Given a time-series observation, SlotFlow jointly infers the number of signal components $K$ and their individual parameters in a single forward pass, achieving millisecond-scale posterior estimation with well-calibrated uncertainties. The architecture combines (i) a dual-stream frequency–time encoder that extracts complementary spectral and temporal representations, (ii) a classifier that predicts the cardinality posterior from spectral features, and (iii) dynamic slot allocation that instantiates exactly $K$ slot contexts, each passed to a single shared conditional normalizing flow that produces per-source posteriors. Training uses permutation-invariant Hungarian matching to handle the inherent label-switching symmetry of multi-source posteriors.

We validate SlotFlow on sinusoidal mixtures with up to 10 overlapping components, a canonical benchmark motivated directly by the quasi-monochromatic nature of LISA galactic binaries. SlotFlow achieves high cardinality accuracy and posteriors in close agreement with RJMCMC across amplitude, phase, and frequency parameters, while reducing inference time from hours to milliseconds. Posterior calibration remains reliable across the full range of source counts and signal-to-noise ratios explored.

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