SlotFlow: Amortized Trans-Dimensional Inference with Slot-Based Normalizing Flows

TL;DR

SlotFlow is a deep learning framework that efficiently performs trans-dimensional inference by estimating the number of components and their parameters in time-series data, significantly speeding up traditional Bayesian methods.

Contribution

The paper introduces SlotFlow, a novel neural architecture for amortized trans-dimensional inference that jointly estimates component count and parameters using slot-based normalizing flows.

Findings

Achieves 99.85% accuracy in component count estimation.

Provides well-calibrated parameter posteriors with low bias.

Runs approximately one million times faster than RJMCMC.

Abstract

Inferring the number of distinct components contributing to an observation, while simultaneously estimating their parameters, remains a long-standing challenge across signal processing, astrophysics, and neuroscience. Classical trans-dimensional Bayesian methods such as Reversible Jump Markov Chain Monte Carlo (RJMCMC) provide asymptotically exact inference but can be computationally expensive. Instead, modern deep learning provides a faster alternative to inference but typically assume fixed component counts, sidestepping the core challenge of trans-dimensionality. To address this, we introduce SlotFlow, a deep learning architecture for trans-dimensional amortized inference. The architecture processes time-series observations, which we represent jointly in the frequency and time domains through parallel encoders. A classifier produces a distribution over component counts K, and its MAP estimate specifies the number of slots instantiated. Each slot is parameterized by a shared conditional normalizing flow trained via permutation-invariant Hungarian matching. On sinusoidal decomposition with up to 10 overlapping components and Gaussian noise, SlotFlow achieves 99.85% cardinality accuracy and well-calibrated parameter posteriors, with systematic biases well below one posterior standard deviation. Direct comparison with RJMCMC shows close agreement in amplitude and phase, with Wasserstein distances $W_2 < 0.01$ and $< 0.03$, indicating that shared global context captures inter-component structure despite a factorized posterior. Frequency posteriors remain centered but exhibit 2-3x broader intervals, consistent with an encoder bottleneck in retaining long-baseline phase coherence. The method delivers a $\sim 10^6\times$ speedup over RJMCMC, suggesting applicability to time-critical workflows in gravitational-wave astronomy, neural spike sorting, and object-centric vision.