Differentiable Systematic Resampling for Variational Sequential Monte Carlo

2026-10-08

AI Summary

This study addresses the inherent discreteness of the resampling step in particle filtering, which impedes end-to-end gradient-based learning. To overcome this limitation, we propose a temperature-controlled Differentiable Systematic Resampling (DSR) method. By integrating variational sequential Monte Carlo with temperature relaxation techniques, DSR enables full gradient propagation while preserving the ordered structure of the cumulative distribution function. We theoretically establish an exponential convergence rate for the proposed approach, which operates without iterative solvers and thereby significantly reduces computational overhead. Experimental evaluations on stochastic dynamical systems and handwritten digit datasets demonstrate that DSR achieves superior filtering accuracy and parameter learning performance.

Abstract

Particle filters are a standard tool for nonlinear state estimation, but their resampling step is discrete, preventing gradient-based learning in variational sequential Monte Carlo. We introduce Differentiable Systematic Resampling (DSR), a temperature-controlled relaxation of systematic resampling, that preserves the CDF-ordered, banded structure of systematic resampling while enabling full gradient flow. DSR converges to exact systematic resampling as the temperature vanishes, and we prove a pointwise exponential convergence rate for the induced bias. Compared to optimal-transport-based differentiable resampling, DSR avoids iterative solvers and has substantially lower computational overhead. Experiments on stochastic dynamical systems and real-world handwriting data show that DSR achieves comparable or superior filtering and dynamics learning performance.

Problem

• Particle filters
• Resampling
• Differentiable
• Variational sequential Monte Carlo
• Nonlinear state estimation

Innovation

• Differentiable Systematic Resampling
• Variational Sequential Monte Carlo
• Particle Filters
• Temperature-controlled Relaxation
• Gradient Flow