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PreprintCC BY 4.0arXiv

Differentiable Systematic Resampling for Variational Sequential Monte Carlo

  • Fredrik Cumlin
  • Saikat Chatterjee
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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.

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Cite

BibTeXRIS
BibTeX
@misc{cumlin2026differentiable,
  title = {{Differentiable Systematic Resampling for Variational Sequential Monte Carlo}},
  author = {Fredrik Cumlin and Saikat Chatterjee},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12094},
  eprint = {2610.12094},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12094},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Differentiable Systematic Resampling for Variational Sequential Monte Carlo
AU  - Fredrik Cumlin
AU  - Saikat Chatterjee
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.12094
UR  - https://arxiv.org/abs/2610.12094
AB  - 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.
ER  -