# SIXO: Smoothing Inference with Twisted Objectives

arXiv: https://arxiv.org/abs/2206.05952 · HTML: https://mlsanity.com/paper/2206.05952/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 55 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Neural Adaptive Sequential Monte Carlo](https://mlsanity.com/paper/1506.03338/) (2015)
- [Energy-Inspired Models: Learning with Sampler-Induced Distributions](https://mlsanity.com/paper/1910.14265/) (2019)
- [Lookahead Strategies for Sequential Monte Carlo](https://mlsanity.com/paper/1302.5206/) (2013)
- [Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter](https://mlsanity.com/paper/1708.08543/) (2017)
- [Particle Smoothing for Hidden Diffusion Processes: Adaptive Path Integral Smoother](https://mlsanity.com/paper/1605.00278/) (2016)
- [Graphical model inference: Sequential Monte Carlo meets deterministic approximations](https://mlsanity.com/paper/1901.02374/) (2019)

## Built on by (most cited first, 22 of 22)

- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [Towards Scalable and Stable Parallelization of Nonlinear RNNs](https://mlsanity.com/paper/2407.19115/) (2024)
- [Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Sampling](https://mlsanity.com/paper/2504.05410/) (2025)
- [Inferring stochastic low-rank recurrent neural networks from neural data](https://mlsanity.com/paper/2406.16749/) (2024)
- [Bayesian Optimization of Antibodies Informed by a Generative Model of Evolving Sequences](https://mlsanity.com/paper/2412.07763/) (2024)
- [Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Series](https://mlsanity.com/paper/2410.05602/) (2024)
- [eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling](https://mlsanity.com/paper/2403.01371/) (2024)
- [On the Power of (Approximate) Reward Models for Inference-Time Scaling](https://mlsanity.com/paper/2602.01381/) (2026)
- [Reinforced sequential Monte Carlo for amortised sampling](https://mlsanity.com/paper/2510.11711/) (2025)
- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [NAS-X: Neural Adaptive Smoothing via Twisting](https://mlsanity.com/paper/2308.14864/) (2023)
- [When are likely answers right? On Sequence Probability and Correctness in LLMs](https://mlsanity.com/paper/2606.27359/) (2026)
- [Reject, Resample, Repeat: Understanding Parallel Reasoning in Language Model Inference](https://mlsanity.com/paper/2603.07887/) (2026)
- [Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers](https://mlsanity.com/paper/2304.14390/) (2023)
- [Robust Inverse Graphics via Probabilistic Inference](https://mlsanity.com/paper/2402.01915/) (2024)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space](https://mlsanity.com/paper/2510.12916/) (2025)
- [Neural Backward Filtering Forward Guiding](https://mlsanity.com/paper/2601.23030/) (2026)
- [Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecasting](https://mlsanity.com/paper/2605.24548/) (2026)
- [PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation](https://mlsanity.com/paper/2609.26890/) (2026)

## Abstract (arXiv)

Sequential Monte Carlo (SMC) is an inference algorithm for state space models that approximates the posterior by sampling from a sequence of target distributions. The target distributions are often chosen to be the filtering distributions, but these ignore information from future observations, leading to practical and theoretical limitations in inference and model learning. We introduce SIXO, a method that instead learns targets that approximate the smoothing distributions, incorporating information from all observations. The key idea is to use density ratio estimation to fit functions that warp the filtering distributions into the smoothing distributions. We then use SMC with these learned targets to define a variational objective for model and proposal learning. SIXO yields provably tighter log marginal lower bounds and offers significantly more accurate posterior inferences and parameter estimates in a variety of domains.