# Reducing Reparameterization Gradient Variance

arXiv: https://arxiv.org/abs/1705.07880 · HTML: https://mlsanity.com/paper/1705.07880/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2017.

## Built on by (most cited first, 27 of 27)

- [Faster Meta Update Strategy for Noise-Robust Deep Learning](https://mlsanity.com/paper/2104.15092/) (2021)
- [Provable convergence guarantees for black-box variational inference](https://mlsanity.com/paper/2306.03638/) (2023)
- [Amortized Variational Inference: A Systematic Review](https://mlsanity.com/paper/2209.10888/) (2022)
- [FedSDG-FS: Efficient and Secure Feature Selection for Vertical Federated Learning](https://mlsanity.com/paper/2302.10417/) (2023)
- [Generalized Doubly Reparameterized Gradient Estimators](https://mlsanity.com/paper/2101.11046/) (2021)
- [Linear Convergence of Black-Box Variational Inference: Should We Stick the Landing?](https://mlsanity.com/paper/2307.14642/) (2023)
- [Contextual Feature Selection with Conditional Stochastic Gates](https://mlsanity.com/paper/2312.14254/) (2023)
- [Practical and Matching Gradient Variance Bounds for Black-Box Variational Bayesian Inference](https://mlsanity.com/paper/2303.10472/) (2023)
- [Variance reduction of diffusion model's gradients with Taylor approximation-based control variate](https://mlsanity.com/paper/2408.12270/) (2024)
- [Fast and Unified Path Gradient Estimators for Normalizing Flows](https://mlsanity.com/paper/2403.15881/) (2024)
- [Calibrated Test-Time Guidance for Bayesian Inference](https://mlsanity.com/paper/2602.22428/) (2026)
- [An Uncertainty-Informed Framework for Trustworthy Fault Diagnosis in Safety-Critical Applications](https://mlsanity.com/paper/2111.00874/) (2021)
- [Graph Reparameterizations for Enabling 1000+ Monte Carlo Iterations in Bayesian Deep Neural Networks](https://mlsanity.com/paper/2202.09478/) (2022)
- [U-Statistics for Importance-Weighted Variational Inference](https://mlsanity.com/paper/2302.13918/) (2023)
- [Accelerating Large Batch Training via Gradient Signal to Noise Ratio (GSNR)](https://mlsanity.com/paper/2309.13681/) (2023)
- [Quasi-Newton Quasi-Monte Carlo for variational Bayes](https://mlsanity.com/paper/2104.02865/) (2021)
- [Marginally calibrated response distributions for end-to-end learning in autonomous driving](https://mlsanity.com/paper/2110.01050/) (2021)
- [Train Less, Infer Faster: Efficient Model Finetuning and Compression via Structured Sparsity](https://mlsanity.com/paper/2602.09169/) (2026)
- [Latent Variable Modelling Using Variational Autoencoders: A survey](https://mlsanity.com/paper/2206.09891/) (2022)
- [Sparse Binarization for Fast Keyword Spotting](https://mlsanity.com/paper/2406.06634/) (2024)
- [Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inference](https://mlsanity.com/paper/2505.21721/) (2025)
- [Revisiting Mixture Policies in Entropy-Regularized Actor-Critic](https://mlsanity.com/paper/2605.09157/) (2026)
- [Radial Spike and Slab Bayesian Neural Networks for Sparse Data in Ransomware Attacks](https://mlsanity.com/paper/2205.14759/) (2022)
- [Joint control variate for faster black-box variational inference](https://mlsanity.com/paper/2210.07290/) (2022)
- [Pathwise Gradient Variance Reduction with Control Variates in Variational Inference](https://mlsanity.com/paper/2410.05753/) (2024)
- [GRAFT: Decoupling Ranking and Calibration for Survival Analysis](https://mlsanity.com/paper/2602.07884/) (2026)
- [Stochastic Gradient Variational Inference with Price's Gradient Estimator from Bures-Wasserstein to Parameter Space](https://mlsanity.com/paper/2602.18718/) (2026)

## Abstract (arXiv)

Optimization with noisy gradients has become ubiquitous in statistics and machine learning. Reparameterization gradients, or gradient estimates computed via the "reparameterization trick," represent a class of noisy gradients often used in Monte Carlo variational inference (MCVI). However, when these gradient estimators are too noisy, the optimization procedure can be slow or fail to converge. One way to reduce noise is to use more samples for the gradient estimate, but this can be computationally expensive. Instead, we view the noisy gradient as a random variable, and form an inexpensive approximation of the generating procedure for the gradient sample. This approximation has high correlation with the noisy gradient by construction, making it a useful control variate for variance reduction. We demonstrate our approach on non-conjugate multi-level hierarchical models and a Bayesian neural net where we observed gradient variance reductions of multiple orders of magnitude (20-2,000x).