# The Generalized Reparameterization Gradient

arXiv: https://arxiv.org/abs/1610.02287 · HTML: https://mlsanity.com/paper/1610.02287/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2016.

## Built on by (most cited first, 30 of 30)

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- [ARMS: Antithetic-REINFORCE-Multi-Sample Gradient for Binary Variables](https://mlsanity.com/paper/2105.14141/) (2021)
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- [Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms](https://mlsanity.com/paper/2310.19927/) (2023)
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- [Calibrated Test-Time Guidance for Bayesian Inference](https://mlsanity.com/paper/2602.22428/) (2026)
- [CARMS: Categorical-Antithetic-REINFORCE Multi-Sample Gradient Estimator](https://mlsanity.com/paper/2110.14002/) (2021)
- [On permutation symmetries in Bayesian neural network posteriors: a variational perspective](https://mlsanity.com/paper/2310.10171/) (2023)
- [The Lie-Group Bayesian Learning Rule](https://mlsanity.com/paper/2303.04397/) (2023)
- [Enhancing Uncertainty Estimation and Interpretability via Bayesian Non-negative Decision Layer](https://mlsanity.com/paper/2505.22199/) (2025)
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- [An Overview on Controllable Text Generation via Variational Auto-Encoders](https://mlsanity.com/paper/2211.07954/) (2022)
- [Parameter Estimation in DAGs from Incomplete Data via Optimal Transport](https://mlsanity.com/paper/2305.15927/) (2023)
- [A New Stochastic Approximation Method for Gradient-based Simulated Parameter Estimation](https://mlsanity.com/paper/2503.18319/) (2025)
- [RAPTOR: End-to-end Risk-Aware MDP Planning and Policy Learning by Backpropagation](https://mlsanity.com/paper/2106.07260/) (2021)
- [Likelihood-based inference and forecasting for trawl processes: a stochastic optimization approach](https://mlsanity.com/paper/2308.16092/) (2023)
- [DBsurf: A Discrepancy Based Method for Discrete Stochastic Gradient Estimation](https://mlsanity.com/paper/2309.03974/) (2023)
- [What to Do When Your Discrete Optimization Is the Size of a Neural Network?](https://mlsanity.com/paper/2402.10339/) (2024)
- [Diagonalisation SGD: Fast & Convergent SGD for Non-Differentiable Models via Reparameterisation and Smoothing](https://mlsanity.com/paper/2402.11752/) (2024)
- [Analytical Approximation of the ELBO Gradient in the Context of the Clutter Problem](https://mlsanity.com/paper/2404.10550/) (2024)
- [Decoupling Task and Behavior: A Two-Stage Reward Curriculum in Reinforcement Learning for Robotics](https://mlsanity.com/paper/2603.05113/) (2026)

## Abstract (arXiv)

The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterization gradient fit Gaussian distributions. In this paper, we introduce the generalized reparameterization gradient, a method that extends the reparameterization gradient to a wider class of variational distributions. Generalized reparameterizations use invertible transformations of the latent variables which lead to transformed distributions that weakly depend on the variational parameters. This results in new Monte Carlo gradients that combine reparameterization gradients and score function gradients. We demonstrate our approach on variational inference for two complex probabilistic models. The generalized reparameterization is effective: even a single sample from the variational distribution is enough to obtain a low-variance gradient.