# Is Backpropagation Optimal? When Synthetic Gradients Improve Sample Efficiency

arXiv: https://arxiv.org/abs/2605.27946 · HTML: https://mlsanity.com/paper/2605.27946/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 58 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximation](https://mlsanity.com/paper/1806.02450/) (2018)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [Decoupled Greedy Learning of CNNs](https://mlsanity.com/paper/1901.08164/) (2019)
- [POPGym: Benchmarking Partially Observable Reinforcement Learning](https://mlsanity.com/paper/2303.01859/) (2023)
- [Empirical Bayes Transductive Meta-Learning with Synthetic Gradients](https://mlsanity.com/paper/2004.12696/) (2020)
- [Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis](https://mlsanity.com/paper/2003.07337/) (2020)
- [Decoupled Parallel Backpropagation with Convergence Guarantee](https://mlsanity.com/paper/1804.10574/) (2018)
- [Understanding Synthetic Gradients and Decoupled Neural Interfaces](https://mlsanity.com/paper/1703.00522/) (2017)
- [Biologically inspired alternatives to backpropagation through time for learning in recurrent neural nets](https://mlsanity.com/paper/1901.09049/) (2019)
- [Accelerated and instance-optimal policy evaluation with linear function approximation](https://mlsanity.com/paper/2112.13109/) (2021)
- [High-probability sample complexities for policy evaluation with linear function approximation](https://mlsanity.com/paper/2305.19001/) (2023)
- [Finite-Time Analysis of Natural Actor-Critic for POMDPs](https://mlsanity.com/paper/2202.09753/) (2022)
- [On the Statistical Benefits of Temporal Difference Learning](https://mlsanity.com/paper/2301.13289/) (2023)
- [The surprising efficiency of temporal difference learning for rare event prediction](https://mlsanity.com/paper/2405.17638/) (2024)
- [Cortico-cerebellar networks as decoupling neural interfaces](https://mlsanity.com/paper/2110.11501/) (2021)
- [A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning](https://mlsanity.com/paper/2205.11831/) (2022)
- [Feed-Forward On-Edge Fine-tuning Using Static Synthetic Gradient Modules](https://mlsanity.com/paper/2009.09675/) (2020)
- [ADA-GP: Accelerating DNN Training By Adaptive Gradient Prediction](https://mlsanity.com/paper/2305.13236/) (2023)

## Abstract (arXiv)

Backpropagation is the default learning rule for artificial neural networks and is often treated as the settled approach whenever differentiability is available. In this work, we revisit this convention through a theoretical lens of sample efficiency. We introduce a unified vectorized feedback framework for loss-based and reward-based learning on computational graphs, in which synthetic gradients emerge as a natural alternative to backpropagation. We characterize the conditions under which synthetic gradients can achieve a lower gradient-estimation mean squared error than backpropagation. We construct examples illustrating that this sample efficiency advantage can be arbitrarily large. Experiments on contextual bandits and reinforcement learning tasks demonstrate the potential of our theoretical findings.