# Safe Mutations for Deep and Recurrent Neural Networks through Output Gradients

arXiv: https://arxiv.org/abs/1712.06563 · HTML: https://mlsanity.com/paper/1712.06563/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2017.

## Built on by (most cited first, 15 of 15)

- [Deep Multiagent Reinforcement Learning: Challenges and Directions](https://mlsanity.com/paper/2106.15691/) (2021)
- [Evolutionary Reinforcement Learning: A Survey](https://mlsanity.com/paper/2303.04150/) (2023)
- [Combining Evolution and Deep Reinforcement Learning for Policy Search: a Survey](https://mlsanity.com/paper/2203.14009/) (2022)
- [Derivative-Free Reinforcement Learning: A Review](https://mlsanity.com/paper/2102.05710/) (2021)
- [MODRL/D-EL: Multiobjective Deep Reinforcement Learning with Evolutionary Learning for Multiobjective Optimization](https://mlsanity.com/paper/2107.07961/) (2021)
- [Improving Deep Policy Gradients with Value Function Search](https://mlsanity.com/paper/2302.10145/) (2023)
- [Competitive Distillation: A Simple Learning Strategy for Improving Visual Classification](https://mlsanity.com/paper/2506.23285/) (2025)
- [Evolutionary Echo State Network: evolving reservoirs in the Fourier space](https://mlsanity.com/paper/2206.04951/) (2022)
- [Selection-Expansion: A Unifying Framework for Motion-Planning and Diversity Search Algorithms](https://mlsanity.com/paper/2104.04768/) (2021)
- [Evolutionary Reinforcement Learning via Cooperative Coevolution](https://mlsanity.com/paper/2404.14763/) (2024)
- [Signal-Adaptive Trust Regions for Gradient-Free Optimization of Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2601.21572/) (2026)
- [Sparse Mutation Decompositions: Fine Tuning Deep Neural Networks with Subspace Evolution](https://mlsanity.com/paper/2302.05832/) (2023)
- [Low Rank Factorizations are Indirect Encodings for Deep Neuroevolution](https://mlsanity.com/paper/2504.03037/) (2025)
- [EvoPref: Multi-Objective Evolutionary Optimization Discovers Diverse LLM Alignments Beyond Gradient Descent](https://mlsanity.com/paper/2605.09777/) (2026)
- [Modular Norm RandOpt: Population-Efficient Ensembling through Architecture-Aware Perturbations](https://mlsanity.com/paper/2609.25745/) (2026)

## Abstract (arXiv)

While neuroevolution (evolving neural networks) has a successful track record across a variety of domains from reinforcement learning to artificial life, it is rarely applied to large, deep neural networks. A central reason is that while random mutation generally works in low dimensions, a random perturbation of thousands or millions of weights is likely to break existing functionality, providing no learning signal even if some individual weight changes were beneficial. This paper proposes a solution by introducing a family of safe mutation (SM) operators that aim within the mutation operator itself to find a degree of change that does not alter network behavior too much, but still facilitates exploration. Importantly, these SM operators do not require any additional interactions with the environment. The most effective SM variant capitalizes on the intriguing opportunity to scale the degree of mutation of each individual weight according to the sensitivity of the network's outputs to that weight, which requires computing the gradient of outputs with respect to the weights (instead of the gradient of error, as in conventional deep learning). This safe mutation through gradients (SM-G) operator dramatically increases the ability of a simple genetic algorithm-based neuroevolution method to find solutions in high-dimensional domains that require deep and/or recurrent neural networks (which tend to be particularly brittle to mutation), including domains that require processing raw pixels. By improving our ability to evolve deep neural networks, this new safer approach to mutation expands the scope of domains amenable to neuroevolution.