# Directions of Curvature as an Explanation for Loss of Plasticity

arXiv: https://arxiv.org/abs/2312.00246 · HTML: https://mlsanity.com/paper/2312.00246/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 48 references that are in the map.
- First posted on arXiv 30 Nov 2023.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [The Primacy Bias in Deep Reinforcement Learning](https://mlsanity.com/paper/2205.07802/) (2022)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Meta-Learning Representations for Continual Learning](https://mlsanity.com/paper/1905.12588/) (2019)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [Understanding plasticity in neural networks](https://mlsanity.com/paper/2303.01486/) (2023)
- [Implicit Under-Parameterization Inhibits Data-Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2010.14498/) (2020)
- [Understanding and Preventing Capacity Loss in Reinforcement Learning](https://mlsanity.com/paper/2204.09560/) (2022)
- [Loss of Plasticity in Continual Deep Reinforcement Learning](https://mlsanity.com/paper/2303.07507/) (2023)
- [Understanding and Improving Convolutional Neural Networks via Concatenated Rectified Linear Units](https://mlsanity.com/paper/1603.05201/) (2016)
- [Continual Backprop: Stochastic Gradient Descent with Persistent Randomness](https://mlsanity.com/paper/2108.06325/) (2021)
- [Transient Non-Stationarity and Generalisation in Deep Reinforcement Learning](https://mlsanity.com/paper/2006.05826/) (2020)
- [Stiffness: A New Perspective on Generalization in Neural Networks](https://mlsanity.com/paper/1901.09491/) (2019)
- [Emergent properties of the local geometry of neural loss landscapes](https://mlsanity.com/paper/1910.05929/) (2019)
- [A study on the plasticity of neural networks](https://mlsanity.com/paper/2106.00042/) (2021)
- [Maintaining Plasticity in Deep Continual Learning](https://mlsanity.com/paper/2306.13812/) (2023)
- [Harnessing Structures for Value-Based Planning and Reinforcement Learning](https://mlsanity.com/paper/1909.12255/) (2019)
- [HesScale: Scalable Computation of Hessian Diagonals](https://mlsanity.com/paper/2210.11639/) (2022)
- [Utility-based Perturbed Gradient Descent: An Optimizer for Continual Learning](https://mlsanity.com/paper/2302.03281/) (2023)

## Built on by (most cited first, 26 of 26)

- [Learning Continually by Spectral Regularization](https://mlsanity.com/paper/2406.06811/) (2024)
- [Mitigating Plasticity Loss in Continual Reinforcement Learning by Reducing Churn](https://mlsanity.com/paper/2506.00592/) (2025)
- [Neuroplastic Expansion in Deep Reinforcement Learning](https://mlsanity.com/paper/2410.07994/) (2024)
- [Optimizers Qualitatively Alter Solutions And We Should Leverage This](https://mlsanity.com/paper/2507.12224/) (2025)
- [Don't flatten, tokenize! Unlocking the key to SoftMoE's efficacy in deep RL](https://mlsanity.com/paper/2410.01930/) (2024)
- [Network Sparsity Unlocks the Scaling Potential of Deep Reinforcement Learning](https://mlsanity.com/paper/2506.17204/) (2025)
- [On-device edge learning for IoT data streams: a survey](https://mlsanity.com/paper/2502.17788/) (2025)
- [Bridging Streaming Continual Learning via In-Context Large Tabular Models](https://mlsanity.com/paper/2512.11668/) (2025)
- [Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning](https://mlsanity.com/paper/2509.22335/) (2025)
- [Activation Function Design Sustains Plasticity in Continual Learning](https://mlsanity.com/paper/2509.22562/) (2025)
- [Reset & Distill: A Recipe for Overcoming Negative Transfer in Continual Reinforcement Learning](https://mlsanity.com/paper/2403.05066/) (2024)
- [Predicting Plasticity in Deep Continual Learning: A Theoretical Perspective](https://mlsanity.com/paper/2605.09044/) (2026)
- [Sparsity-Driven Plasticity in Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2508.06871/) (2025)
- [Do Neural Networks Lose Plasticity in a Gradually Changing World?](https://mlsanity.com/paper/2602.09234/) (2026)
- [The Rank and Gradient Lost in Non-stationarity: Sample Weight Decay for Mitigating Plasticity Loss in Reinforcement Learning](https://mlsanity.com/paper/2604.01913/) (2026)
- [SPHERE: Mitigating the Loss of Spectral Plasticity in Mixture-of-Experts for Deep Reinforcement Learning](https://mlsanity.com/paper/2605.04712/) (2026)
- [Silent Neuron Theory and Plasticity Preservation for Deep Reinforcement Learning in Adaptive Video Streaming](https://mlsanity.com/paper/2505.01584/) (2025)
- [A Unified Noise-Curvature View of Loss of Trainability](https://mlsanity.com/paper/2509.19698/) (2025)
- [Continual Learning with Query-Only Attention](https://mlsanity.com/paper/2510.00365/) (2025)
- [Beyond Single-Model Optimization: Preserving Plasticity in Continual Reinforcement Learning](https://mlsanity.com/paper/2604.15414/) (2026)
- [Rethinking Plasticity in Deep Reinforcement Learning](https://mlsanity.com/paper/2603.21173/) (2026)
- [Attribution-Based Neuron Utility for Plasticity Restoration in Deep Networks](https://mlsanity.com/paper/2605.06834/) (2026)
- [Agentic Safety is an Epistemic Property, Not a Behavioral One](https://mlsanity.com/paper/2606.28347/) (2026)
- [Sustaining Plasticity via Learnable Wavelet Activations in Continual Learning](https://mlsanity.com/paper/2608.12874/) (2026)
- [SingularClip: Preventing Spectral Collapse to Maintain Plasticity in Continual and Reinforcement Learning](https://mlsanity.com/paper/2608.18319/) (2026)
- [Rare Gate Disagreements Can Limit Plasticity: When Gradient Flow Mispredicts Finite-Batch SGD](https://mlsanity.com/paper/2610.11475/) (2026)

## Abstract (arXiv)

Loss of plasticity is a phenomenon in which neural networks lose their ability to learn from new experience. Despite being empirically observed in several problem settings, little is understood about the mechanisms that lead to loss of plasticity. In this paper, we offer a consistent explanation for loss of plasticity: Neural networks lose directions of curvature during training and that loss of plasticity can be attributed to this reduction in curvature. To support such a claim, we provide a systematic investigation of loss of plasticity across continual learning tasks using MNIST, CIFAR-10 and ImageNet. Our findings illustrate that loss of curvature directions coincides with loss of plasticity, while also showing that previous explanations are insufficient to explain loss of plasticity in all settings. Lastly, we show that regularizers which mitigate loss of plasticity also preserve curvature, motivating a simple distributional regularizer that proves to be effective across the problem settings we considered.