# Dimensionless Controls of Plasticity Under Alternating Tasks: From Evolutionary Biology to Continual Learning

arXiv: https://arxiv.org/abs/2608.23889 · HTML: https://mlsanity.com/paper/2608.23889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Linear Mode Connectivity in Multitask and Continual Learning](https://mlsanity.com/paper/2010.04495/) (2020)
- [Loss of Plasticity in Continual Deep Reinforcement Learning](https://mlsanity.com/paper/2303.07507/) (2023)
- [A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix](https://mlsanity.com/paper/2010.04003/) (2020)
- [Deep neural networks have an inbuilt Occam's razor](https://mlsanity.com/paper/2304.06670/) (2023)
- [Analysis of Stochastic Gradient Descent in Continuous Time](https://mlsanity.com/paper/2004.07177/) (2020)
- [Why flatness does and does not correlate with generalization for deep neural networks](https://mlsanity.com/paper/2103.06219/) (2021)
- [A PAC-Bayesian Link Between Generalisation and Flat Minima](https://mlsanity.com/paper/2402.08508/) (2024)
- [When Representations Align: Universality in Representation Learning Dynamics](https://mlsanity.com/paper/2402.09142/) (2024)
- [Commute Your Domains: Trajectory Optimality Criterion for Multi-Domain Learning](https://mlsanity.com/paper/2501.15556/) (2025)
- [Out-of-distribution forgetting: vulnerability of continual learning to intra-class distribution shift](https://mlsanity.com/paper/2306.00427/) (2023)
- [On the curvature of the loss landscape](https://mlsanity.com/paper/2307.04719/) (2023)
- [Amplitude response and square wave describing functions](https://mlsanity.com/paper/2412.01579/) (2024)

## Abstract (arXiv)

Plasticity under changing environments is central to both evolutionary biology and continual learning. Motivated by recent work on genotype--phenotype maps, we study a minimal deep-learning analogue where a network is trained alternately on two Boolean label sets, and ask which biological controls of plasticity survive the translation to gradient descent. Reinterpreting four proposed biological factors as quantities of training dynamics, we find the system reduces to two dimensionless controls: the task disagreement r, the fraction of disagreeing labels, and the reach η T, the product of learning rate and switching period. We derive two bounds on plasticity: r alone fixes an extremal geometric floor on the utopia distance, while r and η T jointly bound forgetting. Across 9,720 trajectories, an ANOVA confirms that r, η, and T dominate, while the effect of neutral-set size (emphasized in the biological setting) is negligible. The optimal reach itself follows an approximate inverse power law η T*propto r-1.18, yielding a heuristic that sets the optimal reach η T^* from the task disagreement alone. The analogy that survives is therefore dynamical rather than geometric, and our setting enables a view of plasticity through the lens of other driven systems in physics and engineering.