# Continual Learning as a Multiphase Moving-Boundary Problem

arXiv: https://arxiv.org/abs/2606.01863 · HTML: https://mlsanity.com/paper/2606.01863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [Meta-Learning Representations for Continual Learning](https://mlsanity.com/paper/1905.12588/) (2019)
- [Functional Regularisation for Continual Learning with Gaussian Processes](https://mlsanity.com/paper/1901.11356/) (2019)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [Continual Deep Learning by Functional Regularisation of Memorable Past](https://mlsanity.com/paper/2004.14070/) (2020)
- [Continually Learning Self-Supervised Representations with Projected Functional Regularization](https://mlsanity.com/paper/2112.15022/) (2021)
- [Deep learning of free boundary and Stefan problems](https://mlsanity.com/paper/2006.05311/) (2020)
- [Continual Neural Mapping: Learning An Implicit Scene Representation from Sequential Observations](https://mlsanity.com/paper/2108.05851/) (2021)
- [Order parameters and phase transitions of continual learning in deep neural networks](https://mlsanity.com/paper/2407.10315/) (2024)
- [Optimal Protocols for Continual Learning via Statistical Physics and Control Theory](https://mlsanity.com/paper/2409.18061/) (2024)
- [Subspace Distillation for Continual Learning](https://mlsanity.com/paper/2307.16419/) (2023)
- [Elephant Neural Networks: Born to Be a Continual Learner](https://mlsanity.com/paper/2310.01365/) (2023)
- [Statistical mechanics of continual learning: variational principle and mean-field potential](https://mlsanity.com/paper/2212.02846/) (2022)
- [Physics-Informed Machine Learning for Two-Phase Moving-Interface and Stefan Problems](https://mlsanity.com/paper/2512.14010/) (2025)
- [InTAct: Interval-based Task Activation Consolidation for Continual Learning](https://mlsanity.com/paper/2511.17439/) (2025)
- [Knowledge Distillation for Continual Learning of Biomedical Neural Fields](https://mlsanity.com/paper/2511.21409/) (2025)

## Abstract (arXiv)

Continual learning struggles to balance retaining past knowledge with absorbing new tasks. Stefan-CL elegantly resolves this stability-plasticity dilemma through the physics of melting. It frames consolidated knowledge as a protected "solid" and unused capacity as an adaptable "liquid." As the network learns, this boundary expands, governed by a "latent heat" tuning dial. By mathematically freezing the learned interior, Stefan-CL cuts forgetting to near zero, matching memory-heavy baselines without storing raw data, forging a beautiful, physics-grounded path for AI.