mlsanityData to 14 Oct 2026

Continual Learning as a Multiphase Moving-Boundary Problem

arXiv 2606.01863 ↗First posted 1 Jun 2026cs.LG math-ph math.MPcited by 0

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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.

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.

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23 of 40 references.

References · 23

  1. 2016Overcoming catastrophic forgetting in neural networkscited by 4,787
  2. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
  3. 2016iCaRL: Incremental Classifier and Representation Learningcited by 2,333
  4. 2017Gradient Episodic Memory for Continual Learningcited by 1,898
  5. 2016Progressive Neural Networkscited by 1,361
  6. 2018Experience Replay for Continual Learningcited by 1,095
  7. 2020Implicit Geometric Regularization for Learning Shapescited by 710
  8. 2018Task-Free Continual Learningcited by 221
  9. 2019Meta-Learning Representations for Continual Learningcited by 189
  10. 2019Functional Regularisation for Continual Learning with Gaussian Processescited by 123
  11. 2022iSDF: Real-Time Neural Signed Distance Fields for Robot Perceptioncited by 109
  12. 2020Continual Deep Learning by Functional Regularisation of Memorable Pastcited by 105
11 more
  1. 2021Continually Learning Self-Supervised Representations with Projected Functional Regularizationcited by 38
  2. 2020Deep learning of free boundary and Stefan problemscited by 35
  3. 2021Continual Neural Mapping: Learning An Implicit Scene Representation from Sequential Observationscited by 30
  4. 2024Order parameters and phase transitions of continual learning in deep neural networkscited by 14
  5. 2024Optimal Protocols for Continual Learning via Statistical Physics and Control Theorycited by 14
  6. 2023Subspace Distillation for Continual Learningcited by 12
  7. 2023Elephant Neural Networks: Born to Be a Continual Learnercited by 10
  8. 2022Statistical mechanics of continual learning: variational principle and mean-field potentialcited by 9
  9. 2025Physics-Informed Machine Learning for Two-Phase Moving-Interface and Stefan Problemscited by 3
  10. 2025InTAct: Interval-based Task Activation Consolidation for Continual Learningcited by 2
  11. 2025Knowledge Distillation for Continual Learning of Biomedical Neural Fieldscited by 2

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