# Intrinsic-Extrinsic Coupling in Learning Dynamics

arXiv: https://arxiv.org/abs/2609.30185 · HTML: https://mlsanity.com/paper/2609.30185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 32 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [An Evaluation Dataset for Intent Classification and Out-of-Scope Prediction](https://mlsanity.com/paper/1909.02027/) (2019)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [AlphaEdit: Null-Space Constrained Knowledge Editing for Language Models](https://mlsanity.com/paper/2410.02355/) (2024)
- [Path-conditioned training: a principled way to rescale ReLU neural networks](https://mlsanity.com/paper/2602.19799/) (2026)
- [Implicit biases in multitask and continual learning from a backward error analysis perspective](https://mlsanity.com/paper/2311.00235/) (2023)
- [Retention analysis of edited knowledge after fine-tuning](https://mlsanity.com/paper/2507.14198/) (2025)
- [Can Neural Networks Learn by Experimenting on Themselves? Self-Interventional Learning from Functional Consequences to Predictive Self-Knowledge](https://mlsanity.com/paper/2608.14894/) (2026)
- [Fiber Fingerprints of Hidden Learning-State Dynamics](https://mlsanity.com/paper/2608.15976/) (2026)
- [Revelation Control](https://mlsanity.com/paper/2608.23860/) (2026)

## Abstract (arXiv)

A learner's current observations need not determine its response to further training. We formulate intrinsic-extrinsic coupling through the continuation-conditioned value of a constrained learning-state intervention, with observation-relative fibers describing present agreement. An executable finite-frame classifier-head write protects current logits while repairing specified historical margins under finite-precision acceptance checks. We distinguish local admissibility, continuation-conditioned intervention value, and complete-policy performance. A matched four-cell contrast identifies readout-specific non-additivity between the same intrinsic intervention and alternative external continuations. In a CLINC-derived class-incremental setting, replay changes the write's 32-update contribution from five correct predictions to zero. Nonzero interactions also occur under output distillation, with a RoBERTa backbone, and under optimizer-native SGDW dynamics. Under SGDW, correct-count interactions are negative in all three activated roots at 128 updates, showing that coupling need not imply positive synergy. The mathematical analysis distinguishes feasible local repairs and favorable terminal outputs from training-reachable repair regions. Separate coordination tests show that content controls match or exceed the development gain, while a five-root fresh-test comparison with Fiber present in every arm shows root-dependent rather than uniformly beneficial correct-count effects. On the secondary cross-entropy readout, guided allocation yields lower mean loss than standard replay in all five pairs. Together, these results make intrinsic-extrinsic coupling operational by connecting executable state geometry to continuation-conditioned value, matched interaction identification, and closed-loop coordination, while separating identified coupling from complete-policy performance.