mlsanityData to 14 Oct 2026

The Kinetics of Training: A Driven-Nucleation Rate Law for Emergence, Plasticity Loss, and Circuit Control in Language Models

arXiv 2607.27281 ↗First posted 29 Jul 2026cs.LGcited by 0

On the map: Mechanistic interpretability → Knowledge and representations inside LLMs

Abstract (arXiv)

A capability appears in a language model when the last parts of its circuit align in one stochastic attempt, and getting all but one right is worth nothing. We show this no-partial-credit joint alignment is the rate-limiting step of capability formation. Two fingerprints: in a shortcut-free apparatus a five-part circuit missing three waits as long as a three-part circuit missing three (1.19-1.37), so the wait counts missing parts, not size; and on Pythia across seven capabilities and three scales, ablating one part leaves a median 17% of the capability in 32 of 32 discriminating cells, where partial credit predicts 50-83% (p = 2e-10), while a random non-part head leaves 100%. One rare event whose barrier grows with missing parts yields a rate equation -- sites x attempts x drive x exp(-beta*K), minus destruction -- read three ways, each preregistered with frozen constants. Forward: a capability flat at baseline ignites at a step of our choosing once the mix passes a concentration floor (10/10 above, 0/12 below), and while still flat its arrival is datable from its precursor to 5% median error on six held-out models. Backward: the delay to learn a withheld capability grows with waiting until, past a critical step, it never ignites -- yet validation loss falls smoothly throughout, so standard monitors are blind to it. We locate the damage (heads commit to the base data) and isolate the cure: re-initializing only the query-key slices restores learnability (6/6) while the value slices do nothing (0/6). We prove the mechanism in a controlled gated-attention model: occupation forces a deadline whose consequences need no mixing assumption. Completed: SGD's noise fails the fluctuation-dissipation test, so we install one and anneal, melt and pin circuits on schedule. Scope: conjunction circuits in transformers to 1.4B.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Knowledge and representations inside LLMs, one of 13 directions in Mechanistic interpretability. Builds on 36 of its 56 references that are in the map. First posted on arXiv 29 Jul 2026.

Builds on

36 of 56 references.

References · 36

  1. 2022Emergent Abilities of Large Language Modelscited by 2,512
  2. 2023Pythia: A Suite for Analyzing Large Language Models Across Training and Scalingcited by 1,786
  3. 2023Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!cited by 1,154
  4. 2022In-context Learning and Induction Headscited by 964
  5. 2024OLMo: Accelerating the Science of Language Modelscited by 613
  6. 2023Are Emergent Abilities of Large Language Models a Mirage?cited by 523
  7. 2023DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretrainingcited by 399
  8. 2017Stochastic Gradient Descent as Approximate Bayesian Inferencecited by 300
  9. 2022Predictability and Surprise in Large Generative Modelscited by 210
  10. 2022Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limitcited by 187
  11. 2024Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performancecited by 184
  12. 2024RegMix: Data Mixture as Regression for Language Model Pre-trainingcited by 177
24 more
  1. 2023The Dormant Neuron Phenomenon in Deep Reinforcement Learningcited by 174
  2. 2015Adding Gradient Noise Improves Learning for Very Deep Networkscited by 145
  3. 2023SGD learning on neural networks: leap complexity and saddle-to-saddle dynamicscited by 143
  4. 2015Stochastic modified equations and adaptive stochastic gradient algorithmscited by 142
  5. 2022The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networkscited by 142
  6. 2020Online stochastic gradient descent on non-convex losses from high-dimensional inferencecited by 119
  7. 2023The mechanistic basis of data dependence and abrupt learning in an in-context classification taskcited by 118
  8. 2017Stochastic gradient descent performs variational inference, converges to limit cycles for deep networkscited by 109
  9. 2024What needs to go right for an induction head? A mechanistic study of in-context learning circuits and their formationcited by 89
  10. 2024Disentangling the Causes of Plasticity Loss in Neural Networkscited by 86
  11. 2023The Transient Nature of Emergent In-Context Learning in Transformerscited by 76
  12. 2024The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponentscited by 52
  13. 2018Fluctuation-dissipation relations for stochastic gradient descentcited by 48
  14. 2023Grokking as a First Order Phase Transition in Two Layer Networkscited by 48
  15. 2024Grokfast: Accelerated Grokking by Amplifying Slow Gradientscited by 41
  16. 2023SGD Finds then Tunes Features in Two-Layer Neural Networks with near-Optimal Sample Complexity: A Case Study in the XOR problemcited by 39
  17. 2023Dynamical versus Bayesian Phase Transitions in a Toy Model of Superpositioncited by 29
  18. 2025Data Mixing Can Induce Phase Transitions in Knowledge Acquisitioncited by 16
  19. 2025What Can Grokking Teach Us About Learning Under Nonstationarity?cited by 8
  20. 2025Predicting the Emergence of Induction Heads in Language Model Pretrainingcited by 7
  21. 2026Noise-Driven Escape from Metastable Phases explains Grokking in Deep Neural Networkscited by 5
  22. 2026Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergencecited by 3
  23. 2026Thermodynamic Irreversibility of Training Algorithmscited by 1
  24. 2026Emergent Capabilities Arise Randomly from Learning Sparse Attention Patternscited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2024Observational Scaling Laws and the Predictability of Language Model Performance
  2. 2025LLM Probability Concentration: How Alignment Shrinks the Generative Horizon
  3. 2026On Distinguishing Capability Elicitation from Capability Creation in Post-Training: A Free-Energy Perspective
  4. 2026Capable but Unreliable: Canonical Path Deviation as a Causal Mechanism of Agent Failure in Long-Horizon Tasks
  5. 2026ReAD: Reinforcement-Guided Capability Distillation for Large Language Models
  6. 2024Revisiting the Superficial Alignment Hypothesis
  7. 2025The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs
  8. 2026Where Cognition Lives: Dissecting Emergent from Computed Function in a Minimal Complete Cognitive Architecture