Human Grokking: Phase Transitions in Semantic Field Saturation

Abstract

In machine learning, grokking denotes a phase transition from memorization to generalization: a neural network discovers the underlying algebraic structure of a task long after achieving perfect training accuracy. We propose a structurally parallel phenomenon in human learning within high-density epistemic environments --- proceeding through accumulation, saturation, phase transition, and generalization --- and ground the parallel in the mechanistic interpretability decomposition of Nanda et al. (2023).

The core claim: if morphism-density (the number and type of structural connections between representations) is the critical parameter for the transition, then optimal pedagogy maximizes relational structure per unit of content, not content-volume per unit of time.

We present a 32-node, 91-edge constellation pedagogy spanning physics, mathematics, electrical engineering, and RF engineering as both the instrument for accelerating the transition and the experimental apparatus for studying it. Five operationalized, falsifiable empirical predictions are specified.

The Paper

Resources

The Constellation Graph

The core experimental apparatus is a 32-node knowledge graph spanning four domains, connected by 91 unique typed morphism edges. Each node is a constellation --- a cluster of 5—14 relationally defined terms with explicit structural connections to adjacent constellations. The graph is the pedagogical tool, the measurement instrument, and the evidence base, all in one artifact.

The four domains and their internal sequences:

• Physics (9 nodes, blue): Newtonian mechanics through quantum field theory
• Mathematics (9 nodes, red/pink): Linear algebra through algebraic topology and fiber bundles
• Electrical Engineering (7 nodes, green): Circuit fundamentals through power systems
• RF Engineering (7 nodes, amber): Electromagnetic waves through information and coding theory

Eleven typed edge classes connect the graph: limit, conservation, duality, transform, quantization, constitutive, embedding, lifting, approximation, composition, and bridge (cross-domain structural identity).

Key Contributions

The Nanda Mapping. We map the three-phase mechanistic decomposition of ML grokking (Nanda et al. 2023) --- memorization circuits, circuit formation, regularization-driven cleanup --- onto observable human cognitive phases. The critical prediction: human grokking should show a measurable plateau in proxy measures (constellation completion accuracy) while self-reported comprehension remains flat, followed by a simultaneous jump. This is the crossing-point signature that distinguishes grokking from expertise.

Cognitive Regularization. We identify dyadic co-creation (sustained collaborative work with an interlocutor) as the human analog of weight decay in neural networks. Communication forces compression; an interlocutor forces coherence checking. These are exactly the regularization pressures that suppress “memorization circuits” (content-level retrieval) in favor of “generalizing circuits” (morphism-level processing). The prediction: stronger regularization (more intense dyadic interaction) should accelerate the transition.

Structural Identity, Not Analogy. The paper defines a precise hierarchy of structural identity --- from isomorphism through equivalence, adjunction, functor, and natural transformation --- and provides a worked example: Kirchhoff’s laws as circuit-graph (co)homology. This is an isomorphism, not a metaphor. The boundary operator $\partial$ with $\partial^2 = 0$ is the same mathematical object in both contexts.

Five Falsifiable Predictions. Constellation completion with null models; explanation directionality shift (deductive to abductive); cross-domain transfer speed; plateau-then-jump temporal signature (the most direct test); and far transfer to held-out domains not on the graph (the “test set” analog from Power et al. 2022).

Citation

@article{close_2026_human_grokking,
  author       = {Close, Larsen},
  title        = {Human Grokking: Phase Transitions in Semantic
                  Field Saturation},
  month        = feb,
  year         = 2026,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.18627239},
  url          = {https://zenodo.org/records/18627239}
}