Natural Ungrokking: Rule Reversal in Pretraining

Updated 5 July 2026

Natural ungrokking is defined as the within-run loss of a generalized rule despite stationary training evidence, distinguishing it from traditional grokking.
Experimental results show that corpus support frequency predicts whether a rule survives or collapses, with precise manipulation through data interventions.
The phenomenon exhibits asymmetric control where rules can be systematically killed but are not recoverable through injected support, highlighting displacement over erasure.

Searching arXiv for the primary paper and closely related grokking/ungrokking work. arXiv search query: Natural Ungrokking Asymmetric Control of Which Rules Survive Pretraining Searching arXiv for the exact title and related grokking papers. Natural ungrokking is a within-run reversal during ordinary pretraining in which a model first learns a rule, generalizes it on held-out probes, and later ceases to apply it even though the training stream is stationary and the rule’s supporting evidence remains present in the corpus (Li et al., 24 Jun 2026). The canonical case is a pronoun-gender rule in a small decoder-only LLM: given a feminine cue such as “Sue cried because,” the model prefers she over the corpus-default he, reaches held-out conflict accuracy $0.94$ by step $925$, and then falls to near $0.00$ by steps $3500$–$4400$ on the same probes, while the agree condition remains solved (Li et al., 24 Jun 2026). The phenomenon is presented as capability-level phase structure that is not visible in the loss curve, is predicted by corpus support frequency, and is asymmetrically controllable: targeted edits can destroy a rule on demand, but injecting support back does not restore it (Li et al., 24 Jun 2026).

1. Definition and relation to grokking

Natural ungrokking is defined as a model’s loss of a previously generalized rule within a single uninterrupted pretraining run, with no dataset swap, no removal of examples, and no change in the stationarity of the training stream (Li et al., 24 Jun 2026). In the focal experiments, the model acquires the rule, applies it correctly on held-out conflict probes, and later regresses while training accuracy on the underlying construction remains intact in agree-condition controls. The paper therefore distinguishes loss of the rule from loss of the construction.

This usage differs from standard grokking, which denotes delayed generalization: training accuracy saturates well before test accuracy rises. It also differs from earlier “ungrokking” in the circuit-efficiency literature, where a grokked model is further trained on a smaller dataset and regresses because memorization becomes more efficient below a critical dataset size (Varma et al., 2023). Natural ungrokking instead occurs within one run on a stationary corpus; the reversal is attributed to corpus-conditioned competition between a learned rule and a competing surface pattern rather than to a between-run change in dataset size (Li et al., 24 Jun 2026).

Conceptually, the term identifies a failure mode of pretraining in which generalization is neither monotone nor terminal. A rule can emerge, dominate behavior for a period, and later be displaced without any obvious trace in the optimization objective.

2. Experimental regime and probe construction

The governed experiments use a fixed small decoder-only transformer with the following architecture and training protocol (Li et al., 24 Jun 2026).

Component	Specification
Model	4-layer decoder-only transformer; $d_{\text{model}} = 256$ ; 2 attention heads; 2048-token context; 8192 BPE vocabulary; 11.5M parameters total; 3.1M excluding embeddings
Training	4400 steps; batch size 32; cosine warmdown over the final 30%; Muon on matrix parameters; AdamW on embeddings and scalars with $\beta = (0.9, 0.95)$
Corpora and budgets	TinyStories and a filtered web corpus derived from ClimbMix; $D/N \in \{1.5, 5\}$ plus uncapped packed runs, roughly $D/N \approx 30$ for TinyStories and $D/N \approx 40$ for web

Within comparisons, architecture, tokenizer, optimizer, and schedule are held fixed. Learning-rate and weight-decay settings differ by corpus: for TinyStories, matrix LR $925$0, embedding LR $925$1, weight decay $925$2; for web, matrix LR $925$3, embedding LR $925$4, weight decay $925$5. Each main cell uses exploratory seeds $925$6, and a quarantined replication set uses seeds $925$7–$925$8, designated before use.

The focal capability is pronoun-gender agreement under conflict with a corpus prior. In a feminine-cue context such as “Sue cried because …,” the rule-conforming continuation is she while the corpus-wide prior prefers he. The agree control is exemplified by “Tom cried because …,” where cue and prior align. This control is central because it shows that a collapsed model can still handle the construction when rule and prior do not conflict.

The main phase grid spans two corpora and three budget regimes. On TinyStories, the focal rule survives in $925$9 runs across all budgets; on the web corpus, it survives in $0.00$0 runs. The loss curve does not reveal this difference in fate (Li et al., 24 Jun 2026).

3. Corpus support frequency as the survival determinant

The paper’s principal empirical law is that the corpus decides which rules survive pretraining through support frequency: how often the training stream shows the rule winning over a competing surface pattern (Li et al., 24 Jun 2026). This is formalized by the support statistic

$0.00$1

For gender families, counts are obtained in a windowed mode: the first she/he within 16 tokens of a single-token gendered cue, counting both space variants of cue tokens. For other families, the counter uses exact bigrams. The TinyStories girl-class support frequency for the focal rule is

$0.00$2

events/token, which later serves as the unit for rescue-dose normalization.

The key claim is not merely that corpus identity matters, but that support frequency predicts the final verdict while the data-to-parameter ratio $0.00$3 only modulates collapse depth. In the authors’ formulation, support frequency decides a rule’s fate; $0.00$4 changes how deeply a doomed rule falls but does not flip survival versus collapse (Li et al., 24 Jun 2026). This is visible in the phase grid: TinyStories yields recovery across packed, $0.00$5, and $0.00$6, whereas web yields no surviving focal-rule cells across the same budgets.

A post-mortem descriptive counter in the appendix reinforces the corpus-statistic view. For the web text, simple bigram ratios include pronoun $0.00$7 and reflexive $0.00$8; these are reported as the only sub-unity ratios in either corpus. The paper uses such ratios to motivate the scale of rescue interventions.

4. Displacement mechanism and the contrast margin

The proposed mechanism is displacement rather than erasure (Li et al., 24 Jun 2026). Two hypotheses are contrasted. Under erasure, the model loses the construction itself. Under displacement, the construction remains available, but a competing surface-default prior out-competes the learned rule at the prediction site. The agree-condition controls favor displacement: collapsed runs continue to solve the construction when rule and prior align, indicating that the failure is specific to the rule-versus-prior conflict.

The central mechanistic observable is the contrast margin

$0.00$9

By definition, $3500$0 means the rule beats the prior, and $3500$1 means the prior beats the rule.

Across the main phase grid, mean final $3500$2 values are positive on TinyStories and negative on web. For TinyStories they are $3500$3 across packed, $3500$4, and $3500$5; for web they are $3500$6 across the same budgets. The sign of final $3500$7 matches final conflict-accuracy status in $3500$8 base runs. The timing is comparably sharp: in instrument-valid web seeds, the zero-crossing occurs at step $3500$9 with collapse at step $4400$0, and at step $4400$1 with collapse at step $4400$2. The paper summarizes this as behavioral collapse occurring within one 100-step checkpoint of the $4400$3 crossing.

Additional decomposition localizes the effect to contextual processing rather than static readout. In web runs, the direct embedding-path term stays near zero while the contextual term rises and later becomes negative; in surviving TinyStories runs, the direct term remains small and the contextual term ends strongly positive. The appendix further reports that gender-cue decodability in final-layer residuals is near chance in collapsed web runs and near ceiling in surviving TinyStories runs. These observations support the interpretation that the cue’s gender signal is no longer transported to the prediction site when natural ungrokking occurs.

5. Asymmetric control: monotone kill, failed rescue

The intervention results establish an asymmetry between destroying a rule and restoring it (Li et al., 24 Jun 2026). In the kill arm, TinyStories support is flipped in place from rule-conforming evidence to counter-evidence while preserving token counts and most other statistics. For pronoun gender, girl-name + she support is flipped to he with doses $4400$4. The causal effect is monotone: at $4400$5 the rule is not killed, at $4400$6 the cell is intervention-invalid because unrelated control families are damaged, and at $4400$7 the rule is fully killed in $4400$8 seeds. Mean $4400$9 moves from $d_{\text{model}} = 256$ 0 at baseline to $d_{\text{model}} = 256$ 1, then $d_{\text{model}} = 256$ 2, then $d_{\text{model}} = 256$ 3, and reported kill monotonicity is $d_{\text{model}} = 256$ 4.

A second rule family, $d_{\text{model}} = 256$ 5 allomorphy, exhibits the same one-way controllability. With doses $d_{\text{model}} = 256$ 6, mean final held-out conflict accuracy falls monotonically: $d_{\text{model}} = 256$ 7 The edit is reported as specific: unrelated families remain within $d_{\text{model}} = 256$ 8 of baseline, while another probe family for the same rule co-degrades.

The rescue arm reverses the edit direction on collapsed web data by injecting matching support documents back in. Doses are $d_{\text{model}} = 256$ 9, with symmetric boy $\beta = (0.9, 0.95)$ 0he documents and removal of neutral documents to preserve token counts. Post-injection support ratios reach $\beta = (0.9, 0.95)$ 1, $\beta = (0.9, 0.95)$ 2, $\beta = (0.9, 0.95)$ 3, and $\beta = (0.9, 0.95)$ 4, compared with $\beta = (0.9, 0.95)$ 5 in the naturally surviving TinyStories base cell. Nevertheless, no dose produces a control-valid behavioral recovery. The paper emphasizes that even when injected support is 450 times the natural sustaining level, the rule does not recover. Rescue monotonicity fails, with $\beta = (0.9, 0.95)$ 6 rather than the registered success threshold.

A timing control addresses the possibility that rescue fails only because support arrives too late. The $\beta = (0.9, 0.95)$ 7 rescue dose is split into an early schedule concentrated in steps $\beta = (0.9, 0.95)$ 8– $\beta = (0.9, 0.95)$ 9 and a late schedule in steps $D/N \in \{1.5, 5\}$ 0– $D/N \in \{1.5, 5\}$ 1. Both yield $D/N \in \{1.5, 5\}$ 2 control-valid recoveries. In the early schedule, one seed temporarily reaches conflict accuracy $D/N \in \{1.5, 5\}$ 3 while the dose is active and then loses the rule once the dose ends. The resulting picture is explicitly asymmetric: removing support is causally sufficient to destroy a rule, but adding support back is not sufficient to restore it. The paper further states that every confirmatory threshold and prediction was pre-registered before the governed data were read.

6. Position within the grokking literature and broader implications

Natural ungrokking sits at the intersection of several lines of grokking research while differing from each in a specific way. The circuit-efficiency account of grokking and ungrokking explains regression as a phase transition between memorizing and generalizing circuits, driven by dataset size and weight-decay-mediated efficiency; ungrokking in that framework occurs when continued training on a smaller dataset makes memorization more efficient than generalization (Varma et al., 2023). Natural ungrokking departs from this regime by showing reversal within one stationary pretraining run, with no between-run shrinkage of the dataset, and with final rule survival predicted by corpus support frequency rather than by the loss curve or an explicit dataset-size threshold (Li et al., 24 Jun 2026).

A thermodynamic heuristic models grokking as stochastic drift on a zero-training-loss manifold toward broader, higher-entropy structured regions, with reverse transitions interpretable through changes in free-energy ordering (Kozyrev, 2024). A global structural account treats grokking as parsimony-driven compression, redundancy collapse, spectral localization, and manifold simplification, implying that reversal would require loss of the sparse structured state (Zhang et al., 31 Mar 2026). Natural ungrokking does not provide a full mechanistic derivation in either language, but it supplies an empirical regime in which a learned rule is later displaced by a competing surface pattern while the loss curve remains silent (Li et al., 24 Jun 2026).

This suggests that pretraining has capability-level phase structure not reducible to aggregate optimization metrics. A plausible implication is that the relevant state variable is neither loss alone nor rule evidence alone, but the corpus-conditioned balance between rule-consistent and prior-consistent continuations at the prediction site. Under that interpretation, natural ungrokking is not generic forgetting and not simple overfitting in a loose sense. It is a selective reversal in which a model retains the construction, loses the conflict-case preference, and exhibits one-way controllability under data interventions.

The broader significance is methodological as well as conceptual. The phenomenon appears in public checkpoints—Pythia $D/N \in \{1.5, 5\}$ 4M– $D/N \in \{1.5, 5\}$ 5B and OLMo-1B—with scale-ordered collapse depth and Spearman $D/N \in \{1.5, 5\}$ 6 across five Pythia sizes (Li et al., 24 Jun 2026). Accordingly, natural ungrokking is presented not as an artifact of one $D/N \in \{1.5, 5\}$ 7M-parameter setup, but as evidence that ordinary pretraining can both create and later eliminate specific rule-like behaviors, with the survival decision written into corpus statistics rather than exposed by the loss curve.