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arxiv: 2605.20602 · v1 · pith:PWMHEGTUnew · submitted 2026-05-20 · 💻 cs.CL · cs.AI· cs.LG

Self-Training Doesn't Flatten Language -- It Restructures It: Surface Markers Amplify While Deep Syntax Dies

Ming Liu This is my paper

Pith reviewed 2026-05-21 05:42 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG
keywords self-trainingstructural depthlanguage model outputssyntactic decayLLM text restructuringsurface markersdeep syntax
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The pith

Self-training on model outputs restructures language by syntactic depth rather than flattening it uniformly.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The common view is that self-training a language model on its own outputs causes uniform flattening with lost diversity and narrower distributions. This paper shows the process instead restructures language asymmetrically, boosting surface markers like connectives and hedges while causing deeper syntactic forms such as questions, passives, and subjunctives to decay. The decay rate of each feature tracks primarily the number of nested syntactic dependencies it requires, with a pooled correlation of 0.540 across 85 feature-model pairs, far stronger than the link to initial frequency. A control using human text fine-tuning shows no such depth-based pattern, indicating the effect is specific to self-training. The result means standard complexity proxies can rise even as underlying syntax erodes, affecting how training data is chosen and how machine text is detected.

Core claim

The Structural Depth Hypothesis states that the per-generation decay rate of a linguistic feature during successive self-training is predicted primarily by its structural depth—the number of nested syntactic dependencies it requires—and only secondarily by its generation-zero output frequency. Tracking 17 features over eleven generations in five models from three architecture families yields a pooled Spearman rho of 0.540 for depth versus 0.225 for frequency, while a matched human-text fine-tuning control yields rho near zero.

What carries the argument

The Structural Depth Hypothesis, which predicts feature decay rates in self-training from the count of nested syntactic dependencies a feature requires.

If this is right

  • Aggregate complexity proxies such as dependency tree depth, type-token ratio, and word length all rise even as clause structure collapses.
  • The resulting text carries rising superficial complexity alongside eroding deep syntax.
  • Training-data curation must account for this depth-driven restructuring to preserve syntactic variety.
  • LLM-text detection methods may need adjustment to track depth-specific markers rather than overall complexity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the pattern holds, repeated self-training cycles could gradually erode a model's capacity for complex clause embedding in ways simple diversity metrics miss.
  • The depth-based decay might appear in other iterative regimes such as reinforcement learning from model feedback, suggesting a broader test across training loops.
  • Explicit interventions during self-training could be designed to protect high-depth structures and slow the observed collapse.

Load-bearing premise

That the 17 linguistic features can be reliably assigned structural depth values based on nested syntactic dependencies in a manner independent of the self-training process.

What would settle it

Finding that frequency predicts per-generation decay rates at least as strongly as structural depth in a replication with additional models or a broader feature set would undermine the primary role assigned to depth.

Figures

Figures reproduced from arXiv: 2605.20602 by Ming Liu.

Figure 1
Figure 1. Figure 1: Core result for GPT-2 124M across 11 self-training generations. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Per-feature decay rate λ(ϕ) vs. structural depth d(ϕ) for GPT-2. Group means (horizontal bars) decrease monotonically with depth. Positive λ indicates amplification; negative indicates collapse. 5.4 Critical pairs The clearest evidence for SDH comes from critical pairs: pairs of features that are matched on lexical surface form or frequency but differ in depth. Past tense, regular vs. irregular. Both are e… view at source ↗
Figure 3
Figure 3. Figure 3: Depth vs. frequency as decay predictors (GPT-2). Each point is one of the 17 features. Depth (Spearman [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Critical pairs: features matched on frequency but differing in depth show opposite fates under self-training. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Cross-model comparison. (a) Group means by depth across five models. The depth gradient is consistent despite different absolute magnitudes. (b) Pooled decay rates (N=85) show a highly significant depth correlation (ρ=0.540, p < 10−6 ). structure) yields a 95% CI of [0.434, 0.634], ex￾cluding zero. Per-feature bootstrap CIs (resam￾pling over models, 104 iterations) show that 12 of 17 features have CIs excl… view at source ↗
Figure 6
Figure 6. Figure 6: Feature-level heatmaps across generations. Each row is a feature (sorted by depth), each column a [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Greedy-to-nucleus ratio τ (ϕ) by feature. d=0 features (red) cluster near zero (high sampling dependence σ ≈ 1), meaning they are absent from greedy templates. Deep features (green, blue) have τ > 1 (σ = 0) but still decay due to the dominant depth penalty. ally significant after Holm correction (Pythia-2.8B: padj=0.010; Pythia-410M: padj=0.036). We note that Fisher’s method assumes independence of the per… view at source ↗
read the original abstract

Successive self-training on a language model's own outputs is widely characterized as a process of flattening: diversity drops, distributions narrow, and the text becomes "more like itself." We provide evidence that this characterization is incomplete. Across eleven generations of self-training on five models (GPT-2 124M, Pythia-410M, Pythia-1.4B, OPT-1.3B, Pythia-2.8B), language is not flattened uniformly -- it is restructured. Surface markers (discourse connectives, hedges, em-dashes) rise, while mid- and deep-syntactic structures (questions, parentheticals, passives, subjunctives) collapse. We formalize this asymmetric collapse as the Structural Depth Hypothesis (SDH): the per-generation decay rate of a linguistic feature is predicted primarily by its structural depth -- the number of nested syntactic dependencies it requires -- and only secondarily by its generation-zero output frequency. Pooling 17-feature panels from five models spanning three architecture families (N=85), the pooled Spearman correlation is rho=0.540 (p < 10^{-6}; cluster-bootstrap 95% CI [0.434, 0.634]), while frequency is a substantially weaker predictor (rho=0.225). A matched human-text fine-tuning control yields rho=0.039 (p=0.88), confirming the gradient is self-training-specific. We further document a Superficial Complexity Paradox: aggregate complexity proxies (dep-tree depth, TTR, word length) all rise as the underlying clause structure dies, with direct implications for training-data curation and LLM-text detection.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript argues that successive self-training on language models does not produce uniform flattening but instead restructures linguistic output: surface markers (e.g., discourse connectives, hedges) increase while mid- and deep-syntactic structures (questions, passives, subjunctives) decay. This is formalized as the Structural Depth Hypothesis (SDH), which posits that per-generation decay rates are predicted primarily by a feature's structural depth (number of nested syntactic dependencies) and only secondarily by its generation-zero frequency. Evidence consists of pooled Spearman correlations across 17 features and five models (N=85) yielding rho=0.540 for depth versus rho=0.225 for frequency, with a human-text fine-tuning control showing rho=0.039; aggregate complexity proxies are also shown to rise despite underlying structural collapse.

Significance. If the SDH holds, the work offers a more precise account of self-training dynamics than the prevailing flattening narrative, with concrete implications for training-data curation and LLM-generated text detection. Strengths include the multi-model, multi-architecture replication, use of cluster-bootstrap confidence intervals, and an external human control that isolates self-training-specific effects. The result supplies falsifiable predictions about which features will decay under continued self-training.

major comments (2)
  1. [Methods / Feature Definition] The manuscript provides no explicit list of the 17 linguistic features nor the pre-specified rule set used to assign structural depth values (number of nested syntactic dependencies) to each. This assignment is load-bearing for the SDH claim and the reported rho=0.540 versus rho=0.225 contrast; without documented criteria, inter-annotator agreement, or evidence that assignments were made independently of observed decay trajectories, the correlation risks circularity.
  2. [Results / Correlation Analysis] It is unclear whether feature selection or depth labeling occurred before or after inspecting per-generation decay rates. The abstract and results report a pooled analysis but do not describe pre-registration, blinding, or a hold-out procedure that would demonstrate the depth predictor was not tuned to the same data used to compute the correlations.
minor comments (2)
  1. [Abstract / Results] The abstract states eleven generations of self-training but the correlation analysis pools 17-feature panels without clarifying how many generations enter each per-feature decay-rate calculation or whether early-generation instability was excluded.
  2. [Discussion] The Superficial Complexity Paradox is introduced but the precise definitions of the aggregate proxies (dep-tree depth, TTR, word length) and their measurement across generations could be stated more explicitly to allow replication.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and detailed review, which has helped us strengthen the clarity and rigor of our presentation of the Structural Depth Hypothesis. Below we respond point-by-point to the major comments. We have revised the manuscript to address the concerns where possible.

read point-by-point responses

  1. Referee: [Methods / Feature Definition] The manuscript provides no explicit list of the 17 linguistic features nor the pre-specified rule set used to assign structural depth values (number of nested syntactic dependencies) to each. This assignment is load-bearing for the SDH claim and the reported rho=0.540 versus rho=0.225 contrast; without documented criteria, inter-annotator agreement, or evidence that assignments were made independently of observed decay trajectories, the correlation risks circularity.

    Authors: We agree that the absence of an explicit feature list and depth-assignment protocol is a significant omission that weakens the transparency of the SDH claim. The depth values were in fact assigned a priori using a syntactic-dependency criterion (counting the maximum number of nested clausal and phrasal dependencies required to realize the construction, drawing on standard treebank annotation guidelines) before any decay-rate analysis was performed. We have added a new Appendix A that lists all 17 features with precise extraction rules, the depth rubric with worked examples for each, and a brief justification for each depth score grounded in syntactic theory rather than observed frequencies or decay. We also note that formal inter-annotator agreement was not computed; this is now acknowledged as a limitation in the revised Methods. revision: yes

  2. Referee: [Results / Correlation Analysis] It is unclear whether feature selection or depth labeling occurred before or after inspecting per-generation decay rates. The abstract and results report a pooled analysis but do not describe pre-registration, blinding, or a hold-out procedure that would demonstrate the depth predictor was not tuned to the same data used to compute the correlations.

    Authors: Feature selection was guided by prior literature on syntactic complexity and was finalized before the self-training runs and decay measurements began. Depth labeling followed the same pre-specified syntactic rubric. However, the study was not pre-registered and no blinding or hold-out validation of the depth predictor was performed. We have inserted a new paragraph in the Methods section that explicitly states the chronological order of decisions and acknowledges the lack of pre-registration. As an additional safeguard, we now report a supplementary analysis restricted to a theoretically motivated subset of six features whose depth assignments were made without reference to any empirical decay data; the depth–decay correlation remains significant in this reduced set. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical correlations rest on independent linguistic depth assignments and external controls.

full rationale

The paper's central claim is the Structural Depth Hypothesis, supported by pooled Spearman correlations (rho=0.540 for depth vs. rho=0.225 for frequency) computed across observed decay rates of 17 features in self-training trajectories from five models, plus a matched human-text fine-tuning control. These are statistical results on measured quantities rather than a derivation that reduces by construction to its inputs. Depth is defined via the number of nested syntactic dependencies as a pre-specified linguistic criterion, with no equations or steps shown that equate the predictor to the outcome or rename a fitted parameter as a prediction. No self-citations, uniqueness theorems, or ansatzes are invoked in a load-bearing way that would make the result equivalent to the input data by definition. The analysis is therefore self-contained against the reported empirical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the domain assumption that linguistic features possess measurable structural depth independent of the training regime, plus standard statistical assumptions for Spearman correlation and cluster bootstrapping. No free parameters or new invented entities are introduced.

axioms (1)
  • domain assumption Linguistic features can be classified by structural depth according to the number of nested syntactic dependencies they require.
    This classification supplies the primary predictor in the Structural Depth Hypothesis and is used to compute the reported correlations.

pith-pipeline@v0.9.0 · 5837 in / 1402 out tokens · 56851 ms · 2026-05-21T05:42:51.877976+00:00 · methodology

discussion (0)

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Reference graph

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