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arxiv: 2606.06888 · v2 · pith:QQNJULOQnew · submitted 2026-06-05 · 💻 cs.LG

Data-Constrained Language Model Pretraining: Improved Regularization and Scaling Laws

Zhiwei Xu , Shihao Wu , Hanseul Cho , Wei Hu , Yixin Wang This is my paper

Pith reviewed 2026-06-27 22:21 UTC · model grok-4.3

classification 💻 cs.LG
keywords data-constrained pretrainingmasked-input regularizationscaling lawslanguage model pretrainingweight decayrepeated dataautoregressive models
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The pith

Masked-input regularization added to weight decay improves language model validation loss under data constraints, with gains equivalent to 1.3 times more unique data according to the SoftQ scaling law.

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

The paper examines pretraining when available text data is limited relative to compute, so models must repeat passes over a fixed corpus. It tests masked-input regularization as an auxiliary loss on randomly masked inputs, applied on top of strong weight decay, and shows this combination reduces validation loss across model sizes from 72M to 1.4B parameters while delivering downstream gains at the largest scale. It also introduces the SoftQ scaling law, which couples model size to the amount of repeated data to capture their interaction, and demonstrates that this form fits the experimental results more closely than additive laws that treat the two factors separately. The new law further translates the regularization benefit into an effective increase of roughly 1.3 times the unique training data.

Core claim

Across 72M to 1.4B parameter models, masked-input regularization added on top of strong weight decay improves validation loss over autoregressive strong-weight-decay-only models, with downstream gains at 1.4B. SoftQ, a scaling law that couples model size and data size to capture their interaction under repeated data, fits data-constrained experiments substantially better than classical alternatives such as the Chinchilla law, and estimates MIR's gains as equivalent to roughly 1.3 times as much unique training data.

What carries the argument

Masked-input regularization (MIR), an auxiliary next-token prediction loss on randomly masked inputs, together with the SoftQ scaling law that couples model size and repeated data size.

If this is right

  • MIR added to strong weight decay reduces validation loss relative to weight decay alone across the tested range of model sizes.
  • At 1.4B parameters MIR produces measurable gains on downstream tasks.
  • SoftQ provides a substantially better fit to data-constrained pretraining runs than additive scaling laws that decouple model size from data repetition.
  • The regularization improvement can be read as equivalent to training on 1.3 times as much unique data.

Where Pith is reading between the lines

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

  • Regularization methods originally developed for diffusion models can transfer to standard autoregressive training without requiring architecture changes or extra inference cost.
  • Coupled scaling laws may help practitioners decide how many epochs to run when the supply of unique text is fixed.
  • The same regularization and scaling approach could be tested in other data-scarce domains such as code or multimodal training.

Load-bearing premise

The functional form of SoftQ correctly captures the interaction between model size and repeated data passes rather than merely fitting the specific experimental conditions tested.

What would settle it

Measuring whether the performance lift from MIR on a new model size or repetition count exactly matches the 1.3 times unique-data multiplier predicted by the SoftQ fit on the original experiments.

Figures

Figures reproduced from arXiv: 2606.06888 by Hanseul Cho, Shihao Wu, Wei Hu, Yixin Wang, Zhiwei Xu.

Figure 1
Figure 1. Figure 1: Overview of the main results. Left: On DataComp-LM (DCLM) dataset [Li et al., 2024] with 100M unique training tokens, MIR improves validation loss over the strongly regularized autoregressive baseline across model sizes. Points show means over five random seeds, error bars show one standard deviation, and faint markers show individual runs. Right: On the strongly regularized baseline grid, we plot the loss… view at source ↗
Figure 2
Figure 2. Figure 2: Validation Loss dynamics on DCLM 100M for the 257M model. Large weight decay substantially improves both multi-epoch AR and dLLM training; with both well regularized, their validation losses become comparable. Recent studies report that dLLMs outperform AR models in the data-constrained regime [Ni et al., 2025, Prabhudesai et al., 2025], using weight de￾cay wd = 0.1 for both. Independently, Kim et al. [202… view at source ↗
Figure 1
Figure 1. Figure 1: Representative tokenlevel examples from the top 0.1% largest improvements in nexttoken loss. In each text window, the red token is the held-out true next token yt. The rows below report the MIR and blidititthith thbbilitid t Figure 3: Left: Absolute token-level loss-gap tails on all validation tokens for the 1.4B models after [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: Validation loss vs. number of epochs. Weight decay is fixed to 0.1, peak learning rate is [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Tuning the mask ratio bounds (rmin, rmax) and regularization coefficient λ. A.8 Auxiliary Experimental Results [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Absolute-loss view of the fitted Chinchilla and SoftQ laws on the [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Regularized baseline validation loss as a function of unique training data size [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Scaling curves across four unique-data budgets for the strongly regularized baseline and [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
read the original abstract

Classical scaling laws for language model pretraining balance model size against training dataset size under a fixed compute budget, assuming abundant data and a single pass over the corpus. As training compute grows faster than the supply of natural language data, pretraining is likely to enter a data-constrained, compute-rich regime where models train for multiple epochs over a finite dataset. We study data-constrained pretraining along two axes, regularization and scaling. For regularization, we study masked-input regularization (MIR), an auxiliary next-token prediction loss on randomly masked inputs. MIR tests whether the random masking central to diffusion language models can benefit autoregressive pretraining without architectural changes or inference overhead. Across 72M to 1.4B parameter models, we find that MIR added on top of strong weight decay improves validation loss over autoregressive strong-weight-decay-only models, with downstream gains at 1.4B. For scaling, we propose SoftQ, a scaling law that couples model size and data size to capture their interaction under repeated data. Classical alternatives such as the Chinchilla law use an additive form that decouples these terms, making them misspecified in the data-constrained regime. We find that SoftQ fits data-constrained experiments substantially better than these alternatives, and estimates MIR's gains as equivalent to roughly 1.3 times as much unique training data. We release our code at https://github.com/yixinw-lab/dc_pretrain.

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

3 major / 3 minor

Summary. The manuscript examines data-constrained language model pretraining in the regime of repeated passes over finite data. It introduces masked-input regularization (MIR), an auxiliary next-token loss on randomly masked inputs, and reports that MIR on top of strong weight decay improves validation loss over weight-decay-only baselines across 72M–1.4B models, with downstream gains at 1.4B. It further proposes the SoftQ scaling law, which couples model size N and effective data D under repetition, and claims that SoftQ fits the data-constrained experiments substantially better than additive alternatives such as the Chinchilla law, with MIR gains estimated as equivalent to roughly 1.3× unique training data. Code is released.

Significance. If the empirical claims hold after addressing experimental reporting and validation details, the work is significant for the emerging data-limited pretraining regime. The code release is a clear strength that supports reproducibility. The reported downstream gains at 1.4B and the proposed functional form for repeated-data scaling could inform practical regularization and compute allocation decisions.

major comments (3)
  1. [Abstract / scaling laws] Abstract and scaling-law section: SoftQ parameters are fitted directly to the same data-constrained runs used to assert superior fit and to derive the 1.3× data-equivalence claim for MIR; this renders the validation of the functional form partially circular, as the claimed advantage over additive forms is not tested on held-out repetition regimes or larger scales.
  2. [MIR experiments] Experimental results (MIR section): the central claim of consistent validation-loss improvement and downstream gains rests on comparisons whose statistical support is not detailed—no run counts, error bars, significance tests, or exact data-exclusion rules are provided, making it impossible to assess whether the reported gains are robust or load-bearing.
  3. [scaling laws / SoftQ fit] Scaling-law validation: the claim that SoftQ correctly captures the N–D interaction under repetition (rather than providing extra degrees of freedom that fit the tested 72M–1.4B, limited-epoch regime) is not supported by out-of-distribution tests or comparison against other flexible functional forms; the 1.3× equivalence therefore inherits the same limitation.
minor comments (3)
  1. [scaling laws] Notation for effective data D under repetition should be defined explicitly before the SoftQ equation to avoid ambiguity with the classical D term.
  2. [figures] Figure captions for loss curves should state the number of independent runs and whether shaded regions represent standard error or min/max.
  3. [code release] The GitHub link is given but the manuscript does not specify which exact scripts reproduce the SoftQ parameter fits and the 1.3× calculation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We agree that additional statistical reporting and independent validation of the scaling law are required to support the claims. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / scaling laws] Abstract and scaling-law section: SoftQ parameters are fitted directly to the same data-constrained runs used to assert superior fit and to derive the 1.3× data-equivalence claim for MIR; this renders the validation of the functional form partially circular, as the claimed advantage over additive forms is not tested on held-out repetition regimes or larger scales.

    Authors: We agree the current validation is partially circular because SoftQ parameters are fit to the same runs used to evaluate fit quality and the MIR equivalence claim. The functional form itself was derived from modeling the interaction between model size and effective data under repetition (rather than chosen purely for flexibility). In revision we will add held-out repetition schedules, cross-validation across different epoch counts, and explicit comparisons against other flexible functional forms with similar parameter counts to test whether the advantage holds out of sample. revision: yes

  2. Referee: [MIR experiments] Experimental results (MIR section): the central claim of consistent validation-loss improvement and downstream gains rests on comparisons whose statistical support is not detailed—no run counts, error bars, significance tests, or exact data-exclusion rules are provided, making it impossible to assess whether the reported gains are robust or load-bearing.

    Authors: The referee correctly notes that the manuscript omits run counts, error bars, significance tests, and precise data-exclusion criteria. We will revise the experimental section to report the number of independent random seeds, include error bars or shaded regions on all loss curves, state the exact data filtering rules, and add statistical significance tests for the reported validation and downstream improvements. revision: yes

  3. Referee: [scaling laws / SoftQ fit] Scaling-law validation: the claim that SoftQ correctly captures the N–D interaction under repetition (rather than providing extra degrees of freedom that fit the tested 72M–1.4B, limited-epoch regime) is not supported by out-of-distribution tests or comparison against other flexible functional forms; the 1.3× equivalence therefore inherits the same limitation.

    Authors: We acknowledge the absence of out-of-distribution tests at scales or repetition regimes beyond the reported 72M–1.4B range. In the revision we will (i) compare SoftQ against additional flexible functional forms with comparable degrees of freedom and (ii) expand the limitations paragraph to explicitly discuss the tested regime. The form remains motivated by the multiplicative interaction between model capacity and repeated data rather than being an arbitrary fit; the 1.3× claim will be presented with the corresponding caveats. revision: partial

Circularity Check

1 steps flagged

SoftQ parameters fitted to data-constrained runs; 1.3x data equivalence derived directly from that fit

specific steps
  1. fitted input called prediction [Abstract]
    "We find that SoftQ fits data-constrained experiments substantially better than these alternatives, and estimates MIR's gains as equivalent to roughly 1.3 times as much unique training data."

    SoftQ functional parameters are obtained by fitting to the identical data-constrained experimental points; the 1.3x equivalence is then computed from those same fitted parameters, so the reported gain is a direct algebraic consequence of the fit rather than a separate prediction or external validation.

full rationale

The paper proposes SoftQ as a coupled scaling law, fits its parameters to the same 72M–1.4B data-constrained experiments used to demonstrate superior fit over Chinchilla-style additive forms, and then extracts the MIR gain as 'roughly 1.3 times as much unique training data' from those fitted parameters. This reduces the claimed equivalence and the superiority claim to a direct output of the fit on the target data rather than an independent derivation or out-of-sample prediction. No other circular steps (self-citation chains, self-definitional terms, or imported uniqueness theorems) are present; the regularization results on MIR appear independent of the scaling-law fit.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Central claims rest on experimental outcomes for MIR gains and on the empirical superiority of the SoftQ functional form; both depend on fitted parameters and the representativeness of the tested regime.

free parameters (1)
  • SoftQ scaling law parameters
    Parameters in the proposed SoftQ law are fitted to match the data-constrained experimental results.
axioms (1)
  • domain assumption The interaction between model size and data repetition in the data-constrained regime is captured by a coupled functional form rather than an additive one.
    Invoked when claiming SoftQ fits experiments substantially better and when deriving the 1.3x data equivalence.

pith-pipeline@v0.9.1-grok · 5802 in / 1569 out tokens · 35798 ms · 2026-06-27T22:21:46.321183+00:00 · methodology

discussion (0)

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Reference graph

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