Infinite Compute Pre-training Insights

• Pre-training under infinite compute is a regime where unlimited computational power exposes the limitations of fixed, saturated datasets, leading to unique overfitting challenges.
• Aggressive tuning of weight decay and ensembling strategies effectively mitigate overfitting, achieving a monotonically decreasing validation loss and improved data efficiency.
• Distillation leverages ensemble benefits to compress model size while preserving generalization, enabling efficient deployment in compute-rich, data-constrained settings.

Pre-training under infinite compute refers to the methodological and algorithmic regime in which computational resources for LLM training are unconstrained, while available web-scale text data is limited and potentially saturated. This setting has emerged as a focal point of research due to the rapid increase in hardware scalability far outpacing the expansion of curated datasets. Central questions in this regime include how to maximize model performance under fixed data, how to avoid overfitting when scaling model size and training epochs, and what interventions yield maximal generalization and data efficiency.

1. Data-Constrained Overfitting and the Failure of Standard Scaling Recipes

In the infinite compute paradigm, simply increasing model size $N$ or re-epoching fixed data $D$ leads to rapid overfitting. When datasets are saturated, scaling the epoch count or parameters with standard regularization settings (e.g., weight decay $\lambda = 0.1$) induces non-monotonic loss curves, with larger models achieving lower training loss but higher validation loss due to memorization and poor generalization. This "double descent" behavior invalidates earlier scaling laws (e.g., Chinchilla), which relied on abundant fresh data for joint scaling of $N$ and $D$.

A critical finding is that unconstrained epoching and parameter scaling—without proper regularization—cannot continuously decrease validation loss under data-limited conditions (Kim et al., 18 Sep 2025).

2. Regularization-Driven Parameter Scaling

The primary intervention identified is the aggressive tuning of regularization—specifically, a substantial increase in weight decay. Empirical results demonstrate that the optimal weight decay in high-epoch, over-parameterized regimes is approximately $30\times$ larger than conventional practice (e.g., from 0.1 up to 3.2 for models with $\sim$1.4B parameters). Grid and coordinate-descent searches over epoch count, learning rate, and weight decay enable jointly optimal hyperparameter settings.

This intervention yields a validation loss that monotonically decreases as model size increases, following a power law:

$\hat{L}_{D,N} = \frac{A_D}{N^{\alpha_D}} + E_D$

where $E_D$ is the estimated loss asymptote as $N \to \infty$, and the improved $\alpha_D$ reaches $\sim$1.02, compared to $\sim$0.34 for classical scaling. The use of elevated weight decay suppresses overfitting and maintains generalization even as epoch count increases (Kim et al., 18 Sep 2025).

3. Ensembling for Improved Loss Asymptotes

Beyond single-model scaling, ensembling emerges as a significant intervention for further reducing the loss asymptote under infinite compute. Independently trained models ${\mathcal{A}(D, N, Z_i, H)}_{i=1}^K$, where $Z$ indexes randomness, are combined at inference via logit averaging:

$$\text{LogitAvg}\left( \left\{ \mathcal{A}(D, N, Z_i, H) \right\}_{i=1}^K \right)$$

As the number of ensemble members $K$ increases, validation loss decreases approximately as $1/K$, achieving an asymptote lower than any single-parameter scaling recipe. For example, the regularized single model’s loss asymptote at $200$M tokens is approximately $3.43$, whereas typical ensembling achieves $3.34$ for moderate $K$, and joint scaling (parameter and ensemble size) yields an even lower asymptote ($\sim$3.17$$) (<a href="/papers/2509.14786" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Kim et al., 18 Sep 2025</a>).</p> <h2 class='paper-heading' id='data-efficiency-gains-via-distillation'>4. Data Efficiency Gains via Distillation</h2> <p>These improvements in asymptotic performance translate directly to data efficiency gains. At$$200$M tokens, the regularized recipe is$2.29\times$$more data efficient than the baseline, and combining ensembling with parameter scaling boosts this to$$5.17\times$$data efficiency. <a href="https://www.emergentmind.com/topics/lora-reconstruction-distillation" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Distillation</a> further amplifies efficiency: a student model distilled from an ensemble retains$$83\%$of the ensembling benefit while being$8\times$$smaller, enabling deployment of highly efficient models for inference.</p> <p>Self-distillation, wherein a model generates synthetic data for its own student, can also lower loss for fixed parameter count (<a href="/papers/2509.14786" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Kim et al., 18 Sep 2025</a>).</p> <h2 class='paper-heading' id='scaling-laws-and-asymptotic-evaluation'>5. Scaling Laws and Asymptotic Evaluation</h2> <p>The empirical trends are formalized as data-efficient scaling laws. Regularized training obeys an approximate$$1/N$law for loss as model size$N$increases:</p> <p>$\hat{L}_{D,N} = \frac{A_D}{N^{\alpha_D}} + E_D$</p> <p>where$A_D$,$\alpha_D$,$E_D$are empirically fit for fixed data$D$$. The central analytic shift posited is to evaluate algorithms by their loss asymptote ($$E_D$$) under the infinite compute regime, rather than performance at a fixed (finite) compute (<a href="/papers/2509.14786" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Kim et al., 18 Sep 2025</a>). This methodology allows direct comparisons between recipes based on their theoretical minima, accounting for both parameter scaling and ensembling.</p> <h2 class='paper-heading' id='downstream-performance-and-generalization'>6. Downstream Performance and Generalization</h2> <p>Validation loss improvements from regularized, ensemble-based, and distilled models correlate robustly with gains on downstream benchmarks. In cross-task evaluations (e.g., on PIQA, SciQ, ARC Easy), the best ensemble model achieves a$$9\%$$average improvement. Furthermore, continued pre-training (<a href="https://www.emergentmind.com/topics/continual-post-training-cpt" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">CPT</a>) on mid-training data (such as math-oriented corpora) with joint scaling yields a$$17.5\times$$data efficiency improvement compared to naive CPT recipes (<a href="/papers/2509.14786" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Kim et al., 18 Sep 2025</a>).</p> <p>These results demonstrate that careful tuning of regularization and ensemble strategies not only minimizes training loss but also improves generalization on real-world tasks.</p> <h2 class='paper-heading' id='practical-implications-and-future-directions'>7. Practical Implications and Future Directions</h2> <p>Given compute growth far outstripping data acquisition, future recipe design under infinite compute should:</p> <ul> <li>Aggressively tune regularization, especially weight decay ($$N$40%%%% higher than legacy values).

Scale parameter count subject to the new power law, targeting steady decrease in validation loss.

Utilize ensembling to achieve lower asymptotic limits, with efficient inference enabled via distillation.

Evaluate pre-training methods by their asymptotic loss, factoring both model and ensemble scaling.

Apply these strategies universally across LLMs and other domains where compute is unconstrained but data is fixed.

A plausible implication is that advances in synthetic data generation, adaptive regularization, and architecture design will further increase data efficiency and generalization capacity in future compute-rich, data-limited model pre-training regimes.

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These findings represent a substantial body of empirical and methodological research into the principles underlying pre-training when compute is, for practical purposes, unlimited, and data is the primary bottleneck (Kim et al., 18 Sep 2025).