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arxiv: 2606.05610 · v1 · pith:RKRKOZTRnew · submitted 2026-06-04 · 💻 cs.CL

Predictable Scaling Laws of Optimal Hyperparameters for LLM Continued Pre-training

Yongwei Zhou , Juncheng Diao , Junlin Shang , Peiguang Li , Rongxiang Weng This is my paper

Pith reviewed 2026-06-28 01:50 UTC · model grok-4.3

classification 💻 cs.CL
keywords scaling lawshyperparameter optimizationcontinued pre-traininglarge language modelscompute efficiency
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The pith

Optimal hyperparameters for LLM continued pre-training follow stable scaling laws discoverable from small proxy models.

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

The paper establishes that optimal learning rates and batch sizes during continued pre-training change in a regular, predictable manner as compute increases. Small proxy models are used to derive explicit functions that map any compute budget to the best hyperparameter values. For any starting checkpoint, its validation loss is inverted through a scaling law to recover the amount of pre-training compute that would produce the same loss from scratch; this equivalent-compute value is then added to the planned budget to select the correct hyperparameters for the target run. If the discovered laws hold, the method eliminates most of the usual grid-search cost while delivering performance at least as good as exhaustive tuning.

Core claim

Optimal hyperparameters follow stable and predictable scaling laws throughout the continued pre-training process. The two-stage framework first trains small proxy models to obtain functions mapping compute budget to optimal hyperparameters, then uses the inverse scaling law on a checkpoint's validation loss to estimate its equivalent pre-training compute; the sum of that quantity and the new budget yields the predicted optimal settings for the target model.

What carries the argument

Inverse scaling law that converts a checkpoint's validation loss into an estimate of its equivalent pre-training compute, combined with proxy-derived functions that map total compute to optimal learning rate and batch size.

If this is right

  • Hyperparameter search overhead drops by up to 90 percent for continued pre-training runs.
  • Performance matches or exceeds that of standard grid-search baselines.
  • The approach applies to any starting checkpoint and generalizes across model architectures.

Where Pith is reading between the lines

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

  • The same proxy-plus-inversion pattern could be tested on other training phases such as supervised fine-tuning if analogous loss-compute relations exist.
  • Training budgets for multi-stage LLM pipelines could be planned in advance with far less repeated search.
  • Continued pre-training would behave more like an extension of the original pre-training curve than a separate tuning task.

Load-bearing premise

Scaling laws found on small proxy models will continue to hold for large target models, and a checkpoint's validation loss can be inverted to recover an accurate equivalent pre-training compute value.

What would settle it

Apply the full prediction procedure to a large target model, then train two versions of that model—one with the predicted hyperparameters and one with hyperparameters found by exhaustive search on the identical run—and observe whether the predicted version reaches substantially lower final performance.

Figures

Figures reproduced from arXiv: 2606.05610 by Juncheng Diao, Junlin Shang, Peiguang Li, Rongxiang Weng, Yongwei Zhou.

Figure 1
Figure 1. Figure 1: Scaling Laws for Optimal Hyperparameters [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The Overall Framework for Optimal Hyperparameters Prediction in continued pre-training [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Optimization analysis of learning rate and batch size [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Validation loss trajectories during continued pre-training. (a) Larger batch sizes (e.g., [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
read the original abstract

The efficacy of continued pre-training for Large Language Models (LLMs) hinges upon hyperparameter configurations, such as learning rate and batch size. However, current practices often rely on heuristics or grid searches, leading to training instability and excessive costs. In this work, we first empirically discover that optimal hyperparameters follow stable and predictable scaling laws throughout the continued pre-training process. Leveraging these insights, we propose a novel framework to establish quantitative relationships between compute budget and optimal hyperparameters for a given checkpoint. Our approach has two stages: (1) \textit{Empirical Law Discovery}, where we train small-scale proxy models to derive functions mapping compute budget to optimal hyperparameters via standard loss-compute scaling laws; and (2) \textit{State-Aware Hyperparameter Prediction}, where we evaluate an initial checkpoint's validation loss and use the inverse scaling law to estimate its \textit{equivalent pre-training compute} -- the compute needed to achieve the same loss from scratch. Combining this with the planned compute budget, we predict optimal hyperparameters for the target run. Empirical results demonstrate that our method reduces the hyperparameter search overhead by up to 90\% while achieving comparable or superior performance relative to baselines. This model-agnostic framework generalizes across architectures, providing a principled and efficient methodology for diverse continued pre-training scenarios starting from any given point.

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 paper claims that optimal learning rate and batch size for LLM continued pre-training obey stable scaling laws that can be discovered on small proxy models; it introduces a two-stage framework (Empirical Law Discovery via loss-compute scaling laws, followed by State-Aware Hyperparameter Prediction that inverts the scaling law on a checkpoint's validation loss to recover equivalent pre-training compute) to predict target hyperparameters from a given compute budget, reporting up to 90% reduction in search overhead with comparable or better performance.

Significance. If the proxy-to-target transfer holds, the framework would materially reduce the cost of hyperparameter selection in continued pre-training, a frequent and expensive step in LLM pipelines. The approach is model-agnostic in principle and supplies an explicit quantitative link between compute budget and optimal hyperparameters.

major comments (2)
  1. [Abstract / Empirical Law Discovery] Abstract, Empirical Law Discovery stage: scaling laws for optimal LR and batch size are fitted exclusively on small-scale proxy models, yet the manuscript contains no direct transfer experiment in which the predicted hyperparameters are applied to a large target model (> few B parameters) and compared against exhaustive search or strong baselines on that same model and data regime. This extrapolation is load-bearing for both the generalization claim and the 90% overhead reduction.
  2. [Abstract / State-Aware Hyperparameter Prediction] Abstract, State-Aware Hyperparameter Prediction stage: the inverse scaling law used to estimate equivalent pre-training compute from validation loss is derived and tested only at proxy scale; no evidence is provided that the recovered compute value remains accurate for checkpoints originating from larger models or different data mixtures, undermining the quantitative relationship asserted between budget and hyperparameters.
minor comments (2)
  1. [Abstract] The abstract states the framework is 'model-agnostic' and 'generalizes across architectures,' but the specific model families, sizes, and datasets used for the proxy experiments and any limited target tests are not enumerated.
  2. [Abstract] Empirical results are summarized without reference to error bars, number of runs, or statistical tests supporting the 'comparable or superior performance' claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the key points where the scope of our empirical validation requires clearer articulation. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract / Empirical Law Discovery] Abstract, Empirical Law Discovery stage: scaling laws for optimal LR and batch size are fitted exclusively on small-scale proxy models, yet the manuscript contains no direct transfer experiment in which the predicted hyperparameters are applied to a large target model (> few B parameters) and compared against exhaustive search or strong baselines on that same model and data regime. This extrapolation is load-bearing for both the generalization claim and the 90% overhead reduction.

    Authors: The referee correctly notes that all reported experiments use proxy models. The manuscript does not contain direct transfer experiments that apply the predicted hyperparameters to models larger than a few billion parameters and compare them against exhaustive search on the same large model and data. Our defense rests on the observation that the scaling laws were recovered consistently across multiple proxy scales and architectures, which we take as evidence that the functional forms are stable. Nevertheless, we agree that this leaves the extrapolation to truly large targets as an assumption rather than a directly verified result. In revision we will (a) state the exact parameter ranges used for the proxy models in the abstract and main text and (b) add an explicit limitations paragraph discussing the untested regime. revision: yes

  2. Referee: [Abstract / State-Aware Hyperparameter Prediction] Abstract, State-Aware Hyperparameter Prediction stage: the inverse scaling law used to estimate equivalent pre-training compute from validation loss is derived and tested only at proxy scale; no evidence is provided that the recovered compute value remains accurate for checkpoints originating from larger models or different data mixtures, undermining the quantitative relationship asserted between budget and hyperparameters.

    Authors: We agree that the inverse scaling law (mapping validation loss back to equivalent pre-training compute) is derived and validated exclusively on the same proxy-scale checkpoints. No experiments are presented that test whether the recovered compute estimate remains accurate when the checkpoint comes from a larger model or from a different data mixture. This is a genuine limitation of the current evidence. In the revision we will restrict the claims about the State-Aware stage to the proxy regime in which it was tested and add a short discussion of the additional assumptions required for transfer to larger models or shifted data distributions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on empirical proxy fits for extrapolation

full rationale

The paper's chain consists of training small proxy models to fit scaling laws (loss vs. compute and optimal hyperparameters vs. compute), then applying the inverse of the loss-compute relation to estimate equivalent pre-training compute for a checkpoint and combining it with a target budget to select hyperparameters. This is a standard empirical extrapolation procedure rather than any reduction of the claimed predictions to the fitted inputs by definition or construction. No self-citations, uniqueness theorems, or ansatzes are invoked in the abstract or described stages, and the central performance claims rest on reported empirical results rather than tautological reuse of the same data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are detailed beyond reliance on standard loss-compute scaling laws and empirical fitting from proxy models.

pith-pipeline@v0.9.1-grok · 5777 in / 1234 out tokens · 42489 ms · 2026-06-28T01:50:14.836693+00:00 · methodology

discussion (0)

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Reference graph

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