Loss-to-Loss Prediction: Scaling Laws for All Datasets (2411.12925v1)

Abstract: While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

Loss-to-Loss Prediction: Scaling Laws for All Datasets

The paper "Loss-to-Loss Prediction: Scaling Laws for All Datasets" presents a paper on scaling laws, extending existing methodologies for predicting train loss across various data distributions. While traditional scaling laws associate model performance with specific data and compute regimes, this work ventures further by proposing a generalized framework for loss-to-loss prediction across differing datasets, both in pre-training and downstream tasks.

Key Insights and Methodologies

The primary contribution is a methodology termed loss-to-loss prediction, which effectively allows translating loss predictions from one dataset to another. This methodology is built upon the observation of simple shifted power law relationships across train-to-train, train-to-test, and test-to-test scenarios. Three core predictions are formulated:

1. Train-to-Train: The paper identifies a shifted power law connecting the train losses of models across two distinct datasets when paired by training compute. This relationship enables the estimation of scaling laws from smaller scales, translating existing laws from a known distribution.
2. Train-to-Test: The train-to-test prediction links a model’s training loss on one dataset to its test loss on a dissimilar dataset. Although these predictions prove less practical due to the limited benefit in predicting unseen train set performances, they offer valuable insights into the transfer dynamics from pre-training to downstream tasks.
3. Test-to-Test: This prediction correlates the test losses of models trained on separate datasets. While noisier than other predictions, it holds significant implications for dataset selection aimed at enhancing performance on specific downstream tasks.

Through these relationships, the authors demonstrate their ability to predict performance even at compute levels 20 times larger than those used for model training, underscoring the robustness of their predictions.

Discussion on Scaling Law Translation and Predictions

The work challenges existing scaling law parameterizations, advocating a form blending attributes from the seminal Equations present in \citet{kaplan2020scaling} and \citet{hoffmann2022training}. This form supports a valuable extrapolation capacity necessary for articulating concrete loss-to-loss predictions. Moreover, the paper underscores the invariance in compute-optimal model sizes irrespective of the data distribution, an understanding crucial for efficient model scaling.

Two practical applications underscore the utility of loss-to-loss predictions:

• Scaling Law Translation: By leveraging a comprehensive set of pre-trained models, new scaling laws can be efficiently extrapolated to new distributions using minimal additional computation. This significantly outperforms conventional independent fitting methods, enhancing prediction accuracy while reducing computational cost.
• Predicting Large Model Test Losses: Here, predictions for larger models trained on novel datasets use loss-to-loss methodologies to improve extrapolative accuracy beyond baseline methods. Such predictions are crucial for data-driven decision-making in model training and deployment.

Implications and Future Directions

This research extends both the practical and theoretical frontiers of scaling laws, offering insights into dataset-specific loss dynamics and performance extrapolation. Practically, loss-to-loss predictions promise impactful efficiencies in model training, informing data selection and guiding pre-training strategies optimally tailored for diverse downstream tasks. Theoretically, it raises questions about the underpinnings of data distribution effects in scaling laws, alluding to potential broader applications in AI model transferability assessments.

Future research could explore resolving the noted limitations, particularly in understanding the underlying mechanics driving train-to-test and test-to-test relationships. Furthermore, investigating more complex data mixtures and generative tasks could amplify these methodologies' robustness and applicability. The intriguing invariant compute-optimal model finding suggests examining other architectural choices could enrich the understanding of data distribution effects.

In summary, the paper contributes a vital toolkit for loss extrapolation across datasets, heralding efficient, data-informed scaling laws essential for modern AI.