Broken Neural Scaling Laws (2210.14891v17)

Abstract: We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest varies as amount of compute used for training (or inference), number of model parameters, training dataset size, model input size, number of training steps, or upstream performance varies) for various architectures & for each of various tasks within a large & diverse set of upstream & downstream tasks, in zero-shot, prompted, & finetuned settings. This set includes large-scale vision, language, audio, video, diffusion, generative modeling, multimodal learning, contrastive learning, AI alignment, AI capabilities, robotics, out-of-distribution (OOD) generalization, continual learning, transfer learning, uncertainty estimation / calibration, OOD detection, adversarial robustness, distillation, sparsity, retrieval, quantization, pruning, fairness, molecules, computer programming/coding, math word problems, "emergent phase transitions", arithmetic, supervised learning, unsupervised/self-supervised learning, & reinforcement learning (single agent & multi-agent). When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set. Moreover, this functional form accurately models & extrapolates scaling behavior that other functional forms are incapable of expressing such as the nonmonotonic transitions present in the scaling behavior of phenomena such as double descent & the delayed, sharp inflection points present in the scaling behavior of tasks such as arithmetic. Lastly, we use this functional form to glean insights about the limit of the predictability of scaling behavior. Code is available at https://github.com/ethancaballero/broken_neural_scaling_laws

An Expert Analysis on "Broken Neural Scaling Laws"

The paper "Broken Neural Scaling Laws," authored by Ethan Caballero et al., offers a substantive advancement in understanding the scaling relations of neural networks, particularly how performance metrics vary with model and dataset scaling. By introducing Broken Neural Scaling Laws (BNSLs), the authors challenge the traditional power-law scaling models that previously attempted to predict the efficacy of extensive neural network training from smaller-scale experiments.

Introduction to Scaling Laws

Scaling laws have long served as a foundational basis for estimating the performance improvements from increasing model size, dataset volume, or compute resources. Historically, these laws have modeled test losses and performance metrics as smooth, power-law functions of scale. However, these traditional scaling laws exhibit limitations, especially when applied to "downstream" tasks, which are essentially model evaluations on new or distinct subsets beyond the training data. Many times, downstream performance does not exhibit the same smooth patterns but instead shows non-linearities, including inflection points and non-monotonic behaviors like double descent, which traditional scaling laws fail to capture.

Contributions of the Paper

The authors propose a new form of scaling law, the Broken Neural Scaling Law, which provides a piecewise linear model on a logarithmic scale plot. This new model captures the essence of performance scaling with high fidelity by incorporating "breaks" that represent transitions in scaling behavior. BNSLs accommodate non-monotonic phenomena, such as double descent and unexpected sharp inflection points common in tasks like arithmetic performance evaluation.

Key Empirical Insights:

• Wide Applicability: The BNSL model is experimentally validated across diverse tasks, architectural paradigms, and scales, including vision, language, arithmetic tasks, reinforcement learning, and more. This comprehensive application underscores the model's robustness compared to erstwhile approaches.
• Accurate Extrapolations: On substantial datasets within the benchmark established by Alabdulmohsin et al., BNSLs achieve state-of-the-art extrapolation accuracy, significantly outperforming previous models across multiple tasks.
• Handling Double Descent: The BNSL's ability to model and predict double descent behavior in neural networks is a particularly noteworthy advancement, reflecting the model's adeptness at handling complex, non-linear training dynamics.

Theoretical and Practical Implications

The shift towards BNSLs reflects a greater understanding of the inherent complexity in scaling behaviors of neural networks. The presence of sharp transitions or "breaks" suggests that scaling behaviors are not universally smooth but depend heavily on various factors like model architecture, task difficulty, and data diversity. Such insights are crucial for designing models intended to safely and predictively scale across AI applications.

In practical terms, BNSLs provide a more reliable predictive model for stakeholders seeking to scale their models efficiently and safely. This includes making informed decisions about when and how to invest resources in scaling architectures. Importantly, the paper provides insights into AI safety, where accurately forecasting emergent capabilities at scale is critical.

Future Directions

Leveraging BNSL could open new avenues for exploring universal scaling laws that further refine these transitional behaviors between different scaling regimens. One notable challenge is understanding the limits of predictability in these scaling behaviors, particularly when dealing with sharp transitions. Future research could explore how new architectural innovations could interact with BNSLs, particularly in domains where AI system interpretability and transparency are paramount.

Finally, the novel use of BNSLs in various domains implies that multi-variate scaling models could be developed, allowing simultaneous scaling across multiple dimensions (e.g., parameters, data, and compute) that mirror real-world neural network scaling scenarios.

Conclusion

The introduction of Broken Neural Scaling Laws marks a pioneering step in understanding the nuanced scaling dynamics of neural networks, surpassing the limited foresight of traditional power laws. With robust empirical validation and theoretical merits, BNSLs provide a more nuanced and accurate framework for predicting AI performance in ever-increasing scales—enabling both improved model design and better stewardship of computational resources. This work lays a foundation for continued investigation into the behaviors of neural architectures as they are geared towards broader and more complex applications.