We propose the Quantization Model of neural scaling laws, explaining both the observed power law dropoff of loss with model and data size, and also the sudden emergence of new capabilities with scale. We derive this model from what we call the Quantization Hypothesis, where network knowledge and skills are quantized into discrete chunks (quanta). We show that when quanta are learned in order of decreasing use frequency, then a power law in use frequencies explains observed power law scaling of loss.

Quantization method plays a crucial role in improving model efficiency and reducing deployment costs, enabling the widespread application of deep learning models on resource-constrained devices. However, the quantization process inevitably introduces accuracy degradation. In this paper, we propose Mixture of Quantization Experts( abbr. MoQE), a quantization inference framework based on the Mixture-of-Experts (MoE) architecture, aiming to jointly improve the performance of quantization models. MoQE combines multiple quantization variants of one full-precision model as specialized "quantization experts" and dynamically routes input data to the most suitable expert based on its characteristics. MoQE alleviates the performance degradation commonly seen in single quantization models through specialization quantization expert models. We design lightweight, structure-aware router models tailored for both CV and NLP tasks. Experimental evaluations on ResNet, LLaMA, and Qwen model families across benchmark datasets including ImageNet, WikiText, C4, and OpenWebText demonstrate that MoQE achieves performance comparable to SOT A quantization model, without incurring significant increases in inference latency. Quantization method plays a pivotal role in the field of machine learning, particularly in enhancing model efficiency and reducing resource consumption. As deep learning models grow increasingly complex, their demand for computational resources escalates, constraining deployment on resource-limited devices and increasing operational costs. Furthermore, quantization method streamlines the model optimization pipeline, enabling developers to achieve efficient deployment within shorter timeframes and accelerating time-to-market for AI-driven products. Consequently, quantization method serves not only as a critical enabler for improving the accessibility and practicality of machine learning models but also as a key facilitator in the broader dissemination of artificial intelligence technologies. However, their practical deployment faces several critical challenges.

We propose the Quantization Model of neural scaling laws, explaining both the observed power law dropoff of loss with model and data size, and also the sudden emergence of new capabilities with scale. We derive this model from what we call the Quantization Hypothesis, where network knowledge and skills are "quantized" into discrete chunks (quanta). We show that when quanta are learned in order of decreasing use frequency, then a power law in use frequencies explains observed power law scaling of loss. We tentatively find that the frequency at which these quanta are used in the training distribution roughly follows a power law corresponding with the empirical scaling exponent for language models, a prediction of our theory.

Neural scaling laws are observed in a range of domains, to date with no clear understanding of why they occur. Recent theories suggest that loss power laws arise from Zipf's law, a power law observed in domains like natural language. One theory suggests that language scaling laws emerge when Zipf-distributed task quanta are learned in descending order of frequency. In this paper we examine power-law scaling in AlphaZero, a reinforcement learning algorithm, using a theory of language-model scaling. We find that game states in training and inference data scale with Zipf's law, which is known to arise from the tree structure of the environment, and examine the correlation between scaling-law and Zipf's-law exponents. In agreement with quanta scaling theory, we find that agents optimize state loss in descending order of frequency, even though this order scales inversely with modelling complexity. We also find that inverse scaling, the failure of models to improve with size, is correlated with unusual Zipf curves where end-game states are among the most frequent states. We show evidence that larger models shift their focus to these less-important states, sacrificing their understanding of important early-game states.