The Capability Manifold and ML Scaling Laws

2026-09-23

AI Summary

本文提出能力流形框架，通过有界缩放函数将下游能力与机器学习生命周期中的资源关联，解决仅用损失无法全面评估模型性能的问题。

Abstract

Existing machine learning (ML) scaling laws relate predictive loss to compute, model parameters, and data. However, as models are increasingly deployed through agentic harnesses, loss alone is insufficient to characterize downstream performance: models with similar loss can exhibit different capabilities in reasoning, retrieval, planning, and adaptation. Yet, no unified framework connects such capabilities to the coupled resources available across the ML lifecycle. We bridge this gap by introducing a capability manifold, a multidimensional framework mapping downstream capabilities to pre-training, post-training, and test-time resources through bounded scaling functions. Analytical Jacobians quantify capability sensitivity to resource changes and interactions. As an initial application, we embed Kaplan- and Chinchilla-type scaling laws and test-time compute within the framework, demonstrating how existing scaling relationships can be unified as trajectories on a common capability manifold.

Problem

• machine learning
• scaling laws
• downstream performance
• capabilities
• resources

Innovation

• capability manifold
• scaling laws
• resource mapping