Neural Scaling Universality: If Exponents Are Fixed, Time to Understand Coefficients
Neural scaling laws describe how pre-training loss decays as power laws with training time, model size, and compute. This position paper argues that the exponents of these power laws are fixed by generic mechanisms: a one-third time scaling due to the strong nonlinearity of Softmax, an inverse width scaling due to representational superposition, and an inverse depth scaling due to ensemble averaging of Transformer layers. These mechanisms are robust to a wide range of data structures and architectural details, placing current large language models in a universality class with fixed exponents. The coefficients, however, are expected to be sensitive to data and architecture details, and dir...
| Authors | Yizhou Liu, Jeff Gore |
|---|---|
| Primary category | cs.LG |
| Published | 23 June 2026 |
| Last updated at source | 23 June 2026 |
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