On Implications of Scaling Laws on Feature Superposition

TL;DR

This paper explores the theoretical implications of scaling laws on feature representations in neural networks, arguing that certain assumptions about feature superposition and universality cannot both hold simultaneously.

Contribution

It presents a theoretical analysis showing the incompatibility of the superposition hypothesis with the universality of features in scaled models.

Findings

Superposition hypothesis and feature universality cannot both be true.

Scaling laws impose fundamental constraints on feature representations.

Theoretical insights challenge existing assumptions in neural network interpretability.

Abstract

Using results from scaling laws, this theoretical note argues that the following two statements cannot be simultaneously true: 1. Superposition hypothesis where sparse features are linearly represented across a layer is a complete theory of feature representation. 2. Features are universal, meaning two models trained on the same data and achieving equal performance will learn identical features.