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The emergence of seemingly similar representations across tasks and neural architectures suggests that convergent properties may underlie sophisticated behavior. One form of representation that seems particularly fundamental to reasoning in many artificial (and perhaps natural) networks is the formation of world models, which decompose observed task structures into re-usable perceptual primitives and task-relevant relations. In this work, we show that auto-regressive transformers tasked with solving mazes learn to linearly represent the structure of mazes, and that the formation of these representations coincides with a sharp increase in generalization performance. Furthermore, we find preliminary evidence for Adjacency Heads which may play a role in computing valid paths through mazes.
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Formation of Representations in Neural Networks
Understanding neural representations will help open the black box of neural networks and advance our scientific understanding of modern AI systems. However, how complex, structured, and transferable representations emerge in modern neural networks has remained a mystery. Building on previous results, we propose the Canonical Representation Hypothesis (CRH), which posits a set of six alignment relations to universally govern the formation of representations in most hidden layers of a neural network. Under the CRH, the latent representations (R), weights (W), and neuron gradients (G) become mutually aligned during training. This alignment implies that neural networks naturally learn compact representations, where neurons and weights are invariant to task-irrelevant transformations. We then show that the breaking of CRH leads to the emergence of reciprocal power-law relations between R, W, and G, which we refer to as the Polynomial Alignment Hypothesis (PAH). We present a minimal-assumption theory demonstrating that the balance between gradient noise and regularization is crucial for the emergence the canonical representation. The CRH and PAH lead to an exciting possibility of unifying major key deep learning phenomena, including neural collapse and the neural feature ansatz, in a single framework.
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- Award ID(s):
- 2134108
- PAR ID:
- 10565432
- Publisher / Repository:
- Center for Brains, Minds and Machines (CBMM)
- Date Published:
- Format(s):
- Medium: X
- Institution:
- Massachusetts Institute of Technology
- Sponsoring Org:
- National Science Foundation
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