Study measures how neural representations form during training
Original title: The Information Geometry of Representation Formation
Path tortuosity, not endpoint displacement, predicted later drift and sensitivity to parameter perturbations.
The paper treats representation learning as a geometric trajectory rather than studying only trained endpoints. Bures geometry measures movement through representation space, and quantum Fisher information characterizes local sensitivity to input factors. Learning concentrated sensitivity on task-relevant factors, and trajectories became less direct when the computation needed higher-order interactions. That pattern held under matched-performance and training-duration controls and transferred from synthetic inputs to residual CNNs on rendered and natural images.
- Changing only the prediction target reorganized geometry around the visual factor.
- The effect persisted under matched performance and training duration.
- Tests used synthetic vectors and residual CNNs on images.
- Representation-aware optimization could shape the trajectories.
From the original article
1 min read at arxiv.orgMost analyses of neural representations focus on trained endpoints, leaving the process by which internal structure forms comparatively unmeasured. We instead treat representation formation itself as an object of study, asking whether the path a representation takes through training reveals information that its endpoint does not.
By Sanjukta Krishnagopal · arxiv.org
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