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We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and con- trastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different represen- tation learning methods is effectively low-dimen- sional; (2) supervised learning on one task results in a surprising amount of progress even on seem- ingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Word- net phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse differ- ent trajectories during training but they fit similar models eventually; (5) contrastive and semi-su- pervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR- 10 and Imagenet datasets to study these phenom- ena. Code is available at https://github.com/grasp- lyrl/picture of space of tasks.
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Randomly Weighted Neuromodulation in Neural Networks Facilitates Learning of Manifolds Common Across Tasks
Geometric Sensitive Hashing functions, a family of Local Sensitive Hashing functions, are neural network models that learn class-specific manifold geometry in supervised learning. However, given a set of supervised learning tasks, understanding the manifold geometries that can represent each task and the kinds of relationships between the tasks based on them has received little attention. We explore a formalization of this question by considering a generative process where each task is associated with a high-dimensional manifold, which can be done in brain-like models with neuromodulatory systems. Following this formulation, we define Task-specific Geometric Sensitive Hashing and show that a randomly weighted neural network with a neuromodulation system can realize this function.
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- Award ID(s):
- 2223839
- PAR ID:
- 10547695
- Publisher / Repository:
- Proceedings of Machine Learning Research
- Date Published:
- Edition / Version:
- 243
- Page Range / eLocation ID:
- 315–325
- Format(s):
- Medium: X
- Location:
- New Orleans, Louisiana, USA
- Sponsoring Org:
- National Science Foundation
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