Representation Learning via Manifold Flattening and Reconstruction

• URL: http://arxiv.org/abs/2305.01777v4
• Date: Fri, 8 Sep 2023 00:31:53 GMT
• Title: Representation Learning via Manifold Flattening and Reconstruction
• Authors: Michael Psenka, Druv Pai, Vishal Raman, Shankar Sastry, Yi Ma
• Abstract summary: This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold. Our such-generated neural networks, called Flattening Networks (FlatNet), are theoretically interpretable, computationally feasible at scale, and generalize well to test data.
• Score: 10.823557517341964
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening Networks (FlatNet), are theoretically interpretable, computationally feasible at scale, and generalize well to test data, a balance not typically found in manifold-based learning methods. We present empirical results and comparisons to other models on synthetic high-dimensional manifold data and 2D image data. Our code is publicly available.

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