A Generative Process for Sampling Contractive Auto-Encoders

TL;DR

This paper introduces a novel sampling procedure for contractive auto-encoders that captures local data structure, enabling efficient generation of data samples and improved invariance learning for better classification.

Contribution

It proposes a new stochastic sampling process based on the Jacobian singular vectors of contractive auto-encoders, enhancing data generation and invariance learning.

Findings

Sampling converges quickly and mixes well between modes.

The method improves invariance learning and classification accuracy.

Samples are consistent with the local manifold structure.

Abstract

The contractive auto-encoder learns a representation of the input data that captures the local manifold structure around each data point, through the leading singular vectors of the Jacobian of the transformation from input to representation. The corresponding singular values specify how much local variation is plausible in directions associated with the corresponding singular vectors, while remaining in a high-density region of the input space. This paper proposes a procedure for generating samples that are consistent with the local structure captured by a contractive auto-encoder. The associated stochastic process defines a distribution from which one can sample, and which experimentally appears to converge quickly and mix well between modes, compared to Restricted Boltzmann Machines and Deep Belief Networks. The intuitions behind this procedure can also be used to train the second layer of contraction that pools lower-level features and learns to be invariant to the local directions of variation discovered in the first layer. We show that this can help learn and represent invariances present in the data and improve classification error.