[Paper Review] Discovering Hidden Factors of Variation in Deep Networks

Brian Cheung, Jesse A. Livezey+2 more|arXiv (Cornell University)|Dec 1, 2014

Face recognition and analysis26 citations

TL;DR

This paper proposes a method using cross-covariance penalty (XCov) regularization in autoencoders to disentangle and explicitly represent hidden factors of variation—such as handwriting style in MNIST digits and subject identity in facial images—beyond the primary classification signal. The approach enables deep networks to discover, represent, and extrapolate unseen variations in data, demonstrated across MNIST, TFD, and Multi-PIE datasets with controllable generation of manipulated data instances.

ABSTRACT

Deep learning has enjoyed a great deal of success because of its ability to learn useful features for tasks such as classification. But there has been less exploration in learning the factors of variation apart from the classification signal. By augmenting autoencoders with simple regularization terms during training, we demonstrate that standard deep architectures can discover and explicitly represent factors of variation beyond those relevant for categorization. We introduce a cross-covariance penalty (XCov) as a method to disentangle factors like handwriting style for digits and subject identity in faces. We demonstrate this on the MNIST handwritten digit database, the Toronto Faces Database (TFD) and the Multi-PIE dataset by generating manipulated instances of the data. Furthermore, we demonstrate these deep networks can extrapolate `hidden' variation in the supervised signal.

Motivation & Objective

• To address the limitation of deep networks in learning disentangled representations of factors beyond the primary classification signal.
• To discover and explicitly represent hidden factors of variation such as handwriting style in digits and identity in facial images.
• To enable deep networks to extrapolate unseen variations in the data using only supervised signals.
• To develop a regularization technique that encourages disentanglement without requiring explicit supervision for each factor.

Proposed method

• Introduces a cross-covariance penalty (XCov) as a regularization term during autoencoder training to minimize statistical dependence between latent factors.
• Applies XCov to standard deep autoencoder architectures to encourage disentanglement of factors like style and content in the learned latent space.
• Uses the regularized autoencoder to generate manipulated data instances by interpolating or modifying specific disentangled factors.
• Trains on standard datasets (MNIST, TFD, Multi-PIE) with only classification labels, yet learns to represent non-classification factors.
• Employs a simple, differentiable penalty term that penalizes cross-covariance between different latent factor components.
• Leverages the disentangled representations to perform zero-shot generation of unseen variations not present in the training data.

Experimental results

Research questions

• RQ1 Can standard deep autoencoders discover and represent hidden factors of variation without explicit supervision for those factors?
• RQ2 How effective is the cross-covariance penalty (XCov) in disentangling factors such as handwriting style and identity in image data?
• RQ3 Can the learned representations extrapolate to unseen variations in the data, even when those variations are not present in the training set?
• RQ4 To what extent can disentangled representations be generated and controlled using only classification labels and the XCov regularization?

Key findings

• The XCov regularization effectively disentangles factors such as handwriting style in MNIST and subject identity in facial images, enabling controlled manipulation of these attributes.
• The model generates plausible and diverse data instances by modifying specific disentangled factors, demonstrating explicit control over hidden variations.
• Even with only classification labels, the network learns to represent and extrapolate to unseen variations in the data, such as new handwriting styles or identities.
• The method achieves disentanglement without requiring weakly supervised or self-supervised signals for individual factors, relying solely on the XCov penalty.
• The approach generalizes across datasets, showing consistent disentanglement performance on MNIST, Toronto Faces Database (TFD), and Multi-PIE.
• Generated samples show meaningful and semantically coherent changes when specific latent factors are altered, confirming the interpretability of the learned representations.