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Discovering Hidden Factors of Variation in Deep Networks (1412.6583v4)

Published 20 Dec 2014 in cs.LG, cs.CV, and cs.NE

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.

Citations (192)
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Summary

Essay on "Discovering Hidden Factors of Variation in Deep Networks"

The paper "Discovering Hidden Factors of Variation in Deep Networks" by Cheung et al. explores the potential of autoencoders for disentangling and representing diverse factors of variation within datasets. This paper addresses the integration of supervised and unsupervised learning modalities within deep neural networks, aiming to discern class-relevant signals from other latent factors of variation, such as style or pose, in visual data.

The paper introduces a novel augmentation of autoencoders through simple regularization terms, specifically employing a cross-covariance penalty (XCov). This penalty seeks to disentangle representations by minimizing the correlation between observed and latent variables. The XCov's formulation delineates factors pertinent to classification from those independent of class labels, which in practice, assists in capturing and manipulating non-class-related variations in data.

The experimental paradigm of this paper is substantively applied to three image datasets: MNIST, Toronto Faces Database (TFD), and Multi-PIE. Through these datasets, the proposed approach demonstrates its efficacy in uncovering factors like handwriting style or facial identity while maintaining competitive classification performance. For instance, the representation of MNIST data shows that the network learns to generate the canonical digit style with class labels and captures stylistic variations with latent variables.

Key to the methodology is the division of encoder outputs into observed variables used for this discriminative task and latent variables reserved for reconstruction. The architecture is trained with a composite objective function balancing reconstruction accuracy, cross-entropy for classification, and the XCov penalty for regularization. Notably, the paper finds that increasing the dimensionality of latent variables alongside regularization enhances the separation of class and non-class factors, improving overall reconstruction and fidelity in disentangled representations.

The implications of these findings are practical and theoretical. Practically, uncovering latent variations can prove invaluable in applications like signal denoising and exploratory data analysis, where understanding hidden structures in data is crucial. Theoretically, the demonstrated ability of neural networks to extrapolate beyond discrete labels to continuous semantically meaningful variations presents an interesting commentary on their intrinsic capability to learn complex manifold transformations.

The authors achieve a robust disentanglement without relying on complex architectures, such as bilinear models, which traditionally require learning weight tensors for multiplicative combinations. Instead, the simplicity and flexibility of autoencoders enhanced by XCov suggest potential pathways for more generalized solutions to complex factor disentanglement problems in feature learning.

Foreseeing future work, ideas stemming from this paper could extend to other domains like natural language processing or auditory data, where underlying factors are similarly composite and hidden. Additionally, integration with semi-supervised or unsupervised transfer learning models might reveal further avenues for employing these disentanglement methods across diverse datasets and tasks.

In conclusion, Cheung et al.’s work contributes significantly to how deep learning methods can be utilized to extract and operate on hidden factors of variation in a given dataset, thereby addressing and clarifying a previously under-explored dimension in representation learning.

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