[Paper Review] Learning Invariant Representations with Local Transformations

Kihyuk Sohn, Honglak Lee|arXiv (Cornell University)|Jun 27, 2012

Domain Adaptation and Few-Shot Learning28 references100 citations

TL;DR

This paper proposes a framework for learning transformation-invariant representations by integrating local linear transformations into feature learning algorithms, such as restricted Boltzmann machines, autoencoders, and sparse coding. By applying probabilistic max pooling over transformed feature weights, the method achieves invariance to spatial and geometric variations, demonstrating state-of-the-art performance on image and speech classification benchmarks including MNIST, CIFAR-10, STL-10, and TIMIT.

ABSTRACT

Learning invariant representations is an important problem in machine learning and pattern recognition. In this paper, we present a novel framework of transformation-invariant feature learning by incorporating linear transformations into the feature learning algorithms. For example, we present the transformation-invariant restricted Boltzmann machine that compactly represents data by its weights and their transformations, which achieves invariance of the feature representation via probabilistic max pooling. In addition, we show that our transformation-invariant feature learning framework can also be extended to other unsupervised learning methods, such as autoencoders or sparse coding. We evaluate our method on several image classification benchmark datasets, such as MNIST variations, CIFAR-10, and STL-10, and show competitive or superior classification performance when compared to the state-of-the-art. Furthermore, our method achieves state-of-the-art performance on phone classification tasks with the TIMIT dataset, which demonstrates wide applicability of our proposed algorithms to other domains.

Motivation & Objective

• To address the challenge of learning robust, invariant features under geometric and spatial transformations in visual and audio data.
• To develop a unified framework that integrates local transformations into existing unsupervised feature learning algorithms.
• To achieve invariance through probabilistic max pooling over transformed weights, enhancing generalization across data variations.
• To extend the framework to diverse models like RBMs, autoencoders, and sparse coding for broad applicability.
• To evaluate performance on standard benchmarks, demonstrating superiority or competitiveness with state-of-the-art methods.

Proposed method

• Incorporates local linear transformations (e.g., rotations, translations) into the weight matrices of feature learning models.
• Introduces the transformation-invariant restricted Boltzmann machine (TIRBM) that learns features and their transformed versions jointly.
• Uses probabilistic max pooling over transformed feature maps to achieve invariance without explicit data augmentation.
• Applies the same principle to autoencoders and sparse coding by modifying their objective functions to include transformed weight terms.
• Employs a shared representation learning mechanism where features are invariant to small local transformations.
• Leverages the statistical structure of transformations to implicitly regularize the feature space and improve robustness.

Experimental results

Research questions

• RQ1 Can local linear transformations be effectively integrated into unsupervised feature learning models to improve invariance?
• RQ2 How does incorporating transformed weights affect the generalization and robustness of learned representations?
• RQ3 Can the proposed framework outperform or match state-of-the-art methods on standard image and speech classification benchmarks?
• RQ4 To what extent does probabilistic max pooling over transformations reduce sensitivity to spatial and geometric variations?
• RQ5 Is the framework extensible to multiple unsupervised learning architectures beyond restricted Boltzmann machines?

Key findings

• The transformation-invariant restricted Boltzmann machine achieves state-of-the-art performance on the MNIST dataset with data variations, outperforming prior methods.
• The method demonstrates competitive performance on CIFAR-10 and STL-10, showing robustness to complex visual variations.
• On the TIMIT phone classification benchmark, the framework achieves state-of-the-art results, confirming its applicability beyond vision.
• The use of probabilistic max pooling over transformed features leads to significant invariance gains without requiring data augmentation.
• The framework generalizes effectively to autoencoders and sparse coding, maintaining strong performance across diverse learning settings.