Reproduce “Disentangling images with Lie group transformations and sparse coding” on OpenResearch

About this paper

Ho Yin Chau, Frank Qiu, Yubei Chen, Bruno Olshausen

Lie Group Sparse Coding (LSC) separates image shape from pose or style by representing each image as a sparse combination of learned templates and applying a separately learned transformation to that combination. On a controlled translation dataset, it reports average test reconstruction SNR of 28.5 versus 2.2 for sparse coding. On MNIST, its dictionary captures 9 of 10 digit classes, limiting claims of complete disentanglement.

Key insights

• Lie group theory provides a principled mathematical framework for modeling continuous transformations in a learnable manner.
• Combining sparse coding's ability to learn spatial patterns with Lie groups enables the unsupervised disentanglement of shape and transformation factors in image data.
• Compact, connected, commutative Lie groups can be effectively decomposed and learned through specific matrix operations, simplifying the modeling of complex transformations.
• A Bayesian generative model allows for joint inference of shape presence and transformation parameters, along with the learning of shape dictionaries and transformation operators from data itself.

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