Dylan M. Paiton

David Klindt, Lukas Schott, Yash Sharma et al.

We construct an unsupervised learning model that achieves nonlinear disentanglement of underlying factors of variation in naturalistic videos. Previous work suggests that representations can be disentangled if all but a few factors in the environment stay constant at any point in time. As a result, algorithms proposed for this problem have only been tested on carefully constructed datasets with this exact property, leaving it unclear whether they will transfer to natural scenes. Here we provide evidence that objects in segmented natural movies undergo transitions that are typically small in magnitude with occasional large jumps, which is characteristic of a temporally sparse distribution. We leverage this finding and present SlowVAE, a model for unsupervised representation learning that uses a sparse prior on temporally adjacent observations to disentangle generative factors without any assumptions on the number of changing factors. We provide a proof of identifiability and show that the model reliably learns disentangled representations on several established benchmark datasets, often surpassing the current state-of-the-art. We additionally demonstrate transferability towards video datasets with natural dynamics, Natural Sprites and KITTI Masks, which we contribute as benchmarks for guiding disentanglement research towards more natural data domains.

Yubei Chen, Dylan M. Paiton, Bruno A. Olshausen

We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility. The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes. When stacked, it also models hierarchical composition. We provide a theoretical description of the transform and demonstrate properties of the learned representation on both synthetic data and natural videos.

Peter F. Schultz, Dylan M. Paiton, Wei Lu et al.

In sparse coding it is common to tile an image into nonoverlapping patches, and then use a dictionary to create a sparse representation of each tile independently. In this situation, the overcompleteness of the dictionary is the number of dictionary elements divided by the patch size. In deconvolutional neural networks (DCNs), dictionaries learned on nonoverlapping tiles are replaced by a family of convolution kernels. Hence adjacent points in the feature maps (V1 layers) have receptive fields in the image that are translations of each other. The translational distance is determined by the dimensions of V1 in comparison to the dimensions of the image space. We refer to this translational distance as the stride. We implement a type of DCN using a modified Locally Competitive Algorithm (LCA) to investigate the relationship between the number of kernels, the stride, the receptive field size, and the quality of reconstruction. We find, for example, that for 16x16-pixel receptive fields, using eight kernels and a stride of 2 leads to sparse reconstructions of comparable quality as using 512 kernels and a stride of 16 (the nonoverlapping case). We also find that for a given stride and number of kernels, the patch size does not significantly affect reconstruction quality. Instead, the learned convolution kernels have a natural support radius independent of the patch size.