Fast and Guaranteed Tensor Decomposition via Sketching

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tensor contractions via FFTs, without explicitly forming the tensors. Such tensor contractions are encountered in decomposition methods such as tensor power iterations and alternating least squares. We also design novel colliding hashes for symmetric tensors to further save time in computing the sketches. We then combine these sketching ideas with existing whitening and tensor power iterative techniques to obtain the fastest algorithm on both sparse and dense tensors. The quality of approximation under our method does not depend on properties such as sparsity, uniformity of elements, etc. We apply the method for topic modeling and obtain competitive results.Comment: 29 pages. Appeared in Proceedings of Advances in Neural Information Processing Systems (NIPS), held at Montreal, Canada in 201

Tactile-Filter: Interactive Tactile Perception for Part Mating

Humans rely on touch and tactile sensing for a lot of dexterous manipulation tasks. Our tactile sensing provides us with a lot of information regarding contact formations as well as geometric information about objects during any interaction. With this motivation, vision-based tactile sensors are being widely used for various robotic perception and control tasks. In this paper, we present a method for interactive perception using vision-based tactile sensors for a part mating task, where a robot can use tactile sensors and a feedback mechanism using a particle filter to incrementally improve its estimate of objects (pegs and holes) that fit together. To do this, we first train a deep neural network that makes use of tactile images to predict the probabilistic correspondence between arbitrarily shaped objects that fit together. The trained model is used to design a particle filter which is used twofold. First, given one partial (or non-unique) observation of the hole, it incrementally improves the estimate of the correct peg by sampling more tactile observations. Second, it selects the next action for the robot to sample the next touch (and thus image) which results in maximum uncertainty reduction to minimize the number of interactions during the perception task. We evaluate our method on several part-mating tasks with novel objects using a robot equipped with a vision-based tactile sensor. We also show the efficiency of the proposed action selection method against a naive method. See supplementary video at https://www.youtube.com/watch?v=jMVBg_e3gLw .Comment: Accepted at RSS202

3D View Prediction Models of the Dorsal Visual Stream

Deep neural network representations align well with brain activity in the ventral visual stream. However, the primate visual system has a distinct dorsal processing stream with different functional properties. To test if a model trained to perceive 3D scene geometry aligns better with neural responses in dorsal visual areas, we trained a self-supervised geometry-aware recurrent neural network (GRNN) to predict novel camera views using a 3D feature memory. We compared GRNN to self-supervised baseline models that have been shown to align well with ventral regions using the large-scale fMRI Natural Scenes Dataset (NSD). We found that while the baseline models accounted better for ventral brain regions, GRNN accounted for a greater proportion of variance in dorsal brain regions. Our findings demonstrate the potential for using task-relevant models to probe representational differences across visual streams.Comment: 2023 Conference on Cognitive Computational Neuroscienc