Doruk Aksoy

We present two new algorithms for approximating and updating the hierarchical Tucker decomposition of tensor streams. The first algorithm, Batch Hierarchical Tucker - leaf to root (BHT-l2r), proposes an alternative and more efficient way of approximating a batch of similar tensors in hierarchical Tucker format. The second algorithm, Hierarchical Tucker - Rapid Incremental Subspace Expansion (HT-RISE), updates the batch hierarchical Tucker representation of an accumulated tensor as new batches of tensors become available. The HT-RISE algorithm is suitable for the online setting and never requires full storage or reconstruction of all data while providing a solution to the incremental Tucker decomposition problem. We provide theoretical guarantees for both algorithms and demonstrate their effectiveness on physical and cyber-physical data. The proposed BHT-l2r algorithm and the batch hierarchical Tucker format offers up to 6.2× compression and 3.7× reduction in time over the hierarchical Tucker format. The proposed HT-RISE algorithm also offers up to 3.1× compression and 3.2× reduction in time over a state of the art incremental tensor train decomposition algorithm.

We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the tensor train incremental core expansion (TT-ICE), improves upon the current state-of-the-art algorithms for compressing in tensor train format by developing a new adaptive approach that incurs significantly slower rank growth and guarantees compression accuracy. This capability is achieved by limiting the number of new vectors appended to the TT-cores of an existing accumulation tensor after each data increment. These vectors represent directions orthogonal to the span of existing cores and are limited to those needed to represent a newly arrived tensor to a target accuracy. We provide two versions of the algorithm: TT-ICE and TT-ICE accelerated with heuristics (TT-ICE). We provide a proof of correctness for TT-ICE and empirically demonstrate the performance of the algorithms in compressing large-scale video and scientific simulation datasets. Compared to existing approaches that also use rank adaptation, TT-ICE achieves higher compression and up to reduction in computational time.

We describe a tensor-network latent-space encoding approach for increasing the scalability of behavioral cloning of a video game player’s actions entirely from video streams of the gameplay. Specifically, we address challenges associated with the high computational requirements of traditional deep-learning based encoders such as convolutional variational autoencoders that prohibit their use in widely available hardware or for large scale data. Our approach uses tensor networks instead of deep variational autoencoders for this purpose, and it yields significant speedups with no loss of accuracy. Empirical results on ATARI games demonstrate that our approach leads to a speedup in the time it takes to encode data and train a predictor using the encodings (between 2.6× to 9.6× compared to autoencoders or variational autoencoders). Furthermore, the tensor train encoding can be efficiently trained on CPU as well, which leads to comparable or better training times than the autoencoder and variational autoencoder trained on GPU (0.9× to 5.4× faster). These results suggest significant possibilities in mitigating the need for cost and time-intensive hardware for training deep-learning architectures for behavioral cloning.