An Incremental Tensor Train Decomposition Algorithm

11/22/2022
by   Doruk Aksoy, et al.
0

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 57× higher compression and up to 95 reduction in computational time.

READ FULL TEXT
research
11/21/2022

Approximation in the extended functional tensor train format

This work proposes the extended functional tensor train (EFTT) format fo...
research
11/19/2021

Parallel algorithms for computing the tensor-train decomposition

The tensor-train (TT) decomposition expresses a tensor in a data-sparse ...
research
08/29/2019

Multi-resolution Low-rank Tensor Formats

We describe a simple, black-box compression format for tensors with a mu...
research
08/31/2023

Efficient Computation of Tucker Decomposition for Streaming Scientific Data Compression

The Tucker decomposition, an extension of singular value decomposition f...
research
12/08/2019

Lossless Compression for 3DCNNs Based on Tensor Train Decomposition

Three dimensional convolutional neural networks (3DCNNs) have been appli...
research
07/15/2019

Tensor train-Karhunen-Loève expansion for continuous-indexed random fields using higher-order cumulant functions

The goals of this work are two-fold: firstly, to propose a new theoretic...
research
01/25/2021

TT-Rec: Tensor Train Compression for Deep Learning Recommendation Models

The memory capacity of embedding tables in deep learning recommendation ...

Please sign up or login with your details

Forgot password? Click here to reset