TensorCodec: Compact Lossy Compression of Tensors without Strong Data Assumptions

• URL: http://arxiv.org/abs/2309.10310v2
• Date: Wed, 20 Sep 2023 07:18:02 GMT
• Title: TensorCodec: Compact Lossy Compression of Tensors without Strong Data Assumptions
• Authors: Taehyung Kwon, Jihoon Ko, Jinhong Jung, and Kijung Shin
• Abstract summary: TENSORCODEC is a lossy compression algorithm for general tensors that do not necessarily adhere to strong input data assumptions. Our analysis and experiments on 8 real-world datasets demonstrate that TENSORCODEC is (a) Concise. It gives up to 7.38x more compact compression than the best competitor with similar reconstruction error.
• Score: 22.937900567884796
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor compression algorithms are available, many of them rely on strong data assumptions regarding its order, sparsity, rank, and smoothness. In this work, we propose TENSORCODEC, a lossy compression algorithm for general tensors that do not necessarily adhere to strong input data assumptions. TENSORCODEC incorporates three key ideas. The first idea is Neural Tensor-Train Decomposition (NTTD) where we integrate a recurrent neural network into Tensor-Train Decomposition to enhance its expressive power and alleviate the limitations imposed by the low-rank assumption. Another idea is to fold the input tensor into a higher-order tensor to reduce the space required by NTTD. Finally, the mode indices of the input tensor are reordered to reveal patterns that can be exploited by NTTD for improved approximation. Our analysis and experiments on 8 real-world datasets demonstrate that TENSORCODEC is (a) Concise: it gives up to 7.38x more compact compression than the best competitor with similar reconstruction error, (b) Accurate: given the same budget for compressed size, it yields up to 3.33x more accurate reconstruction than the best competitor, (c) Scalable: its empirical compression time is linear in the number of tensor entries, and it reconstructs each entry in logarithmic time. Our code and datasets are available at https://github.com/kbrother/TensorCodec.

Related papers

• Unlocking Data-free Low-bit Quantization with Matrix Decomposition for KV Cache Compression [87.5604418100301]
  Key-value( KV) caching is an important technique to accelerate the inference of large language models. Existing methods often compromise precision or require extra data for calibration. We introduce textbfDecoQuant, a novel data-free low-bit quantization technique based on tensor decomposition methods.
  arXiv  Detail & Related papers  (2024-05-21T08:35:10Z)
• "Lossless" Compression of Deep Neural Networks: A High-dimensional Neural Tangent Kernel Approach [49.744093838327615]
  We provide a novel compression approach to wide and fully-connected emphdeep neural nets. Experiments on both synthetic and real-world data are conducted to support the advantages of the proposed compression scheme.
  arXiv  Detail & Related papers  (2024-03-01T03:46:28Z)
• Compression of Structured Data with Autoencoders: Provable Benefit of Nonlinearities and Depth [83.15263499262824]
  We prove that gradient descent converges to a solution that completely disregards the sparse structure of the input. We show how to improve upon Gaussian performance for the compression of sparse data by adding a denoising function to a shallow architecture. We validate our findings on image datasets, such as CIFAR-10 and MNIST.
  arXiv  Detail & Related papers  (2024-02-07T16:32:29Z)
• Multi-Dictionary Tensor Decomposition [5.733331864416094]
  We propose a framework for Multi-Dictionary Decomposition (MDTD) We derive a general optimization algorithm for MDTD that handles both complete input and input with missing values. It can impute missing values in billion-entry tensors more accurately and scalably than state-of-the-art competitors.
  arXiv  Detail & Related papers  (2023-09-18T12:31:56Z)
• DiffRate : Differentiable Compression Rate for Efficient Vision Transformers [98.33906104846386]
  Token compression aims to speed up large-scale vision transformers (e.g. ViTs) by pruning (dropping) or merging tokens. DiffRate is a novel token compression method that has several appealing properties prior arts do not have.
  arXiv  Detail & Related papers  (2023-05-29T10:15:19Z)
• Latent Matrices for Tensor Network Decomposition and to Tensor Completion [8.301418317685906]
  We propose a novel higher-order tensor decomposition model that decomposes the tensor into smaller ones and speeds up the computation of the algorithm. Three optimization algorithms, LMTN-PAM, LMTN-SVD and LMTN-AR, have been developed and applied to the tensor-completion task. Experimental results show that our LMTN-SVD algorithm is 3-6 times faster than the FCTN-PAM algorithm and only a 1.8 points accuracy drop.
  arXiv  Detail & Related papers  (2022-10-07T08:19:50Z)
• Augmented Tensor Decomposition with Stochastic Optimization [46.16865811396394]
  Real-world tensor data are usually high-ordered and have large dimensions with millions or billions of entries. It is expensive to decompose the whole tensor with traditional algorithms. This paper proposes augmented tensor decomposition, which effectively incorporates data augmentations to boost downstream classification.
  arXiv  Detail & Related papers  (2021-06-15T06:29:05Z)
• Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation [53.95297550117153]
  We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking emphat a fraction of their entries only. The proposed approach is particularly useful for large-scale multidimensional grid data, and for tasks that require context over a large receptive field.
  arXiv  Detail & Related papers  (2021-05-29T08:39:57Z)
• DeepReduce: A Sparse-tensor Communication Framework for Distributed Deep Learning [79.89085533866071]
  This paper introduces DeepReduce, a versatile framework for the compressed communication of sparse tensors. DeepReduce decomposes tensors in two sets, values and indices, and allows both independent and combined compression of these sets. Our experiments with large real models demonstrate that DeepReduce transmits fewer data and imposes lower computational overhead than existing methods.
  arXiv  Detail & Related papers  (2021-02-05T11:31:24Z)
• Distributed Non-Negative Tensor Train Decomposition [3.2264685979617655]
  High-dimensional data is presented as multidimensional arrays, aka tensors. The presence of latent (not directly observable) structures in the tensor allows a unique representation and compression of the data. We introduce a distributed non-negative tensor-train and demonstrate its scalability and the compression on synthetic and real-world big datasets.
  arXiv  Detail & Related papers  (2020-08-04T05:35:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.