This work presents a method to accelerate the optimization of learning high dimensional functions using deep neural network (DNN), and studies the effect of adding features which distill pretrained DNN into TNs using a discretize and decompose strategy.
Abstract
In this work we present a method to accelerate the optimization of learning high dimensional functions using deep neural network (DNN). This optimization procedure introduces contextual features into the first layer of a DNN. The parameters of DNN are optimized via standard gradient descent while keeping the input-feature basis fixed. After optimization of the DNN parameters, the feature layer is provided a chance to update and change before DNN optimization resumes. The feature layer has two types of functions: those that can be evaluated quickly in a matrix-free way on the domain (i.e. rank-1 features) and more complex features that must first be decomposed using tensor network (TN) decomposition strategies (tensor features). In particular, we study the effect of adding features which distill pretrained DNN into TNs using a discretize and decompose strategy. To efficiently decompose high-dimensional functions constructed from discretized DNN, we leverage a randomized tensor decomposition strategy. Using randomization, we are able to reduce the storage cost of decomposing high dimensional functions by at least 8 orders of magnitude. Using this approach, we are able to efficiently train models between 5 and 40 dimensions.
An efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format and observing that the proposed NTT fitting procedure exhibits drastically faster convergence than an alternative multiplicative update method that has been previously proposed is observed.
Xun Tang, R. Dwaraknath, Lexing Ying· SIAM Journal on Scientific C...· 0 citations
Traditional model reduction techniques for neural network compression usually leverage existing matrix/tensor decomposition methods to explore the redundancy among model parameters, which may overlook the local structures of the models. In this work, we propose a novel low-rank approximation algorithm, called Dimension-Augmented Tensor-Train (DATT) decomposition, which integrates dimension slicing with the Tensor-Train decomposition. DATT allows different partitions to be represented using distinct, non-shared spanning sets. This enables the decomposition to adapt more flexibly to localized structure, potentially achieving better compression. With the localized low-rank structures, DATT provides a more compact representation of neural network weights. We evaluated the performance of DATT with the other state-of-the-art low-rank approximation-based model compression algorithms, and demonstrated that DATT outperforms them in terms of parameter reduction and model accuracy. In particular, for compressing ResNet-20 on CIFAR-10, DATT achieves a 77.00% reduction in parameters with only a 0.37% drop in top-1 accuracy.
Yu-Chuan Tai, Cheng-Yu Sie, Che-Rung Lee· Annual International Compute...· 0 citations
A transfer parameterization is developed and validated for GNNs trained with SGD, Adam, and AdamW that yields stable feature updates, learning rate transfer, and improved performance as width and depth increase, and provides a practical recipe for scaling GNNs across a variety of learning tasks and training scenarios.
This paper proposes a novel Tensor Train (TT)-based tensor-on-tensor regression optimization framework for variable selection based on mode-1 hyperslice sparsity. The formulation incorporates an l2,0-regularized term on the first TT-core while imposing Stiefel manifold constraints on the remaining M−1 TT-cores. Leveraging the property that the group sparsity of the first core is equivalent to the hyperslice sparsity of the global structure, we establish theoretical guarantees for the uniform variable-selection consistency of the proposed model. To efficiently solve the proposed model, we design an alternating iterative algorithm equipped with a preconditioned metric and prove its convergence to a critical point. Extensive numerical experiments on both synthetic and real-world datasets demonstrate that the numerical solutions generated by our algorithm exhibit exact support recovery in practice, tightly aligning with our theoretical analysis.
Developing nonlinear models that are both expressive and computationally efficient remains a challenge in machine learning and nonlinear system identification. Tensor network kernel machines (TNKM) address this challenge by combining nonlinear feature representations with compact low-rank tensor-network parameterizations. However, practical and extensible software frameworks for developing TNKM models remain limited. In this work, we introduce"tnkm", an open-source Python library for constructing and training TNKM models using JAX. The library provides a unified interface for combining different feature maps, tensor-network architectures, and optimization strategies, including alternating least squares and gradient-based methods. We demonstrate the capabilities of"tnkm"on nonlinear benchmark problems, showing that the implemented models achieve competitive prediction accuracy while retaining compact parameterizations and efficient training. The proposed framework facilitates reproducible development and application of tensor-network-based learning methods.
Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise evaluation of elementary and nonlinear filtering functions on data encoded as tensor trains (TTs), a class of tensor networks. Our approach operates entirely in the compressed domain, enabling efficient computation on exponentially large datasets while maintaining a controlled computational cost. We demonstrate its power in two key areas: (I) evaluating highly nonlinear elementary and filtering functions on a 3D reactive flow field, enabling high-fidelity reaction rate computation and region filtering, and (II) finding extrema in complex optimization problems, such as solving Max-SAT instances on spaces up to $2^{70}$ configurations. These results establish ITNT as a foundational tool that provides tensor network methods with the capability for general-purpose data science and large-scale optimization.
Xiao Wang, Tomohiro Hashizume, Pia Siegl et al.· 2 citations