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Tensor-Featured Networks Accelerate High-Dimensional Function Learning

Karl Pierce, Yuehaw Khoo, Haizhao Yang· August 12, 2026 View original

Key takeaways

  • Tensor-featured training networks accelerate the learning of high-dimensional functions in DNNs.
  • Contextual tensor features are introduced into the first layer, with periodic updates.
  • Randomized tensor decomposition significantly reduces storage costs for high-dimensional functions.
  • The method is effective for models between 5 and 40 dimensions.

Who benefits

Scientific ComputingMaterials ScienceFinanceEngineeringData Science

Summary

This work presents a method to accelerate the optimization of learning high-dimensional functions using deep neural networks (DNNs) by introducing contextual tensor features into the first layer. It leverages randomized tensor decomposition to efficiently handle high-dimensional functions, reducing storage costs significantly.

Researchers have developed a new method to significantly accelerate the learning and optimization of high-dimensional functions using deep neural networks (DNNs). The core innovation involves integrating contextual features, specifically tensor features, into the initial layer of a DNN. This approach allows the DNN parameters to be optimized via standard gradient descent, while the input-feature basis is periodically updated and refined. The feature layer incorporates two types of functions: quickly evaluable rank-1 features and more complex tensor features that require tensor network (TN) decomposition. To efficiently decompose high-dimensional functions derived from pre-trained DNNs, the method employs a randomized tensor decomposition strategy. This randomization drastically reduces the storage cost, by at least eight orders of magnitude, for decomposing high-dimensional functions. The approach has proven effective in training models across 5 to 40 dimensions, demonstrating accelerated learning.

Why it matters

Professionals in scientific computing, machine learning, and data science dealing with high-dimensional data or complex function approximation can benefit from this method to accelerate training and reduce computational resource requirements.

How to implement this in your domain

  1. 1Explore integrating tensor-featured layers into existing DNN architectures for high-dimensional function approximation tasks.
  2. 2Investigate randomized tensor decomposition techniques to reduce memory footprint and computational cost in large-scale models.
  3. 3Apply this method to problems in scientific simulations, materials science, or financial modeling that involve complex high-dimensional functions.
  4. 4Benchmark the training speed and accuracy improvements against traditional DNNs for specific high-dimensional datasets.

Original post by Karl Pierce, Yuehaw Khoo, Haizhao Yang

"arXiv:2608.10351v1 Announce Type: new 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 pa…"

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Originally posted by Karl Pierce, Yuehaw Khoo, Haizhao Yang on X · view source

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