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The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

Data encoding remains a fundamental bottleneck in quantum machine learning, where amplitude encoding of high-dimensional classical vectors into quantum states incurs exponential cost. In this work, we propose a pre-trained tensor-train (TT)…

Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…

Binary semirings such as the tropical, log, and probability semirings form a core algebraic tool in classical and modern neural inference systems, supporting tasks like Viterbi decoding, dynamic programming, and probabilistic reasoning.…

We introduce canonical weight normalization for convolutional neural networks. Inspired by the canonical tensor decomposition, we express the weight tensors in so-called canonical networks as scaled sums of outer vector products. In…

Quantization of deep neural networks (DNN) has been proven effective for compressing and accelerating DNN models. Data-free quantization (DFQ) is a promising approach without the original datasets under privacy-sensitive and confidential…

Visual tokenizers are fundamental to image generation. They convert visual data into discrete tokens, enabling transformer-based models to excel at image generation. Despite their success, VQ-based tokenizers like VQGAN face significant…

Foundation models in language and vision benefit from a unified discrete token interface that converts raw inputs into sequences for scalable pre-training and inference. For graphs, an effective tokenizer should yield reusable discrete…

Ascertaining whether a classical model can efficiently replace a given quantum model -- dequantization -- is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function…

These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on…

Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…

This work proposes QNet, a novel sequence encoder model that entirely inferences on the quantum computer using a minimum number of qubits. Let $n$ and $d$ represent the length of the sequence and the embedding size, respectively. The…

This work introduces Semantically Masked Vector Quantized Generative Adversarial Network (SQ-GAN), a novel approach integrating semantically driven image coding and vector quantization to optimize image compression for…

The ability to encode and manipulate data structures with distributed neural representations could qualitatively enhance the capabilities of traditional neural networks by supporting rule-based symbolic reasoning, a central property of…

ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…