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Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
In a previous paper, we showed that a compartmental stochastic process model of SARS-CoV-2 transmission could be fit to time series data and then reinterpreted as a collection of interacting branching processes drawn from a dynamic degree…
Born-rule generative modeling, a central task in quantum machine learning, seeks to learn probability distributions that can be efficiently sampled by measuring complex quantum states. One hope is for quantum models to efficiently capture…
The use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the…
Inspired by the ConvNets with structured hidden representations, we propose a Tensor-based Neural Network, TCNN. Different from ConvNets, TCNNs are composed of structured neurons rather than scalar neurons, and the basic operation is neuron…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and…
With the proliferation of knowledge graphs, modeling data with complex multirelational structure has gained increasing attention in the area of statistical relational learning. One of the most important goals of statistical relational…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
Recurrent Neural Networks (RNNs), which are a powerful scheme for modeling temporal and sequential data need to capture long-term dependencies on datasets and represent them in hidden layers with a powerful model to capture more information…
We present a generative diffusion model specifically tailored to the discovery of surface structures. The generative model takes into account substrate registry and periodicity by including masked atoms and $z$-directional confinement.…
This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…
Generative models are typically trained on grid-like data such as images. As a result, the size of these models usually scales directly with the underlying grid resolution. In this paper, we abandon discretized grids and instead…
Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…
We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…
A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent…
Tensor structured Markov chains are part of stochastic models of many practical applications, e.g., in the description of complex production or telephone networks. The most interesting question in Markov chain models is the determination of…