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Tensor networks have recently found applications in machine learning for both supervised learning and unsupervised learning. The most common approaches for training these models are gradient descent methods. In this work, we consider an…

We consider the problem of approximating a function by an element of a nonlinear manifold which admits a differentiable parametrization, typical examples being neural networks with differentiable activation functions or tensor networks.…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit…

In this work, we study the Neural Tangent Kernel (NTK) of Matrix Product States (MPS) and the convergence of its NTK in the infinite bond dimensional limit. We prove that the NTK of MPS asymptotically converges to a constant matrix during…

Natural Gradient Descent (NGD) has emerged as a promising optimization algorithm for training neural network-based solvers for partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs). However, its practical…

Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…

Natural gradient descent (NGD) is a powerful optimization technique for machine learning, but the computational complexity of the inverse Fisher information matrix limits its application in training deep neural networks. To overcome this…

We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of 1D quantum systems, to simulate the time-evolution of non-equilibrium stochastic systems. We describe this method in detail; a…

We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the…

Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by…

We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…

In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss…

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…

Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…

One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies…

Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks…

A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based…

Quantum circuit Born machines based on instantaneous quantum polynomial-time (IQP) circuits are natural candidates for quantum generative modeling, both because of their probabilistic structure and because IQP sampling is provably…