Related papers: Loss-aware state space geometry for quantum variat…

Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large…

Natural gradient descent (NGD) provided deep insights and powerful tools to deep neural networks. However the computation of Fisher information matrix becomes more and more difficult as the network structure turns large and complex. This…

We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less…

In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state…

Gradient descent, or negative gradient flow, is a standard technique in optimization to find minima of functions. Many implementations of gradient descent rely on discretized versions, i.e., moving in the gradient direction for a set step…

Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the…

We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural networks (PINNs) and the deep Ritz method. As a main…

Bayesian neural networks (BNNs) are most commonly optimised with first-order optimisers such as stochastic gradient descent. However, when optimising for parameters of probabilistic models, incorporating second order information during…

The optimization of parametric quantum circuits is technically hindered by three major obstacles: the non-convex nature of the objective function, noisy gradient evaluations, and the presence of barren plateaus. As a result, the selection…

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We…

In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…

In this paper we investigate how gradient-based algorithms such as gradient descent, (multi-pass) stochastic gradient descent, its persistent variant, and the Langevin algorithm navigate non-convex loss-landscapes and which of them is able…

Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires…

We consider machine learning tasks with low-rank functional tree tensor networks (TTN) as the learning model. While in the case of least-squares regression, low-rank functional TTNs can be efficiently optimized using alternating…

Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…

The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the…