相关论文: Information geometry of nonmonotonic quantum natur…

A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…

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…

The heart of Quantum Federated Learning (QFL) is associated with a distributed learning architecture across several local quantum devices and a more efficient training algorithm for the QFL is expected to minimize the communication overhead…

The multinomial logistic regression (MLR) model is widely used in statistics and machine learning. Stochastic gradient descent (SGD) is the most common approach for determining the parameters of a MLR model in big data scenarios. However,…

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.…

We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based optimization problems. Our technique represents the natural gradient direction as a…

Natural Gradient Descent (NGD) helps to accelerate the convergence of gradient descent dynamics, but it requires approximations in large-scale deep neural networks because of its high computational cost. Empirical studies have confirmed…

Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically…

Studies about Quantum Information Theory continue actively in many research institutions. Very recently, pratical setups of large scale quantum computers are widely studied e.g. quantum repeaters, memories and processors. Entanglement…

Quantum natural gradient has emerged as a superior minimisation technique in quantum variational algorithms. Classically simulating the algorithm running on near-future quantum hardware is paramount in its study, as it is for all…

Quantum convolutional neural networks (QCNNs) represent a promising approach in quantum machine learning, paving new directions for both quantum and classical data analysis. This approach is particularly attractive due to the absence of the…

I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…

Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…

In optimization, the natural gradient method is well-known for likelihood maximization. The method uses the Kullback-Leibler divergence, corresponding infinitesimally to the Fisher-Rao metric, which is pulled back to the parameter space of…

We address the problem of quantum reinforcement learning (QRL) under model-free settings with quantum oracle access to the Markov Decision Process (MDP). This paper introduces a Quantum Natural Policy Gradient (QNPG) algorithm, which…

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…

Many supervised learning tasks have intrinsic symmetries, such as translational and rotational symmetry in image classifications. These symmetries can be exploited to enhance performance. We formulate the symmetry constraints into a concise…

In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by…

Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…

Quantum Fisher Information (QFI) is a ubiquitous quantity with applications ranging from quantum metrology and resource theories to condensed matter physics. In equilibrium local quantum many-body systems, the QFI of a subsystem with…