arXiv research

New method learns quantum states using neural networks, revealing hidden dynamics.

Develops an analytic theory for quantum imaginary time evolution.

The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.

Noise can affect the overparametrization of QNNs, enabling new directions but also suppressing sensitivity.

Overparametrization improves QNN trainability by reducing spurious local minima.

NG+ method improves deep learning efficiency and accuracy.

We introduce DQFIM to quantify and improve generalization of quantum machine learning models.

Market strategies minimize Fisher information to minimize risk.

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 distribution of outputs. The space of parameters consisting of weights and biases i…

Machine learning approximates phase transitions using Fisher information.

A new measure of model complexity based on Fisher Information.

Noise-resilient optimization on noisy quantum computers.

Two Fisher information matrix estimators are analyzed for neural networks, focusing on their variances and trade-offs.

Quantum machine learning tackles large datasets with randomized measurements.

NGD improves multivariate Gaussian inference by optimizing Fisher information.

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $ΔG$ of the graph and try to improve generalization. Based on quantum information geometry, $ΔG$ can be characterized by the eigendecomposition of the graph Laplaci…

The Fisher-Rao geometry is applied to elliptical distributions for optimization and classification.

Natural gradient descent, which preconditions a gradient descent update with the Fisher information matrix of the underlying statistical model, is a way to capture partial second-order information. Several highly visible works have advocated an approximation known as the empirical Fisher, drawing connections between ap…

One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGL…

We propose a modified $χ^β$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cramér-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimat…

We study two types of preconditioners and preconditioned stochastic gradient descent (SGD) methods in a unified framework. We call the first one the Newton type due to its close relationship to the Newton method, and the second one the Fisher type as its preconditioner is closely related to the inverse of Fisher inform…

Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M. In this paper, we show that the Frechet manifold D is equipped with a Riemannian metric g^{D} and an affine connection \nabla^{D} which are infinite dimensional analogues of the Fisher…

We introduce RSE to measure robustness in estimation problems.

Develops a new geometric framework for quantum metrics.

New methods improve Fisher Matrix approximations for neural networks at low cost.

Early training phase affects deep neural network optimization and generalization.

Researchers develop a new quantum invariant using a matrix dilogarithm for 3-manifolds.

The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we d…

Paper identifies key function spaces for ReLU networks based on Fisher information.

We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed quantum state. We also introduce quantum flows, the quantum analog of normalizing flow…

Reverse annealing boosts quantum matrix factorization performance.

A family of probability distributions parametrized by an open domain $Λ$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix tensor is positive definite defining in this way a Riemannia…

Optimal preconditioning improves Langevin sampling efficiency.

Paper improves matrix-valued data classification using nonparametric LDA.

This article gives matrix factorizations for the trivalent diagrams and double line appearing in $\mathfrak{sl}_n$ quantum link invariant. These matrix factorizations reconstruct Khovanov-Rozansky homology. And we show that the Euler characteristic of the matrix factorization for a double loop equals the quantum dimens…

Unified approach for learning quantum operations from measurements.

This paper solves the intractability barrier in non-parametric information geometry by introducing a novel framework.

Study asymptotics of unitary matrix elements in quantum mechanics.

New neural networks for non-commutative data.

A new iterative K-FAC algorithm reduces training time and memory usage.

We compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves.

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 analyze this method and its properties, and show how it can be viewed as a type of 2…

Sketch Tomography improves quantum state estimation accuracy.

Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.

New method for natural policy gradients converges linearly.

Paper presents a rank-1 approximation method for natural policy gradients in deep RL.

Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive it…

A new method improves uncertainty estimation in deep learning, especially for hard-to-label samples.