相关论文: Semigroup Consistency as a Diagnostic for Learned …

We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…

Fully symmetric learning rules for principal component analysis can be derived from a novel objective function suggested in our previous work. We observed that these learning rules suffer from slow convergence for covariance matrices where…

Most modern learning problems are highly overparameterized, meaning that there are many more parameters than the number of training data points, and as a result, the training loss may have infinitely many global minima (parameter vectors…

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and…

Few-shot image classification requires the classifier to robustly cope with unseen classes even if there are only a few samples for each class. Recent advances benefit from the meta-learning process where episodic tasks are formed to train…

Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned…

Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…

Estimating the parameters of a model describing a set of observations using a neural network is in general solved in a supervised way. In cases when we do not have access to the model's true parameters this approach can not be applied.…

In order to leverage and profit from unlabelled data, semi-supervised frameworks for semantic segmentation based on consistency training have been proven to be powerful tools to significantly improve the performance of purely supervised…

Precise control in modern robotic applications is always an open issue due to unknown time-varying disturbances. Existing meta-learning-based approaches require a shared representation of environmental structures, which lack flexibility for…

We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…

This work is devoted to the problem of distributed target tracking when a team of robots detect the target through a variable perception-latency mechanism. A reference for the robots to track is constructed in terms of a desired formation…

The reconstruction theorem and the multilevel Schauder estimate have central roles in the analytic theory of regularity structures [17]. Inspired by [26], we provide elementary proofs for them by using the semigroup of operators.…

We derive a simple and model-independent formula for the change in the generalization gap due to a gradient descent update. We then compare the change in the test error for stochastic gradient descent to the change in test error from an…

The ability to simulate and predict the outcome of contacts is paramount to the successful execution of many robotic tasks. Simulators are powerful tools for the design of robots and their behaviors, yet the discrepancy between their…

By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the…

A general condition for the self-consistency of a semiclassical approximation to a given system is suggested. It is based on the eigenvalue distribution of the relevant Hessian evaluated at the streamline configurations (configurations that…

While developments in machine learning led to impressive performance gains on big data, many human subjects data are, in actuality, small and sparsely labeled. Existing methods applied to such data often do not easily generalize to…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…