Related papers: Invariance Measures for Neural Networks

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…

Neural networks (NNs) whose subnetworks implement reusable functions are expected to offer numerous advantages, including compositionality through efficient recombination of functional building blocks, interpretability, preventing…

We first exhibit a multimodal image registration task, for which a neural network trained on a dataset with noisy labels reaches almost perfect accuracy, far beyond noise variance. This surprising auto-denoising phenomenon can be explained…

The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…

Convolutional Neural Networks (CNNs) perform very well in image classification and object detection in recent years, but even the most advanced models have limited rotation invariance. Known solutions include the enhancement of training…

Recent results show that deep neural networks achieve excellent performance even when, during training, weights are quantized and projected to a binary representation. Here, we show that this is just the tip of the iceberg: these same…

A reliable perception has to be robust against challenging environmental conditions. Therefore, recent efforts focused on the use of radar sensors in addition to camera and lidar sensors for perception applications. However, the sparsity of…

Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework…

In an attempt to better understand generalization in deep learning, we study several possible explanations. We show that implicit regularization induced by the optimization method is playing a key role in generalization and success of deep…

Computer vision research has long aimed to build systems that are robust to spatial transformations found in natural data. Traditionally, this is done using data augmentation or hard-coding invariances into the architecture. However, too…

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

Although numerous methods to reduce the overfitting of convolutional neural networks (CNNs) exist, it is still not clear how to confidently measure the degree of overfitting. A metric reflecting the overfitting level might be, however,…

Latent representations are used extensively for downstream tasks, such as visualization, interpolation or feature extraction of deep learning models. Invariant and equivariant neural networks are powerful and well-established models for…

A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…

Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We…

There is currently a paradigm shift in several power system monitoring applications, such as incipient fault detection and monitoring inverter-based resources, to transition from traditional phasor analytics to more informative waveform…

We propose a nonparametric parameter estimation of confidence intervals when the underlying has large or infinite variance. We explain the method by a simple numerical example and provide an application to estimate the coupling strength in…

Training deep neural networks is known to require a large number of training samples. However, in many applications only few training samples are available. In this work, we tackle the issue of training neural networks for classification…