Related papers: Learning advanced mathematical computations from e…

Neural Networks sequentially build high-level features through their successive layers. We propose here a new neural network model where each layer is associated with a set of candidate mappings. When an input is processed, at each layer,…

Machine learning has been widely applied to clearly defined problems of astronomy and astrophysics. However, deep learning and its conceptual differences to classical machine learning have been largely overlooked in these fields. The broad…

Convolutional Neural Networks (CNNs) define an exceptionally powerful class of models for image classification, but the theoretical background and the understanding of how invariances to certain transformations are learned is limited. In a…

Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…

Though neural network models demonstrate impressive performance, we do not understand exactly how these black-box models make individual predictions. This drawback has led to substantial research devoted to understand these models in areas…

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of…

Training deep neural networks may be challenging in real world data. Using models as black-boxes, even with transfer learning, can result in poor generalization or inconclusive results when it comes to small datasets or specific…

We investigate the problem of learning to generate complex networks from data. Specifically, we consider whether deep belief networks, dependency networks, and members of the exponential random graph family can learn to generate networks…

Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…

The ability of humans and animals to quickly adapt to novel tasks is difficult to reconcile with the standard paradigm of learning by slow synaptic weight modification. Here we show that fixed-weight neural networks can learn to generate…

Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…

In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…

This paper describes the use of neural networks to enhance simulations for subsequent training of anomaly-detection systems. Simulations can provide edge conditions for anomaly detection which may be sparse or non-existent in real-world…

We train deep generative models on datasets of reflexive polytopes. This enables us to compare how well the models have picked up on various global properties of generated samples. Our datasets are complete in the sense that every single…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

Interpreting how does deep neural networks (DNNs) make predictions is a vital field in artificial intelligence, which hinders wide applications of DNNs. Visualization of learned representations helps we humans understand the vision of DNNs.…

We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…

Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to…

Physics models typically contain adjustable parameters to reproduce measured data. While some parameters correspond directly to measured features in the data, others are unobservable. These unobservables can, in some cases, cause…