Related papers: Another look at the Gardner problem
Many of today's most interesting questions involve understanding and interpreting complex relationships within graph-based structures. For instance, in materials science, predicting material properties often relies on analyzing the…
Despite their success and widespread adoption, the opaque nature of deep neural networks (DNNs) continues to hinder trust, especially in critical applications. Current interpretability solutions often yield inconsistent or oversimplified…
Statistical-physics calculations in machine learning and theoretical neuroscience often involve lengthy derivations that obscure physical interpretation. Here, we give concise, non-replica derivations of several key results and highlight…
Adoption of deep neural networks in fields such as economics or finance has been constrained by the lack of interpretability of model outcomes. This paper proposes a generative neural network architecture - the parameter encoder neural…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
In this research, we aim to compare the performance of different classical machine learning models and neural networks in identifying the frequency of occurrence of each digit in a given number. It has various applications in machine…
This work addresses the challenge of using a deep learning model to prune graphs and the ability of this method to integrate explainability into spatio-temporal problems through a new approach. Instead of applying explainability to the…
We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with…
This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are…
A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…
Dealing with an unbounded data stream involves overcoming the assumption that data is identically distributed and independent. A data stream can, in fact, exhibit temporal dependencies (i.e., be a time series), and data can change…
We use a binary search tree and the simplex algorithm to measure the fraction of patterns that can be stored by an Ising perceptron. The algorithm is much faster than exhaustive search and allows us to obtain accurate statistics up to a…
Recurrent neural networks (RNN) are powerful tools to explain how attractors may emerge from noisy, high-dimensional dynamics. We study here how to learn the ~N^(2) pairwise interactions in a RNN with N neurons to embed L manifolds of…
The packing problem, also known as cutting or nesting, has diverse applications in logistics, manufacturing, layout design, and atlas generation. It involves arranging irregularly shaped pieces to minimize waste while avoiding overlap.…
Many real-world problems, e.g. object detection, have outputs that are naturally expressed as sets of entities. This creates a challenge for traditional deep neural networks which naturally deal with structured outputs such as vectors,…
Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including…
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…
Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important…
A central question of network science is how functional properties of systems arise from their structure. For networked dynamical systems, structure is typically quantified with network measures. A functional property that is of theoretical…
We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa). The main difficulty of using a…