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Transformer networks have lead to important progress in language modeling and machine translation. These models include two consecutive modules, a feed-forward layer and a self-attention layer. The latter allows the network to capture long…
We investigate the long-time behaviour of solutions of a class of singular-degenerate porous medium type equations in bounded domains with homogeneous Dirichlet boundary conditions. The existence of global attractors is shown under very…
Somehow, the revised version of our paper \cite{KY} does not appear on journals' home page. Here we present the revised version altered to reflect the corrections and/or additions to that paper. In this note, we consider self-affine…
The well-posedness of a generalized Coleman--Gurtin equation equipped with dynamic boundary conditions with memory was recently established by the author with C.G. Gal. In this article we report advances concerning the asymptotic behavior…
While advances in artificial intelligence and neuroscience have enabled the emergence of neural networks capable of learning a wide variety of tasks, our understanding of the temporal dynamics of these networks remains limited. Here, we…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
A longstanding challenge for the Machine Learning community is the one of developing models that are capable of processing and learning from very long sequences of data. The outstanding results of Transformers-based networks (e.g., Large…
We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…
We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…
Traditional analytical reflectance models, while compact and interpretable, lack the capacity to accurately represent physical measurements. Recent neural models, which closely fit input data, are less generalizable and often more expensive…
A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional…
Machine learning and deep learning in particular has advanced tremendously on perceptual tasks in recent years. However, it remains vulnerable against adversarial perturbations of the input that have been crafted specifically to fool the…
Artificial neurons with arbitrarily complex internal structure are introduced. The neurons can be described in terms of a set of internal variables, a set activation functions which describe the time evolution of these variables and a set…
Artificial neural networks in general and deep learning networks in particular established themselves as popular and powerful machine learning algorithms. While the often tremendous sizes of these networks are beneficial when solving…
We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The…
Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
Opponent modeling is necessary in multi-agent settings where secondary agents with competing goals also adapt their strategies, yet it remains challenging because strategies interact with each other and change. Most previous work focuses on…
In this paper, we address the problem of dynamic scene deblurring in the presence of motion blur. Restoration of images affected by severe blur necessitates a network design with a large receptive field, which existing networks attempt to…
A recent experiment suggests that neural circuits may alternatively implement continuous or discrete attractors, depending on the training set up. In recurrent neural network models, continuous and discrete attractors are separately modeled…