Related papers: Threshold Disorder as a Source of Diverse and Comp…
Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…
We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path $\ell_{\rm opt}$ in a disordered Erd\H{o}s-R\'enyi (ER) random network and scale-free (SF) network. Each link $i$ is…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
Recurrent Neural Network (RNN) and its variations such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), have become standard building blocks for learning online data of sequential nature in many research areas, including…
In the past few years, neural networks have evolved from simple Feedforward Neural Networks to more complex neural networks, such as Convolutional Neural Networks and Recurrent Neural Networks. Where CNNs are a perfect fit for tasks where…
Hierarchically structured materials, which possess distinct features on different length scales, are ubiquitous in nature and engineering. In many cases, one structural level may be ordered while another structural level may be disordered.…
Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of…
Regulatory networks (RNs) are a well-accepted modelling formalism in computational systems biology. The control of RNs is currently receiving a lot of attention because it provides a computational basis for cell reprogramming -- an…
The presence of Long Distance Dependencies (LDDs) in sequential data poses significant challenges for computational models. Various recurrent neural architectures have been designed to mitigate this issue. In order to test these…
Recurrent neural networks (RNNs) are complex dynamical systems, capable of ongoing activity without any driving input. The long-term behavior of free-running RNNs, described by periodic, chaotic and fixed point attractors, is controlled by…
This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are…
Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…
Discrete gene regulatory networks (GRNs) play a vital role in the study of robustness and modularity. A common method of evaluating the robustness of GRNs is to measure their ability to regulate a set of perturbed gene activation patterns…
Performance of trained neural network (NN) models, in terms of testing accuracy, has improved remarkably over the past several years, especially with the advent of deep learning. However, even the most accurate NNs can be biased toward a…
The architecture of a neural network constrains the potential dynamics that can emerge. Some architectures may only allow for a single dynamic regime, while others display a great deal of flexibility with qualitatively different dynamics…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
The optical properties of materials are strongly influenced by disorder. Control of disorder in photonic materials can unveil interesting optical properties. We have found an engineered photonic structure for which the average light…
In dynamic graphs, preserving temporal continuity is critical. However, Memory-based Dynamic Graph Neural Networks (MDGNNs) trained with large batches often disrupt event sequences, leading to temporal information loss. This discontinuity…
Predictive multiplicity and chaotic dynamics represent two fundamental challenges in machine learning that have evolved independently despite their conceptual connections. We bridge this gap by introducing horizon-constrained Rashomon sets,…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…