相关论文: The Coupling Strength Is a Scale Parameter in Thre…

The rapid scaling of Large Language Models (LLMs) has pushed training workloads far beyond the limits of single-node analysis, demanding a deeper understanding of how these models behave across large-scale, multi-GPU systems. In this paper,…

Increased coupling between critical infrastructure networks, such as power and communication systems, will have important implications for the reliability and security of these systems. To understand the effects of power-communication…

Reservoir computing (RC), first applied to temporal signal processing, is a recurrent neural network in which neurons are randomly connected. Once initialized, the connection strengths remain unchanged. Such a simple structure turns RC into…

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…

Artificial Recurrent Neural Networks are a powerful information processing abstraction, and Reservoir Computing provides an efficient strategy to build robust implementations by projecting external inputs into high dimensional dynamical…

Usually, reservoir computing shows an exponential memory decay. This paper investigates under which circumstances echo state networks can show a power law forgetting. That means traces of earlier events can be found in the reservoir for…

The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…

In this paper, we study the trainability of rectified linear unit (ReLU) networks. A ReLU neuron is said to be dead if it only outputs a constant for any input. Two death states of neurons are introduced; tentative and permanent death. A…

Reservoir computing is a promising neuromorphic paradigm, and its quantum implementation using spin networks has shown some advantage when entanglement is present. Here, we consider a distributed scenario in which two distinct input time…

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…

Recurrent neural networks (RNNs) trained on low-dimensional tasks have been widely used to model functional biological networks. However, the solutions found by learning and the effect of initial connectivity are not well understood. Here,…

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…

We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a perturbative expansion of the neural equations, where the…

Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…

Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…

Unsupervised pretraining and dropout have been well studied, especially with respect to regularization and output consistency. However, our understanding about the explicit convergence rates of the parameter estimates, and their dependence…

Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…

In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…

The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…