Related papers: Networks with complex weights: Green function and …
We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…
Expressive querying of machine learning models - viewed as a form of intentional data - enables their verification and interpretation using declarative languages, thereby making learned representations of data more accessible. Motivated by…
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…
Random walks on simple graphs in connection with electrical resistor networks lead to the definition of Markov chains with transition probability matrix in terms of electrical conductances. We extend this definition to an effective…
We give an analogy between non-reversible Markov chains and electric networks much in the flavour of the classical reversible results originating from Kakutani, and later Kem\'eny-Snell-Knapp and Kelly. Non-reversibility is made possible by…
An interesting approach to analyzing neural networks that has received renewed attention is to examine the equivalent kernel of the neural network. This is based on the fact that a fully connected feedforward network with one hidden layer,…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
We show how well known rules of back propagation arise from a weighted combination of finite automata. By redefining a finite automata as a predictor we combine the set of all $k$-state finite automata using a weighted majority algorithm.…
During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…
A very interesting matter of Network Science is assessing how complex a given network is. In other words, by how much does such a network departs from any general patterns which could be evoked for its description. Among other choices,…
A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In…
We study the connection between weighted Bergman kernel and Green's function on a domain W lying in C for which the Green's function exists.
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of feed-forward networks and their theoretical…
The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda, is classically estimated using the capacity of Lambda with respect to the Green kernel G(x,y). We show that replacing the Green kernel by…
On the basis of the tight-binding formalism and Green function technique we obtain all the Green functions matrix elements for a biased chain with a linear variation of the electron on-site energy. Their dependence on the system parameters…
We demonstrate that any Euclidean-time quantum mechanical theory may be represented as a neural network, ensured by the Kosambi-Karhunen-Lo\`eve theorem, mean-square path continuity, and finite two-point functions. The additional constraint…
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…
In this paper we explore a connection between deep networks and learning in reproducing kernel Krein space. Our approach is based on the concept of push-forward - that is, taking a fixed non-linear transform on a linear projection and…
A central question in deep learning is to understand the functions learned by deep networks. What is their approximation class? Do the learned weights and representations depend on initialization? Previous empirical work has evidenced that…
I aim to show that models, classification or generating functions, invariances and datasets are algorithmically equivalent concepts once properly defined, and provide some concrete examples of them. I then show that a) neural networks (NNs)…