Directed percolation in random temporal network models with heterogeneities

Abstract

Fully decentralised federated learning enables collaborative training of individual machine learning models on distributed devices on a network while keeping the training data localised. This approach enhances data privacy and eliminates both the single point of failure and the necessity for central coordination. Our research highlights that the effectiveness of decentralised federated learning is significantly influenced by the network topology of connected devices. A simplified numerical model for studying the early behaviour of these systems leads us to an improved artificial neural network initialisation strategy, which leverages the distribution of eigenvector centralities of the nodes of the underlying network, leading to a radically improved training efficiency. Additionally, our study explores the scaling behaviour and choice of environmental parameters under our proposed initialisation strategy. This work paves the way for more efficient and scalable artificial neural network training in a distributed and uncoordinated environment, offering a deeper understanding of the intertwining roles of network structure and learning dynamics.

Reticula: A temporal network and hypergraph analysis software package

“…[22] used it to estimate constrained reachability on large real-world temporal networks, while Ref. [23] applied the same methodology to a variety of random temporal network models to show that limited waiting-time adjacency has a directed percolation reachability phase transition in many temporal networks. Furthermore, Ref.…”

“…Reticula can also be used for generating various synthetic and random static and temporal networks, such as regular ring lattices, d-dimensional square lattices, G(n, p) [26], Barabási-Albert [27], k-regular, (directed or undirected) degree-sequence [28] and (directed or undirected) expected degree-sequence random graphs [29,30], as well as fully-mixed and activation model temporal networks with any static ''base'' and exponential, geometric, self-exciting and power-law inter-event time distributions [23]. It is also possible to start from a (possibly realworld) temporal network and randomise certain features away using various microcanonical randomised reference models implemented in the library [31].…”

Reticula: A temporal network and hypergraph analysis software package

“…[15] used it to estimate constrained reachability on large real-world temporal networks, while Ref. [16] applied the same methodology to a variety of random temporal network models to show that limited waiting-time adjacency has a directed percolation reachability phase transition in many temporal networks. Furthermore, Ref.…”

“…Reticula can also be used for generating various synthetic and random static and temporal networks, such as regular ring lattices, d-dimensional square lattices, G(n, p) [20], Barabási-Albert [21], k-regular, (directed or undirected) degree-sequence [22] and (directed or undirected) expected degreesequence random graphs [23,24], as well as fully-mixed and activation model temporal networks with any static "base" and exponential, geometric, selfexciting and power-law inter-event time distributions [16]. It is also possible to start from a (possibly real-world) temporal network and randomise certain features away using various microcanonical randomised reference models implemented in the library [25].…”

“…Similarly, for temporal networks it is possible to calculate the event graph representation [29], and to calculate the temporal reachability cluster starting from a single vertex at a specified time in O(|E|), or estimate it in one pass for all vertices at all possible starting times in O(|E| log |E|) [28]. The resulting temporal clusters include reachability information, and characteristic quantities such as cluster mass, volume and lifetime [16,15].…”