Related papers: Adapted Topologies and Higher Rank Signatures

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…

Federated fine-tuning for Large Language Models (LLMs) faces significant challenges due to the heavy communication overhead of transmitting large model updates. Although Low Rank Adaptation (LoRA) has been proposed as a solution, yet its…

In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…

Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…

We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Parallel combinations of adaptive filters have been effectively used to improve the performance of adaptive algorithms and address well-known trade-offs, such as convergence rate vs. steady-state error. Nevertheless, typical combinations…

The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and…

In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…

We consider stochastic convex optimization problems, where several machines act asynchronously in parallel while sharing a common memory. We propose a robust training method for the constrained setting and derive non asymptotic convergence…

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

In Part I \cite{Zhao13TSPasync1}, we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We…

For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `learn' the network are faced with a very large number (in…

Reconfigurable optical topologies are a promising new technology to improve datacenter network performance and cope with the explosive growth of traffic. In particular, these networks allow to directly and adaptively connect racks between…

The signature of a path, introduced by K.T. Chen [5] in $1954$, has been extensively studied in recent years. The $2010$ paper [12] of Hambly and Lyons showed that the signature is injective on the space of continuous finite-variation paths…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil new fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are…

We introduce the notion of weak decreasing stochastic (WDS) ordering for real-valued processes with negative means, which, to our knowledge, has not been studied before. Thanks to Madan-Yor's argument, it follows that the WDS ordering is a…