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Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

In two dimensions, $U(N_c)$ gauge theories exhibit a non-trivial topological structure, while $SU(N_c)$ theories are topologically trivial. Hence, for $G = U(N_c)$ the phase space is divided into topological sectors, characterized by a…

We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…

We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex…

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most…

We construct neural networks that work for any Lie group and maintain gauge covariance, enabling smooth, invertible gauge field transformations. We implement these transformations for 4D SU(3) lattice gauge fields and explore their use in…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Existing convolution techniques in artificial neural networks suffer from huge computation complexity, while the biological neural network works in a much more powerful yet efficient way. Inspired by the biological plasticity of dendritic…

This paper introduces a heuristic topology optimization framework for thin-walled, 2D extruded lattice structures subject to complex high-speed loading. The proposed framework optimizes the wall thickness distribution in the lattice cross…

Critical slowing down, where autocorrelation grows rapidly near the continuum limit due to Hybrid Monte Carlo (HMC) moving through configuration space inefficiently, still challenges lattice gauge theory simulations. Combining neural field…

Federated Learning (FL) algorithms commonly sample a random subset of clients to address the straggler issue and improve communication efficiency. While recent works have proposed various client sampling methods, they have limitations in…

The recent introduction of Machine Learning techniques, especially Normalizing Flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional Hybrid Monte Carlo (HMC) algorithm.…

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or…

We investigate SU(2) gauge fields topology using new approach, which exploits the well known connection between SU(2) gauge theory and quaternionic projective sigma-models and allows to formulate the topological charge density entirely in…

In the symplectic Lagrangian framework we newly embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and…

In this paper, we present a new MTL framework that searches for structures optimized for multiple tasks with diverse graph topologies and shares features among tasks. We design a restricted DAG-based central network with read-in/read-out…

We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in…

This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…