Related papers: Spectral Networks and Snakes
We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical…
Fix an odd prime $p$. Let $X$ be a pointed space whose $p$-completed K-theory $\mathrm{KU}_p^*(X)$ is an exterior algebra on a finite number of odd generators; examples include odd spheres and many H-spaces. We give a…
Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…
We introduce Sprecher Networks (SNs), a family of trainable architectures derived from David Sprecher's 1965 constructive form of the Kolmogorov-Arnold representation. Each SN block implements a "sum of shifted univariate functions" using…
Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the…
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…
We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
In this paper we investigate the relation between complexified Fenchel-Nielsen coordinates and spectral network coordinates on Seiberg-Witten moduli space. The main technique is the comparison of exact expressions for the expectation value…
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take…
A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*. We study the relationship between certain pairs of such theories which…
We study the spectral sequence associated to the filtration by powers of the augmentation ideal on the (twisted) equivariant chain complex of the universal cover of a connected CW-complex X. In the process, we identify the d^1 differential…
Combinatorial methods are developed to find the cluster coordinates for moduli space of flat connections which is describing the Coulomb branch of higher rank N=2 theories derived by compactifying six dimensional (2,0) theory on a punctured…
In this paper, we define some Markov Chains associated to Vershik maps on Bratteli diagrams. We study probabilistic and spectral properties of their transition operators and we prove that the spectra of these operators are connected to…
A framework is developed to describe the Zariski topologies on the prime and primitive spectra of a quantum algebra $A$ in terms of the (known) topologies on strata of these spaces and maps between the collections of closed sets of…
The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a "weighted…
We study the Coulomb branch of class $\mathcal{S}_k$ $\mathcal{N} = 1$ SCFTs by constructing and analyzing their spectral curves.
The $SU_3$-skein algebra of a surface $F$ is spanned by isotopy classes of certain framed graphs in $F\times I$ called $3$-webs subject to the skein relations encapsulating relations between $U_q(sl(3))$-representations. These skein…
Graph neural networks (GNNs) have achieved impressive impressions for graph-related tasks. However, most GNNs are primarily studied under the cases of signal domain with supervised training, which requires abundant task-specific labels and…
We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical…