Related papers: Two-mode geometry controls multiscale organization…

The node set of a two-mode network consists of two disjoint subsets and all its links are linking these two subsets. The links can be weighted. We developed a new method for identifying important sub-networks in two-mode networks. The…

We define a second-order neural network stochastic gradient training algorithm whose block-diagonal structure effectively amounts to normalizing the unit activations. Investigating why this algorithm lacks in robustness then reveals two…

Effective generalization in robotic manipulation requires representations that capture invariant patterns of interaction across environments and tasks. We present a self-supervised framework for learning hierarchical manipulation concepts…

Layered control is essential for managing complexity in large-scale systems, employing progressively coarser models at higher layers. While significant advances have been made for fully observable systems, the theoretical foundations of…

Microstructural evolution in structural materials is known to occur in response to mechanical loading and can often accommodate substantial plastic deformation through the coupled motion of grain boundaries (GBs). This can produce desirable…

Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics,…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…

We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

A bipartite network is a graph structure where nodes are from two distinct domains and only inter-domain interactions exist as edges. A large number of network embedding methods exist to learn vectorial node representations from general…

The Marginally Rigid State is a candidate paradigm for what makes granular material a state of matter distinct from both liquid and solid. Coordination number is identified as a discriminating characteristic, and for rough-surfaced…

Learning the graphical structure of Bayesian networks is key to describing data-generating mechanisms in many complex applications but poses considerable computational challenges. Observational data can only identify the equivalence class…

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…

We use information geometry, in which the local distance between models measures their distinguishability from data, to quantify the flow of information under the renormalization group. We show that information about relevant parameters is…

Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…

A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural…

Control architectures and autonomy stacks for complex engineering systems are often divided into layers to decompose a complex problem and solution into distinct, manageable sub-problems. To simplify designs, uncertainties are often ignored…