Related papers: Garland's Technique for Posets and High Dimensiona…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
The generalised Garfinkle-Vachaspati transform (GGV) introduced in our previous work (arXiv:1808.04981) is a powerful technique to add hair modes to a class of known D1-D5 solutions. The richest and most interesting examples of D1-D5…
The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small categories. Existing theories require that such a poset…
Generalization is important for peg-in-hole assembly, a fundamental industrial operation, to adapt to dynamic industrial scenarios and enhance manufacturing efficiency. While prior work has enhanced generalization ability for pose…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any…
A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a \nu\- domain, i.e. a superdomain with an odd involution,…
In this paper, we propose a new covering technique localized for the trajectories of SGD. This localization provides an algorithm-specific complexity measured by the covering number, which can have dimension-independent cardinality in…
We study a variant of the down-up and up-down walks over an $n$-partite simplicial complex, which we call expanderized higher order random walks -- where the sequence of updated coordinates correspond to the sequence of vertices visited by…
We establish a conjecture of Defant, Hopkins, Poznanovi\'{c}, and Propp concerning the dimensions of toggleability spaces for products of chains, shifted staircases, type-A root posets, and type-B posets. Generalizing this result, we show…
We create a framework for studying symmetric chain decompositions of families of finite posets based on the geometry of polytopes. Our framework unifies almost all known results regarding symmetric chain decompositions of the Young posets…
When applying a pre-trained 2D-to-3D human pose lifting model to a target unseen dataset, large performance degradation is commonly encountered due to domain shift issues. We observe that the degradation is caused by two factors: 1) the…
Finding the mode of a high dimensional probability distribution $D$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $D$ is…
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…
We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions among multiple entities. Our framework covers several popular models in recent network analysis literature,…
We show that hypernetworks can be regarded as posets which, in their turn, have a natural interpretation as simplicial complexes and, as such, are endowed with an intrinsic notion of curvature, namely the Forman Ricci curvature, that…
Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…
We establish a Karhunen-Lo`eve expansion for generic centered, second order stochastic processes, which does not rely on topological assumptions. We further investigate in which norms the expansion converges and derive exact average rates…
In this paper, we extend original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally…
Optimization techniques are at the core of many scientific and engineering disciplines. The steepest descent methods play a foundational role in this area. In this paper we studied a generalized steepest descent method on Riemannian…