10 citations · 38 across the 13 of their papers we have counts for
15 papers
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction
Luis Scoccola, Hitesh Gakhar, Johnathan Bush +4
The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a -dimensional hole in the…
Supervised Homogeneity Fusion: a Combinatorial Approach
Wen Wang, Shihao Wu, Ziwei Zhu +2
Fusing regression coefficients into homogenous groups can unveil those coefficients that share a common value within each group. Such groupwise homogeneity reduces the intrinsic di…
Persistent Cup-Length
Marco Contessoto, Facundo Mémoli, Anastasios Stefanou +1
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Rip…
Persistent Homotopy Groups of Metric Spaces
Facundo Mémoli, Ling Zhou
We study notions of persistent homotopy groups of compact metric spaces together with their stability properties in the Gromov-Hausdorff sense. We pay particular attention to the c…
Gauge theory and twins paradox of disentangled representations
X. Dong, L. Zhou
Achieving disentangled representations of information is one of the key goals of deep network based machine learning system. Recently there are more discussions on this issue. In t…
Understanding over-parameterized deep networks by geometrization
Xiao Dong, Ling Zhou
A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networ…
Geometrization of deep networks for the interpretability of deep learning systems
Xiao Dong, Ling Zhou
How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge…
Reducing Parameter Space for Neural Network Training
Tong Qin, Ling Zhou, Dongbin Xiu
For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifical…
Spacetime as the optimal generative network of quantum states: a roadmap to QM=GR?
Xiao Dong, Ling Zhou
The idea that spacetime geometry is built from quantum entanglement has been widely accepted in the last years. But how exactly the geometry is related with quantum states is still…
Time from quantum state complexity and the pace of time flow
X. Dong, L. Zhou
Based on the hypothesis that the thermodynamic arrow of time is an emergent phenomenon of quantum state complexity evolution, we further propose that the natural pace of time flow…
Quantum state complexity and the thermodynamic arrow of time
Xiao Dong, Ling Zhou
Why time is a one-way corridor? What's the origin of the arrow of time? We attribute the thermodynamic arrow of time as the direction of increasing quantum state complexity. Inspir…
Demystifying AlphaGo Zero as AlphaGo GAN
Xiao Dong, Jiasong Wu, Ling Zhou
The astonishing success of AlphaGo Zero\cite{Silver_AlphaGo} invokes a worldwide discussion of the future of our human society with a mixed mood of hope, anxiousness, excitement an…
Ralph's equivalent circuit model, revised Deutsch's maximum entropy rule and discontinuous quantum evolutions in D-CTCs
Xiao Dong, Hanwu Chen, Ling Zhou
We examine Ralph's equivalent circuit model of D-CTCs, which was proposed to derive Deutsch's maximum entropy rule of D-CTCs. By constructing counterexamples we show that the equiv…
How deep learning works --The geometry of deep learning
Xiao Dong, Jiasong Wu, Ling Zhou
Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system…