arXiv research

In L^3, cuspidal edges can have bounded mean curvature under specific conditions.

Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field $ν$ is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of the cuspidal edge (as a regul…

This paper proposes a method to learn graph representations by partitioning edges into communities.

SAM improves generalization by operating near the edge of stability.

In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space $\boldsymbol R^3$ preserving their singular set images and first fundamental forms, was given. Here, we call this an `isometric duality'. When the singular set image has no symmetries and d…

EDG generates Boltzmann samples from latent variables efficiently.

New framework for disentangling graph node and edge features.

Study on planar graph braid groups' second homology.

New geometric approach realizes 5D bulk theories with 4D edge modes.

This paper tackles graph translation challenges by predicting both node and edge attributes simultaneously.

This work estimates edge weights of edge-reinforced random walks using observed data.

New method constructs tilings of the plane using directed edges and alignments.

Paper detects anomalous edges in social networks using edge exchangeability.

It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural networks, the foundation of this hypothesis on generic non-linear systems remain…

Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. Fleming and the author introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the constituent 2-component algebraically split li…

An edge tessellation is a tiling of the plane generated by reflecting a polygon in its edges. We prove that a polygon generating an edge tessellation is one the following eight types: a rectangle; an equilateral, 60-right, isosceles right, or 120-isosceles triangle; a 120-rhombus; a 60-90-120 kite; or a regular hexagon…

Executing deep neural networks for inference on the server-class or cloud backend based on data generated at the edge of Internet of Things is desirable due primarily to the limited compute power of edge devices and the need to protect the confidentiality of the inference neural networks. However, such a remote inferen…

On-device federated learning updates edge models by exchanging trained results.

The paper extends Bour's theorem to helicoidal surfaces with singularities.

Study detects edge correlation between unlabeled random graphs.

In matrix factorization, available graph side-information may not be well suited for the matrix completion problem, having edges that disagree with the latent-feature relations learnt from the incomplete data matrix. We show that removing these $\textit{contested}$ edges improves prediction accuracy and scalability. We…

Polynomial-time algorithm estimates edge density of random graphs with privacy and robustness.

Paper determines Assouad-Nagata dimension for all minor-closed metrics.

Previously in 2014, we proposed the Nearest Descent (ND) method, capable of generating an efficient Graph, called the in-tree (IT). Due to some beautiful and effective features, this IT structure proves well suited for data clustering. Although there exist some redundant edges in IT, they usually have salient features …

Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the 2-component constituent algebraically split links and show examples…

Graph pruning improves neural network performance by addressing squashing and smoothing issues.

New findings show mini-batch SGD operates in a 'Edge of Stochastic Stability' regime.

Efficient framework for training machine learning models at edge without data movement.

We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an $n$ node multilayer neural net that has degree at most $n^γ$ for some $γ<1$ and each edge has a random edge weight in $[-1,1]$. Our algorithm learns {\em …

Improved KAN model explains brain dynamics through edge learning and synaptic strength.

Resource-constrained IoT devices, such as sensors and actuators, have become ubiquitous in recent years. This has led to the generation of large quantities of data in real-time, which is an appealing target for AI systems. However, deploying machine learning models on such end-devices is nearly impossible. A typical so…

We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homology by the polynomial ring generated by the set of edges, and we show that this homology module is finitely generated. An analogue of class…

We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify relations between singularities of parallel and dual surfaces and differential geometri…

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networ…

OL4EL optimizes edge learning on resource-constrained servers.

New GPs model edge functions on complex networks, capturing divergence and curl.

Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this paper we use elliptic theory for edge-degenerate differential operators on singular manifolds to study the moduli space of deformations of special Lagrangian submanifolds with ed…

Letting $C$ be a compact $C^ω$-curve embedded in $\boldsymbol R^3$ ($C^ω$ means real analyticity), we consider a $C^ω$-cuspidal edge $f$ along $C$. When $C$ is non-closed, in the authors' previous works, the local existence of three distinct cuspidal edges along $C$ whose first fundamental forms coincide with that of $…

Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…

Edge augmentation connects disconnected graphs by elevating eigenvalues.

We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…

The paper solves pentagon equations using triangulations and edge transformations.

Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge, the extent to which the edge is embedded in a surrounding structure, and the age…

Survey on pruning CNN models to reduce size for edge devices.

IIC decouples causal identification into two phases, significantly reducing the HTC gap in linear SEMs.

Federated learning technique improves convergence speed with communication delays.

In the emerging advancement in the branch of autonomous robotics, the ability of a robot to efficiently localize and construct maps of its surrounding is crucial. This paper deals with utilizing thermal-infrared cameras, as opposed to conventional cameras as the primary sensor to capture images of the robot's surroundi…

Study of cuspidal edges on focal surfaces of regular surfaces.