arXiv research

Study on typical knots and links using grid diagrams, focusing on size, components, and writhe.

The paper examines linking numbers in grid models and finds polynomial moments.

This work refines grid size selection for non-interactive private $K$-means clustering.

Determining the appropriate batch size for mini-batch gradient descent is always time consuming as it often relies on grid search. This paper considers a resizable mini-batch gradient descent (RMGD) algorithm based on a multi-armed bandit for achieving best performance in grid search by selecting an appropriate batch s…

SKI accelerates GP inference with sparse grids to handle higher dimensions.

New method constructs moduli spaces of Lagrangian surfaces in CP^2 from grid diagrams.

In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex grid structures, and define a new vertex convolution operation by adopting a set of…

Study non-monotonic loss functions in CRC, achieving valid risk control with large calibration samples.

Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…

In this paper, we investigate the significance of choosing an appropriate tessellation strategy for a spatio-temporal taxi demand-supply modeling framework. Our study compares (i) the variable-sized polygon based Voronoi tessellation, and (ii) the fixed-sized grid based Geohash tessellation, using taxi demand-supply GP…

The increasing penetration of distributed energy resources poses numerous reliability issues to the urban distribution grid. The topology estimation is a critical step to ensure the robustness of distribution grid operation. However, the bus connectivity and grid topology estimation are usually hard in distribution gri…

The paper develops a stationary-distribution theory for Random Forest ensemble size selection.

M-CaStLe discovers causal structures in multivariate space-time data.

Study finds optimal learning rate schedules for sub-100M quantization-aware training across bit-widths.

Computes elastic grids that approximate 3D surfaces without physical simulations.

A new method uses SVM classification to efficiently compute confidence sets.

Proposes learning regularization strength directly from data.

New method uses tensor networks to price multi-asset options efficiently.

Insights in power grid pixel maps (PGPMs) refer to important facility operating states and unexpected changes in the power grid. Identifying insights helps analysts understand the collaboration of various parts of the grid so that preventive and correct operations can be taken to avoid potential accidents. Existing sol…

This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transit…

A new approach models exploration in continuous-time RL using random measures.

In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation ass…

Generative models learn distributions of continuous functions.

New insights into data geometry reveal manifold structure in grid-cell activity.

We address the problem of maintaining high voltage power transmission networks in security at all time. This requires that power flowing through all lines remain below a certain nominal thermal limit above which lines might melt, break or cause other damages. Current practices include enforcing the deterministic "N-1" …

Sparse grids reduce xVA exposure evaluations by up to 6000 times.

This paper improves GNN efficiency for large-scale graph applications.

Neural sequence-to-sequence models, particularly the Transformer, are the state of the art in machine translation. Yet these neural networks are very sensitive to architecture and hyperparameter settings. Optimizing these settings by grid or random search is computationally expensive because it requires many training r…

The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces `…

We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that gr…

A new method improves ridesharing efficiency using QMIX.

In recent scene recognition research images or large image regions are often represented as disorganized "bags" of features which can then be analyzed using models originally developed to capture co-variation of word counts in text. However, image feature counts are likely to be constrained in different ways than word …

Quantum algorithm for multi-asset option pricing under different volatility models.

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier feat…

The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.

Half grid diagrams prove every link can be represented by a special type of grid diagram.

Grid homology confirms the Upsilon invariant in knot theory.

GridPyM handles grid diagrams for knot theory.

Grid homology theory for spatial graphs extends skein sequence.

Extends knot invariant to filtered grid complexes.

New method finds grid diagrams for many fibered knots.

Grid homology properties for MOY graphs studied.

Grid homology invariant proved for lens space links.

New trading strategy beats traditional grid in crypto markets.

Recently it has been shown that the step sizes of a family of variance reduced gradient methods called the JacSketch methods depend on the expected smoothness constant. In particular, if this expected smoothness constant could be calculated a priori, then one could safely set much larger step sizes which would result i…

Develops equivariant grid homology for strongly invertible knots.

Grid homology shows knot unknotting lower bound.

Computes homology of an obstruction chain complex in grid homology.