A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The abstract discusses parallels between Galois theory and Stone-Weierstrass theorem in various fields.
kth-order invariant graph networks are as powerful as kth-order WL in distinguishing graphs.
4-Legendrian permutation racks can't distinguish knots but recover classical invariants.
PathNNs improve graph neural networks by distinguishing non-isomorphic graphs.
Robo-advisors estimate clients' risk aversion using interactive questionnaires.
Geometric GNNs improve graph discrimination through GWL.
Paper compares GCNs and MPNNs, finding GCNs are one step ahead of WL algorithm.
Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there have been increasing interests in studying their expressive power. One line of work studies the capability of GNNs to approximate permutation-invariant functions on graphs, and another focuses on the their power as…
New MPNNs match 2-WL, faster distinguishing graphs.
Graphs indistinguishable by GNNs are fully characterized.
GCNs distinguish graph models based on embeddings, but depth matters.
It is known that the first two-variable Links--Gould quantum link invariant is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Here we report investigations which greatly expand the set of evaluations o…
Meta two-sample testing uses auxiliary data to quickly find powerful tests from limited samples.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
This study compares GNNs and GA-MLPs, finding GA-MLPs can distinguish graphs but not count walks.
Deep-learning method improves hypothesis testing for independence.
This paper explores what causal structures can be distinguished by observational and interventional probing schemes.
We prove that many pretzel knots of the form are not topologically slice, even though their positive mutants are ribbon. We use the sliceness obstruction of Kirk and Livingston related to the twisted Alexander polynomials associated to prime power cyclic covers of knots.
ESAN improves graph neural networks by processing subgraphs.
In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 22 matrices with entries in a possibly non-commutative ring, for example the quaternions. These polynomials are sufficiently powerful to distinguish the Kishino knot from …
Detects dense subhypergraphs in heterogeneous random hypergraphs.
The paper sets thresholds for testing correlation in hypergraphs, distinguishing between independent and correlated states.
Modern machine learning techniques can be used to construct powerful models for difficult collider physics problems. In many applications, however, these models are trained on imperfect simulations due to a lack of truth-level information in the data, which risks the model learning artifacts of the simulation. In this …
A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.
We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range cross-correlated processes. Utilizing a heteroskedasticity and auto-correlation robust est…
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…
The first part of this paper discusses general procedures for finding numerical approximations to distinguished Kahler metrics, such as Calabi-Yau metrics, on complex projective manifolds. These procedures are closely related to ideas from Geometric Invariant Theory, and to the asymptotics of high powers of positive li…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the distinguishability of the distributions, by optimizing a lower bound on test power f…
CTT compresses samples to test distributions near-linearly, outperforming existing methods.
Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many s…
We examine open books with powers of fibered Dehn twists as monodromy. The resulting contact manifolds can be thought of as Boothby-Wang orbibundles over symplectic orbifolds. Using the mean Euler characteristic of equivariant symplectic homology we can distinguish these contact manifolds and hence show that some fiber…
SciSports is a Dutch startup company specializing in football analytics. This paper describes a joint research effort with SciSports, during the Study Group Mathematics with Industry 2018 at Eindhoven, the Netherlands. The main challenge that we addressed was to automatically process empirical football players' traject…
Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been pro…
GNNs with random node initialization are shown to be universally expressive.
A great deal of attention has been recently given to Machine Learning (ML) techniques in many different application fields. This paper provides a vision of what ML can do in Power Line Communications (PLC). We firstly and briefly describe classical formulations of ML, and distinguish deterministic from statistical lear…
DE improves GNNs by distinguishing graph substructures, enhancing accuracy.
To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various lengths. We find that GCNs are rather restrictive in learning graph moments. Without c…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by …
Adding random features to GNNs improves their performance.
We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD is applied to the setting of unsupervised learning by generative adversarial ne…
Study the hanging chain shape around a circle.
We consider components of Hurwitz moduli space of G-Galois covers and set up a powerful algebraic framework to study the set of corresponding equivalence classes of monodromy maps. Within that we study geometric stabilisation by various G-covers branched over the disc. Our results addresses the problem to decide equiva…
Differential privacy is a de facto standard in data privacy, with applications in the public and private sectors. A way to explain differential privacy, which is particularly appealing to statistician and social scientists is by means of its statistical hypothesis testing interpretation. Informally, one cannot effectiv…
Given any oriented link diagram, two types of new knot invariants are constructed. They satisfy some generalized skein relations. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations of those rings define new link invariants. For example, the HOMFLYPT polynomial with three va…
Machine learning predicts CO2 emissions in power grids, reducing uncertainty.
Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of distinguishing non-isomorphic graphs. However, it was recently shown that this test cannot…
A new algorithm of the analysis of correlation among economy time series is proposed. The algorithm is based on the power law classification scheme (PLCS) followed by the analysis of the network on the percolation threshold (NPT). The algorithm was applied to the analysis of correlations among GDP per capita time serie…
Unified framework for online LLM watermark detection using e-processes.