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.
This paper tackles selection bias in recommender systems by considering the neighborhood effect.
Learn conditional averages in PAC framework for better predictions.
Data poisoning attacks can fool neighborhood-based recommender systems.
Neighborhood sampling affects graph neural network training outcomes.
In this paper, we consider recommender systems with side information in the form of graphs. Existing collaborative filtering algorithms mainly utilize only immediate neighborhood information and have a hard time taking advantage of deeper neighborhoods beyond 1-2 hops. The main caveat of exploiting deeper graph informa…
Proposes a novel network-based neighborhood regression for biological systems.
PGRec improves recommendation by modeling user-item preferences as a graph and embedding it for better predictions.
In this paper, we develop Leray-Serre-type spectral sequences to compute the intersection homology of the regular neighborhood and deleted regular neighborhood of the bottom stratum of a stratified PL-pseudomanifold. The E^2 terms of the spectral sequences are given by the homology of the bottom stratum with a local co…
Improved RL for knowledge graph reasoning with entity types.
In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff billiard. Using this system we get new results on algebraic Birkhoff conjecture …
Survey simplifies embedding theorems for manifolds.
Caratheodory's axiom limits arbitrage in resource-limited systems.
Identifies half-space neighborhoods of pleating rays in the Riley slice of Schottky groups.
This is the first part of a trilogy where we apply the theory of virtual manifold/orbifolds developed by the first named author and Tian to study the Gromov-Witten moduli spaces. In this paper, we resolve the main analytic issue arising from the lack of differentiability of $PSL(2, \C)$-action on spaces of -m…
Many machine learning problems can be formulated as consensus optimization problems which can be solved efficiently via a cooperative multi-agent system. However, the agents in the system can be unreliable due to a variety of reasons: noise, faults and attacks. Providing erroneous updates leads the optimization process…
New method constructs Stein surfaces using topological isotopy.
Solves initial value problem for harmonic maps on specific manifolds.
We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equat…
Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believe…
We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include regular neighborhoods in PL stratified spaces.
Making an adaptive prediction based on one's input is an important ability for general artificial intelligence. In this work, we step forward in this direction and propose a semi-parametric method, Meta-Neighborhoods, where predictions are made adaptively to the neighborhood of the input. We show that Meta-Neighborhood…
We present a neighborhood similarity layer (NSL) which induces appearance invariance in a network when used in conjunction with convolutional layers. We are motivated by the observation that, even though convolutional networks have low generalization error, their generalization capability does not extend to samples whi…
Mathematical analysis of SNE and t-SNE for dimension reduction.
Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and -neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of param…
Flexible outlier detection using graph communities for robust performance.
In this paper Hamiltonian system of time dependent periodic Newton equations is studied. It is shown that for dimensions and higher the following rigidity results holds true: If all the orbits in a neighborhood of infinity are action minimizing then the potential must be constant. This gives a generalization of the…
Study geodesics entering a fixed cusp neighborhood multiple times.
Urban2Vec combines street view imagery and POIs for better urban neighborhood embeddings.
We explore the task of local music recommendation: provide listeners with personalized playlists of relevant tracks by artists who play most of their live events within a small geographic area. Most local artists tend to be obscure, long-tail artists and generally have little or no available user preference data associ…
Feed-forward networks are widely used in cross-modal applications to bridge modalities by mapping distributed vectors of one modality to the other, or to a shared space. The predicted vectors are then used to perform e.g., retrieval or labeling. Thus, the success of the whole system relies on the ability of the mapping…
Skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations (under dimension and compactness assumptions). In general, the stratified approximate fibrations cannot be replaced by bundles, and the teardrops cannot be replaced by ma…
New framework distinguishes knots via neighborhood invariants.
The paper presents a model-free method for stabilizing unknown control systems.
Maximally hyperbolic solutions contain future neighborhoods of intersecting hypersurfaces.
Many prediction problems can be phrased as inferences over local neighborhoods of graphs. The graph represents the interaction between entities, and the neighborhood of each entity contains information that allows the inferences or predictions. We present an approach for applying machine learning directly to such graph…
Proposes a new NMF method incorporating neighborhood structure for better anomaly detection.
Study on transverse knots and their neighborhoods, proving unique standard neighborhoods and destabilization results.
Revises GNN neighborhood aggregation for more accurate node classification.
The study proves a neighborhood theorem for mean curvature flow in higher dimensions.
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to th…
GraphAIR improves graph representation learning by capturing non-linear interactions.
We first show that the connected sum along submanifolds introduced by the second author for compact initial data sets of the vacuum Einstein system can be adapted to the asymptotically Euclidean and to the asymptotically hyperbolic context. Then, we prove that in any case, and generically, the gluing procedure can be l…
The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and construct a collection of implicitly defined functions and reduced equations describi…
Learning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis and data mining. Recent GNN algorithms are based on neural message passing, which enables GNNs to integrate loc…
We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where edges are created over time, which induces an order. Combining convolutional subgra…
We present a new construction of tubular neighborhoods in (possibly infinite dimensional) Riemannian manifolds M, which allows us to show that if G is an arbitrary group acting isometrically on M, then every G-invariant submanifold with locally trivial normal bundle has a G-invariant total tubular neighborhood. We appl…
A conjecture of Hirschowitz's predicts that a globally generated vector bundle on a compact complex manifold satisfies the formal principle, i.e., the formal neighborhood of its zero section determines the germ of neighborhoods in the underlying complex manifold of the vector bundle . By applying Cartan's eq…
VisitHGNN predicts visit probabilities between neighborhoods and POIs using graph neural networks.