InfoTuple efficiently selects larger tuple queries for ranking multiple objects, improving efficiency and consistency.
problem Efficiently selecting and ranking multiple objects for similarity learning.
method Adaptive selection method using mutual information maximization.
result InfoTuple outperforms state-of-the-art methods on synthetic and human response datasets.
In this paper we address cardinality estimation problem which is an important subproblem in query optimization. Query optimization is a part of every relational DBMS responsible for finding the best way of the execution for the given query. These ways are called plans. The execution time of different plans may differ b…
Data compression is a popular technique for improving the efficiency of data processing workloads such as SQL queries and more recently, machine learning (ML) with classical batch gradient methods. But the efficacy of such ideas for mini-batch stochastic gradient descent (MGD), arguably the workhorse algorithm of moder…
Shows uniqueness of irreducible generating tuples for Fuchsian groups.
problem Identifying irreducible generating tuples in Fuchsian groups.
method Variation of ideas from \cite{W2} to show uniqueness of almost orbifold covers with rigid generating tuples.
result Irreducible generating tuples are unique up to equivalence and are irreducible.
Rk-means clusters relational data without full matrix, speeding up clustering.
problem Clustering relational data without full matrix computation.
method Constructs a grid coreset for clustering, avoiding expensive feature extraction queries.
result Orders-of-magnitude speedup in clustering relational data.
Unified framework for N-tuples learning improves weakly supervised tasks.
problem Reducing annotation burden in supervised learning.
method Empirical risk minimization framework integrating pointwise unlabeled data.
result Framework improves generalization across various N-tuples learning tasks.
As previously known, all 3-manifolds of genus two can be represented by edge-coloured graphs uniquely defined by 6-tuples of integers satisfying simple conditions. The present paper describes an ``elementary transformation'' on these 6-tuples which changes the associated graph but does not change the represented manifo…
Study Gromov-Hausdorff convergence of metric pairs and tuples.
problem Understanding convergence in metric spaces.
method Prove equivalence of definitions, embedding, completeness, and compactness theorems.
result Relative version of Fukaya's theorem and finiteness theorem for stratified spaces.
We develop the concept of a double (more generally n-tuple) principal bundle departing from a compatibility condition for a principal action of a Lie group on a groupoid.
The paper generalizes Nielsen equivalence to 2-orbifolds.
problem Proving Nielsen equivalence for closed 2-orbifold groups.
method Proving that generating tuples of orbifold fundamental groups are represented by almost orbifold coverings.
result Generalization of Louder's Theorem to closed 2-orbifolds.
We compute the A-polynomial 2-tuple of twisted Whitehead links. As applications, we determine canonical components of twisted Whitehead links and give a formula for the volume of twisted Whitehead link cone-manifolds.
The paper analyzes orbits of integer tuples using braid diagrams.
problem Determining orbits of integer tuples under braid diagram actions.
method Monoid action of braid diagrams on integer tuples.
result Orbits of integer tuples under up-down action of braid diagrams.
A new approach to Morse theory using folded ribbon trees.
problem Applying Morse theory on symmetric products of surfaces.
method Introducing an A-infinity category with objects as κ-tuples of Morse functions, and showing conditions for the endomorphism to be a Hecke algebra.
result The endomorphism of a specific type of κ-tuple of Morse functions on T*R^2 is the Hecke algebra associated to the symmetric group.
A collection of U(∈N) data vectors is called a U-tuple, and the association strength among the vectors of a tuple is termed as the \emph{hyperlink weight}, that is assumed to be symmetric with respect to permutation of the entries in the index. We herein propose Bregman hyperlink regression (BHLR), …
DSRGAN learns independent structure and rendering without tuple supervision.
problem Learning disentangled representation for natural image generation without tuple supervision.
method Introducing an auxiliary domain with a common underlying-structure space, and designing a parallel generative network with a common Progressive Rendering Architecture.
result DSRGAN significantly outperforms state-of-the-art methods in disentanglability.
Develops slope detection for 3-manifolds with torus boundaries.
problem Determining slopes on the boundary of 3-manifolds with torus boundaries.
method Introduces order-detection and representation-detection of slopes, proving their equivalence.
result Shows how slopes' behavior changes with cabling, improving previous results.
This work extends GNNs to handle multiple graphs with non-commuting operators, proving transferability.
problem Handling multiple graphs with non-commuting operators in graph neural networks.
method Developed a mathematical theory for graph-tuple neural networks (GtNNs) with non-commuting non-expansive operators.
result Proved universal transferability of GtNNs, ensuring no non-transferable energy under convergence.
Optimal sample complexity for contrastive learning of distances.
problem Minimum labeled tuples needed for high accuracy in learning distances.
method Analyzes sample complexity in various distance settings, proving tight bounds.
result Almost optimal bound on sample complexity for learning ℓp distances. Researchers solve the realization of Jordan-Kronecker invariants in Lie algebras.
problem Identifying which Jordan-Kronecker invariants can be realized by Lie algebras.
method Analyzing the Kronecker and Jordan cases, proving impossibility for certain invariants, and describing realizability for others.
result Complete solution for Jordan and Kronecker cases, partial answers for others.
We study the local invariants that a meromorphic k-differential on a Riemann surface of genus g≥0 can have. These local invariants are the orders of zeros and poles, and the k-residues at the poles. We show that for a given pattern of orders of zeroes, there exists, up to a few exceptions, a primitive k-diff…
The paper provides an algorithm to create curves touching a smooth cubic at specific intersection points.
problem Creating curves that touch a smooth cubic at specific intersection points.
method Algorithm based on divisions and Zariski tuples to produce n-contact curves. result An algorithm to generate n-contact curves to a smooth cubic. We show that for every n≥2 there exists a torsion-free one-ended word-hyperbolic group G of rank n admitting generating n-tuples (a1,…,an) and (b1,…,bn) such that the (2n−1)-tuples $$(a_1,\ldots ,a_n, \underbrace{1,\ldots ,1}_{n-1 \text{times}})\hbox{ and }(b_1,\ldots, b_n, \underbrace{…
Let G be a group given by the presentation [<a_1,...,a_k,b_1,... b_k\,| a_i=u_i(\bar b), b_i=v_i(\bar a) \hbox{for} 1\le i\le k>,] where k≥2 and where the ui∈F(b1,...,bk) and wi∈F(a1,...,ak) are random words. Generically such a group is a small cancellation group and it is clear that $(a_1,...,…
Improved analysis for extreme multi-class CRL with better sample complexity.
problem Theoretical sample complexity of CRL in extreme multi-class settings is poorly understood.
method Improved U-Statistics estimator to capture class concentration, proving O(k) sample complexity. result Sample complexity is O(k) for extreme multi-class learning, independent of class distribution. The paper introduces Absolute Shapley Value to handle negative contributions in machine learning model training.
problem Negative marginal contributions in machine learning model training.
method Investigates three philosophies: Original Shapley Value, Zero Shapley Value, and Absolute Shapley Value.
result Absolute Shapley Value significantly outperforms other definitions in evaluating data importance.
Curves in Lagrange Grassmannians naturally appear when one studies intrinsically "the Jacobi equations for extremals", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of fin…
The study connects polygon areas and projective structures in 3D space.
problem Relating polygon areas and projective structures in 3D space.
method Investigates positive tuples of complete flags in R^3 and their associated polygons in RP^2.
result Establishes a relationship between Holmes-Thompson area and projective structures.
In this paper we present short algebraic proofs of the Linear Conway--Gordon--Sachs and the Linear van Kampen--Flores theorems in the spirit of the Radon theorem on convex hulls. {\bf Theorem.} {\it Take any n+3 general position points in Rn. If n is odd, then there are two linked (n+1)/2-simplices wi…
Let Vi be a finite dimensional Hermitian vector space of holomorphic sections of a line bundle Li on a complex n-dimensional manifold X. We associate to Vi the non-negative Hermitian quadratic form gi on X, define a Hermitian mixed volume of X for a "mixing tuple" of n non-negative Hermitian forms…
Let (G) be a connected compact non-abelian Lie-group and (T) a maximal torus of (G). A torus manifold with (G)-action is defined to be a smooth connected closed oriented manifold of dimension (2\dim T) with an almost effective action of (G) such that (M^T\neq \emptyset). We show that if there is a torus manifold (M) wi…
Δ-UQ uses anchoring to estimate uncertainty in models.
problem Estimating uncertainty in predictive models.
method Anchoring input into a tuple for uncertainty estimation.
result Δ-UQ outperforms baselines in various use-cases.
Sparse hypergraph neural networks improve reasoning in large knowledge graphs.
problem Reasoning about relationships in large, real-world domains using sparse and local inferences.
method Sparse and local hypergraph neural networks (SpaLoc) exploiting relational inferences that are usually local and sparse.
result State-of-the-art performance on real-world knowledge graph reasoning benchmarks.
Paper analyzes CRL generalization under non-i.i.d. settings, providing bounds for practical data reuse.
problem Limited theoretical understanding of CRL generalization under non-i.i.d. data conditions.
method Inspired by U-statistics, derives generalization bounds for CRL under non-i.i.d. settings.
result Required number of samples scales logarithmically with class covering number.
Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
problem Classifying 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
method Classifies vertical 3-manifolds as preimages of arcs on the plane for simplified (2,0)-trisection maps.
result Each 6-tuple of vertical 3-manifolds determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms.
Detects synchronized behavior in streaming data.
problem Tracking synchronized behavior in time-stamped tuples.
method AugSplicing algorithm for streaming dense block detection.
result Effective and robust in detecting anomalous behavior.
Extends geostatistical simulation method to handle multiple variables and large grids.
problem Scalability and handling of multiple variables in geostatistical simulation.
method Uses Sinkhorn optimal transport with sparse matcher and FFT-MA Gaussian backbone.
result MST-Direct reproduces joint distribution with zero histogram error and accurately preserves spatial correlation.
A mathematical isomorphism connects Floer homology to DAHA representations.
problem Connecting Floer homology to DAHA representations.
method Isomorphism between Floer homology and DAHA module structure.
result Establishes equivalence between DAHA polynomial representation and Floer homology module structure.
The paper explores the transitivity of orbifold diffeomorphisms.
problem Understanding the transitivity of orbifold diffeomorphisms.
method Investigates the group of compactly supported diffeomorphisms of orbifolds.
result The group of orbifold diffeomorphisms is n-transitive. Smooth manifolds have been always understood intuitively as spaces with an affine geometry on the infinitesimal scale. In Synthetic Differential Geometry this can be made precise by showing that a smooth manifold carries a natural structure of an infinitesimally affine space. This structure is comprised of two pieces o…
Study meromorphic k-differentials with prescribed singularities on Riemann surfaces.
problem Understanding local invariants of meromorphic k-differentials on Riemann surfaces.
method Analyzing orders of zeros and poles, and k-residues at poles.
result For a given pattern of zeros, there exists a primitive holomorphic k-differential with these zeros.
We consider Lie groups SU(n,1) and Sp(n,1) that act as the isometries of the complex and quaternionic hyperbolic spaces respectively. We classify pairs of semisimple elements in Sp(n,1) and SU(n,1) up to conjugacy. This gives local parametrization of the representations ρ in $Hom(F_2, …
We provide a formula for the Dubrovnik polynomial of a rational knot in terms of the entries of the tuple associated with a braid-form diagram of the knot. Our calculations can be easily carried out using a computer algebra system.
The paper introduces a test to distinguish spatial graphs based on their knot diagrams.
problem Distinguishing isotopic spatial graphs from diagrams.
method Using the writhe of knot diagrams from cycles in the graph.
result A necessary condition for distinguishing isotopic spatial graphs.
Solves TOD systems' query annotation problem without explicit annotations.
problem Training TOD systems without explicit KB query annotation.
method Reinforcement learning (RL) and pipelined approach for query prediction and system training.
result Improved RL agent with modifications for TOD tasks.
The paper tackles sequential mode estimation with oracle queries.
problem Adaptively PAC-learning a probability distribution's mode.
method Two query models: index queries and pair queries. Sequential algorithms for mode estimation.
result Lower bounds on optimal query complexity for both models.
Study exact community recovery in noisy SBM with limited queries.
problem Community recovery in noisy stochastic block models with limited queries.
method Balanced uniform querying, two-stage adaptive strategy, sublinear queries, subsampled graph.
result Adaptive querying can improve exact recovery limits in noisy SBM.
Efficiently classifies binary labels with XOR queries, even under noisy conditions.
problem Binary classification with unknown labels using XOR queries.
method Effective query type and an efficient inference algorithm for noisy conditions.
result Achieves information-theoretic limit on optimal number of queries.
Proposes a new query autocompletion method that maximizes retrieval performance.
problem Users often select suboptimal queries due to unknown best retrieval performance.
method Formulates query autocompletion as ranking item rankings, uses counterfactual learning.
result Empirical results show improved query suggestions for better retrieval performance.