New gaps found in metric curvature.
problem Negative curvature metrics with separated length spectra.
method Topology-based separation of length spectra.
result Exponential gaps in length spectra for negatively curved metrics.
On-device research index
arXiv research
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.
169,051 papers · 148 categories
Trend · papers per month
48 results for “gap properties”
Characterizes Anosov representations and strongly convex cocompact groups with eigenvalue gaps.
problem Understanding Anosov representations and their properties.
method Characterizations via equivariant limit maps, Cartan property, and uniform gap summation.
result Characterizations of Anosov representations and strongly convex cocompact subgroups.
Machine learning predicts band gaps for large organic crystals.
problem Predicting band gaps for complex organic crystal structures.
method Released a dataset of 12,500 crystal structures and their band gaps. Trained two state-of-the-art models to achieve a mean absolute error of 0.388 eV.
result Trained models predict band gaps with 13% error for an average gap of 3.05 eV.
We construct finite-gap solutions to the modified Novikov-Veselov equations, describe their spectral properties and the reduction to the modified Korteweg--de Vries equation and explain its relation to soliton deformations of tori and the Willmore conjecture.
Price gap, defined as the logarithmic price difference between the first two occupied price levels on the same side of a limit order book (LOB), is a key determinant of market depth, which is one of the dimensions of liquidity. However, the properties of price gaps have not been thoroughly studied due to the less avail…
The paper proves gap properties for critical metrics under specific conditions.
problem Proving gap properties for critical metrics under divergence-free Bach tensor condition.
method Analyzing critical point equation of total scalar curvature with divergence-free Bach tensor.
result Proves gap properties for and a similar condition for .
Study equilibrium measures on manifolds without conjugate points with visibility covering.
problem Uniqueness and properties of equilibrium measures on manifolds without conjugate points.
method Analysis of geodesic flows, study of equilibrium measures, ergodic properties, and pressure gap.
result Equilibrium measures satisfy a weak pressure gap under certain conditions.
New method for conformal prediction under Markovian data reduces coverage gap.
problem Reducing coverage gap in conformal prediction for Markovian data.
method Split Conformal Prediction method adapted to Markovian data, with K-split CP for improved performance.
result Coverage gap typically scales as √(t_mix * ln(n) / n) for general Markov chains, and can be reduced to t_mix / (n * ln(n)) with K-split CP.
New Dynkin condition for manifolds with boundary yields bi-Lipschitz equivalence and spectral properties.
problem Characterizing smooth Riemannian manifolds with boundary.
method Introducing a Dynkin-type condition and proving its equivalence to a weighted manifold.
result Bi-Lipschitz equivalence and various spectral properties of manifolds with boundary.
Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.
problem Gap between upper and lower bounds on sample complexity for fat-shattering dimension.
method Provided an improved uniform convergence bound.
result Closed the gap between existing upper and lower bounds on sample complexity.
simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct new complexes from existing ones and an extensive library of triangulations of …
Resolves gap problem for quaternion-Hermitian structures.
problem Determine maximal and submaximal symmetry dimensions for quaternion-Hermitian structures.
method Classifies structures with specific symmetry dimensions and studies geometric properties of submaximally symmetric spaces.
result Identifies locally conformally quaternion-Kähler and quaternion-Kähler with torsion structures.
Study spectral properties on manifolds with conical singularities, proving new inequalities.
problem Analyzing spectral properties and geometric inequalities on manifolds with conical singularities.
method Develops new inequalities for manifolds with conical singularities, not covered by existing methods.
result Proves a Bakry-Émery inequality, Hardy inequality, and spectral gap estimate.
Improved gap-dependent bounds for reinforcement learning with linear approximations.
problem Achieving nearly minimax-optimal performance with linear function approximation.
method Developed and analyzed the LSVI-UCB++ algorithm and its concurrent variant.
result First gap-dependent regret bound for nearly minimax-optimal algorithm LSVI-UCB++.
In this paper, we study the properties of the first global term in the polyhomogeneous expansions for Liouville's equation. We obtain rigidity and gap results for the boundary integral of the global coefficient. We prove that such a boundary integral is always nonpositive, and is zero if and only if the underlying doma…
CR method improves convergence for nonconvex optimization under KL property.
problem Improving convergence rate for nonconvex optimization problems.
method Cubic-regularized Newton's method exploiting Kurdyka-Lojasiewicz (KL) property.
result Asymptotic convergence rates of various optimality measures are fully characterized.
Develops correlation number for specific potentials and Hitchin representations.
problem Analyzing correlation numbers for potentials with entropy gaps and Hitchin representations.
method Defines a correlation number for pairs of cusped Hitchin representations and explores its connection to the Manhattan curve.
result Establishes a connection between the correlation number and the Manhattan curve, revealing rigidity properties.
The paper proposes a method to test properties of the optimal assortment in multinomial logit models.
problem Uncertainty quantification for the optimal assortment in multinomial logit models.
method The paper proposes a novel inferential framework to test properties of the optimal assortment in multinomial logit models, reducing the problem to detecting the sign change point of marginal revenue gaps.
result The asymptotic normality of the marginal revenue gap estimator and the construction of a maximum statistic to detect the sign change point.
Isobenefit Lines can offer a certain range of applicability in Location Theory and Gravitational Models for Urban and Geography Economics, in positional decision processes made by citizens, and, last but not least, in land value and property market theories and analysis. The value of a land, or a property, in a generic…
Study estimates gaps in semigroup products, proving embedding properties.
problem Estimating singular value gaps in semigroup products.
method Lower estimates for singular value gaps of free products of semigroups in ping-pong position.
result Groups generated by semigroups in ping-pong position are quasi-isometrically embedded.
The study examines hyperbolic 3-manifolds with uniform spectral gaps for coclosed 1-forms.
problem Understanding the spectral gap for coclosed 1-forms in hyperbolic 3-manifolds.
method Constructing sequences of manifolds and analyzing their spectral properties and homology growth.
result Sequences of hyperbolic manifolds can have uniform spectral gaps for coclosed 1-forms but unbounded torsion homology growth.
Discover gaps in q-series exponents for 3d N=2 theories.
problem Understanding statistical properties of BPS q-series for 3d N=2 theories.
method Used principal component analysis with machine learning to calculate and analyze feature saliencies.
result Gaps in q-series exponents are statistically more significant at the beginning compared to higher powers.
Study on geodesics on high genus expander surfaces, proving filling and non-simple properties.
problem Properties of geodesics on expander surfaces of high genus.
method Adapting Margulis' counting strategy to low length scales.
result Almost every geodesic of certain lengths is filling or non-simple.
Jones polynomial gaps removed for quasi-alternating links.
problem Proving Jones polynomial gaps for quasi-alternating links.
method Proving Jones polynomial properties through link twisting and conjecturing for prime quasi-alternating links.
result Jones polynomial gaps removed for certain quasi-alternating links.
Solves the Wiegold problem by showing free products of left-orderable groups have normal rank > 1.
problem Wiegold problem about groups of normal rank > 1
method Topological argument and intricate construction of left-orders
result Free products of nontrivial left-orderable groups have normal rank > 1
New study on neural network calibration, linking it to generalization gap.
problem Neural networks lack strong guarantees on calibration.
method Decomposed calibration error into train set and generalization gap.
result Models with small generalization gap are well-calibrated.
Reply to Tetlock et al. on tail risk and probability gap.
problem Expert judgment fails to account for tail risk.
method Comparison of forecasting tournaments and extreme value theory.
result Greater gap between tail expectation and probability properties.
Learn2Extend: Extending sequences by retaining their statistical properties with mixture modelscs.LG
The paper extends sequences while preserving statistical properties using a mixture model.
problem Extending sequences while retaining their statistical properties.
method Auto-regressive Sequence Extension Mixture Model (SEMM) using deep learning.
result The mixture model outperforms traditional neural networks in sequence extension with statistical property retention.
This paper connects ultrametric overlap gap properties to parametric RDT for symmetric binary perceptrons.
problem Characterizing statistical computational gaps in symmetric binary perceptrons.
method Developed an analytical union-bounding program to rigorously upper-bound constraint densities of ultrametric overlap gap properties.
result Obtained tightest bounds at the first two levels of ultrametric overlap gap properties, closely approaching parametric RDT estimates.
The paper examines properties of generalized τ-quasi Ricci-harmonic metrics and proves rigidity results.
problem Characterizing and proving rigidity of generalized τ-quasi Ricci-harmonic metrics.
method Exploring conditions for harmonic-Einstein metrics, obtaining rigidity results, and proving gap theorems.
result Rigidity results for compact generalized τ-quasi Ricci-harmonic metrics.
Uniform counting formulas for orthogeodesics in Kleinian groups converge.
problem Counting orthogeodesics in Kleinian groups converging to a limit.
method Spectral gap of the limit manifold and geodesic flow mixing property.
result Asymptotically uniform counting formulas for orthogeodesics.
The trace set of a Fuchsian group ist the set of length of closed geodesics in the surface . Luo and Sarnak showed that the trace set of a cofinite arithmetic Fuchsian group satisfies the bounded clustering property. Sarnak then conjectured that the B-C property actually characterizes arithm…
Generative model for 3D molecules respects symmetry for targeted properties.
problem Infeasibility of exhaustive exploration in chemical space.
method Symmetry-adapted 3D point set generation neural network.
result Model generates molecules with desired properties like small HOMO-LUMO gap.
New bounds close the score matching gap for diffusion models.
problem The difference between sample quality and score matching loss in diffusion models.
method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.
result The quality of score approximation impacts closing the score matching gap for low noise scales.
New empirical PAC-Bayes bound for Markov chains with finite state space.
problem Lack of empirical bounds for Markov chains with temporal dependence.
method Proved a new PAC-Bayes bound for Markov chains, providing an empirical pseudo-spectral gap.
result First fully empirical PAC-Bayes bound for Markov chains with finite state space.
We study the spectral gap of the Erdős--Rényi random graph through the connectivity threshold. In particular, we show that for any fixed if then the normalized graph Laplacian of an Erdős--Rényi graph has all of its nonzero eigenvalues tightly concentrated around . We est…
New complexity measure explains neural network generalization gap.
problem Understanding the generalization gap between neural networks and linear models.
method Introducing a new complexity measure for functions that governs PAC-Bayes bounds and relates to neural network complexity.
result Demonstrates a separation in sample complexity between 2 and 4-layer neural networks for periodic functions.
Study spectral properties of sub-Laplacians in Carnot groups.
problem Spectral properties of sub-Laplacians in Carnot groups.
method Proved pure point spectrum and spectral gap; applied to small ball problem and heat content.
result Proved existence of spectral gap and pure point spectrum.
Convex clustering can only learn convex clusters, with significant gaps between clusters.
problem Understanding the limitations and capabilities of convex clustering.
method Analyzing convex clustering solutions, proving properties, and characterizing clusters.
result Convex clustering can only learn convex clusters with significant gaps between clusters.
Study develops a new method for creating fair models.
problem Ensuring equal outcomes for different protected groups.
method Introduces a new group-fair constraint based on transport maps.
result Develops a novel algorithm FTM for training group-fair models.
On ergodic properties of geodesic flows on uniform visibility manifolds without conjugate pointsmath.DS
Study ergodic properties of geodesic flows on specific manifolds without conjugate points.
problem Ergodic properties of geodesic flows on uniform visibility manifolds without conjugate points.
method Comprehensive study including geometric properties, entropy gap assumption, and symbolic approach.
result Geodesic flow is ergodic with respect to Liouville measure under certain conditions.
The paper improves tensor completion bounds using spectral gap.
problem Theoretical limitations in tensor completion, especially for deterministic sampling.
method Bounding the generalization error of tensor completion methods using spectral gap.
result Improved bounds on tensor completion error, reducing rank dependence.
We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented.
We show that there exists a universal positive constant with the following property: Let be a positive Einstein metric on . If the Yamabe constant of the conformal class satisfies where denot…
The paper analyzes sparse PCA for incomplete data and proves support recovery conditions.
problem Support recovery in sparse PCA with non-random missing data.
method Semidefinite relaxation of the -regularized PCA problem.
result Support of the sparse leading eigenvector can be recovered with high probability.
Random feature model shows slow self-correction of generalization gap.
problem Slow deterioration of generalization error in random feature model.
method Examined the dynamic behavior of gradient descent in the model's resonance regime.
result Gradient descent exhibits a self-correction mechanism, reducing generalization gap over time.
We prove a Liouville theorem for the plurisubharmonic functions on complete Kaelher manifolds. As the applications, we prove a splitting theorem for complete Kaehler manifolds with nonnegative biscetional curvature in terms of the linear growth harmonic functions and a optomal gap theorem for such manifolds.
Free adversarial training reduces the generalization gap compared to vanilla method.
problem Improving generalization in adversarial training.
method Analysis of algorithmic stability in free adversarial training.
result Free adversarial training shows a lower generalization gap.