New example of manifolds with monotonic heat kernels found.
problem Understanding monotonicity of heat kernels on manifolds.
method Analyzing new examples and classifying flat tori.
result Generic metrics fail monotonicity at large times.
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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.
168,742 papers · 148 categories
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48 results for “Monotonic generation”
New models ensure monotonicity in preference learning, improving accuracy especially with limited data.
problem Failure of widely used preference learning models to maintain monotonicity.
method Proposed Linear Generalized Bradley-Terry models with Diffusion Priors.
result New models improve accuracy, especially with limited data.
Study examines explainable machine learning for monotonic models, finding Integrated gradients better for strong monotonicity.
problem Applying explainable machine learning to science-informed models.
method Proposed axioms for monotonicity, tested Shapley value and Integrated gradients methods.
result Integrated gradients provides better explanations for strong monotonicity.
Paper investigates monotonicity issues in AI preference learning.
problem AI models may violate monotonicity when learning preferences.
method Investigates root causes of non-monotonicity in comparison-based preference learning.
result Proves local pairwise monotonicity under mild assumptions.
Monotone functions and mapsmath.LO
In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all translated coordinate cones in R^n. In this paper we develop this theory further by d…
New PDE systems generalize Hawking mass monotonicity.
problem Generalizing Hawking mass monotonicity to initial data sets.
method Introduced new systems of PDE on initial data sets .
result Generalized Geroch's monotonicity formula to initial data sets.
In this paper we generalize the monotonicity formulas of [C] for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., [A], [CM1] and [GL] for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green's function on …
Study shows rigidity for entropy minimizers in non-monotone cases.
problem Rigidity of entropy minimizers in non-monotone settings.
method Elementary proofs in non-monotone situations.
result Showed rigidity for minimizers of generalized Colding-Minicozzi entropies.
COMET learns monotonic neural networks by incorporating counterexamples.
problem Enforcing monotonicity constraints in neural networks for real-world tasks.
method Counterexample-guided learning technique for ReLU neural networks.
result COMET achieves state-of-the-art results and improves model quality.
In this paper, we study monotonicity formulas of eigenvalues and entropies along the rescaled List's extended Ricci flow. We derive some monotonicity formulas of eigenvalues of Laplacian which generalize those of Li in [8] and Cao-Hou-Ling in [3]. Moreover, we also consider monotonicity formulas of -func…
Investigates polar tangential angles of curves and their monotonicity.
problem Behavior of polar tangential angles of plane curves.
method Proof of monotonicity for certain curves of monotone curvature.
result Nonexistence results for an obstacle problem involving free elasticae.
Non-affine aggregation rules cannot preserve monotonicity in convex learning.
problem Designing non-affine aggregation rules that maintain monotonicity in convex learning.
method Proving that monotonicity of aggregated gradients is preserved only if the aggregation rule is positively affine.
result Non-affine aggregation prevents steady convergence and substantially degrades algorithmic stability.
New formulas derived for scalar curvature in generalized Ricci flow.
problem Scalar curvature in generalized Ricci flow.
method Derivation of weighted scalar curvature monotonicity formulas and Perelman-type energy/entropy formulas.
result New convex Nash entropies and pseudolocality principles.
Monotonic relationship found between in-distribution and out-of-distribution performance.
problem Understanding performance of machine learning models under distribution shifts.
method Analyzing ridge-regularized models and linear inverse problems under covariate shift.
result Monotonic relationship between in-distribution and out-of-distribution performance for certain models.
Study derives new equation for reserves in non-monotone information scenarios.
problem Modeling reserves in situations where information is not always increasing.
method Infinitesimal approach to derive generalized stochastic Thiele equation.
result New equation allows for information discarding and solves open problems.
The paper addresses monotonicity in machine learning models for fairness and accountability.
problem Ensuring fairness and accountability in transparent machine learning models.
method Study of three types of monotonicity (individual, weak pairwise, strong pairwise) and propose monotonic groves of neural additive models.
result Monotonic groves of neural additive models maintain transparency, accountability, and fairness.
The paper extends intersection theory for b-divisors, proving monotonicity and volume inequalities.
problem Intersection theory for b-divisors and monotonicity of intersection products.
method Developed general intersection theory of nef b-divisors, defined restricted volume, proved monotonicity.
result Proved quantitative monotonicity of intersection product and new volume inequalities.
Study shows configuration spaces' homological dimension increases monotonically.
problem Understanding the homological properties of configuration spaces of manifolds.
method Analyzing the homological monotonicity of unordered configuration spaces of manifolds.
result Homological dimension of configuration spaces increases monotonically in each degree.
This paper introduces a novel monotone curve estimation framework based on convex duality.
problem Estimating smooth, continuous, and monotonic curves in data.
method Convex duality and optimal transport theories.
result Established statistical guarantees for monotone curve estimates.
New algorithms avoid non-monotonic risk curves in statistical learning.
problem Non-monotonic behavior of risk curves in statistical learning.
method Derive risk-monotonic algorithms under weak assumptions.
result Risk monotonicity does not necessarily lead to worse excess risk rates.
Derive monotone quantities for harmonic functions on asymptotically flat 3-manifolds with nonnegative scalar curvature.
problem Derive monotone quantities for harmonic functions on asymptotically flat 3-manifolds with nonnegative scalar curvature.
method Follow the strategy developed in Miao.
result Derive monotone quantities for harmonic functions on asymptotically flat 3-manifolds with nonnegative scalar curvature.
New formulas limit minimal submanifolds' area in curved spaces.
problem Bounding minimal submanifolds' area in curved spaces.
method Developed new monotonicity formulae involving energy-like integrals over non-geodesic sets.
result Imply sharp area bounds for minimal submanifolds through a prescribed point.
The paper tackles non-monotonic learning performance and proposes algorithms to make models more monotone.
problem Non-monotonic learning performance where more data does not always improve model quality.
method Proposes three algorithms to make supervised learning models more monotone, proving consistency and monotonicity with high probability.
result The algorithm MT-HT reduces less than 1% non-monotonic decisions on MNIST while maintaining competitive error rates.
Framework mitigates risk non-monotonicity in high-dimensional predictions.
problem Risk non-monotonicity in high-dimensional predictions.
method Model-agnostic framework using cross-validation and data-driven methodologies (zero- and one-step).
result Modified prediction procedures achieve monotonic asymptotic risk behavior.
Researchers propose a non-monotone quantum natural gradient for quantum systems.
problem Applying natural gradient methods to quantum systems without monotonicity.
method Introducing a non-monotone quantum natural gradient (QNG) and demonstrating its superiority over conventional QNG.
result Non-monotone QNG outperforms conventional QNG in terms of convergence speed.
In this paper, we study monotonicity of eigenvalues of Laplacian-type operator , where is a constant, along the Ricci-Bourguignon flow. For , We derive monotonicity of the lowest eigenvalue of Laplacian-type operator which generalizes some results of Cao \cite{Cao2007}. For , We derive m…
Semi-monotone setsmath.LO
A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of R^n such that its intersection with any translation of any coordinate cone is connected. This can be viewed as a …
Paper defines parabolic frequency for Ricci flow solutions, proving monotonicity and uniqueness.
problem Backwards uniqueness for solutions of parabolic equations on Ricci flows.
method Defines and proves monotonicity of parabolic frequency for Ricci flow solutions.
result Backwards uniqueness for solutions of parabolic equations on Ricci flows.
We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the first author for mean curvature flow and other nonlinear diffusions. Our results apply in particular to Ricci flow, where they yield a local mo…
Probit Monotone BARTstat.ML
Probit Monotone BART estimates binary outcomes using monotonic functions.
problem Estimating conditional mean functions for binary outcomes with monotonicity constraints.
method Proposes a new BART variant that incorporates monotonicity constraints for binary outcomes.
result Allows for more precise estimation of monotonic functions in binary outcome models.
In this paper, we establish a general monotonicity formula of the following elliptic system $$ Δu_i+f_i(u_1,...,u_m)=0 \quad {\rm in} Ω, \label{0.1} $$ where is a bounded domain, , and is a given smooth function of …
In general, Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. In this paper, we initiate the study of monotone orbifold Hurwitz numbers. These are simultaneously variations of the or…
Paper characterizes monotonic mean-deviation risk measures.
problem Developing consistent risk measures from mean-deviation models.
method Applying a risk-weighting function to the deviation part of a mean-deviation model.
result Characterizes monotonic mean-deviation measures as consistent risk measures.
The paper proves learning-curve monotonicity for maximum likelihood estimators in various parametric settings.
problem Establishing monotonicity guarantees for maximum likelihood estimators.
method Variants of GPT-5.2 Pro were used to derive the results.
result The paper proves monotonicity for maximum likelihood estimators in Gaussian and Gamma variables.
The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.
problem Calculating and understanding Weyl entropy in spacetime regions.
method Introducing a candidate density for Weyl entropy in perfect fluid regions and analyzing its behavior in compact spacetime regions.
result Weyl entropy is shown to be monotonic in time and maximal in vacuum static metrics.
New risk control method for non-monotonic losses in complex parameters.
problem Controlling risk for non-monotonic losses with multidimensional parameters.
method Stability-based guarantees for generic algorithms applied to non-monotonic losses.
result Guarantees depend on algorithm stability, with looser guarantees for unstable algorithms.
Monotone neural networks can approximate and interpolate functions efficiently.
problem Understanding the efficiency and expressiveness of monotone neural networks.
method Solving the monotone interpolation problem using depth-4 networks and comparing size bounds with arbitrary networks.
result Monotone neural networks can approximate and interpolate functions efficiently, but may require exponential size in high dimensions.
Euler's elastica with monotone curvature is uniquely minimal.
problem Global minimality of planar elastica with monotone curvature.
method Proof of global minimality using clamped boundary conditions and length penalization.
result Every planar elastica with non-constant monotone curvature is uniquely minimal.
Productivity and credit limits affect aggregate production in non-monotonic ways.
problem Understanding how aggregate production is influenced by individual characteristics and financial constraints.
method Analytical proof of non-monotonic effects of productivity and credit limits on aggregate production in a general equilibrium model.
result Equilibrium aggregate production can be non-monotonic in both individual productivity and credit limit.
Develops a new geometric framework for quantum metrics.
problem Quantum metric generalization for pure two-qubit states.
method Support-projected Petz monotone geometry for pure two-qubit families.
result Strictly generalizes SLD/Bures case and includes other metrics.
Study on -Green functions on specific manifolds, proving monotonicity.
problem Monotonicity of -Green functions on certain 3D manifolds.
method Sharp monotonicity formula for -Green functions along level sets.
result Established monotonicity for on specific manifolds.
Improves k-NN for monotonic data with robustness against noise.
problem Class noise in real-life data violates monotonic constraints in k-NN.
method Monotonic Fuzzy k-NN (MonFkNN) with new fuzzy membership calculation.
result Significant accuracy improvements and robustness against monotonic noise.
This work shows MLPs can approximate monotonic functions without bounded activations.
problem Optimizing MLPs with monotonic constraints and bounded activations.
method Generalized theoretical results showing MLPs with non-negative weights and saturating activations are universal approximators.
result MLPs with non-negative weights and saturating activations are universal approximators for monotonic functions.
Constructs families of monotone Lagrangians in Brieskorn-Pham hypersurfaces.
problem Constructing compact monotone Lagrangians in Brieskorn-Pham hypersurfaces.
method Inspired by monodromy considerations, techniques for controlling homology, Maslov class, and monotonicity constant.
result Infinite families of monotone Lagrangian in for .
Researchers extend monotonicity formulas for harmonic functions in RCD(0,N) spaces.
problem Generalizing monotonicity formulas for harmonic functions in spaces.
method New estimates for harmonic functions and a functional version of the outer volume cone theorem.
result Proven rigidity and almost rigidity statements for harmonic functions in spaces.
Brenier Isotonic Regressionstat.ML
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
The paper proves a transformation theorem under a monotone property of almost Euclidean factors of geodesic balls.
problem The non-increasing property of numbers of almost Euclidean factors of geodesic balls.
method Proves a transformation theorem under a non-decreasing property compared to the non-increasing property.
result Shows that for a manifold with nonnegative Ricci curvature, if its universal cover is polar at infinity and the number of almost Euclidean factors is monotone, then its fundamental group is finitely generated and virtually abelian.
Formula proves monotonicity for anisotropic minimal hypersurfaces.
problem Understanding anisotropic minimal hypersurfaces.
method Proved a monotonicity formula under a sign assumption on the Minkowski norm.
result Monotonicity formula for anisotropic minimal hypersurfaces.