Study convexity of geodesics and balls in Outer space.
problem Convexity properties of geodesics and balls in Outer space.
method Introduced balanced folding paths and used them to show weak convexity of out-going balls.
result Weak convexity of out-going balls in Outer space.
Quasi-geodesics in Out(F_n) are not always geodesics, with backtracking in free factors.
problem Characterizing quasi-geodesics in Out(F_n) and their properties.
method Analysis of various paths in Out(F_n) and construction of counterexamples.
result Quasi-geodesics in Out(F_n) can backtrack in free factors, unlike in mapping class groups.
The paper extends Lipschitz metric isometries between Outer Spaces of virtually free groups.
problem Extending isometry properties of Lipschitz metric to virtually free groups.
method Analyzing finite-index subgroups and their covers, identifying folding paths, and using deformation retraction.
result Existence of candidates for Lipschitz distance and deformation retraction of spine.
We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…
Existence proved for complex 3-folds equation on a specific phase range.
problem Existence of solutions for a specific equation on complex 3-folds.
method New continuity path and Monge-Ampère equation with mixed sign coefficients.
result Existence result for the deformed Hermitian Yang-Mills equation on compact complex three-folds.
We develop the geometry of folding paths in Outer space and, as an application, prove that the complex of free factors of a free group of finite rank is hyperbolic.
Paper constructs solutions to a system using Aeppli class without auxiliary gauge connection.
problem Constructing solutions to the Hull-Strominger system without auxiliary gauge connection.
method Deforming conformally balanced metric and tuning by Aeppli class to satisfy anomaly cancellation condition.
result Existence of family of solutions obtained via implicit function theorem.
Paper improves zero-shot protein stability prediction by clarifying free-energy foundations.
problem Improving zero-shot protein stability prediction using inverse folding models.
method Clarifying the free-energy foundations of inverse folding models and proposing better estimates of relative stability.
result Significant gains in zero-shot performance can be achieved with simple methods.
A new cross-validation method reduces redundancy and improves model performance.
problem Redundancy in traditional k-fold cross-validation leads to biased results.
method Irredundant k-fold cross-validation, where each instance is used exactly once for training and testing.
result Consistent performance estimates with reduced variance and lower computational cost.
Given a compact complex n-fold X satisfying the ∂∂ˉ-lemma and supposed to have a trivial canonical bundle KX and to admit a balanced (=semi-Kähler) Hermitian metric ω, we introduce the concept of deformations of X that are {\bf co-polarised} by the balanced class $[ω^{n-1}]\in H^{n-1,\,n-1…
Handel and Mosher have proved that the free splitting complex FS for the free group is Gromov hyperbolic. This is a deep and much sought-after result, since it establishes FS as a good analogue of the curve complex for surfaces. We give a shorter alternative proof of this theorem, using surgery paths in Hatcher's spher…
Kirigami-inspired math reveals shortest paths and ultimate shapes of cut paper.
problem Geodesics and isometric immersions in paper with cuts.
method Constructive proof of geodesics and rectification of polygonal geodesics.
result Polygonal geodesics can be rectified into a straight line by flat-folding.
Model predicts electron paths in chemical reactions.
problem Predicting electron movements in chemical reactions.
method Designing a model to learn electron paths from raw reaction data.
result Model achieves excellent performance on USPTO reaction dataset.
A new sampling method called Restart improves both speed and quality of generative processes.
problem Balancing speed and quality in generative processes involving differential equations.
method Alternates between adding noise and following ODE, improving both speed and quality.
result Surpasses previous SDE and ODE samplers in both speed and accuracy.
New geometric analysis of PWSPDs balances density and geometry in high-dimensional data.
problem Balancing density and geometry in high-dimensional data.
method Power-weighted shortest-path distances (PWSPDs) and their geometric and computational analyses.
result High probability guarantees on the equivalence of PWSPDs on complete and nearest neighbor graphs.
The paper explores moduli space of heterotic system using two deformation paths.
problem Exploring the moduli space of the heterotic system.
method Considering two dual deformation paths starting from a Kähler solution, one along Bott-Chern cohomology class and the other along Aeppli cohomology class. Using the implicit function theorem to prove local existence of heterotic solutions.
result Established an initial step to construct local moduli coordinates around a Kähler solution.
We give a description of the boundary of a complex of free factors that is analogous to E. Klarreich's description of the boundary of a curve complex. The argument uses the geometry of folding paths developed by Bestvina and Feighn as well as structural results about very small trees developed by Coulbois, Hilion, Lust…
Study of stability conditions on 3-folds, focusing on walls and intersections.
problem Understanding stability conditions and numerical walls on 3-folds.
method Differential geometry analysis of numerical walls, proving intersections and maximum turning points.
result Gieseker semistability equivalent to asymptotic semistability along paths in the upper half plane.
Develops balanced linear contextual bandit algorithms to reduce estimation bias.
problem Estimation bias in contextual bandits with rich heterogeneity or complex models.
method Integrates balancing methods from causal inference to reduce estimation bias.
result First regret bound analyses for linear contextual bandits with balancing.
New research confirms conjecture for balanced BTP 4-folds.
problem Constant holomorphic sectional curvature in non-Kähler geometry.
method Classification and analysis of balanced BTP manifolds.
result Conjecture holds for all balanced BTP 4-folds.
Solutions to Strominger system found for square of Kähler class.
problem Finding solutions to Strominger system with specific balanced classes.
method Deforming Calabi-Yau and Hermitian-Yang-Mills metrics.
result Classes that are squares of Kähler metrics admit solutions.
Proposes a DRL-based MLB for UDNs to balance large-scale traffic.
problem Large-scale load balancing in ultra-dense networks (UDNs).
method Two-layer architecture with DRL for intra-cluster load balancing.
result Empirical results show superior load balancing performance.
Survey of recent geometric flows in complex geometry.
problem Preserving conformally balanced property of Hermitian metrics.
method Anomaly flow, a flow of (2,2)-forms on a 3-fold. result Anomaly flow is a higher order extension of the Ricci flow.
Synthetic tabular data synthesis models balance utility and risk.
problem Generating synthetic tabular data for regulated domains.
method Latent flow models with various learning targets, paths, and sampling methods.
result Velocity and posterior matching objectives yield higher utility, while score and noise matching achieve lower risk.
New meta-learning method improves domain generalization by balancing parameters closer to domain centroids.
problem Improving domain generalization by reducing overfitting to specific domains.
method Arithmetic meta-learning with arithmetic-weighted gradients to balance parameters closer to domain centroids.
result Experimental validation of improved domain generalization performance.
Study finds almost contact structures in thermal QCD-like theories at intermediate coupling.
problem Understanding (Almost) Contact Structures in thermal QCD-like theories.
method Explicitly obtained (Almost) Contact Structures and SU(3) structures.
result Subspaces of C3S and AC3S are not mutually 'N-path connected' in the Infra-Red.
Proposes a method to balance fairness and utility in ranking models.
problem Systematic disparity across protected groups in ranking models.
method Model-agnostic post-processing framework using dynamic programming.
result Achieves a balance between fairness and utility across various metrics and datasets.
Q-learning is a simple and powerful tool in solving dynamic problems where environments are unknown. It uses a balance of exploration and exploitation to find an optimal solution to the problem. In this paper, we propose using four basic emotions: joy, sadness, fear, and anger to influence a Qlearning agent. Simulation…
This paper formalizes and compares different CV methods for estimating classifier performance.
problem Variations of cross-validation methods for estimating classifier performance are not well understood.
method Mathematical formalization and analysis of different CV methods, proving their properties and suggesting a smooth estimator.
result The repeated K-fold CV is the only smooth estimator, but it estimates both conditional and mean performance accurately. SVM used for estimating treatment effects without confounding.
problem Estimating average treatment effects in the presence of confounding variables.
method Adapts SVM classifier as a kernel-based weighting procedure to balance covariates and estimate causal effects.
result SVM provides a continuous relaxation of the quadratic integer program for balancing covariates and maximizing effective sample size.
Optimizes exploration in networks by interpolating between random and deterministic paths.
problem Balancing exploitation and exploration in network routing with constraints.
method Developed a constrained randomized shortest-paths framework using Lagrangian duality and iterative procedures.
result Optimal routing policy that interpolates between random and deterministic paths while satisfying constraints.
A Seifert surgery is an integral surgery on a knot in S^3 producing a Seifert fiber space which may contain an exceptional fiber of index 0. The Seifert Surgery Network is a 1-dimensional complex whose vertices correspond to Seifert surgeries; its edges correspond to single twistings along "seiferters" or "annular pair…
NEXT learns efficient paths in high dimensions using neural exploration-exploitation trees.
problem Learning efficient path planning in high-dimensional spaces.
method Neural Exploration-Exploitation Trees (NEXT) integrating neural architecture and UCB algorithm.
result NEXT achieves better sample efficiency and outperforms state-of-the-art methods.
CARP speeds up convex clustering by 100x and offers better visualization.
problem Computational intensity and lack of compelling visualizations in convex clustering.
method Algorithmic Regularization for iterative approximation of regularization paths.
result CARP delivers over 100-fold speed-up and finer approximation grid.
In this paper, we study the problem of author identification under double-blind review setting, which is to identify potential authors given information of an anonymized paper. Different from existing approaches that rely heavily on feature engineering, we propose to use network embedding approach to address the proble…
We consider a generalised complex Monge-Ampère equation on a compact Kähler manifold and treat it using the method of continuity. For complex surfaces, we prove an easy existence result. We also prove that (for three-folds and a related real PDE in a ball), as long as the Hessian is bounded below by a pre-determined co…
Improved transfer learning method considers target and source data balance.
problem Improving transfer learning performance with varying target and source data.
method Weighted Multisource Tradaboost builds on Multisource Tradaboost, weighting datapoint importance based on data availability.
result The proposed method outperforms the base method as target sample count increases.
Proposes a method to improve graph neural networks on heterogeneous graphs using meta-paths.
problem Improving graph neural networks on heterogeneous graphs with auxiliary tasks.
method Self-supervised auxiliary learning with meta-paths for heterogeneous graphs.
result Consistently improves link prediction and node classification on heterogeneous graphs.
PFOPS extends PFO to multi-objective optimization.
problem Current PFO algorithms only handle single-objective optimization; real problems often require multiple objectives.
method PFOPS uses path sampling to balance multiple objectives within the PFO framework.
result PFOPS successfully handles convex, concave, and discontinuous Pareto fronts in MOO experiments.
Study on positivity properties of vector bundle Monge-Ampère equation.
problem Analyzing positivity in vector bundle Monge-Ampère equation.
method Investigates MA-positivity and MA-semi-positive solutions for different ranks of holomorphic bundles over complex surfaces and manifolds.
result Positivity preservation in rank-two holomorphic bundles but not in higher ranks.
This paper introduces PSI-flatness to better understand ReLU neural networks' flatness and generalization.
problem Existing flatness definitions fail to account for ReLU neural networks' Positively Scale-Invariant (PSI) property.
method Formalizes PSI-flatness on basis path values, proving its relation to generalization.
result Minimums with balanced basis path values are flatter and generalize better.
This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this trade-off is determined by one crucial design parameter. The main contribution is a methodology to app…
The space of metrics with positive Ricci curvature on spheres has special algebraic structures.
problem Understanding the space of metrics with positive Ricci curvature on spheres.
method Using H-space and loop space structures, and operad theory.
result The space of metrics with positive Ricci curvature on spheres is homotopy equivalent to an n-fold loop space.
Subsurface projection has become indispensable in studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is sometimes called relative twisting. We give two alternate versions of relative twisting for the outer automorphism group of a free …
A new method uses string method to explore diffusion models.
problem Understanding the geometry of learned distributions in diffusion models.
method String method to compute continuous paths between samples.
result The string method identifies realistic morphing sequences and transition pathways.
This work proposes a fast ALM model approximation using signature theory.
problem High computational cost in ALM model outputs for large-scale sensitivity analyses.
method Approximation of ALM outputs using signature terms derived from economic scenarios.
result The proposed surrogate model reduces computational costs significantly while maintaining strong predictive performance.
When two free factors A and B of a free group F_n are in "general position" we define the projection of B to the splitting complex (alternatively, the complex of free factors) of A. We show that the projections satisfy properties analogous to subsurface projections introduced by Masur and Minsky. We use the subfactor p…
DiffGBM improves tree-based models for tabular regression by making their design defaults explicit and tunable.
problem Improving tree-based models for tabular regression without neural density estimators.
method Explicitly exposes and makes tunable the design defaults of tree-based models, using a Gaussian-path flow-matching trainer and a score-flex space.
result Selected configurations of DiffGBM outperform the published baseline on all eleven tabular benchmarks, with the best aggregate CRPS skill.