A theorem on the existence of the unique minimal topologic handle decomposition of differentiable simply connected five-dimensional manifolds is proved. For a decomposition of this sort, the number of handles of each index is given.
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48 results for “topological sort”
ARCS learns Bayesian networks by optimizing a regularized Cholesky score over permutations.
problem Learning Bayesian networks from data.
method Annealing on regularized Cholesky score (ARCS) for topological sorting.
result ARCS outperforms existing methods in learning Bayesian networks.
TopRank algorithm improves online ranking with better performance and insights.
problem Sequential decision-making in online learning to rank with user feedback.
method Generalized click model and topological sort-based algorithm.
result TopRank outperforms existing algorithms in terms of performance and proof insight.
New ML-based sorting algorithm for big data.
problem Sorting large datasets efficiently.
method Machine Learning approach to achieve complexity.
result Significantly faster sorting for big data.
Monotonic differentiable sorting networks improve upon previous methods.
problem Non-monotonicity in differentiable sorting networks.
method Relaxation of conditional swap operations using sigmoid functions to ensure monotonicity.
result Monotonic differentiable sorting networks improve upon previous methods.
Neural sorting network improves sorting accuracy for complex inputs.
problem Sorting complex inputs like multi-digit images.
method Differentiable swap function and permutation-equivariant Transformer network.
result Our method outperforms baseline methods on various sorting benchmarks.
In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets which contain no (immersed) marginally outer trapped surfaces in their interior must have simple topolo…
Differentiable sorting framework using optimal transport.
problem Piecewise constant sorting function without gradient information.
method Linking sorting to optimal transport, adding entropic regularization, and approximating with Sinkhorn iterations.
result Differentiable sorting operators (S-sorts, S-CDFs, S-quantiles) for machine learning applications.
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with corners, there seem to be poor general notions to deal with them. Moreover, we want…
This paper compares spike sorting techniques for rat brain neuronal activity.
problem Improving the accuracy of spike sorting for neuronal activity analysis.
method Three-step spike sorting process: detection, feature extraction, and clustering. Various methods are compared.
result Kernel PCA outperforms in feature extraction, leading to better spike sorting results.
NeuralSort optimizes sorting networks using continuous relaxations.
problem Non-differentiability of sorting operator hinders gradient-based optimization.
method Continuous relaxation of sorting operator to unimodal row-stochastic matrices, enabling gradient-based optimization.
result Gradient-based stochastic optimization over permutations is achieved.
SORTE optimizes systemic performance over individual rationality.
problem Systemic risk and optimal risk transfer.
method Endogenous determination of budget constraints through systemic utility maximization.
result Existence, uniqueness, and Pareto optimality of SORTE.
New algorithm speeds up spike sorting for large datasets.
problem Numerical complexity limits processing large scale neuroscience datasets.
method Windowed active set Lasso algorithm for convolutional spike sorting.
result Linear complexity ensures scalability and opens online sorting.
We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking, the optimal solution is to use an efficient sorting algorithm, such as Quicksor…
Learning from Data to Speed-up Sorted Table Search Procedures: Methodology and Practical Guidelinescs.LG
Machine learning speeds up search procedures for sorted tables.
problem Improving the speed of sorted table search procedures.
method Systematic experimental comparison of efficient implementations with learned counterparts.
result Learned data structures can significantly speed up search procedures.
Paper introduces differentiable sorting and ranking with time complexity.
problem Non-differentiability of sorting and ranking operations in machine learning.
method Differentiable proxies constructed as projections onto the permutahedron and reduction to isotonic optimization.
result First differentiable sorting and ranking operators with time and space complexity.
This paper uses Bayesian networks to analyze label correlations for improving multi-label classifier chains.
problem Improving multi-label classifier chain performance by discovering label correlations and determining the label order.
method Bayesian network (BN) to model label correlations, scoring function to evaluate BN structure, heuristic algorithm to optimize BN, topological sorting to derive label order.
result The proposed BNCC method enhances multi-label classifier chain performance through optimized label order and correlation analysis.
DSPO optimizes portfolio construction from raw stock data efficiently.
problem Manual design and misalignment in traditional portfolio construction methods.
method End-to-end neural network framework with Monotonical Logistic Regression loss.
result DSPO constructs optimal sorted portfolios with high performance metrics.
The paper sorts big data by revealed preferences, improving consumer and policy decisions.
problem Sorting diverse consumer preferences for big data objects like colleges.
method Endogenous weighting of revealed preferences, considering spillover effects.
result Consistent steady-state solution to counterbalance equilibrium.
Diffsurv extends differentiable sorting to handle censored time-to-event data.
problem Handling censored time-to-event data in survival analysis.
method Extending differentiable sorting methods to account for censored samples.
result Diffsurv outperforms established baselines in various risk prediction scenarios.
Study on efficient algorithms for sorting with noisy data.
problem Learning permutation-based ranking models from noisy comparisons.
method Established optimal rates and provided an efficient algorithm.
result Near-optimal rates achieved with independent observations.
Framework for sorting with diverse value models and valued assignment examples.
problem Sorting with diverse value models and valued assignment examples.
method Optimization model for constructing preference model from valued examples, regularization techniques, and efficient algorithm.
result Improved predictive ability and flexibility in classification performance.
We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular CW-complex, generalizing the concept of regular CW-complex, and prove that the h-regu…
Improved asset pricing using uncertainty-adjusted sorting in machine learning models.
problem Ignoring asset-specific estimation uncertainty in portfolio construction.
method Uncertainty-adjusted prediction bounds for sorting assets.
result Improves portfolio performance across various ML models and equity panels.
New estimators show consistent estimation is possible with randomized item assignment.
problem Estimating underlying comparison probabilities from noisy pairwise comparisons.
method Study permutation-based models under strong stochastic transitivity, randomized item assignment.
result Rates of estimators are optimal for a large class of graphs.
Review and compare sorting model selection methods for preference disaggregation.
problem Selecting a representative sorting model from multiple compatible models.
method Reviewed and proposed new procedures for selecting sorting models, including robust assignment rule.
result Identified most efficient procedures in terms of classification accuracy and robustness.
SoDeep learns approximations of ranking metrics for deep learning tasks.
problem Non-differentiable metrics in machine learning tasks.
method Sorting deep (SoDeep) net trained to approximate sorting of scores.
result Competitive results on Cross-modal text-image retrieval, multi-label image classification, and visual memorability ranking tasks.
There are many theorems in the differential geometry literature of the following sort. Let M be a complete Riemannian manifold with some conditions on various curvatures, diameters, volumes, etc. Then M is homotopy equivalent to a finite CW complex, or M is the interior of a compact, topological manifold with boundary.…
Mass in Kähler Geometrymath.DG
We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) Kähler manifold, assuming only the sort of weak fall-off conditions required for the mass to actually be well-defined. For ALE scalar-flat Kähler manifolds, the mass turns out to be a topological invariant, depending only on …
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
problem Incompatibility between differentiable sorting and rank normalization.
method Formalized admissibility through monotone invariance, batch independence, and rank-space stability conditions.
result Different gap-sensitive and batchwise relaxations of rank normalization violate the conditions for admissibility.
Extends SORTE to multivariate risk functions.
problem Analyzing systemic risk in financial institutions or insurance-reinsurance markets.
method Develops a new framework for multivariate utility functions and applies duality theory.
result Proves existence, uniqueness, and Nash Equilibrium property of Multivariate Systemic Optimal Risk Transfer Equilibrium.
Universal Euler characteristic defined for V-manifolds.
problem Defining a universal Euler characteristic for V-manifolds.
method Generalizing the Euler characteristic to V-manifolds and equivariant CW-complexes.
result The universal Euler characteristic is a universal additive invariant for V-manifolds and equivariant CW-complexes.
The Maxwell Demon and Market Efficiencyphysics.class-ph
This paper addresses two seemingly unrelated problems, (a) What is the entropy and energy accounting in the Maxwell Demon problem? and (b) How can the efficiency of markets be measured? Here we show, in a simple model for the Maxwell Demon, the entropy of the universe increases by an amount eta=0.839995520 in going fro…
CLASSIX is a fast and explainable clustering method that sorts data and merges groups.
problem Clustering of data with various shapes and dimensions.
method Greedy aggregation followed by cluster merging with scalar parameters.
result CLASSIX performs competitively with state-of-the-art algorithms and provides intuitive explanations.
A new method reduces memory requirements for sorting high-dimensional data.
problem Efficiently sorting and organizing high-dimensional data with low memory usage.
method Iteratively shuffles N indices and applies SoftSort optimization steps.
result Significantly improves sorting quality for multidimensional data.
A new method sorts models to find the best one with minimal risk.
problem Finding the best model with minimal risk among nested models.
method Nested Empirical Risk (NER) and Sorted NER (S-NER) methods.
result The S-NER method selects the true model order and the most parsimonious model.
FSPool improves set prediction accuracy and convergence.
problem Set prediction models struggle with simple datasets due to the responsibility problem.
method Featurewise sort pooling to construct a permutation-equivariant auto-encoder.
result FSPool improves reconstructions and representations on various datasets.
IArxiv sorts daily papers by user preference using LDA.
problem Harder for scientists to stay updated with diverse research.
method LDA on paper corpus to extract topics, user preference learning.
result Sorts papers by user preference on underlying topics.
Neural model learns efficient, general algorithms for various problems.
problem Learning efficient algorithms that generalize well.
method Carefully designed neural model with imitation and reinforcement learning.
result Neural model outperforms custom solutions on sorting and knapsack problems.
SCQRNN prevents quantile crossing and improves computational efficiency.
problem Quantile crossing issue in regression models.
method Integrates ad hoc sorting in training to prevent quantile crossing and enhance computational efficiency.
result SCQRNN achieves faster convergence and non-intersecting quantiles.
New method for sorting with interacting criteria using value functions and convex programming.
problem Learning models for sorting with interacting criteria.
method Additive piecewise-linear value function, convex quadratic programming, regularization, classification methods.
result The proposed method outperforms classical methods in sorting tasks.
SLOPE optimizes portfolios by grouping similar assets and estimating weights with sorted -Norm.
problem Optimizing financial portfolios with sparse selection.
method Sorted -Norm penalization (SLOPE) and Alternating Direction Method of Multipliers (ADMM).
result SLOPE optimizes portfolios from minimum variance to equally weighted, improving out-of-sample performance.
OrderNet learns to sort sequences from training data.
problem Sorting unordered sequences where correct order is not easily defined.
method OrderNet is a neural architecture designed to be permutation equivariant and capable of rich interactions.
result OrderNet outperforms previous techniques in generalizing to longer sequences.
Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedurestat.ME
New method estimates mixture model components efficiently.
problem Estimating the number of components in finite mixture models.
method Group-Sort-Fuse (GSF) procedure for simultaneous estimation of order and mixing measure.
result GSF achieves consistent estimation of true mixture order and convergence rate.
Refines online learning to rank algorithm with tighter bounds.
problem Online learning to rank in machine learning.
method Utilized method of mixtures and asymptotic expansions to refine inequalities.
result Improved algorithm and performance estimation.
Persistent homology improves fingerprint classification accuracy.
problem Classifying fingerprints into arch, loop, and whorl groups.
method Applying topological data analysis (TDA) to 3D point clouds of oriented minutiae points and ink-roll images, using supervised learning.
result Achieves near state-of-the-art classification accuracy rates.
The paper studies Gauss sums and their applications in algebra and topology.
problem Computing signatures of bilinear forms and Poincaré spaces.
method Investigates properties of Gauss sums and applies them to algebraic and topological problems.
result Reproves and generalizes results on signatures mod 8 of bilinear and Poincaré spaces.
NLM combines neural networks and logic programming for complex reasoning.
problem Complex reasoning tasks involving logic and properties.
method Neural-symbolic architecture combining neural networks and logic programming.
result NLM achieves perfect generalization on various tasks.