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 sorting”
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.
We propose an sorting algorithm by Machine Learning method, which shows a huge potential sorting big data. This sorting algorithm can be applied to parallel sorting and is suitable for GPU or TPU acceleration. Furthermore, we discuss the application of this algorithm to sparse hash table.
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…
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.
Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is however piece-wise constant (the sorting permutation of a vector does not change if th…
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.
Bayesian networks are a class of popular graphical models that encode causal and conditional independence relations among variables by directed acyclic graphs (DAGs). We propose a novel structure learning method, annealing on regularized Cholesky score (ARCS), to search over topological sorts, or permutations of nodes,…
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.
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.
Pairwise comparison data arises in many domains, including tournament rankings, web search, and preference elicitation. Given noisy comparisons of a fixed subset of pairs of items, we study the problem of estimating the underlying comparison probabilities under the assumption of strong stochastic transitivity (SST). We…
Sorting input objects is an important step in many machine learning pipelines. However, the sorting operator is non-differentiable with respect to its inputs, which prohibits end-to-end gradient-based optimization. In this work, we propose NeuralSort, a general-purpose continuous relaxation of the output of the sorting…
The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here we discuss a universal additive topological invariant of V-manifolds: the univers…
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.
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.
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.
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.
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.
Several tasks in machine learning are evaluated using non-differentiable metrics such as mean average precision or Spearman correlation. However, their non-differentiability prevents from using them as objective functions in a learning framework. Surrogate and relaxation methods exist but tend to be specific to a given…
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.
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.
We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifier…
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.
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.
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.
Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed for this problem that assume a specific click model connecting rankings and user b…
The paper examines the stability of Fama-French multi-factor models over time.
problem Stability of Fama-French multi-factor models over time.
method Rolling window method, Fama and MacBeth's two-step estimation, generalized GRS statistics.
result The effectiveness of Fama-French factors is not stable over time in all countries.
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichmüller space and is quasi-isometric to the underlying mapping class group. We study this space…
In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It is based on fitting K-nearest neighbor regression to the unsupervised regressio…
A new sorting method using values improves causal discovery from noisy data.
problem Improving causal discovery from noisy observational data.
method Introducing -sortability and an algorithm, -SortnRegress, to find causal order.
result Sorting variables by increasing yields a close-to-causal order.
Traditional set prediction models can struggle with simple datasets due to an issue we call the responsibility problem. We introduce a pooling method for sets of feature vectors based on sorting features across elements of the set. This can be used to construct a permutation-equivariant auto-encoder that avoids this re…
In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for manifolds with c…