Novel algorithm estimates local permutations in unlabeled multi-view sensing.
problem Estimating local permutations in unlabeled multi-view sensing.
method Graph alignment and Gromov-Wasserstein alignment exploiting multiple views.
result The proposed algorithm is scalable and applicable to challenging SNR regimes.
Minimal triangulations of circle bundles linked to circular permutations.
problem Which circle bundles can be triangulated over a given base triangulation?
method Minimal triangulations encoded by local systems of circular permutations of vertices.
result Classical Huntington transitivity axiom for cyclic orders expressed as a binary Chern cocycle.
We tackle permutation in linear regression with a new inference framework.
problem Statistical investigation of permutation in linear regression models.
method Localization step followed by conditional Monte Carlo test and coefficient inference.
result Valid statistical inference procedures for permutation and regression coefficients.
The paper encodes local shapes of polynomial curves using permutations.
problem Measuring non-convexity of real algebraic plane curves.
method Generic projections avoiding specific tangencies.
result Local shapes of curves can be encoded in alternating permutations.
The paper introduces a new method to improve model generalization by routing model copies through permutations.
problem Improving model generalization in machine learning.
method The method replicates a model \(M\) times and rewire the contexts in which local learning messages are computed using permutations.
result The method improves generalization by structured message sharing rather than coupling parameters.
Proposes neuron alignment to optimize mode connectivity in neural networks.
problem Understanding and optimizing mode connectivity in deep neural networks.
method Introduces neuron alignment to approximate optimal weight permutations and improve mode connectivity.
result Neuron alignment significantly alleviates robust loss barriers and improves model robustness and accuracy.
A new test for conditional independence adapts to nonlinear dependencies efficiently.
problem Testing conditional independence in nonlinear and high-dimensional data.
method Nearest-neighbor estimator of conditional mutual information combined with local permutation scheme.
result The test reliably simulates null distribution and is better calibrated for non-smooth densities.
New research limits what GNNs can compute and generalizes their performance.
problem Limits of GNNs in computing graph properties and generalization bounds.
method Novel graph-theoretic formalism and data-dependent generalization bounds.
result Proves GNNs can't compute certain graph properties and provides tighter generalization bounds.
Theoretical guarantees for permutation-equivariant QNNs avoid barren plateaus.
problem Excessive local minima and barren plateaus in QNNs training landscapes.
method Designing Sn-equivariant QNNs to encode permutation symmetry. result Equivariant QNNs do not suffer from barren plateaus, quickly reach overparametrization, and generalize well.
PiNet learns graph representations invariant to node permutations.
problem Graph classification and representation learning invariant to node permutations.
method Differentiable node attention pooling, permutation invariant graph neural network.
result Significant accuracy improvement in isomorphic graph classification with limited training data.
New graph foundation models respect symmetries for broader applicability.
problem Tailored graph machine learning architectures limit broader applicability.
method Investigates symmetries for label and feature permutations, proving network universal approximator.
result Universal approximator on multisets respecting node and feature permutations.
Deep networks exhibit permutation saddles and valleys between equivalent minima.
problem Understanding the structure of loss landscapes in deep neural networks.
method Geometric approach to constructing paths between equivalent minima and saddle points.
result Existence of permutation saddles and valleys in deep neural networks.
New Poisson bracket connects to logarithmic manifolds.
problem Constructing a new Poisson bracket compatible with existing structures.
method Developed a new local Poisson bracket compatible with Adler-Gelfand-Dickey brackets, leading to a dispersionless limit.
result Leading term defines a logarithmic Dubrovin-Frobenius manifold.
Signed-permutation coordinate transport improves model alignment across checkpoints.
problem Improper alignment of coordinate-indexed objects across model checkpoints.
method Introduces sign-marginalized Hungarian matching and coordinate-preserving transport.
result Recovering signed-permutation gauge improves coordinate alignment and model performance.
Enhances graph neural networks with structural message-passing for better generalization.
problem Limited representation power and inability to learn basic graph topological properties.
method Proposes a framework that includes a one-hot encoding of nodes and parametrized message and update functions ensuring permutation equivariance.
result Achieves state-of-the-art results on molecular graph regression on the ZINC dataset.
New model preserves symmetry in multivariate time series, improving performance.
problem Implicit ordering in MTS models violates inherent exchangeability.
method Permutation-equivariant 2D state space model with canonical architecture.
result Eliminates sequential dependency chains and simplifies stability analysis.
HKConv learns hyperbolic features by aggregating kernel points.
problem Challenges in learning good hyperbolic representations using Euclidean operations.
method Proposes HKConv, a trainable hyperbolic convolution that correlates local features with kernel points and aggregates them.
result HKConv learns expressive local features according to hyperbolic geometry and enjoys equivariance to permutation and invariance to parallel transport.
A new kernel test avoids permutations for independence testing.
problem Intractable null distributions of kernel statistics.
method Developed xHSIC and xdCov, avoiding permutations.
result New tests have limiting Gaussian distributions under null.
This work tackles Bayesian neural networks by addressing loss landscape symmetries.
problem Understanding and optimizing the loss landscape of Bayesian neural networks.
method The approach involves extending marginalized loss barrier formalism to BNNs, proposing a matching algorithm to search for linearly connected solutions using permutation matrices and combinatorial optimization.
result Nearly zero marginalized loss barriers for linearly connected solutions were found.
New method uses exponential family priors to handle shuffled data problems.
problem Handling mismatch errors in record linkage of two data files.
method Flexible exponential family prior on the permutation group for regularization.
result The proposed method outperforms competing methods in synthetic and real data.
Study groups acting on trees with specific local actions, proving cohomology vanishing or infinite.
problem Understanding bounded cohomology of groups with prescribed local actions.
method Proving vanishing or infinite bounded cohomology based on the 2-transitivity of F′. result Vanishing or infinite bounded cohomology depending on F′'s 2-transitivity. Model learns set representations through optimized permutations.
problem Challenges in learning set representations due to permutation-invariance.
method Proposes a Permutation-Optimisation module to learn set permutations.
result Achieves state-of-the-art results on various set learning tasks.
Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynam- ics simulation. Best performance is achieved when the known physical constraints are encoded in the mac…
Reverse-weighted portfolios outperform in commodity futures markets.
problem Efficiency of commodity futures markets.
method Permutation-weighted portfolios, rank-based methods.
result Reverse-weighted portfolio outperforms price-weighted portfolio.
The study examines how permutation-based optimization performance varies across different function representations.
problem Understanding how the order of function evaluations affects optimization performance.
method Iterative search setting with sampling without replacement, algebraic function recombination, correlation analysis, hierarchical clustering, PCA, ANOVA.
result Algebraically modified benchmarks yield stable re-rankings and coherent clusters of functions and sampling policies, indicating non-additive search effort.
C-OPH improves One Permutation Hashing by using a shorter circulant permutation.
problem Improving the accuracy of One Permutation Hashing (OPH) for Jaccard similarity estimation.
method Develops a new densification method using a shorter circulant permutation.
result Achieves the smallest estimation variance for Jaccard similarity.
Cheap permutation tests speed up distribution testing without sacrificing accuracy.
problem Efficiently testing distribution differences and independence.
method Group datapoints into bins and permute only these bins, using stored sufficient statistics.
result Cheap permutation tests maintain the accuracy and optimality of standard tests but are significantly faster.
Random permutations can offer faster convergence than with-replacement sampling for some functions.
problem Understanding when and how random permutations outperform with-replacement sampling in SGD convergence.
method Analyzing convergence rates for different function classes (1D strongly convex, general strongly convex, quadratic strongly convex).
result The optimal convergence gap between random and permutation-based SGD varies from exponential to nonexistent, depending on the function class.
TIME explains temporal models by analyzing feature importance.
problem Existing methods struggle with temporal models and feature importance.
method Model-agnostic permutation-based approach, temporal feature importance, hypothesis testing.
result TIME provides statistical rigor for explaining temporal models.
Permutations linked to knots and links, with unknots counted by Schröder numbers.
problem Understanding permutations as knots and links.
method Using grid diagrams and Bennequin's inequality.
result Permutations corresponding to unknots and links are counted by Schröder numbers.
NERS improves RL by sampling diverse transitions considering local and global contexts.
problem Sampling biases in experience replay lead to redundant transitions.
method Neural Experience Replay Sampler (NERS) that considers both local and global contexts.
result NERS significantly improves RL performance by sampling diverse and meaningful transitions.
Regularizes RNNs to be invariant to input order.
problem Making RNNs invariant to input order.
method Stochastic regularization to enforce permutation invariance.
result Improves model performance on permutation invariant tasks.
Permutability of surface transforms yields discrete analogs.
problem Discretization of smooth surfaces with specific properties.
method Permutability of transforms of smooth surfaces.
result Discrete surfaces with discrete analogs of original properties.
Janossy pooling averages permutation-sensitive functions over all sequences to create invariant functions.
problem Creating deep, invariant functions for variable-size inputs.
method Janossy pooling: average permutation-sensitive functions over all reorderings.
result Improved performance over state-of-the-art methods.
AutoShuffleNet learns permutation matrices in CNNs for improved accuracy.
problem Manual design of channel shuffling in ShuffleNet.
method Learning permutation matrices via an exact Lipschitz continuous penalty in deep learning.
result Improved classification accuracies on CIFAR-10 and ImageNet datasets.
Dynamic systems linked to infinite permutation matrices.
problem Dynamic equivalence of control systems.
method Association of infinite permutation matrices.
result Relationship between dynamic equivalences and permutation matrices.
A new permutation method improves two-sample testing power.
problem Two-sample testing with improved power and validity.
method Structured block-restricted cross-swaps.
result Block-restricted permutations achieve higher power than full permutations.
Recently, the method of b-bit minwise hashing has been applied to large-scale linear learning and sublinear time near-neighbor search. The major drawback of minwise hashing is the expensive preprocessing cost, as the method requires applying (e.g.,) k=200 to 500 permutations on the data. The testing time can also be ex…
New link topology connects permutation discrepancies to Diaconis-Graham inequalities.
problem Characterize permutations for which Diaconis-Graham inequalities hold with equality.
method Relate permutation discrepancies to the Euler characteristic of their associated links.
result Permutation discrepancies are directly related to the Euler characteristic of their associated links.
Study links and quivers, proving polynomial equality conjecture.
problem Link and quiver invariants and their relations.
method Cluster algebra invariants, point count polynomials, skein relations.
result Equality conjecture between plabic graph link polynomial and quiver point count polynomial proved for specific cases.
The paper uses permutation representations to visualize group extensions and subgroups.
problem Visualizing and understanding group extensions and subgroups.
method Developing metaphoric rope-thread diagrams to represent semi-direct products and their constituents.
result Injective homomorphisms into semi-direct products are established.
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.
A new test statistic speeds up MMD while maintaining power.
problem Efficiently testing two distributions without permutations.
method Cross-MMD statistic based on sample-splitting and studentization.
result Cross-MMD has a limiting standard Gaussian distribution under the null.
A theorem connects knot permutations with specific moves.
problem Understanding isotopy classes of knots through permutations.
method Defines and studies petal diagrams and two types of moves.
result Any isotopic knots can be transformed into each other via defined moves.
We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Ga…
New kernels for permutations improve accuracy in ranking tasks.
problem Improving ranking accuracy in permutation-based tasks.
method Introduced weighted Kendall kernel, supervised learning for weights, and higher-order permutation kernels.
result Supervised learning of weights enhances kernel performance for permutation tasks.
Paper addresses regression with permuted data, proposing robust methods.
problem Regression with permuted data, where response and predictor variables are mismatched.
method Proposes robust regression methods to handle inconsistent least squares estimators.
result Robust regression methods can recover permutation and estimate regression parameters.
SPG learns policies on permutation matrices using Sinkhorn layers.
problem Optimizing permutations for tasks like sorting, ranking, and matching.
method Introduces Sinkhorn Policy Gradient (SPG) algorithm with a temperature-controlled Sinkhorn layer.
result SPG agents perform competitively and are more data-efficient than baseline methods on matching tasks.