We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to rela…
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48 results for “permutation weights”
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.
Extend CPS to non-exchangeable settings with observation-specific permutation weights
problem Calibrated predictive bands under distributional shifts
method Encoding distributional shifts through observation-specific permutation weights
result Shift-aware predictive systems remain valid
New method connects neural networks to diagrammatic algebra.
problem Constructing permutation equivariant neural networks.
method Schur-Weyl duality between symmetric group and partition algebra.
result Simple diagrammatic method for calculating weight matrices.
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.
Bayesian optimization method for permutations accelerates combinatorial search.
problem Optimizing expensive-to-evaluate objectives on permutation problems.
method LAW2ORDER, a batch Bayesian optimization method based on the acquisition weighted kernel.
result LAW2ORDER achieves sublinear batch cumulative regret, demonstrating accelerated search.
Variational inference struggles with weight symmetries in neural networks, leading to biased posteriors.
problem Weight space symmetries in neural networks cause multimodal posteriors, challenging variational inference.
method Developed a symmetrization mechanism to create permutation invariant variational posteriors.
result Symmetrized variational posteriors have a better fit to the true posterior and improved predictive performance.
A new tensor ring mixture model improves density estimation efficiency.
problem Efficient probability density estimation in statistical machine learning.
method Tensor ring decomposition with mixture model for adaptive weights.
result Enhanced expressive capability and flexibility in density estimation.
The permutation symmetry of neurons in each layer of a deep neural network gives rise not only to multiple equivalent global minima of the loss function, but also to first-order saddle points located on the path between the global minima. In a network of hidden layers with neurons in layers $k = 1, \ldots, …
New bounds for SGD show improved performance in various settings.
problem Improving convergence bounds for SGD with random permutations.
method Analyzing convergence of SGD with random reshuffling and arbitrary permutations.
result Tighter lower bounds for weighted average iterates in both convex and strongly-convex cases.
Paper presents a method to summarize HMC samples for neural networks, providing meaningful uncertainty estimates.
problem Lack of interpretable summary statistics for HMC samples in neural networks due to permutation symmetry.
method Introducing a transpositions metric to quantify permutations and using rebasin method to summarize HMC samples.
result Compact representation of HMC samples provides meaningful uncertainty estimates for each weight in a neural network.
ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, …
A new method trains deep networks by separating weight locations from values.
problem Training deep networks efficiently and effectively.
method Lookahead Permutation (LaPerm) to train DNNs by reconnecting weights.
result LaPerm can train DNNs with random and dense, sparse, or single-valued initial weights.
This paper compresses neural networks by permuting and quantizing weights.
problem Efficiently compressing large neural networks for resource-constrained platforms.
method Permuting and quantizing weights, connecting to rate-distortion theory, and using annealed quantization.
result Significant compression with minimal accuracy loss, e.g., 40-70% reduction in gap with uncompressed model.
New algorithm improves PPS for multi-object matching.
problem Efficiently synchronize partial permutations for multi-object matching.
method Proposed CEMP-Partial algorithm for partial permutation synchronization (PPS). Uses sparse matrix operations and nonconvex weighted projected power method.
result Proves CEMP-Partial can exactly classify corrupted and clean partial permutations under adversarial corruption.
Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the conjugacy problem that is successful for random braids in overwhelming probabilit…
A Randomized Permutation Whole-Model Test Heuristic for Self-Validated Ensemble Models (SVEM)stat.ME
A new test validates ensemble models against the null hypothesis.
problem Validating ensemble models against the null hypothesis of a constant response.
method Randomized permutation test on SVEM model predictions.
result The test maintains Type I error rate even with more parameters than observations.
A widely applied diversification paradigm is the naive diversification choice heuristic. It stipulates that an economic agent allocates equal decision weights to given choice alternatives independent of their individual characteristics. This article provides mathematically and economically sound choice theoretic founda…
New basis for permutation equivariant layers reduces computation costs.
problem Efficiently computing permutation equivariant layers in neural networks.
method Generalized partition algebra basis with low-rank tensors.
result Low-rank tensors enable faster computation compared to orbit basis.
New neural network architectures use signed permutation representations for finite groups, improving performance.
problem Designing and optimizing neural networks for finite groups with signed permutation representations.
method Introduces -invariant deep neural networks with densely connected layers and signed permutation representations.
result Signed permutation representations lead to significantly better performance in classification tasks.
Paper defines and computes a new weight system for gl_N Lie algebra.
problem Understanding the weight system of Lie algebra gl_N.
method Two approaches: Kazarian's invariant and Harish-Chandra isomorphism.
result Computes the gl_N weight system on chord diagrams.
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.
A new DP algorithm improves privacy in hashing and sampling for search and learning.
problem Improving privacy in hashing and sampling for large-scale applications.
method Combines differential privacy with one permutation hashing and bin-wise consistent weighted sampling.
result Proposes DP-OPH and DP-BCWS algorithms that enhance privacy while maintaining utility.
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with appropriate weights. We also discuss relations between curves, Grothendieck dessins d'enfa…
New method improves transfer and robustness of supervised contrastive learning.
problem Class collapse in supervised contrastive learning leads to poor representation quality.
method Adding a weighted class-conditional InfoNCE loss and a class-conditional autoencoder.
result Improves transfer and robustness on 5 standard datasets and 3 worst-group robustness datasets.
Improved Bayesian neural network inference by selectively removing redundant modes.
problem Redundant modes in Bayesian neural network posteriors complicate approximate inference.
method Structured partial stochasticity and deterministic subset selection of weights.
result Improved performance of approximate inference schemes with simplified posterior distribution.
Graphs of neural networks are represented to preserve symmetry, improving performance across various tasks.
problem Lack of equivariance in neural network representations of other neural networks.
method Represent neural networks as computational graphs and use graph neural networks to preserve permutation symmetry.
result Single model encodes diverse neural architectures, outperforming state-of-the-art methods.
We propose a novel approach to addressing the vanishing (or exploding) gradient problem in deep neural networks. We construct a new architecture for deep neural networks where all layers (except the output layer) of the network are a combination of rotation, permutation, diagonal, and activation sublayers which are all…
We propose an algorithm to separate simultaneously speaking persons from each other, the "cocktail party problem", using a single microphone. Our approach involves a deep recurrent neural networks regression to a vector space that is descriptive of independent speakers. Such a vector space can embed empirically determi…
In this paper, we propose a listwise approach for constructing user-specific rankings in recommendation systems in a collaborative fashion. We contrast the listwise approach to previous pointwise and pairwise approaches, which are based on treating either each rating or each pairwise comparison as an independent instan…
Sharp threshold found for aligning Gaussian-weighted graphs.
problem Reconstructing planted permutations in Gaussian-weighted graphs.
method Analysis of MAP estimator and second moment method.
result Sharp information-theoretic threshold for exact recovery.
Cheap Permutation Testingmath.ST
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.
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.
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.
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoid…
Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collectio…
Unknotted cyclesmath.CO
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.
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.
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.
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.
Proposes FMS for more efficient neural network hyperparameter optimization.
problem Efficient hyperparameter optimization for deep learning models.
method Uses logged checkpoints of trained weights to guide hyperparameter selections.
result Proposes Forecasting Model Search (FMS) method.
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…
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or permuted during the protocol. In this work, we propose a framework that treats the un…
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.
The paper explores weight systems and their applications to graph and embedded graph invariants.
problem Developing weight systems for graphs and embedded graphs.
method Construction of weight systems from graph invariants and metrized Lie algebras, and extending to arbitrary embedded graphs.
result Explicit forms of generating functions and recurrence relations for weight systems on chord diagrams and embedded graphs.
We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This …
This paper improves model fusion by training-time neuron alignment, reducing barriers in multi-model fusion.
problem Diverse neuron permutations across different settings hinder model fusion performances.
method Training-time neuron alignment using fixed neuron anchors to reduce training-time permutations.
result Training-time neuron alignment improves fusion of pretrained models and federated learning performances.