A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
Faster algorithm for generalized mean densest subgraph problem.
problem Finding subgraphs with highest average p p p -th-power degree. method GENPEEL++ algorithm, which yields ( 2 ( p + 1 ) ) 1 / p (2(p+1))^{1/p} ( 2 ( p + 1 ) ) 1/ p -approximation for p ∈ [ 1 , + ∞ ) p \in [1, +\infty) p ∈ [ 1 , + ∞ ) with time complexity O ( m ( log n ) ) O(m(\log n)) O ( m ( log n )) . result GENPEEL++ algorithm provides faster and more efficient solution for generalized mean densest subgraph problem.
New method for causal discovery using peeling algorithms for various data types.
problem Challenges in causal discovery due to unmeasured confounders.
method Two peeling algorithms (bottom-up and top-down) for causal discovery with generalized structural equation models.
result Valid discovery of causal relationships and parent-child effects in diverse data types.
One-Class Boundary Peeling detects outliers efficiently and robustly.
problem Unsupervised outlier detection in diverse data distributions.
method One-Class Boundary Peeling uses flexible boundaries generated by one-class SVMs and iteratively peels them.
result One-Class Boundary Peeling outperforms state-of-the-art methods in synthetic data simulations.
Study peels tensor equations on Schwarzschild spacetime.
problem Analyzing the asymptotic behavior of tensorial wave equations on Schwarzschild spacetime.
method Combining conformal compactification and vector field techniques to estimate tensorial field energies.
result Obtains optimal initial data for peeling at all orders.
New model explains neural collapse and limits on minority classes in imbalanced datasets.
problem Understanding and predicting performance limits of deep learning models on imbalanced datasets.
method Layer-Peeled Model, a nonconvex optimization program isolating top layers and applying constraints.
result Reveals a new phenomenon called Minority Collapse that limits deep learning models on minority classes.
Study of Dirac fields on Kerr spacetimes using peeling method.
problem Understanding decay and regularity of Dirac fields on Kerr spacetimes.
method Penrose conformal compactification and geometric energy estimates.
result Optimal initial data spaces for peeling of Dirac fields on Kerr spacetimes.
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be sufficiently large (in particular, Ω ~ ( n ) \tildeΩ(\sqrt{n}) Ω ~ ( n ) where n n n is the number of nodes …
New supervised and unsupervised NFLTs for elliptical distributions.
problem Understanding unsupervised No Free Lunch Theorems for elliptical distributions.
method Proved two equally optimal strategies for elliptical distributions, inspired PRIM-based bump-hunting algorithms.
result Optimal strategies for selecting principal components based on variance or volume.
A lamination of a graph embedded on a surface is a collection of pairwise disjoint non-contractible simple closed curves drawn on the graph. In the case when the surface is a sphere with three punctures (a.k.a. a pair of pants), we first identify the lamination space of a graph embedded on that surface as a lattice pol…
In this paper we study an experimentally-observed connection between two seemingly unrelated processes, one from computational geometry and the other from differential geometry. The first one (which we call "grid peeling") is the convex-layer decomposition of subsets G ⊂ Z 2 G\subset \mathbb Z^2 G ⊂ Z 2 of the integer grid, previous…
In this paper, we show that the peeling property still holds for Bondi-Sachs metrics with nonzero cosmological constant under the boundary condition given by Sommerfeld's radiation condition together with three nontrivial Λ Λ Λ -independent functions B B B , a a a , b b b . This should indicate the new boundary condition is natura…
The paper uncovers symmetries in large language models through layer-peeled optimization.
problem Understanding geometric structure in large language model weights and context embeddings.
method Constrained layer-peeled optimization program to analyze symmetries in next-token distributions.
result Symmetries in target next-token distributions are transferred to optimal model weights and context embeddings.
New method speeds up solving L0-regularized least-squares problems.
problem Solving L0-regularized least-squares problems efficiently.
method Safe peeling for Branch-and-Bound algorithm.
result Significant gains in solving time and node exploration.
Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.
problem Analyzing the Bondi-Sachs formalism for Einstein's massless scalar field equations.
method Asymptotic expansions and peeling property for Bondi-Sachs metrics and scalar fields.
result Positivity of Bondi energy-momentum under specific conditions.
Proposes a privacy-preserving sign selection method for distributed systems.
problem Sign selection in distributed differentially private settings.
method Iterative peeling of stability function combined with exponential mechanism.
result Recovery of support and signs with optimal signal-to-noise ratio.
Starting from an arbitrary sequence of polygons whose total perimeter is 2 n 2n 2 n , we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov and Pittel (arXiv:1503.01816) have shown that, regardless of the configuration of polygons we started with, the degree sequence of the graph obtained thi…
The Sample Compression Conjecture of Littlestone & Warmuth has remained unsolved for over two decades. This paper presents a systematic geometric investigation of the compression of finite maximum concept classes. Simple arrangements of hyperplanes in Hyperbolic space, and Piecewise-Linear hyperplane arrangements, are …
Paper explains neural collapse in neural networks using a new model.
problem Understanding neural collapse in neural networks during training.
method Introducing the unconstrained layer-peeled model (ULPM) to prove gradient flow convergence to critical points of a minimum-norm separation problem.
result Proves that all critical points are strict saddle points except the global minimizers exhibiting neural collapse.
The paper develops a robust algorithm for contextual bandits with heavy-tailed rewards.
problem Contextual bandits with heavy-tailed rewards.
method Develops an algorithm based on Catoni's estimator for robust statistics, applying it to contextual bandits with general function approximation.
result Establishes regret bounds that depend on cumulative reward variance and logarithmically on the reward range and number of rounds.
A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an N N N dimensional signal with a K K K -sparse WHT, where N N N is a power of two and K = O ( N α ) K = O(N^α) K = O ( N α ) , scales sub-linearly in N N N for some 0 < α < 1 0 < α< 1 0 < α < 1 . Assuming a random support model for the non-zero transform domain…
Significant improvements in regret analysis for adaptive online learning problems.
problem Exploiting low variance in online learning problems without known variances.
method Novel peeling-based regret analysis leveraging elliptical potential `count` lemma.
result Significant improvements in regret bounds for linear bandits and linear mixture MDPs.
Paper introduces efficient top-k selection with differential privacy.
problem Efficiently selecting top-k elements with differential privacy.
method Oneshot Laplace mechanism, generalizing Report Noisy Max.
result Noise level of O(sqrt(k)/eps) for approximate differential privacy.
Paper proposes a privacy-preserving method to control false discoveries.
problem Protecting individual information in hypothesis tests while controlling false discoveries.
method Differentially private adaptive FDR control method with privacy guarantee.
result The method controls the FDR metric exactly at a user-specified level with privacy.
Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we give the first polynomial time algorithm for provably learning the parameters of…
The paper analyzes generalization in deep contrastive learning.
problem Generalization analysis for unsupervised deep contrastive representation learning.
method Parameter-counting and norm-based bounds derived for neural networks of varying sizes and depths.
result Bounds are independent of network depth and size, reducing dependency on matrix norms.
New method reduces multi-armed bandit regret to near-optimal levels.
problem Improving regret bounds for KL-regularized multi-armed bandits.
method Sharp analysis of KL-UCB with peeling argument.
result First high-probability regret bound with linear dependence on K.
Study explains how noisyGD with DP improves feature learning despite high dimensionality.
problem Improving feature learning in differential privacy settings with noisyGD.
method Layer-peeled model in representation learning, error bound analysis, feature normalization, PCA.
result Misclassification error is independent of dimension in NC, and PCA improves testing accuracy.
We consider the estimation of treatment effects in settings when multiple treatments are assigned over time and treatments can have a causal effect on future outcomes or the state of the treated unit. We propose an extension of the double/debiased machine learning framework to estimate the dynamic effects of treatments…
New method TLC improves transductive learning bounds.
problem Sharp generalization bounds for transductive learning.
method Transductive Local Complexity (TLC) framework.
result Nearly sharp bounds consistent with inductive results.
Logarithmic corrections to Price's law near black hole event horizon.
problem Failure of smooth null infinity in black hole spacetimes.
method Analyzing linear wave equation on Schwarzschild background with specific initial conditions.
result Leading-order asymptotics of solutions near future null infinity and event horizon are logarithmically modified.
Gradient descent converges to a small neighborhood of the true parameter in logistic regression with Gaussian design.
problem Estimating the parameter in logistic regression with Gaussian design.
method Gradient descent with small stepsize and large stepsize, using approximate invertibility condition and eigenvalue analysis.
result Gradient descent achieves an ℓ 2 \ell_2 ℓ 2 error of order O ( ∥ θ ∗ ∥ 2 5 d / n ) O(\sqrt{\|θ^*\|_2^5d/n}) O ( ∥ θ ∗ ∥ 2 5 d / n ) . Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
problem Limited theoretical understanding of line graph transformation's impact on GNN models.
method Examined CFI and strongly regular graphs, showing line graph transformation helps WL tests distinguish these graphs.
result Line graph transformation aids WL tests in distinguishing challenging graph properties.
Proposes MGMN for end-to-end graph similarity learning.
problem Lack of cross-level interactions in graph similarity learning.
method Multi-level graph matching network (MGMN) combining node-graph matching and siamese graph neural networks.
result MGMN outperforms state-of-the-art models on graph-graph classification and regression tasks.
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
MxPool learns graph features from diverse graphs using a hierarchical structure.
problem Learning graph features from diverse graphs with varying properties and sizes.
method MxPool uses a multiplex structure with multiple graph convolution/pooling networks in a hierarchical learning structure.
result MxPool outperforms state-of-the-art methods on graph classification benchmarks.
Study the geometry of graph product extension graphs.
problem Properties of graph products.
method Introduce and study the extension graph of graph products of groups.
result Extension graph is isomorphic to crossing graph of a quasi-median graph and exhibits asymptotic dimension similar to quasi-trees.
Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
problem Quasi-transitive graphs quasi-isometric to planar graphs need to be upgraded to Cayley graphs.
method Upgrading a planar graph to a Cayley graph.
result Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
Customized-GNN generates model-specific for each graph.
problem Graphs in the same dataset have distinct structures.
method Proposes Customized-GNN framework to generate model-specific for each graph.
result Demonstrates effectiveness on various graph classification benchmarks.
Graph embedding leaks sensitive graph properties and subgraphs.
problem Privacy risks in graph embedding sharing.
method Three inference attacks and a defense mechanism.
result High accuracy in inferring graph properties and subgraphs.
Characterizes graphs with leveled embeddings and introduces new graph invariants.
problem Understanding the properties of leveled embeddings in spatial graphs.
method Characterization of graphs with leveled embeddings, introduction of new invariants.
result Characterization of graphs with low level number and determination of specific invariants for complete graphs and complete bipartite graphs.
The paper shows conflict graphs of Petersen family graphs are mostly unbalanced.
problem Understanding the balance of conflict graphs in Petersen family graphs.
method Analyzing maximally planar subgraphs and their conflict graphs.
result All but three strong conflict graphs from Petersen Family Graphs are unbalanced.
Two new methods improve graph embedding without needing a complete graph structure.
problem Graph autoencoders' performance depends on the adjacency matrix quality.
method BAGE and VBAGE: unsupervised graph embedding via adaptive graph learning.
result The methods expand GAEs' applicability to datasets without graph structure.
We define a pseudo-inverse for line graphs using linear integer programming.
problem Not all graphs have a corresponding root graph, making the line graph operation non-invertible.
method Propose a linear integer program to edit the smallest number of edges in the line graph to recover a root graph.
result The pseudo-inverse operation is well-behaved and works in practice as shown by empirical experiments.
Develops method to create non-Abelian Ricci-flat graphs via bundles.
problem Creating non-Abelian Ricci-flat graphs.
method Develops systematic way via graph bundles with constraints.
result Non-trivial graph bundles are not isomorphic to product of base and fiber.
New method uses graph generative models for graph classification.
problem Graph classification for non-relational i.i.d. data.
method Derive classification formulas from GGM, train generative graph auto-encoder model.
result New conditional ELBO for training graph auto-encoder model.
MathNet uses wavelets for graph representation and learning.
problem Graph Neural Networks (GNNs) for graph classification and regression.
method Multiresolution Haar-like wavelets, graph convolution, and pooling.
result MathNet achieves notable accuracy gains on graph classification and regression tasks.
Unified framework for graph coarsening using node features and graph matrices.
problem Dimensionality reduction of large graphs while preserving node features.
method Optimization-based framework that unifies graph learning and dimensionality reduction.
result The learned coarsened graph is ε-similar to the original graph, where ε is a small positive number.