LCNs use Lovasz embeddings to capture global graph properties.
problem Semi-supervised learning on graph data.
method LCNs use Lovasz embeddings to incorporate global graph properties.
result LCNs outperform GCNs on various graph models and real-world datasets.
Novel convex surrogate for submodular losses with tractable computation.
problem Learning with non-modular losses for set prediction.
method Proposed Lovász hinge loss function for submodular losses.
result First tractable convex surrogates for submodular losses.
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes 2012) in several ways. We show that they represent a distortion between a "score" and an "ordering", thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show ho…
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes, 2012) in several ways. We show that they represent a distortion between a 'score' and an 'ordering', thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show h…
CNN improves salt body interpretation in seismic imaging.
problem Manual salt body interpretation is time-consuming and prone to bias.
method U-Net and ResNet with ELU activation and Lovász-Softmax loss.
result CNN predictions match manual interpretations well, especially in weak reflection areas.
We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lovasz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of…
Paper develops privacy-preserving algorithms for online submodular optimization.
problem Online submodular optimization under differential privacy constraints.
method Develops algorithms for both full information and bandit feedback settings, using Lovasz extensions and unbiased estimates.
result Achieves low expected regret with differential privacy guarantees in both settings.
We prove Csorba's conjecture that the Lovász complex Hom(C_5,K_n) of graph multimorphisms from the 5-cycle C_5 to the complete graph K_n is Z/2Z-equivariantly homeomorphic to the Stiefel manifold, V(n-1,2), the space of (ordered) orthonormal 2-frames in R^{n-1}. The equivariant piecewise-linear topology that we need is…
Characterizes 3D embeddability of certain 2D complexes via excluded minors.
problem Characterizing embeddability of specific 2D complexes in 3-space.
method Using Kuratowski-type characterisation via excluded minors.
result Answers Lovász, Pardon, and Wagner's questions about embeddability.
The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability, graph structured anomaly detection serves as a case study in the difficulty of bal…
The paper introduces a method to decorrelate circular coordinates using lattice reduction.
problem Geometric correlation between circle-valued maps when multiple cohomology classes are used.
method Systematic procedure using the Lenstra--Lenstra--Lovász algorithm for constructing low energy torus-valued maps.
result A method to obtain less correlated maps from cohomology classes using integer linear combinations.
We extend several Cheeger-type isoperimetric bounds for convex sets in Euclidean space, due to Bobkov and Kannan-Lovász-Simonovits, to Riemannian manifolds having non-negative Ricci curvature. In order to extend Bobkov's bound, we require in addition an upper bound on the sectional curvature of the space, which permits…
New simplicial complexes show unavoidable link of spheres in high dimensions.
problem Finding unavoidable links of spheres in high-dimensional spaces.
method Simple argument in piecewise linear topology and application of the van Kampen--Flores theorem.
result Existence of additional simplicial complexes with unavoidable links of spheres.
The study characterizes embeddable 2-complexes in 3-space.
problem Characterizing embeddable 2-dimensional simplicial complexes in 3-space.
method Characterization through excluded minors and extensions.
result Characterized embeddable 2-complexes in 3-space, including cones over K5 and K3,3, and related constructions. A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is natural to formulate structured sparsity inducing priors using submodular functions,…
Paper proposes a new method to minimize submodular functions with fewer calls to simpler oracles.
problem Minimizing the sum of submodular set functions with limited information.
method Introduces a modified convex problem requiring constrained total variation oracles that can be solved with fewer calls to minimization oracles.
result Shows significant reduction in the number of calls to minimization oracles.
Algorithm learns CNF formulas from random solutions under specific conditions.
problem Learning a CNF formula from uniform random solutions.
method Revisits Valiant's algorithm and applies Lovász local lemma conditions.
result Significantly reduces sample complexity for learning CNFs.
Topology helps estimate chromatic numbers of random graphs on spheres.
problem Estimating chromatic numbers of random graphs on spheres.
method Topology, specifically connectivity of Lóvasz's neighborhood complex.
result Connectivity bound is useful in dimensions 1 and 2, but generally poor.
Deep learning improves salt deposits segmentation in seismic data.
problem Segmenting salt deposits in seismic reflection data for hydrocarbon exploration.
method A novel deep learning approach combining U-Net with ResNeXt-50 encoder, Spatial-Channel Squeeze & Excitation, Lovasz loss, CoordConv, and Hypercolumn methods.
result Achieved 27th place in Kaggle competition for salt deposits segmentation.
We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their \lova extensions. We show that the Lovasz extension may be seen as the convex envelope of a function that depends …
Universal tester-learner for halfspaces over structured distributions.
problem Learning halfspaces over a wide class of structured distributions.
method Uses a fully polynomial tester-learner based on hypercontractivity and sum-of-squares (SOS) programs.
result Achieves error O(opt)+ε on any labeled distribution that the tester accepts. The paper derives upper hedging prices for multivariate contingent claims using game-theoretic probability and submodularity.
problem Deriving upper hedging prices for complex financial contracts.
method Game-theoretic approach, optimization over simplexes, Lovász extension, Black-Scholes-Barenblatt equations.
result Upper and lower hedging prices can be calculated efficiently for submodular or supermodular payoff functions.
Efficiently poisons offline RLHF models by flipping preference labels.
problem Vulnerability of offline RLHF models to preference label flipping attacks.
method Developed two attack methods: BAL-A and BMP-A, solving a structured binary sparse approximation problem.
result Demonstrated that flipping one preference label induces a parameter-independent shift in the DPO gradient, enabling structured binary sparse approximation.
New technique connects graph matching complexes to Morse theory for better topology understanding.
problem Understanding the topology of matching complexes of complete graphs.
method Developed discrete Morse theory technique to analyze Mn. result Showed Mn is geometrically (νn−1)-connected, improving on previous homotopical results. Unified solution to Goodman-Pollack transversal problem using matroids and topology.
problem Existence of an affine k-dimensional transversal to convex sets.
method Matroidal joins and topological methods.
result Unified solution including colorful Helly theorem and Holmsen's theorem.
Faster algorithm for sampling logconcave densities in high dimensions.
problem Cubic barrier in sampling logconcave densities from a cold start.
method Two key ingredients: weaker distance sampling and refined log-Sobolev inequality.
result First sub-cubic sampling algorithms for isotropic position.
A graph (digraph) G=(V,E) with a set T⊆V of terminals is called inner Eulerian if each nonterminal node v has even degree (resp. the numbers of edges entering and leaving v are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint T-paths in an inner Eulerian graph $G…
A guide simplifies convolutional neural network properties.
problem Understanding and manipulating convolutional neural network architectures.
method Clarifying relationships between properties of convolutional, pooling, and transposed convolutional layers.
result Intuitive relationships between various convolutional and transposed convolutional layers.
DeepCAM learns convolutional dictionaries for image processing.
problem Processing high-dimensional signals like images efficiently.
method Introduces a Deep Convolutional Analysis Dictionary Model (DeepCAM) using convolutional dictionaries.
result DeepCAM achieves performance comparable to other methods on single image super-resolution.
Improved generative models using flexible convolutions.
problem Generating high-quality images efficiently.
method Generalized 1 x 1 convolutions to d x d convolutions, chaining autoregressive and periodic convolutions.
result Flexible d x d convolutions significantly improve generative flow models' performance.
Proposes a new interpretation of separable convolutions.
problem Lack of a thorough explanation for the efficacy of separable convolutions.
method Hybrid interpretation combining depthwise and pointwise convolutions.
result Proposes a new model for understanding separable convolutions.
Introduces Finslerian convolution metrics and their properties.
problem No specific problem stated; focuses on new metric concept.
method Definition and study of Finslerian convolution metrics.
result Characterization of Finslerian convolution metrics of Riemannian, Minkowskian, and Randers types.
DSGC unifies graph and grid convolutions.
problem Lack of understanding between graph and grid convolutions.
method Depthwise separable graph convolution.
result DSGC outperforms existing methods on benchmark datasets.
LNMC improves link prediction on social networks by considering log-normal degree distributions.
problem Link prediction in social networks with log-normal degree distributions.
method Log-Normal Matrix Completion (LNMC) using Alternating Direction Method of Multipliers.
result Up to 5% AUC increase over non-structured sparsity based methods.
TAGCN improves graph CNN performance without approximation.
problem Performance loss in spectral graph convolutional neural networks.
method Topology adaptive graph convolutional network (TAGCN) with adaptive filters.
result TAGCN outperforms existing spectral CNNs on various datasets.
New PTC convolution preserves properties of Euclidean convolutions on manifolds.
problem Lack of generalizable convolutions on curved domains with desirable properties.
method Parallel transport convolution (PTC) on Riemannian manifolds.
result PTC preserves compactly supported filters and directionality.
VC dimensions of group CNNs are infinite for certain kernels and groups.
problem Estimating the generalization capacity of group convolutional neural networks.
method Identifying precise VC dimension estimates for simple sets of group CNNs.
result Two-parameter families of convolutional neural networks have an infinite VC dimension for infinite groups and certain kernels.
ConvNets can be translated into CKNs that perform similarly.
problem The distinction between ConvNets and kernel-based methods.
method Translation of ConvNets into CKNs using a new gradient algorithm.
result CKNs perform as well as ConvNets, supporting the translation.
G-CNNs reduce sample complexity by exploiting symmetries.
problem Reducing sample complexity in neural networks.
method Group equivariant convolutions that exploit symmetries.
result Achieve state-of-the-art results on CIFAR10 and rotated MNIST.
Spectral Convolution Networks speed up computation by applying convolution and activation in the frequency domain.
problem Performance increase in convolution networks comes with repeated transform computations.
method Implement convolution and activation in the frequency domain using Fourier or Laplace transformations.
result Reduced number of transforms and overall complexity by computing both convolution and activation in the frequency domain.
Enhances group convolutional networks with attention to learn meaningful relationships.
problem Lack of explicit means to learn meaningful relationships among symmetry patterns.
method Introduces attentive group equivariant convolutions, applying attention during convolution.
result Consistently outperforms conventional group convolutional networks on benchmark datasets.
New algorithm recovers high-dimensional linear regression vectors without sparsity assumptions.
problem Efficiently recovering unknown vector β* from noisy linear observations in high dimensions.
method Proposes a polynomial-time algorithm based on LLL lattice basis reduction assuming rational entries with the same denominator.
result Algorithm successfully recovers β* for a large class of distributions and non-zero noise, even with small noise and one observation.
Deep convolutional nets are essential for accurate learning on CIFAR-10.
problem Training shallow models to mimic deep convolutional nets on CIFAR-10.
method Used distillation to train shallow feed-forward nets on CIFAR-10, demonstrating the necessity of multiple convolutional layers.
result Accurate models on CIFAR-10 require multiple convolutional layers, even when trained with distillation.
Proves DCNNs with expansive convolution are strongly universally consistent.
problem Theoretical consistency of deep convolutional neural networks (DCNNs).
method Empirical risk minimization on DCNNs with expansive convolution (with zero-padding).
result DCNNs with expansive convolution are strongly universally consistent.
New framework for manifold convolutions using toric embeddings.
problem Computational intractability of manifold convolutions.
method Isometric embeddings into tori for global manifold convolutions.
result Global definition of manifold convolutions on finite approximations.
Paper improves graph convolutional networks by adjusting filter size.
problem Improving predictive performance of graph convolutional networks.
method Introducing a hyper-parameter to influence filter size in graph convolutions.
result Improves predictive performance of Deep Graph Convolutional Networks.
Functor connects Lie groupoid algebras to bornological structures.
problem Establishing a functorial relationship between Lie groupoid convolution algebras and bornological structures.
method Developed a monoidal functor from differentiable stacks to Morita 2-category of complete bornological algebras.
result Convolution algebras are self-induced and convolution modules are smooth.
IEA improves CNN models by averaging multiple convolutional layers.
problem Improving CNN model accuracy through ensemble learning.
method Replacing single convolutional layers with Inner Average Ensembles (IEA) of multiple convolutional layers.
result CNN models using IEA outperform those with regular convolutional layers.