arXiv research

Differentially private algorithms for submodular maximization under various constraints.

A new method, VIF, calculates influence for non-decomposable losses efficiently.

Introduces robust and decomposable AP for image retrieval.

The paper explores when and why value decomposition algorithms work in cooperative multi-agent reinforcement learning.

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and hypergraphs settings, such as graph-based semi-supervised learning and PageRank. We ap…

A new method for optimizing non-decomposable metrics with constraints.

Analyzes first exit times in a modified Barndorff-Nielsen and Shephard model.

The paper develops axioms for uniquely decomposing functions with real arguments.

Study private submodular maximization in streaming data.

Recently, researchers have started decomposing deep neural network models according to their semantics or functions. Recent work has shown the effectiveness of decomposed functional blocks for defending adversarial attacks, which add small input perturbation to the input image to fool the DNN models. This work proposes…

Study on polyhedra rigidity, finding non-existence of flexible weakly convex decomposable polyhedra.

Modern applications in sensitive domains such as biometrics and medicine frequently require the use of non-decomposable loss functions such as precision@k, F-measure etc. Compared to point loss functions such as hinge-loss, these offer much more fine grained control over prediction, but at the same time present novel c…

The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.

New methods decompose manifolds into submanifolds via fold maps.

We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as mono…

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs. The problem exhibits close ties to decomposable submodular function minimization (DSFM), yet is much more challenging to sol…

Researchers classify and decompose valuations on convex functions.

Develops gradient boosting for multi-label classification.

Regular sliceness implies once-stably decomposable sliceness in symplectizations.

We present a class of algorithms capable of directly training deep neural networks with respect to large families of task-specific performance measures such as the F-measure and the Kullback-Leibler divergence that are structured and non-decomposable. This presents a departure from standard deep learning techniques tha…

Study extends Lévy models to capture market propagation delays.

New method combines value function decomposition and policy gradients for cooperative multi-agent reinforcement learning.

Study on functional ellipsoids to decompose the identity.

We study consistency of learning algorithms for a multi-class performance metric that is a non-decomposable function of the confusion matrix of a classifier and cannot be expressed as a sum of losses on individual data points; examples of such performance metrics include the macro F-measure popular in information retri…

The paper defines new types of positivity and proves properties of Schur forms for vector bundles.

In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard splitting, we show that an incompressible subsurface of the Heegaard splitting can be found, by decomposing the 3-manifold along the separating …

Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…

Researchers establish bounds and continuity of decomposed Möbius energies using cosine formula.

Study shows Khovanov homology's relation to decomposable Lagrangian cobordisms.

In this paper we explore coarse properties of cusp-decomposable manifolds first defined by Nguyên Phan. We describe the large scale geometry of the universal cover of a cusp-decomposable manifold and of quasi-isometries between two such universal covers. This description will provide us the tools to prove quasi-isometr…

Study finds conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structure without invoking any assumptions about decomposability. The majority…

The study shows how to embed cusp-decomposable manifolds quasi-isometrically.

Study on tensor nuclear norm's decomposability and subdifferential.

New manifold types defined on quotient spaces.

Study on gamma-related OU processes with simulation methods.

A Seifert surface F for a knot K is disk decomposable if there is a taut sutured manifold heirarchy for the complement of F, whose decomposing surfaces are all disks. It follows that F has minimal genus for the knot K, and has handlebody complement, i.e., F is free. We show that these necessary conditions for disk deco…

This paper tackles unbiased loss functions for multilabel classification with missing labels.

Aitchison and Rubinstein constructed two knot complements that can be decomposed into two regular ideal dodecahedra. This paper shows that these knot complements are the only knot complements that decompose into n regular ideal dodecahedra, providing a partial solution to a conjecture of Neumann and Reid.

Segmentation maps of medical images annotated by medical experts contain rich spatial information. In this paper, we propose to decompose annotation maps to learn disentangled and richer feature transforms for segmentation problems in medical images. Our new scheme consists of two main stages: decompose and integrate. …

The classes of Monge-Ampère systems, decomposable and bi-decomposable Monge-Ampère systems, including equations for improper affine spheres and hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are studied by the clear geometric setting of Lagrangian contact structures, based on the existence of …

Reinforcement learning encounters major challenges in multi-agent settings, such as scalability and non-stationarity. Recently, value function factorization learning emerges as a promising way to address these challenges in collaborative multi-agent systems. However, existing methods have been focusing on learning full…

We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z) and replacing large elementary matrices by "shortcuts," we obtain words of a particular form, and we use combinatorial tec…

The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a complete characterization of the stably decomposable torus fiber bundle of fiber-dimens…

A robust method for decomposing spectral peaks robust to distortion and interference.

We propose a new class of transforms that we call {\it Lehmer Transform} which is motivated by the {\it Lehmer mean function}. The proposed {\it Lehmer transform} decomposes a function of a sample into their constituting statistical moments. Theoretical properties of the proposed transform are presented. This transform…

We study some properties of decomposable exact Lagrangian cobordisms between Legendrian links in $\mathbb{R}^3$ with the standard contact structure. In particular, for any decomposable exact Lagrangian filling $L$ of a Legendrian link $K$, we may obtain a normal ruling of $K$ associated with $L$. We prove that the asso…

Quadratic Killing tensors on Lie groups are always decomposable.