A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper proves that the support norm of tight contact structures adds up.
The -support norm is a regularizer which has been successfully applied to sparse vector prediction problems. We show that it belongs to a general class of norms which can be formulated as a parameterized infimum over quadratics. We further extend the -support norm to matrices, and we observe that it is a special …
We study a regularizer which is defined as a parameterized infimum of quadratics, and which we call the box-norm. We show that the k-support norm, a regularizer proposed by [Argyriou et al, 2012] for sparse vector prediction problems, belongs to this family, and the box-norm can be generated as a perturbation of the fo…
The spectral -support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral -support norm, whose additional para…
Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function uses L2 norm or L1 norm on slack variables. The number of support vectors is a me…
In this note we observe that the no two of the three invariants defined for contact structures by Etnyre and Ozbagci -- that is, the support genus, binding number and support norm -- determine the third.
We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an penalty. We show that this new {\em -support norm} provides a tighter relaxation than the elastic net and is thus a good replacement for the Lasso or the elastic net in sparse prediction problems. Through …
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…
Proposes a new SVM model for binary classification with theoretical and practical advantages.
The L 1-Sobolev inequality states that the L n/(n--1)-norm of a compactly supported function on Euclidean n-space is controlled by the L 1-norm of its gradient. The generalization to differential forms (due to Lanzani & Stein and Bourgain & Brezis) is recent, and states that a the L n/(n--1)-norm of a compactly support…
New method selects variables in groups with few nonzeros, improving support recovery.
IRKSN algorithm achieves sparse recovery with wider applicability conditions.
In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter vector which represents prior knowledge on supports, and (b) regularized in Lp-n…
We describe Milnor open books and Legendrian surgery diagrams for canonical contact structures of links of some rational surface singularities. We also describe an infinite family of Milnor fillable contact 3-manifolds so that the Milnor genus (resp. Milnor norm) is strictly greater than the support genus (resp. suppor…
Proves singular support of sheaves is γ-coisotropic, with implications for symplectic homeomorphisms.
Paper introduces new risk norms based on ES with flexible distortion functions.
Single ReLU neuron's gradient dynamics reveal support vectors as key to generalization.
Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by replacing the cardinality function by its convex envelope (tightest c…
A new method classifies color images using quaternion algebra.
Carnot groups can be polarized if they have specific coordinate systems.
We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spe…
We exhibit an infinite family of tight contact structures with the property that none of the supporting open books minimizes the genus and maximizes the Euler characteristic of the page simultaneously, answering a question of Baldwin and Etnyre in arXiv:0910.5021 .
In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components…
Adversarial training linked to operator norm regularization, proving network sensitivity to attacks.
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Alg…
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discont…
In this paper, we study the evolution of one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the norm of a smooth one form with compact support is non-increasing along the Ricci flow with bounded curvature. The norm is showed to…
Improved greedy 2-coordinate updates for optimization problems with constraints.
Gradient flow on softmax attention minimizes nuclear norm of weight matrices.
Geodesics of contactomorphisms on a specific manifold are characterized by Hamiltonian functions.
The aim of this paper is to discuss some applications of the relation between Seiberg-Witten theory and two natural norms defined on the first cohomology group of a closed 3-manifold N - the Alexander and Thurston norms. We start by giving a "new" proof of McMullen's inequality between these norms, and then use these n…
Deep neural networks with adversarial training achieve sup-norm convergence for nonparametric regression.
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and scalability. Unfortunately, this 1-norm MKL is rarely observed to outperform tr…
We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected based on data. The result supports the empirical observation that minimum-norm …
The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recently, polynomial time algorithms have been proposed where statistically optimal estimates of the singular subspaces …
It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus is an unbounded group. It follows that the fragmentation norm of is unbounded.
SMM preserves matrix data structure for SVM classification.
We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity --- the Fisher-Rao norm --- that possesses desirable invariance properties and is motivated by Information Geometry. We discover an analytical characterization of…
New evidence supports the Euler class one conjecture for tight contact structures.
Neyshabur and Srebro proposed Simple-LSH, which is the state-of-the-art hashing method for maximum inner product search (MIPS) with performance guarantee. We found that the performance of Simple-LSH, in both theory and practice, suffers from long tails in the 2-norm distribution of real datasets. We propose Norm-rangin…
Given a normed plane , we call -cycloids the planar curves which are homothetic to their double -evolutes. It turns out that the radius of curvature and the support function of a -cycloid satisfy a differential equation of Sturm-Liouville type. By studying this equati…
Optimal scaling found to depend on operator norm across large models and datasets.
Study shows unusual non-monotonic risk behavior in minimum-norm interpolants for various data scaling.
We give examples illustrating the fact that the different space/time splittings of the tangent bundle of a semi-Riemannian spin manifold give rise to non-equivalent norms on the space of compactly supported sections of the spinor bundle, and as a result, to different completions. We give a necessary and sufficient cond…
Constructs a solution operator for hyperbolic gluing in higher dimensions.
SVR analyzed within RQ framework for risk management.
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a constrained optimization problem wherein the sum of the norm of the weights in each…
AdaGrad-Norm achieves optimal convergence rates for non-convex objectives without tuning.