arXiv research

Future robots should follow human social norms in order to be useful and accepted in human society. In this paper, we leverage already existing social knowledge in human societies by capturing it in our framework through the notion of social norms. We show how norms can be used to guide a reinforcement learning agent t…

SAM improves generalization in overparameterized models, but its behavior in tensorized models is less understood.

Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…

Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods where feature selection is effected via mixed-norms. Several mixed-norm based spar…

General $(α, β)$ norms are an important class of Minkowski norms which contains the original $(α, β)$ norms. In this note, by studying the behavior of the Darboux curves of the indicatrix, we give a characterization of 3-dimensional general $(α, β)$ norms. By studying the isoperimetric properties of the indicatrix, as …

We study the deformation of the three-dimensional conformal structures by the Ricci flow. We drive the evolution equation of Cotton-York tensor and the L1-norm of it under the Ricci flow. In particular, we investigate the behavior of the L1-norm of the Cotton-York tensor under the Ricci flow on three-dimensional simply…

New method stabilizes FQE by reweighting Bellman targets.

RL agent learns to avoid market spoofing.

We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method …

The paper studies the minimum ℓ₁-norm interpolator's risk behavior in over-parameterized settings.

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, ca…

The paper examines torsions in Minkowskian product of Finsler metrics.

Adversarial attacks aim to confound machine learning systems, while remaining virtually imperceptible to humans. Attacks on image classification systems are typically gauged in terms of $p$-norm distortions in the pixel feature space. We perform a behavioral study, demonstrating that the pixel $p$-norm for any $0\le p …

In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose $y = Az + η$ where $A$ satisfies the restricted isometry property (RIP) with a sufficiently small constant, and $\Vert η\Vert_2 \leq ε$. Then minimizing $\Vert z \Vert_1$ subject to $\Vert y - Az \Ver…

New study shows how model complexity affects test risk, challenging classical theory.

We prove a spanning result for vector-valued Poincaré series on a bounded symmetric domain. We associate a sequence of holomorphic automorphic forms to a submanifold of the domain. When the domain is the unit ball in ${\Bbb{C}}^n$, we provide estimates for the norms of these automorphic forms and we find asymptotics of…

We discuss structured Schatten norms for tensor decomposition that includes two recently proposed norms ("overlapped" and "latent") for convex-optimization-based tensor decomposition, and connect tensor decomposition with wider literature on structured sparsity. Based on the properties of the structured Schatten norms,…

It is shown that the Hilbert geometry $(D,h_D)$ associated to a bounded convex domain $D\subset \mathbb{E}^n$ is isometric to a normed vector space $(V,||\cdot ||)$ if and only if $D$ is an open $n$-simplex. One further result on the asymptotic geometry of Hilbert's metric is obtained with corollaries for the behavior …

This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with Kähler metrics $ω_ε$ when $ε\to 0$. Here $ω_ε$ are flat and have areas $ε$ and $ε^{-1}$ on the two elliptic curves …

The existence of adversarial examples has led to considerable uncertainty regarding the trust one can justifiably put in predictions produced by automated systems. This uncertainty has, in turn, lead to considerable research effort in understanding adversarial robustness. In this work, we take first steps towards separ…

Religious adherence reduces corporate greenwashing behavior.

Paper develops a framework for learning interpretable representations of sequential decision behavior.

Study investigates overparametrization in survival models, revealing complex loss behavior.

Improved online PCA algorithm learns from evolving norm of parameter vector.

We show precompactness results for solutions to parabolic fourth order geometric evolution equations. As part of the proof we obtain smoothing estimates for these flows in the presence of a curvature bound, an improvement on prior results which also require a Sobolev constant bound. As consequences of these results we …

New method certifies neural network function space norms from point evaluations.

In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows.

Anisotropic curvature flow of networks shows unique solutions and behavior under finite time.

Two approaches detect EV charging patterns at stations.

New method improves stability of soft FQI for offline RL.

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional predictor variable. To control the complexity of the model, we employ a functional fo…

Batching stabilizes risk in high-dimensional linear regression models.

We model how Lipschitz continuity changes during neural network training.

We analyze computational limits of modern Hopfield models based on pattern norms.

We investigate the low-energy behavior of the gradient flow of the $L^2$ norm of the Riemannian curvature on four-manifolds. Specifically, we show long time existence and exponential convergence to a metric of constant sectional curvature when the initial metric has positive Yamabe constant and small initial energy.

The paper studies heat behavior on curved spaces without radiality assumption.

Let M be an oriented irreducible 3-manifold with infinite fundamental group and empty or toroidal boundary. Consider any element φin the first cohomology of M with integral coefficients. Then one can define the φ-twisted L^2-torsion function of the universal covering which is a function from the set of positive real nu…

Growth of spinors in 4D and 3D generalized Seiberg-Witten equations.

Deep linear networks can closely approximate interpolants without improving risk.

Advances robust principal component analysis with transformed ℓ1 regularization.

This work studies the implicit bias of mini-batch SGD in classification.

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this paper, we first bring together various probabilistic inequalities for sums of in…

Paper addresses LSTM stability for thermal systems using infinity-norm.

Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.

Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.

We establish a relation between the "large r" asymptotics of the Turaev-Viro invariants $TV_r$ and the Gromov norm of 3-manifolds. We show that for any orientable, compact 3-manifold $M$, with (possibly empty) toroidal boundary, $\log |TV_r (M)|$ is bounded above by a function linear in $r$ and whose slope is a positiv…

The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a non-trivial proximit…

The Hitchin-Simpson equations are first-order non-linear equations for a pair consisting of a connection and a Higgs field. In this paper, we study the behavior of sequences of solutions to the Hitchin-Simpson equations on closed Kähler manifolds with unbounded $L^2$ norms of the Higgs fields. We prove a compactness re…