arXiv research

New classifier combines locally linear kernels for fast and accurate non-linear classification.

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…

Non-linear Hopf manifolds can be embedded into linear ones and admit LCK metrics.

This paper achieves optimal regret bounds for locally private linear contextual bandit.

In this paper we describe the local Ricci and Bianchi identities for an h-normal N-linear connection DΓ(N) on the dual 1-jet space J^{1*}(T,M). To reach this aim, we firstly give the expressions of the local distinguished (d-) adapted components of torsion and curvature tensors produced by DΓ(N), and then we analyze th…

Study local properties of Chern-scalar curvature through linearization stability.

This paper discusses topological and locally linear actions of finite groups on $S^4$. Local linearity of the orientation preserving actions on $S^4$ forces the group to be a subgroup of $SO(5)$. On the other hand, orientation reversing topological actions of "exotic" groups $G$ (i.e. $G\not\subset O(5)$) on $S^4$ are …

Piecewise linear activations create many spurious local minima in neural networks.

The Gronwall conjecture states that a planar 3-web of foliations which admits more than one distinct linearizations is locally equivalent to an algebraic web. We propose an analogue of the Gronwall conjecture for the 3-web of foliations by Legendrian curves in a contact three manifold. The Legendrian Gronwall conjectur…

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from learning sparse (generalized) linear models to network models. Efficient implementatio…

Study Loday algebroids, prove splitting theorem, and linearize problems.

Local SGD proves efficient in overparameterized linear regression.

Paper addresses linear regression with partially mismatched data using local search with theoretical guarantees.

Extends Calabi operator to Riemannian locally symmetric spaces.

Local model for Poisson manifolds around submanifolds.

This paper analyzes a simplified strategy for nonlinear control using local linear models and iLQR updates.

For their ability to capture non-linearities in the data and to scale to large training sets, local Support Vector Machines (SVMs) have received a special attention during the past decade. In this paper, we introduce a new local SVM method, called L$^3$-SVMs, which clusters the input space, carries out dimensionality r…

Locally adaptive interpretable regression improves linear regression's predictability.

In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each set. We show that the resulting random feature map, when used in conjunction with …

The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.

Survey of Locally Linear Embedding and its variants.

Local LMO optimizes constrained problems using local linear minimization.

This paper introduces a new method for semi-supervised learning on high dimensional nonlinear manifolds, which includes a phase of unsupervised basis learning and a phase of supervised function learning. The learned bases provide a set of anchor points to form a local coordinate system, such that each data point $x$ on…

New insights into continual learning for deep models, showing convergence issues but local linear solutions.

This paper simplifies deep ReLU networks into local linear models for better interpretability.

Study proposes Local Linear Encoding for better feature discretization.

We consider deep linear networks with arbitrary convex differentiable loss. We provide a short and elementary proof of the fact that all local minima are global minima if the hidden layers are either 1) at least as wide as the input layer, or 2) at least as wide as the output layer. This result is the strongest possibl…

This paper improves Bayesian neural nets by using local linearization.

New GP model estimates piecewise continuous functions.

A new method simplifies HLLE for better robustness.

We investigate the loss surface of neural networks. We prove that even for one-hidden-layer networks with "slightest" nonlinearity, the empirical risks have spurious local minima in most cases. Our results thus indicate that in general "no spurious local minima" is a property limited to deep linear networks, and insigh…

Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary conditions for exponentiation to compact Lie groups are established. Applications…

FedSARSA converges with heterogeneous agents, achieving linear speed-up.

LLE produces unwanted results without regularization, which can be prevented with regularization.

New algorithms improve Bayesian linear regression with spike-and-slab priors.

This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamenta…

Policy gradient converges linearly with Hadamard parameterization in tabular settings.

Posterior collapse in Variational Autoencoders (VAEs) arises when the variational posterior distribution closely matches the prior for a subset of latent variables. This paper presents a simple and intuitive explanation for posterior collapse through the analysis of linear VAEs and their direct correspondence with Prob…

We show LLMs can be locally linear, enabling better control of activations.

Generative LLE modifies LLE to generate stochastic embeddings.

We modify previous quasi-local mass definition. The new definition provides expressions of the quasi-local energy, the quasi-local linear momentum and the quasi-local mass. And they are equal to the ADM expressions at spatial infinity. Moreover, the new quasi-local energy has the positivity property.

The paper develops predictors for functional data on manifolds.

We show that for any convex differentiable loss, a deep linear network has no spurious local minima as long as it is true for the two layer case. This reduction greatly simplifies the study on the existence of spurious local minima in deep linear networks. When applied to the quadratic loss, our result immediately impl…

In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node up…

NGSLL combines DNN accuracy with linear model interpretability.

Gradient descent converges linearly in finite-width networks with positive NTK and compatible conditions.

This paper develops a new method to model treatment effects that are heterogeneous across different quantiles.