arXiv subjects

Rixon Crane

Publications and source records attributed to Rixon Crane.

4 recordsLinked to original sources

arXiv2026

Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy

We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg-Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.

cs.CV↗

arXiv2021

Invexifying Regularization of Non-Linear Least-Squares Problems

We consider regularization of non-convex optimization problems involving a non-linear least-squares objective. By adding an auxiliary set of variables, we introduce a novel regularization framework whose corresponding objective function is not only provably invex, but it also satisfies the highly desirable Polyak--Lojasiewicz inequality for any choice of the regularization parameter. Although our novel framework is entirely different from the classical $\ell_2$-regularization, an interesting connection is established for the special case of under-determined linear least-squares. In particular, we show that gradient descent applied to our novel regularized formulation converges to the same solution as the linear ridge-regression problem. Numerical experiments corroborate our theoretical results and demonstrate the method's performance in practical situations as compared to the typical $\ell_2$-regularization.

math.OC↗

arXiv2020

DINO: Distributed Newton-Type Optimization Method

We present a novel communication-efficient Newton-type algorithm for finite-sum optimization over a distributed computing environment. Our method, named DINO, overcomes both theoretical and practical shortcomings of similar existing methods. Under minimal assumptions, we guarantee global sub-linear convergence of DINO to a first-order stationary point for general non-convex functions and arbitrary data distribution over the network. Furthermore, for functions satisfying Polyak-Lojasiewicz (PL) inequality, we show that DINO enjoys a linear convergence rate. Our proposed algorithm is practically parameter free, in that it will converge regardless of the selected hyper-parameters, which are easy to tune. Additionally, its sub-problems are simple linear least-squares, for which efficient solvers exist. Numerical simulations demonstrate the efficiency of DINO as compared with similar alternatives.

math.OC↗

arXiv2019

DINGO: Distributed Newton-Type Method for Gradient-Norm Optimization

For optimization of a sum of functions in a distributed computing environment, we present a novel communication efficient Newton-type algorithm that enjoys a variety of advantages over similar existing methods. Similar to Newton-MR, our algorithm, DINGO, is derived by optimization of the gradient's norm as a surrogate function. DINGO does not impose any specific form on the underlying functions, and its application range extends far beyond convexity. In addition, the distribution of the data across the computing environment can be arbitrary. Further, the underlying sub-problems of DINGO are simple linear least-squares, for which a plethora of efficient algorithms exist. Lastly, DINGO involves a few hyper-parameters that are easy to tune. Moreover, we theoretically show that DINGO is not sensitive to the choice of its hyper-parameters in that a strict reduction in the gradient norm is guaranteed, regardless of the selected hyper-parameters. We demonstrate empirical evidence of the effectiveness, stability and versatility of our method compared to other relevant algorithms.

math.OC↗