arXiv subjects

Bryce A. Christopherson

Publications and source records attributed to Bryce A. Christopherson.

3 recordsLinked to original sources

arXiv2026

Double-Scoring: Reliable Extraction of Strong Lottery Tickets

The lottery ticket hypothesis proposes that large random neural networks contain sparse subnetworks that can match the performance of dense models after comparable training. A stronger version asserts that sufficiently overparameterized random networks contain subnetworks that are already accurate before any weight training. Existing theory establishes that such strong lottery tickets exist, but reliable extraction remains difficult. We revisit edge-popup, a frozen-weight score-training method for extracting strong tickets, and identify layerwise sparsity selection as a central bottleneck. We introduce double-scoring, an augmented score-space parameterization that replaces a layerwise sparsity search with optimization over enlarged score tensors. We prove that fixed-density masking in an augmented score space preserves access to all original-coordinate masks, and we show that the resulting method can be interpreted as edge-popup on a zero-augmented network. In controlled experiments, double-scoring substantially improves strong-ticket extraction over fixed-density edge-popup and pruning-at-initialization baselines, improves on the performance of rewound sparse-training topologies, and exhibits markedly lower sensitivity to sparsity hyperparameters. Ablations show that the gain is not merely due to additional trainable score parameters, but is tied to the augmented score-space competition that induces the effective original sparsity.

cs.LG↗

arXiv2021

Feedback Stabilization of Nonlinear Control Systems by Composition Operators

Feedback asymptotic stabilization of control systems is an important topic of control theory and applications. Broadly speaking, if the system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, then there exists a feedback control $u(x)$ ensuring the convergence to an equilibrium for any trajectory starting from a point sufficiently close to the equilibrium state. In this paper, we develop a reasonably natural and general composition operator approach to stabilizability. To begin with, we provide an extension of the classical Hautus lemma to the generalized context of composition operators and show that Brockett's theorem is still necessary for local asymptotic stabilizability in this generalized framework. Further, we employ a powerful version of the implicit function theorem--as given by Jittorntrum and Kumagai--to cover stabilization without differentiability requirements in this expanded context. Employing the obtained characterizations, we establish relationships between stabilizability in the conventional sense and in the generalized composition operator sense. This connection allows us to show that the stabilizability of a control system is equivalent to the stability of an associated system. That is, we reduce the question of stabilizability to that of stability.

math.OC↗

arXiv2019

A Variational Approach to Local Asymptotic and Exponential Stabilization of Nonlinear Systems

Local asymptotic stabilizability is a topic of great theoretical interest and practical importance. Broadly, if a system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, we are guaranteed a feedback controller $u(x)$ that forces convergence to an equilibrium for trajectories initialized sufficiently close to it. A necessary condition was given by Brockett: such controllers exist only when $f$ is open at the equilibrium. Recently, Gupta, Jafari, Kipka and Mordukhovich considered a modification to this condition, replacing Brockett's topological openness by the linear openness property of modern variational analysis. In this paper, we show that under the linear openness assumption there is a local diffeomorphism of neighborhoods of the equilibirum on which the system is exponentially stabilizable by means of continuous stationary feedback laws. Introducing a transversality property and relating it to the above diffeomorphism, we prove that linear openness and transversality on a punctured neighborhood of an equilibrium is sufficient for local exponential stabilizability of systems with a rank deficient linearization.The main result goes beyond the usual Kalman and Hautus criteria for the existence of exponential stabilizing feedback laws, since it allows us to handle systems for which exponential stabilization is achieved through higher-order terms. However, it is implemented so far under a rather restrictive row-rank conditions. This suggests a twofold approach to the use of these properties: a point-wise version is enough to ensure stability via the linearization, while a local version is enough to overcome deficiencies in the linearization.

math.DS↗