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Researcher profile

David Grimsman

David Grimsman contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
eess.SYSystems and ControlMultiagent SystemsArtificial IntelligenceComputer Science and Game TheoryData Structures and AlgorithmsDistributed, Parallel, and Cluster ComputingMachine LearningNetworking and Internet ArchitectureRobotics

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Published work

5 published item(s)

preprint2026arXiv

A Generalized Singular Value Theory for Neural Networks

Building on the abstract Generalized Singular Value Decomposition (GSVD) theory of Brown et al. [2025], we prove that most modern neural architectures admit a generalized SVD representation in which they are left-invertible before a final linear layer, with no change in input-output behavior. Furthermore, the left-invertible nonlinear portion of the input-output behavior can be made to be \emph{norm preserving}, meaning that perturbations in the left-invertible ``embedding'' (the activations prior to the final linear layer in this representation) correspond proportionally to changes in the input, i.e., distance in feature space can be calibrated directly to distance in input space. We provide a data-driven algorithm for estimating this representation from trained models and propose a model architecture that naturally facilitates the decomposition. We then provide a proof-of-concept that the learned representation can be used to identify adversarial perturbations to model inputs, and develop the theory necessary for future applications to areas such as model bias and invertibility.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Trajectories for the Optimal Collection of Information

We study a scenario where an aircraft has multiple heterogeneous sensors collecting measurements to track a target vehicle of unknown location. The measurements are sampled along the flight path and our goals to optimize sensor placement to minimize estimation error. We select as a metric the Fisher Information Matrix (FIM), as "minimizing" the inverse of the FIM is required to achieve small estimation error. We propose to generate the optimal path from the Hamilton-Jacobi (HJ) partial differential equation (PDE) as it is the necessary and sufficient condition for optimality. A traditional method of lines (MOL) approach, based on a spatial grid, lends itself well to the highly non-linear and non-convex structure of the problem induced by the FIM matrix. However, the sensor placement problem results in a state space dimension that renders a naive MOL approach intractable. We present a new hybrid approach, whereby we decompose the state space into two parts: a smaller subspace that still uses a grid and takes advantage of the robustness to non-linearities and non-convexities, and the remaining state space that can by found efficiently from a system of ODEs, avoiding formation of a spatial grid.

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preprint2022arXiv

The Impact of Message Passing in Agent-Based Submodular Maximization

This paper considers a set of sensors, which as a group are tasked with taking measurements of the environment and sending a small subset of the measurements to a centralized data fusion center, where the measurements will be used to estimate the overall state of the environment. The sensors' goal is to send the most informative set of measurements so that the estimate is as accurate as possible. This problem is formulated as a submodular maximization problem, for which there exists a well-studied greedy algorithm, where each sensor sequentially chooses a set of measurements from its own local set, and communicates its decision to the future sensors in the sequence. In this work, sensors can additionally share measurements with one another, in order to augment the decision set of each sensor. We explore how this increase in communication can be exploited to improve the results of the nominal greedy algorithm. Specifically, we show that this measurement passing can improve the quality of the resulting measurement set by up to a factor of $n+1$, where $n$ is the number of sensors.

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preprint2020arXiv

Distributed Submodular Maximization with Parallel Execution

The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy algorithm which guarantees approximation at least 1/2 of the optimal solution. This greedy algorithm can be implemented with a set of agents, each making a decision sequentially based on the choices of all prior agents. In this paper, we consider a generalization of the greedy algorithm in which agents can make decisions in parallel, rather than strictly in sequence. In particular, we are interested in partitioning the agents, where a set of agents in the partition all make a decision simultaneously based on the choices of prior agents, so that the algorithm terminates in limited iterations. We provide bounds on the performance of this parallelized version of the greedy algorithm and show that dividing the agents evenly among the sets in the partition yields an optimal structure. We additionally show that this optimal structure is still near-optimal when the objective function exhibits a certain monotone property. Lastly, we show that the same performance guarantees can be achieved in the parallelized greedy algorithm even when agents can only observe the decisions of a subset of prior agents.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Stackelberg Equilibria for Two-Player Network Routing Games on Parallel Networks

We consider a two-player zero-sum network routing game in which a router wants to maximize the amount of legitimate traffic that flows from a given source node to a destination node and an attacker wants to block as much legitimate traffic as possible by flooding the network with malicious traffic. We address scenarios with asymmetric information, in which the router must reveal its policy before the attacker decides how to distribute the malicious traffic among the network links, which is naturally modeled by the notion of Stackelberg equilibria. The paper focuses on parallel networks, and includes three main contributions: we show that computing the optimal attack policy against a given routing policy is an NP-hard problem; we establish conditions under which the Stackelberg equilibria lead to no regret; and we provide a metric that can be used to quantify how uncertainty about the attacker's capabilities limits the router's performance.

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