David Grimsman

David Grimsman, Mohd. Shabbir Ali, João P. Hespanha et al.

The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm is implemented in a distributed way, agents sequentially make decisions based on the decisions of all previous agents. This work explores how limited access to the decisions of previous agents affects the quality of the solution of the greedy algorithm. Specifically, we provide tight upper and lower bounds on how well the algorithm performs, as a function of the information available to each agent. Intuitively, the results show that performance roughly degrades proportionally to the size of the largest group of agents which make decisions independently. Additionally, we consider the case where a system designer is given a set of agents and a global limit on the amount of information that can be accessed. Our results show that the best designs partition the agents into equally-sized sets and allow agents to access the decisions of all previous agents within the same set.

Brian Charles Brown, Robert Bridges, David Grimsman et al.

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.

Justin Tackett, Benjamin Francis, Luis Garcia et al.

Critical infrastructures are becoming increasingly complex as our society becomes increasingly dependent on them. This complexity opens the door to new possibilities for attacks and a need for new defense strategies. Our work focuses on instability attacks on the power grid, wherein an attacker causes cascading outages by introducing unstable dynamics into the system. When stress is place on the power grid, a standard mitigation approach is load-shedding: the system operator chooses a set of loads to shut off until the situation is resolved. While this technique is standard, there is no systematic approach to choosing which loads will stop an instability attack. This paper addresses this problem using a data-driven methodology for load shedding decisions. We show a proof of concept on the IEEE 14 Bus System using the Achilles Heel Technologies Power Grid Analyzer, and show through an implementation of modified Prony analysis (MPA) that MPA is a viable method for detecting instability attacks and triggering defense mechanisms.