Sean Warnick

Ye Yuan, Guy-Bart Stan, Sean Warnick et al.

Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics and engineering. In some previous work, we introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not measured, in many situations it is important to estimate the minimal number of hidden states in order to understand the complexity of the network under investigation and help identify potential targets for measurements. Estimating the minimal number of hidden states is also crucial to obtain the simplest state-space model that captures the network structure and is coherent with the measured data. This paper characterizes minimal order state-space realizations that are consistent with a given dynamical structure function by exploring properties of dynamical structure functions and developing an algorithm to explicitly obtain such a minimal realization.

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.

Caleb Bradshaw, Caelen Miller, Sean Warnick

This paper introduces distribution-based prediction, a novel approach to using Large Language Models (LLMs) as predictive tools by interpreting output token probabilities as distributions representing the models' learned representation of the world. This distribution-based nature offers an alternative perspective for analyzing algorithmic fidelity, complementing the approach used in silicon sampling. We demonstrate the use of distribution-based prediction in the context of recent United States presidential election, showing that this method can be used to determine task specific bias, prompt noise, and algorithmic fidelity. This approach has significant implications for assessing the reliability and increasing transparency of LLM-based predictions across various domains.

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.

Serban Sabau, Cristian Oara, Sean Warnick et al.

We introduce a novel distributed control architecture for heterogeneous platoons of linear time--invariant autonomous vehicles. Our approach is based on a generalization of the concept of {\em leader--follower} controllers for which we provide a Youla--like parameterization while the sparsity constraints are imposed on the controller's left coprime factors, outlying a new concept of structural constraints in distributed control. The proposed scheme is amenable to optimal controller design via norm based costs, it guarantees string stability and eliminates the accordion effect from the behavior of the platoon. We also introduce a synchronization mechanism for the exact compensation of the time delays induced by the wireless broadcasting of information.