Craig Bakker

Craig Bakker, Arnab Bhattacharya, Samrat Chatterjee et al.

The identification of the Stuxnet worm in 2010 provided a highly publicized example of a cyber attack used to damage an industrial control system physically. This raised public awareness about the possibility of similar attacks against other industrial targets -- including critical infrastructure. In this paper, we use hypergames to analyze how adversarial perturbations, like those used by Stuxnet, can be used to manipulate a system that employs optimal control. Hypergames form an extension of game theory that enables us to model strategic interactions where the players may have significantly different perceptions of the game(s) they are playing. Past work with hypergames has been limited to relatively simple interactions consisting of a small set of discrete choices for each player, but here, we apply hypergames to larger systems with continuous variables. We find that manipulating constraints can be a more effective attacker strategy than directly manipulating objective function parameters. Moreover, the attacker need not change the underlying system to carry out a successful attack -- it may be sufficient to deceive the defender controlling the system. It is possible to scale our approach up to even larger systems, but the ability to do so will depend on the characteristics of the system in question, and we identify several characteristics that will make those systems amenable to hypergame analysis.

Jeremy Zucker, Kaushal Paneri, Sara Mohammad-Taheri et al. · oxford

Counterfactual inference is a useful tool for comparing outcomes of interventions on complex systems. It requires us to represent the system in form of a structural causal model, complete with a causal diagram, probabilistic assumptions on exogenous variables, and functional assignments. Specifying such models can be extremely difficult in practice. The process requires substantial domain expertise, and does not scale easily to large systems, multiple systems, or novel system modifications. At the same time, many application domains, such as molecular biology, are rich in structured causal knowledge that is qualitative in nature. This manuscript proposes a general approach for querying a causal biological knowledge graph, and converting the qualitative result into a quantitative structural causal model that can learn from data to answer the question. We demonstrate the feasibility, accuracy and versatility of this approach using two case studies in systems biology. The first demonstrates the appropriateness of the underlying assumptions and the accuracy of the results. The second demonstrates the versatility of the approach by querying a knowledge base for the molecular determinants of a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-induced cytokine storm, and performing counterfactual inference to estimate the causal effect of medical countermeasures for severely ill patients.

Craig Bakker, Steven Rosenthal, Kathleen E. Nowak

The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow of the system onto a space of observables where the dynamics are linear (and possibly infinte). This paper focuses on the development of consistent Koopman representations for controlled dynamical system. We introduce the concept of dynamical consistency for Koopman representations and analyze several existing and proposed representations deriving necessary constraints on the dynamical system, observables, and Koopman operators. Our main result is a hybrid formulation which independently and jointly observes the state and control inputs. This formulation admits a relatively large space of dynamical systems compared to earlier formulations while keeping the Koopman operator independent of the state and control inputs. More generally, this work provides an analysis framework to evaluate and rank proposed simplifications to the general Koopman representation for controlled dynamical systems.

Craig Bakker, Michael J. Henry, Nathan O. Hodas

In this paper, we show that feedforward and recurrent neural networks exhibit an outer product derivative structure but that convolutional neural networks do not. This structure makes it possible to use higher-order information without needing approximations or infeasibly large amounts of memory, and it may also provide insights into the geometry of neural network optima. The ability to easily access these derivatives also suggests a new, geometric approach to regularization. We then discuss how this structure could be used to improve training methods, increase network robustness and generalizability, and inform network compression methods.