Claudia K Petritsch

Navin Khoshnan, Claudia K Petritsch, Bryce-Allen Bagley

The identification of high-dimensional nonlinear dynamical systems via the Volterra series has significant potential, but has been severely hindered by the curse of dimensionality. Tensor Network (TN) methods such as the Modified Alternating Linear Scheme (MVMALS) have been a breakthrough for the field, offering a tractable approach by exploiting the low-rank structure in Volterra kernels. However, these techniques still encounter prohibitive computational and memory bottlenecks due to high-order polynomial scaling with respect to input dimension. To overcome this barrier, we introduce the Tensor Head Averaging (THA) algorithm, which significantly reduces complexity by constructing an ensemble of localized MVMALS models trained on small subsets of the input space. In this paper, we present a theoretical foundation for the THA algorithm. We establish observable, finite-sample bounds on the error between the THA ensemble and a full MVMALS model, and we derive an exact decomposition of the squared error. This decomposition is used to analyze the manner in which subset models implicitly compensate for omitted dynamics. We quantify this effect, and prove that correlation between the included and omitted dynamics creates an optimization incentive which drives THA's performance toward accuracy superior to a simple truncation of a full MVMALS model. THA thus offers a scalable and theoretically grounded approach for identifying previously intractable high-dimensional systems.

Bryce Allen Bagley, Claudia K Petritsch

The rapid advancement in neurotechnology in recent years has created an emerging critical intersection between neurotechnology and security. Implantable devices, non-invasive monitoring, and non-invasive therapies all carry with them the prospect of violating the privacy and autonomy of individuals' cognition. A growing number of scientists and physicians have made calls to address this issue, but applied efforts have been relatively limited. A major barrier hampering scientific and engineering efforts to address these security issues is the lack of a clear means of describing and analyzing relevant problems. In this paper we develop Cognitive Neurosecurity, a mathematical framework which enables such description and analysis by drawing on methods and results from multiple fields. We demonstrate certain statistical properties which have significant implications for Cognitive Neurosecurity, and then present descriptions of the algorithmic problems faced by attackers attempting to violate privacy and autonomy, and defenders attempting to obstruct such attempts.

Bryce Allen Bagley, Navin Khoshnan, Claudia K Petritsch

As Evolutionary Dynamics moves from the realm of theory into application, algorithms are needed to move beyond simple models. Yet few such methods exist in the literature. Ecological and physiological factors are known to be central to evolution in realistic contexts, but accounting for them generally renders problems intractable to existing methods. We introduce a formulation of evolutionary games which accounts for ecology and physiology by modeling both as computations and use this to analyze the problem of directed evolution via methods from Reinforcement Learning. This combination enables us to develop first-of-their-kind results on the algorithmic problem of learning to control an evolving population of cells. We prove a complexity bound on eco-evolutionary control in situations with limited prior knowledge of cellular physiology or ecology, give the first results on the most general version of the mathematical problem of directed evolution, and establish a new link between AI and biology.