PID Control of Biochemical Reaction Networks

Principles of feedback control have been shown to naturally arise in biological systems and successfully applied to build synthetic circuits. In this work we consider Biochemical Reaction Networks (CRNs) as a paradigm for modelling biochemical systems and provide the first implementation of a derivative component in CRNs. That is, given an input signal represented by the concentration level of some species, we build a CRN that produces as output the concentration of two species whose difference is the derivative of the input signal. By relying on this component, we present a CRN implementation of a feedback control loop with Proportional-Integral-Derivative (PID) controller and apply the resulting control architecture to regulate the protein expression in a microRNA regulated gene expression model.Comment: 8 Pages, 4 figures, Submitted to CDC 201

Identifying the Best Haploidentical Donor: Are We There?

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Promises of Deep Kernel Learning for Control Synthesis

Deep Kernel Learning (DKL) combines the representational power of neural networks with the uncertainty quantification of Gaussian Processes. Hence, it is potentially a promising tool to learn and control complex dynamical systems. In this work, we develop a scalable abstraction-based framework that enables the use of DKL for control synthesis of stochastic dynamical systems against complex specifications. Specifically, we consider temporal logic specifications and create an end-to-end framework that uses DKL to learn an unknown system from data and formally abstracts the DKL model into an Interval Markov Decision Process (IMDP) to perform control synthesis with correctness guarantees. Furthermore, we identify a deep architecture that enables accurate learning and efficient abstraction computation. The effectiveness of our approach is illustrated on various benchmarks, including a 5-D nonlinear stochastic system, showing how control synthesis with DKL can substantially outperform state-of-the-art competitive methods.Comment: 9 pages, 4 figures, 3 table

Formal Abstraction of General Stochastic Systems via Noise Partitioning

Verifying the performance of safety-critical, stochastic systems with complex noise distributions is difficult. We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with non-standard (e.g., non-affine, non-symmetric, non-unimodal) noise distributions for verification purposes. The method uses a finite partitioning of the noise domain to construct an interval Markov chain (IMC) abstraction of the system via transition probability intervals. Noise partitioning allows for a general class of distributions and structures, including multiplicative and mixture models, and admits both known and data-driven systems. The partitions required for optimal transition bounds are specified for systems that are monotonic with respect to the noise, and explicit partitions are provided for affine and multiplicative structures. By the soundness of the abstraction procedure, verification on the IMC provides guarantees on the stochastic system against a temporal logic specification. In addition, we present a novel refinement-free algorithm that improves the verification results. Case studies on linear and nonlinear systems with non-Gaussian noise, including a data-driven example, demonstrate the generality and effectiveness of the method without introducing excessive conservatism.Comment: 6 pages, 6 figures, submitted jointly to IEEE Control Systems Letters and 2024 AC

Adversarial Robustness Certification for Bayesian Neural Networks

We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$, we define two notions of robustness for BNNs in an adversarial setting: probabilistic robustness and decision robustness. Probabilistic robustness is the probability that for all points in $T$ the output of a BNN sampled from the posterior is in $S$. On the other hand, decision robustness considers the optimal decision of a BNN and checks if for all points in $T$ the optimal decision of the BNN for a given loss function lies within the output set $S$. Although exact computation of these robustness properties is challenging due to the probabilistic and non-convex nature of BNNs, we present a unified computational framework for efficiently and formally bounding them. Our approach is based on weight interval sampling, integration, and bound propagation techniques, and can be applied to BNNs with a large number of parameters, and independently of the (approximate) inference method employed to train the BNN. We evaluate the effectiveness of our methods on various regression and classification tasks, including an industrial regression benchmark, MNIST, traffic sign recognition, and airborne collision avoidance, and demonstrate that our approach enables certification of robustness and uncertainty of BNN predictions

Individual Fairness in Bayesian Neural Networks

We study Individual Fairness (IF) for Bayesian neural networks (BNNs). Specifically, we consider the $\epsilon$-$\delta$-individual fairness notion, which requires that, for any pair of input points that are $\epsilon$-similar according to a given similarity metrics, the output of the BNN is within a given tolerance $\delta>0.$ We leverage bounds on statistical sampling over the input space and the relationship between adversarial robustness and individual fairness to derive a framework for the systematic estimation of $\epsilon$-$\delta$-IF, designing Fair-FGSM and Fair-PGD as global,fairness-aware extensions to gradient-based attacks for BNNs. We empirically study IF of a variety of approximately inferred BNNs with different architectures on fairness benchmarks, and compare against deterministic models learnt using frequentist techniques. Interestingly, we find that BNNs trained by means of approximate Bayesian inference consistently tend to be markedly more individually fair than their deterministic counterparts

Statistical Guarantees for the Robustness of Bayesian Neural Networks

We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i.e., with a priori error and confidence bounds. We provide experimental comparison for several approximate BNN inference techniques on image classification tasks associated to MNIST and a two-class subset of the GTSRB dataset. Our results enable quantification of uncertainty of BNN predictions in adversarial settings.Comment: 9 pages, 6 figure