Self-Improving Cyber-Physical Systems (NSF CPS Small)

Machine learning methods such as deep neural networks (DNNs), despite their success across different domains, are known to often generate incorrect predictions with high confidence on inputs outside their training distribution. The deployment of DNNs in safety-critical domains requires detection of out-of-distribution (OOD) data so that DNNs can abstain from making predictions on those. A number of methods have been recently developed for OOD detection, but there is still room for improvement. We propose the new method iDECODe, leveraging in-distribution equivariance for conformal OOD detection. It relies on a novel base non-conformity measure and a new aggregation method, used in the inductive conformal anomaly detection framework, thereby guaranteeing a bounded false detection rate. We demonstrate the efficacy of iDECODe by experiments on image and audio datasets, obtaining state-of-the-art results. We also show that iDECODe can detect adversarial examples.

It has recently been shown that neural SDEs with Brownian motion as noise lead to smoother attributions than traditional ResNets. Various attribution methods such as saliency maps, integrated gradients, DeepSHAP and DeepLIFT have been shown to be more robust for neural SDEs than ResNets using the recently proposed sensitivity metric. In this paper, we show that neural SDEs with adaptive attribution-driven noise lead to even more robust attributions and smaller sensitivity metrics than traditional neural SDEs with Brownian motion as noise. In particular, attribution-driven shaping of noise leads to 6.7%, 6.9% and 19.4% smaller sensitivity metric for integrated gradients computed on three discrete approximations of neural SDEs with standard Brownian motion noise- stochastic ResNet-50, WideResNet-101 and ResNeXt-101 models respectively. The neural SDE model with adaptive attribution-driven noise leads to 25.7% and 4.8% improvement in the SIC metric over traditional ResNets and Neural SDEs with Brownian motion as noise. To the best of our knowledge, we are the first to propose the use of attributions for shaping the noise injected in neural SDEs, and demonstrate that this process leads to more robust attributions than traditional neural SDEs with standard Brownian motion as noise.

This paper presents an approach to detect out-of-context (OOC) objects in an image. Given an image with a set of objects, our goal is to determine if an object is inconsistent with the scene context and detect the OOC object with a bounding box. In this work, we consider commonly explored contextual relations such as co-occurrence relations, the relative size of an object with respect to other objects, and the position of the object in the scene. We posit that contextual cues are useful to determine object labels for in-context objects and inconsistent context cues are detrimental to determining object labels for out-of-context objects. To realize this hypothesis, we propose a graph contextual reasoning network (GCRN) to detect OOC objects. GCRN consists of two separate graphs to predict object labels based on the contextual cues in the image - 1) a representation graph to learn object features based on the neighboring objects and 2) a context graph to explicitly capture contextual cues from the neighboring objects. GCRN explicitly captures the contextual cues to improve the detection of in-context objects and identify objects that violate contextual relations. In order to evaluate our approach, we create a large-scale dataset by adding OOC object instances to the COCO images. We also evaluate on recent OCD benchmark. Our results show that GCRN outperforms competitive baselines in detecting OOC objects and correctly detecting in-context objects.

Normalizing flows map an independent set of latent variables to their samples using a bijective transformation. Despite the exact correspondence between samples and latent variables, their high level relationship is not well understood. In this paper we characterize the geometric structure of flows using principal manifolds and understand the relationship between latent variables and samples using contours. We introduce a novel class of normalizing flows, called principal component flows (PCF), whose contours are its principal manifolds, and a variant for injective flows (iPCF) that is more efficient to train than regular injective flows. PCFs can be constructed using any flow architecture, are trained with a regularized maximum likelihood objective and can perform density estimation on all of their principal manifolds. In our experiments we show that PCFs and iPCFs are able to learn the principal manifolds over a variation of datasets. Additionally, we show that PCFs can perform density estimation on data that lie on a manifold with variable dimensionality, which is not possible with existing normalizing flows.

Despite the remarkable strides over the last decade in the performance of machine learning techniques, their applications are typically limited to nonadversarial benign environments. The use of deep learning in applications such as biometric recognition, and intrusion detection, require them to operate in adversarial environments. But the overwhelming empirical studies and theoretical results have shown that these methods are extremely fragile and susceptible to adversarial attacks. The rationale for why these methods make the decisions they do are also notoriously difficult to interpret; understanding such rationale may be crucial for the aforementioned applications. In this chapter, we discuss the connections between these related challenges, and describe a novel integrated approach, Trinity (Trust, Resilience and INterpretabilITY ), for analyzing these models.

Quantum algorithms are notoriously hard to design and require significant human ingenuity and insight. We present a new methodology called Quantum Automated Synthesizer (QUASH) that can automatically synthesize quantum circuits using decision procedures that perform symbolic reasoning for combinatorial search. Our automated synthesis approach constructs finite symbolic abstract models of the quantum gates automatically and discovers a quantum circuit as a composition of quantum gates using these symbolic models. Our key insight is that most current quantum algorithms work on a finite number of classical inputs, and hence, their correctness proof relies only on reasoning about a finite set of quantum states that can be represented using finite symbolic systems. We demonstrate the potential of our approach by automatically synthesizing four quantum circuits and re-discovering the Bernstein-Vazirani quantum algorithm using state-of-the-art decision procedures. Our synthesis approach only requires distinguishing between a finite set of symbolic quantum states; for example, the synthesis of the Bernstein-Vazirani quantum algorithm only requires reasoning about the following qubit states- |0, |1, -i|0, i|1, |+, |-, e 1/2 |1i, e iπ/4 |1 and a remaining symbolic state representing all other possible quantum states. Our approach leverages decision procedures and theorem provers to assist in the discovery of new quantum algorithms and is a step towards the automation of quantum algorithm design.

ML algorithms or models, especially deep neural networks (DNNs), have shown significant promise in several areas. However, recently researchers have demonstrated that ML algorithms, especially DNNs, are vulnerable to adversarial examples (slightly perturbed samples that cause mis-classification). Existence of adversarial examples has hindered deployment of ML algorithms in safety-critical sectors, such as security. Several defenses for adversarial examples exist in the literature. One of the important classes of defenses are manifold-based defenses, where a sample is “pulled back” into the data manifold before classifying. These defenses rely on the manifold assumption (data lie in a manifold of lower dimension than the input space). These defenses use a generative model to approximate the input distribution. This paper asks the following question- do the generative models used in manifold-based defenses need to be topology-aware? Our paper suggests the answer is yes. We provide theoretical and empirical evidence to support our claim.

Several methods have recently been developed for computing attributions of a neural network’s prediction over the input features. However, these existing approaches for computing attributions are noisy and not robust to small perturbations of the input. This paper uses the recently identified connection between dynamical systems and residual neural networks to show that the attributions computed over neural stochastic differential equations (SDEs) are less noisy, visually sharper, and quantitatively more robust. Using dynamical systems theory, we theoretically analyze the robustness of these attributions. We also experimentally demonstrate the efficacy of our approach in providing smoother, visually sharper and quantitatively robust attributions by computing attributions for ImageNet images using ResNet-50, WideResNet-101 models and ResNeXt-101 models.

We present TrojDRL, a tool for exploring and evaluating backdoor attacks on deep reinforcement learning agents. TrojDRL exploits the sequential nature of deep reinforcement learning (DRL) and considers different gradations of threat models. We show that untargeted attacks on state-of-the-art actor-critic algorithms can circumvent existing defenses built on the assumption of backdoors being targeted. We evaluated TrojDRL on a broad set of DRL benchmarks and showed that the attacks require only poisoning as little as 0.025% of the training data. Compared with existing works of backdoor attacks on classification models, TrojDRL provides a first step towards understanding the vulnerability of DRL agents.

In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed.

Given a Boolean formula ϕ(x) in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly e clauses, for all values of e. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the hardness of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.

The functions of an autonomous system can generally be partitioned into those concerned with perception and those concerned with action. Perception builds and maintains an internal model of the world (i.e., the system’s environment) that is used to plan and execute actions to accomplish a goal established by human supervisors. Accordingly, assurance decomposes into two parts- a) ensuring that the model is an accurate representation of the world as it changes through time and b) ensuring that the actions are safe (and effective), given the model. Both perception and action may employ AI, including machine learning (ML), and these present challenges to assurance. However, it is usually feasible to guard the actions with traditionally engineered and assured monitors, and thereby ensure safety, given the model. Thus, the model becomes the central focus for assurance. We propose an architecture and methods to ensure the accuracy of models derived from sensors whose interpretation uses AI and ML. Rather than derive the model from sensors bottom-up, we reverse the process and use the model to predict sensor interpretation. Small prediction errors indicate the world is evolving as expected and the model is updated accordingly. Large prediction errors indicate surprise, which may be due to errors in sensing or interpretation, or unexpected changes in the world (e.g., a pedestrian steps into the road). The former initiate error masking or recovery, while the latter requires revision to the model. Higher-level AI functions assist in diagnosis and execution of these tasks. Although this two-level architecture where the lower level does “predictive processing” and the upper performs more reflective tasks, both focused on maintenance of a world model, is derived by engineering considerations, it also matches a widely accepted theory of human cognition.

ML algorithms or models, especially deep neural networks (DNNs), have shown significant promise in several areas. However, recently researchers have demonstrated that ML algorithms, especially DNNs, are vulnerable to adversarial examples (slightly perturbed samples that cause mis-classification). Existence of adversarial examples has hindered deployment of ML algorithms in safety-critical sectors, such as security. Several defenses for adversarial examples exist in the literature. One of the important classes of defenses are manifold-based defenses, where a sample is “pulled back” into the data manifold before classifying. These defenses rely on the manifold assumption (data lie in a manifold of lower dimension than the input space). These defenses use a generative model to approximate the input distribution. This paper asks the following question- do the generative models used in manifold-based defenses need to be topology-aware? Our paper suggests the answer is yes. We provide theoretical and empirical evidence to support our claim.

Deep neural networks (DNNs) have been shown to be brittle to inputs outside the distribution of training data, and to adversarial examples. This fragility is compounded by a lack of effectively computable measures of prediction confidence that correlate with the accuracy of DNNs. The direct use of logits severely overestimates confidence. These factors have impeded the adoption of DNNs in high-assurance systems. In this paper, we propose a novel confidence metric that does not require access to the training data, the use of model ensembles, or the need to train a calibration model on a held-out validation set, and hence, is usable even when only a trained model is available at inference time. A lightweight approach to quantify uncertainty in the output of a model and define a confidence metric is to measure the conformance of the model’s decision in the neighborhood of the input. But measuring conformance by sampling in the neighborhood of an input becomes exponentially difficult with increase in the dimension of the input. We use the feature concentration observed in robust models for local dimensionality reduction and attribution-based sampling over the features to compute the confidence metric. We mathematically motivate the proposed metric, and evaluate its effectiveness with two sets of experiments. First, we study the change in accuracy and the associated confidence over out-of-distribution inputs and evaluate the correlation between the accuracy and computed confidence. We also compare our results with the use of logits to estimate uncertainty. Second, we consider attacks such as FGSM, CW, DeepFool, PGD, and adversarial patch generation methods. The computed confidence metric is found to be low on out-of-distribution data and adversarial examples where the accuracy of the model is also low. These experiments demonstrate the effectiveness of the proposed confidence metric to make DNNs more transparent with respect to uncertainty of prediction.

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set asa set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk(CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis).

Deep neural networks (DNNs) are known to produce incorrect predictions with very high confidence on out-of-distribution inputs (OODs). This limitation is one of the key challenges in the adoption of DNNs in high-assurance systems such as autonomous driving, air traffic management, and medical diagnosis. This challenge has received significant attention recently, and several techniques have been developed to detect inputs where the model’s prediction cannot be trusted. These techniques detect OODs as datapoints with either high epistemic uncertainty or high aleatoric uncertainty. We demonstrate the difference in the detection ability of these techniques and propose an ensemble approach for detection of OODs as datapoints with high uncertainty (epistemic or aleatoric). We perform experiments on vision datasets with multiple DNN architectures, achieving state-of-the-art results in most cases.

We present Sherlock a tool for verification of deep neural networks along with some recent applications of the tool to verification and control problems for autonomous systems. Deep Neural Networks have emerged as an ubiquitous choice of concept representation in machine learning, and are commonly used as function approximators in many learning tasks. Learning methods using deep neural networks are often referred to as deep learning, and they have reached human-level accuracy on benchmark data-sets for several tasks such as image classification and speech recognition. This has inspired the adoption and integration of deep learning methods into safety-critical systems. For example, deep learning is often used in perception and several decision-making modules in automated vehicles. This has created a challenge in verifying and certifying these systems using traditional approaches developed for software and hardware verification. Further, these models are known to be brittle and prone to adversarial examples. Establishing robustness of these models is, thus, an important challenge. For safe integration of learning into critical systems, we must be able to encapsulate these models into assumption-guarantee contracts by verifying guarantees on the outputs of the model given the assumptions on its inputs. We discuss some of our recent work on this topic of verifying deep neural networks that is currently available as an open-source tool, Sherlock.

We propose a novel passive learning approach, TeLex, to infer signal temporal logic (STL) formulas that characterize the behavior of a dynamical system using only observed signal traces of the system. First, we present a template-driven learning approach that requires two inputs- a set of observed traces and a template STL formula. The unknown parameters in the template can include time-bounds of the temporal operators, as well as the thresholds in the inequality predicates. TeLEx finds the value of the unknown parameters such that the synthesized STL property is satisfied by all the provided traces and it is tight. This requirement of tightness is essential to generating interesting properties when only positive examples are provided and there is no option to actively query the dynamical system to discover the boundaries of legal behavior. We propose a novel quantitative semantics for satisfaction of STL properties which enables TeLEx to learn tight STL properties without multidimensional optimization. The proposed new metric is also smooth. This is critical to enable the use of gradient-based numerical optimization engines and it produces a 30x to 100x speed-up with respect to the state-of-art gradient-free optimization. Second, we present a novel technique for automatically learning the structure of the STL formula by incrementally constructing more complex formula guided by the robustness metric of subformula. We demonstrate the effectiveness of the overall approach for learning STL formulas from only positive examples on a set of synthetic and real-world benchmarks.

This paper investigates data-efficient methods for learning robust control policies. Reinforcement learning has emerged as an effective approach to learn control policies by interacting directly with the plant, but it requires a significant number of example trajectories to converge to the optimal policy. Combining model-free reinforcement learning with model-based control methods achieves better data-efficiency via simultaneous system identification and controller synthesis. We study a novel approach that exploits the existence of approximate physics models to accelerate the learning of control policies. The proposed approach consists of iterating through three key steps- evaluating a selected policy on the real-world plant and recording trajectories, building a Gaussian process model to predict the reality-gap of a parametric physics model in the neighborhood of the selected policy, and synthesizing a new policy using reinforcement learning on the refined physics model that most likely approximates the real plant. The approach converges to an optimal policy as well as an approximate physics model. The real world experiments are limited to evaluating only promising candidate policies, and the use of Gaussian processes minimizes the number of required real world trajectories. We demonstrate the effectiveness of our techniques on a set of simulation case-studies using OpenAI gym environments.

Models produced by machine learning, particularly deep neural networks, are state-of-the-art for many machine learning tasks and demonstrate very high prediction accuracy. Unfortunately, these models are also very brittle and vulnerable to specially crafted adversarial examples. Recent results have shown that accuracy of these models can be reduced from close to hundred percent to below 5% using adversarial examples. This brittleness of deep neural networks makes it challenging to deploy these learning models in security-critical areas where adversarial activity is expected, and cannot be ignored. A number of methods have been recently proposed to craft more effective and generalizable attacks on neural networks along with competing efforts to improve robustness of these learning models. But the current approaches to make machine learning techniques more resilient fall short of their goal. Further, the succession of new adversarial attacks against proposed methods to increase neural network robustness raises doubts about a foolproof approach to robustify machine learning models against all possible adversarial attacks. In this paper, we consider the problem of detecting adversarial examples. This would help identify when the learning models cannot be trusted without attempting to repair the models or make them robust to adversarial attacks. This goal of finding limitations of the learning model presents a more tractable approach to protecting against adversarial attacks. Our approach is based on identifying a low dimensional manifold in which the training samples lie, and then using the distance of a new observation from this manifold to identify whether this data point is adversarial or not. Our empirical study demonstrates that adversarial examples not only lie farther away from the data manifold, but this distance from manifold of the adversarial examples increases with the attack confidence.

We propose an automatic synthesis technique to generate provably correct controllers of stochastic linear dynamical systems for Signal Temporal Logic (STL) specifications. While formal synthesis problems can be directly formulated as exists-forall constraints, the quantifier alternation restricts the scalability of such an approach. We use the duality between a system and its proof of correctness to partially alleviate this challenge. We decompose the controller synthesis into two subproblems, each addressing orthogonal concerns - stabilization with respect to the noise, and meeting the STL specification. The overall controller is a nested controller comprising of the feedback controller for noise cancellation and an open loop controller for STL satisfaction. The correct-by-construction compositional synthesis of this nested controller relies on using the guarantees of the feedback controller instead of the controller itself. We use a linear feedback controller as the stabilizing controller for linear systems with bounded additive noise and over-approximate its ellipsoid stability guarantee with a polytope. We then use this over-approximation to formulate a mixed-integer linear programming (MILP) problem to synthesize an open-loop controller that satisfies STL specifications.

Real-world applications often naturally decompose into several sub-tasks. In many settings (e.g., robotics) demonstrations provide a natural way to specify the sub-tasks. However, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the sub-tasks can be safely recombined or limit the types of composition available. Motivated by this deficit, we consider the problem of inferring Boolean non-Markovian rewards (also known as logical trace properties or specifications) from demonstrations provided by an agent operating in an uncertain, stochastic environment. Crucially, specifications admit well-defined composition rules that are typically easy to interpret. In this paper, we formulate the specification inference task as a maximum a posteriori (MAP) probability inference problem, apply the principle of maximum entropy to derive an analytic demonstration likelihood model and give an efficient approach to search for the most likely specification in a large candidate pool of specifications. In our experiments, we demonstrate how learning specifications can help avoid common problems that often arise due to ad-hoc reward composition.

In this paper, we consider the problem of learning Boolean formulae from examples obtained by actively querying an oracle that can label these examples as either positive or negative. This problem has received attention in both machine learning as well as formal methods communities, and it has been shown to have exponential worst-case complexity in the general case as well as for many restrictions. In this paper, we focus on learning sparse Boolean formulae which depend on only a small (but unknown) subset of the overall vocabulary of atomic propositions. We propose two algorithms—first, based on binary search in the Hamming space, and the second, based on random walk on the Boolean hypercube, to learn these sparse Boolean formulae with a given confidence. This assumption of sparsity is motivated by the problem of mining explanations for decisions made by artificially intelligent (AI) algorithms, where the explanation of individual decisions may depend on a small but unknown subset of all the inputs to the algorithm. We demonstrate the use of these algorithms in automatically generating explanations of these decisions. These explanations will make intelligent systems more understandable and accountable to human users, facilitate easier audits and provide diagnostic information in the case of failure. The proposed approach treats the AI algorithm as a black-box oracle; hence, it is broadly applicable and agnostic to the specific AI algorithm. We show that the number of examples needed for both proposed algorithms only grows logarithmically with the size of the vocabulary of atomic propositions. We illustrate the practical effectiveness of our approach on a diverse set of case studies.

We present an approach to learn and formally verify feedback laws for data-driven models of neural networks. Neural networks are emerging as powerful and general data-driven representations for functions. This has led to their increased use in data-driven plant models and the representation of feedback laws in control systems. However, it is hard to formally verify properties of such feedback control systems. The proposed learning approach uses a receding horizon formulation that samples from the initial states and disturbances to enforce properties such as reachability, safety and stability. Next, our verification approach uses an over-approximate reachability analysis over the system, supported by range analysis for feedforward neural networks. We report promising results obtained by applying our techniques on several challenging nonlinear dynamical systems.

Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus, there is a pressing need for developing techniques to verify neural networks to check whether certain user-expected properties are satisfied. In this paper, we study a specific verification problem of computing a guaranteed range for the output of a deep neural network given a set of inputs represented as a convex polyhedron. Range estimation is a key primitive for verifying deep NNs. We present an efficient range estimation algorithm that uses a combination of local search and linear programming problems to efficiently find the maximum and minimum values taken by the outputs of the NN over the given input set. In contrast to recently proposed “monolithic” optimization approaches, we use local gradient descent to repeatedly find and eliminate local minima of the function. The final global optimum is certified using a mixed integer programming instance. We implement our approach and compare it with Reluplex, a recently proposed solver for deep neural networks. We demonstrate the effectiveness of the proposed approach for verification of NNs used in automated control as well as those used in classification.

We propose a novel passive learning approach, TeLex, to infer signal temporal logic (STL) formulas that characterize the behavior of a dynamical system using only observed signal traces of the system. First, we present a template-driven learning approach that requires two inputs- a set of observed traces and a template STL formula. The unknown parameters in the template can include time-bounds of the temporal operators, as well as the thresholds in the inequality predicates. TeLEx finds the value of the unknown parameters such that the synthesized STL property is satisfied by all the provided traces and it is tight. This requirement of tightness is essential to generating interesting properties when only positive examples are provided and there is no option to actively query the dynamical system to discover the boundaries of legal behavior. We propose a novel quantitative semantics for satisfaction of STL properties which enables TeLEx to learn tight STL properties without multidimensional optimization. The proposed new metric is also smooth. This is critical to enable the use of gradient-based numerical optimization engines and it produces a 30x to 100x speed-up with respect to the state-of-art gradient-free optimization. Second, we present a novel technique for automatically learning the structure of the STL formula by incrementally constructing more complex formula guided by the robustness metric of subformula. We demonstrate the effectiveness of the overall approach for learning STL formulas from only positive examples on a set of synthetic and real-world benchmarks.