arXiv subjects

Thomas A. Henzinger

Publications and source records attributed to Thomas A. Henzinger.

At least 73 records · Page 4Linked to original sources

arXiv2022

Are All Vision Models Created Equal? A Study of the Open-Loop to Closed-Loop Causality Gap

There is an ever-growing zoo of modern neural network models that can efficiently learn end-to-end control from visual observations. These advanced deep models, ranging from convolutional to patch-based networks, have been extensively tested on offline image classification and regression tasks. In this paper, we study these vision architectures with respect to the open-loop to closed-loop causality gap, i.e., offline training followed by an online closed-loop deployment. This causality gap typically emerges in robotics applications such as autonomous driving, where a network is trained to imitate the control commands of a human. In this setting, two situations arise: 1) Closed-loop testing in-distribution, where the test environment shares properties with those of offline training data. 2) Closed-loop testing under distribution shifts and out-of-distribution. Contrary to recently reported results, we show that under proper training guidelines, all vision models perform indistinguishably well on in-distribution deployment, resolving the causality gap. In situation 2, We observe that the causality gap disrupts performance regardless of the choice of the model architecture. Our results imply that the causality gap can be solved in situation one with our proposed training guideline with any modern network architecture, whereas achieving out-of-distribution generalization (situation two) requires further investigations, for instance, on data diversity rather than the model architecture.

cs.CV↗

arXiv2022

Synthesis of Parametric Hybrid Automata from Time Series

We propose an algorithmic approach for synthesizing linear hybrid automata from time-series data. Unlike existing approaches, our approach provides a whole family of models. Each model in the family is guaranteed to capture the input data up to a precision error ε, in the following sense: For each time series, the model contains an execution that is ε-close to the data points. Our construction allows to effectively choose a model from this family with minimal precision error ε. We demonstrate the algorithm's efficiency and its ability to find precise models in two case studies.

cs.FL↗

arXiv2022

Entangled Residual Mappings

Residual mappings have been shown to perform representation learning in the first layers and iterative feature refinement in higher layers. This interplay, combined with their stabilizing effect on the gradient norms, enables them to train very deep networks. In this paper, we take a step further and introduce entangled residual mappings to generalize the structure of the residual connections and evaluate their role in iterative learning representations. An entangled residual mapping replaces the identity skip connections with specialized entangled mappings such as orthogonal, sparse, and structural correlation matrices that share key attributes (eigenvalues, structure, and Jacobian norm) with identity mappings. We show that while entangled mappings can preserve the iterative refinement of features across various deep models, they influence the representation learning process in convolutional networks differently than attention-based models and recurrent neural networks. In general, we find that for CNNs and Vision Transformers entangled sparse mapping can help generalization while orthogonal mappings hurt performance. For recurrent networks, orthogonal residual mappings form an inductive bias for time-variant sequences, which degrades accuracy on time-invariant tasks.

cs.LG↗

arXiv2022

Learning Stabilizing Policies in Stochastic Control Systems

In this work, we address the problem of learning provably stable neural network policies for stochastic control systems. While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of how to learn such policies is little explored. Here, we study the effectiveness of jointly learning a policy together with a martingale certificate that proves its stability using a single learning algorithm. We observe that the joint optimization problem becomes easily stuck in local minima when starting from a randomly initialized policy. Our results suggest that some form of pre-training of the policy is required for the joint optimization to repair and verify the policy successfully.

cs.LG↗

arXiv2022

Scalable Verification of Quantized Neural Networks (Technical Report)

Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an idealized model of the actual network which works over real arithmetic and ignores rounding imprecisions. This idealization is in stark contrast to network quantization, which is a technique that trades numerical precision for computational efficiency and is, therefore, often applied in practice. Neglecting rounding errors of such low-bit quantized neural networks has been shown to lead to wrong conclusions about the network's correctness. Thus, the desired approach for verifying quantized neural networks would be one that takes these rounding errors into account. In this paper, we show that verifying the bit-exact implementation of quantized neural networks with bit-vector specifications is PSPACE-hard, even though verifying idealized real-valued networks and satisfiability of bit-vector specifications alone are each in NP. Furthermore, we explore several practical heuristics toward closing the complexity gap between idealized and bit-exact verification. In particular, we propose three techniques for making SMT-based verification of quantized neural networks more scalable. Our experiments demonstrate that our proposed methods allow a speedup of up to three orders of magnitude over existing approaches.

cs.AI↗

arXiv2021

Stability Verification in Stochastic Control Systems via Neural Network Supermartingales

We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the literature, verifying stability in stochastic control systems is an open problem. The few existing works on this topic either consider only specialized forms of stochasticity or make restrictive assumptions on the system, rendering them inapplicable to learning algorithms with neural network policies. In this work, we present an approach for general nonlinear stochastic control problems with two novel aspects: (a) instead of classical stochastic extensions of Lyapunov functions, we use ranking supermartingales (RSMs) to certify a.s.~asymptotic stability, and (b) we present a method for learning neural network RSMs. We prove that our approach guarantees a.s.~asymptotic stability of the system and provides the first method to obtain bounds on the stabilization time, which stochastic Lyapunov functions do not. Finally, we validate our approach experimentally on a set of nonlinear stochastic reinforcement learning environments with neural network policies.

cs.LG↗

arXiv2021

GoTube: Scalable Stochastic Verification of Continuous-Depth Models

We introduce a new stochastic verification algorithm that formally quantifies the behavioral robustness of any time-continuous process formulated as a continuous-depth model. Our algorithm solves a set of global optimization (Go) problems over a given time horizon to construct a tight enclosure (Tube) of the set of all process executions starting from a ball of initial states. We call our algorithm GoTube. Through its construction, GoTube ensures that the bounding tube is conservative up to a desired probability and up to a desired tightness. GoTube is implemented in JAX and optimized to scale to complex continuous-depth neural network models. Compared to advanced reachability analysis tools for time-continuous neural networks, GoTube does not accumulate overapproximation errors between time steps and avoids the infamous wrapping effect inherent in symbolic techniques. We show that GoTube substantially outperforms state-of-the-art verification tools in terms of the size of the initial ball, speed, time-horizon, task completion, and scalability on a large set of experiments. GoTube is stable and sets the state-of-the-art in terms of its ability to scale to time horizons well beyond what has been previously possible.

cs.LG↗

arXiv2021

Into the Unknown: Active Monitoring of Neural Networks

Neural-network classifiers achieve high accuracy when predicting the class of an input that they were trained to identify. Maintaining this accuracy in dynamic environments, where inputs frequently fall outside the fixed set of initially known classes, remains a challenge. The typical approach is to detect inputs from novel classes and retrain the classifier on an augmented dataset. However, not only the classifier but also the detection mechanism needs to adapt in order to distinguish between newly learned and yet unknown input classes. To address this challenge, we introduce an algorithmic framework for active monitoring of a neural network. A monitor wrapped in our framework operates in parallel with the neural network and interacts with a human user via a series of interpretable labeling queries for incremental adaptation. In addition, we propose an adaptive quantitative monitor to improve precision. An experimental evaluation on a diverse set of benchmarks with varying numbers of classes confirms the benefits of our active monitoring framework in dynamic scenarios.

cs.LG↗

arXiv2021

Infinite Time Horizon Safety of Bayesian Neural Networks

Bayesian neural networks (BNNs) place distributions over the weights of a neural network to model uncertainty in the data and the network's prediction. We consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with infinite time horizon systems. Compared to the existing sampling-based approaches, which are inapplicable to the infinite time horizon setting, we train a separate deterministic neural network that serves as an infinite time horizon safety certificate. In particular, we show that the certificate network guarantees the safety of the system over a subset of the BNN weight posterior's support. Our method first computes a safe weight set and then alters the BNN's weight posterior to reject samples outside this set. Moreover, we show how to extend our approach to a safe-exploration reinforcement learning setting, in order to avoid unsafe trajectories during the training of the policy. We evaluate our approach on a series of reinforcement learning benchmarks, including non-Lyapunovian safety specifications.

cs.LG↗

arXiv2021

Flavours of Sequential Information Flow

Information-flow policies prescribe which information is available to a given user or subsystem. We study the problem of specifying such properties in reactive systems, which may require dynamic changes in information-flow restrictions between their states. We formalize several flavours of sequential information-flow, which cover different assumptions about the semantic relation between multiple observations of a system. Information-flow specification falls into the category of hyperproperties. We define different variants of sequential information-flow specification using a first-order logic with both trace quantifiers and temporal quantifiers called Hypertrace Logic. We prove that HyperLTL, equivalent to a subset of Hypertrace Logic with restricted quantifier prefixes, cannot specify the majority of the studied two-state independence variants. For our results, we introduce a notion of equivalence between sets of traces that cannot be distinguished by certain classes of formulas in Hypertrace Logic. This presents a new approach to proving inexpressiveness results for logics such as HyperLTL.

cs.LO↗

arXiv2021

Adversarial Training is Not Ready for Robot Learning

Adversarial training is an effective method to train deep learning models that are resilient to norm-bounded perturbations, with the cost of nominal performance drop. While adversarial training appears to enhance the robustness and safety of a deep model deployed in open-world decision-critical applications, counterintuitively, it induces undesired behaviors in robot learning settings. In this paper, we show theoretically and experimentally that neural controllers obtained via adversarial training are subjected to three types of defects, namely transient, systematic, and conditional errors. We first generalize adversarial training to a safety-domain optimization scheme allowing for more generic specifications. We then prove that such a learning process tends to cause certain error profiles. We support our theoretical results by a thorough experimental safety analysis in a robot-learning task. Our results suggest that adversarial training is not yet ready for robot learning.

cs.LG↗

arXiv2021

Synthesis of Hybrid Automata with Affine Dynamics from Time-Series Data

Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series data, we present an algorithmic approach to synthesize a hybrid automaton exhibiting behavior that is close to the data, up to a specified precision, and changes in synchrony with the data. A fundamental problem in our synthesis algorithm is to check membership of a time series in a hybrid automaton. Our solution integrates reachability and optimization techniques for affine dynamical systems to obtain both a sufficient and a necessary condition for membership, combined in a refinement framework. The algorithm processes one time series at a time and hence can be interrupted, provide an intermediate result, and be resumed. We report experimental results demonstrating the applicability of our synthesis approach.

eess.SY↗

arXiv2021

Determinacy in Discrete-Bidding Infinite-Duration Games

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a non-terminating system and its environment. In bidding games the players bid for the right to move the token: in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Bidding games are known to have a clean and elegant mathematical structure that relies on the ability of the players to submit arbitrarily small bids. Many applications, however, require a fixed granularity for the bids, which can represent, for example, the monetary value expressed in cents. We study, for the first time, the combination of discrete-bidding and infinite-duration games. Our most important result proves that these games form a large determined subclass of concurrent games, where determinacy is the strong property that there always exists exactly one player who can guarantee winning the game. In particular, we show that, in contrast to non-discrete bidding games, the mechanism with which tied bids are resolved plays an important role in discrete-bidding games. We study several natural tie-breaking mechanisms and show that, while some do not admit determinacy, most natural mechanisms imply determinacy for every pair of initial budgets.

cs.GT↗

arXiv2020

Formal Methods with a Touch of Magic

Machine learning and formal methods have complimentary benefits and drawbacks. In this work, we address the controller-design problem with a combination of techniques from both fields. The use of black-box neural networks in deep reinforcement learning (deep RL) poses a challenge for such a combination. Instead of reasoning formally about the output of deep RL, which we call the {\em wizard}, we extract from it a decision-tree based model, which we refer to as the {\em magic book}. Using the extracted model as an intermediary, we are able to handle problems that are infeasible for either deep RL or formal methods by themselves. First, we suggest, for the first time, combining a magic book in a synthesis procedure. We synthesize a stand-alone correct-by-design controller that enjoys the favorable performance of RL. Second, we incorporate a magic book in a bounded model checking (BMC) procedure. BMC allows us to find numerous traces of the plant under the control of the wizard, which a user can use to increase the trustworthiness of the wizard and direct further training.

cs.LO↗

arXiv2020

Multi-dimensional Long-Run Average Problems for Vector Addition Systems with States

A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating.

cs.FL↗

arXiv2020

Information-Flow Interfaces

Contract-based design is a promising methodology for taming the complexity of developing sophisticated systems. A formal contract distinguishes between assumptions, which are constraints that the designer of a component puts on the environments in which the component can be used safely, and guarantees, which are promises that the designer asks from the team that implements the component. A theory of formal contracts can be formalized as an interface theory, which supports the composition and refinement of both assumptions and guarantees. Although there is a rich landscape of contract-based design methods that address functional and extra-functional properties, we present the first interface theory that is designed for ensuring system-wide security properties, thus paving the way for a science of safety and security co-engineering. Our framework provides a refinement relation and a composition operation that support both incremental design and independent implementability. We develop our theory for both stateless and stateful interfaces. We illustrate the applicability of our framework with an example inspired from the automotive domain. Finally, we provide three plausible trace semantics to stateful information-flow interfaces and we show that only two correspond to temporal logics for specifying hyperproperties, while the third defines a new class of hyperproperties that lies between the other two classes.

cs.FL↗

arXiv2020

Outside the Box: Abstraction-Based Monitoring of Neural Networks

Neural networks have demonstrated unmatched performance in a range of classification tasks. Despite numerous efforts of the research community, novelty detection remains one of the significant limitations of neural networks. The ability to identify previously unseen inputs as novel is crucial for our understanding of the decisions made by neural networks. At runtime, inputs not falling into any of the categories learned during training cannot be classified correctly by the neural network. Existing approaches treat the neural network as a black box and try to detect novel inputs based on the confidence of the output predictions. However, neural networks are not trained to reduce their confidence for novel inputs, which limits the effectiveness of these approaches. We propose a framework to monitor a neural network by observing the hidden layers. We employ a common abstraction from program analysis - boxes - to identify novel behaviors in the monitored layers, i.e., inputs that cause behaviors outside the box. For each neuron, the boxes range over the values seen in training. The framework is efficient and flexible to achieve a desired trade-off between raising false warnings and detecting novel inputs. We illustrate the performance and the robustness to variability in the unknown classes on popular image-classification benchmarks.

cs.LG↗

arXiv2020

Infinite-Duration Poorman-Bidding Games

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. Such games are central in formal verification since they model the interaction between a non-terminating system and its environment. We study {\em bidding games} in which the players bid for the right to move the token. Two bidding rules have been defined. In {\em Richman} bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. {\em Poorman} bidding is similar except that the winner of the bidding pays the "bank" rather than the other player. While poorman reachability games have been studied before, we present, for the first time, results on {\em infinite-duration} poorman games. A central quantity in these games is the {\em ratio} between the two players' initial budgets. The questions we study concern a necessary and sufficient ratio with which a player can achieve a goal. For reachability objectives, such {\em threshold ratios} are known to exist for both bidding rules. We show that the properties of poorman reachability games extend to complex qualitative objectives such as parity, similarly to the Richman case. Our most interesting results concern quantitative poorman games, namely poorman mean-payoff games, where we construct optimal strategies depending on the initial ratio, by showing a connection with {\em random-turn based games}. The connection in itself is interesting, because it does not hold for reachability poorman games. We also solve the complexity problems that arise in poorman bidding games.

cs.GT↗