TY - CONF AB - Fixed-point arithmetic is a popular alternative to floating-point arithmetic on embedded systems. Existing work on the verification of fixed-point programs relies on custom formalizations of fixed-point arithmetic, which makes it hard to compare the described techniques or reuse the implementations. In this paper, we address this issue by proposing and formalizing an SMT theory of fixed-point arithmetic. We present an intuitive yet comprehensive syntax of the fixed-point theory, and provide formal semantics for it based on rational arithmetic. We also describe two decision procedures for this theory: one based on the theory of bit-vectors and the other on the theory of reals. We implement the two decision procedures, and evaluate our implementations using existing mature SMT solvers on a benchmark suite we created. Finally, we perform a case study of using the theory we propose to verify properties of quantized neural networks. AU - Baranowski, Marek AU - He, Shaobo AU - Lechner, Mathias AU - Nguyen, Thanh Son AU - Rakamarić, Zvonimir ID - 8194 SN - 03029743 T2 - Automated Reasoning TI - An SMT theory of fixed-point arithmetic VL - 12166 ER - TY - JOUR AB - A central goal of artificial intelligence in high-stakes decision-making applications is to design a single algorithm that simultaneously expresses generalizability by learning coherent representations of their world and interpretable explanations of its dynamics. Here, we combine brain-inspired neural computation principles and scalable deep learning architectures to design compact neural controllers for task-specific compartments of a full-stack autonomous vehicle control system. We discover that a single algorithm with 19 control neurons, connecting 32 encapsulated input features to outputs by 253 synapses, learns to map high-dimensional inputs into steering commands. This system shows superior generalizability, interpretability and robustness compared with orders-of-magnitude larger black-box learning systems. The obtained neural agents enable high-fidelity autonomy for task-specific parts of a complex autonomous system. AU - Lechner, Mathias AU - Hasani, Ramin AU - Amini, Alexander AU - Henzinger, Thomas A AU - Rus, Daniela AU - Grosu, Radu ID - 8679 JF - Nature Machine Intelligence TI - Neural circuit policies enabling auditable autonomy VL - 2 ER - TY - CONF AB - Traditional robotic control suits require profound task-specific knowledge for designing, building and testing control software. The rise of Deep Learning has enabled end-to-end solutions to be learned entirely from data, requiring minimal knowledge about the application area. We design a learning scheme to train end-to-end linear dynamical systems (LDS)s by gradient descent in imitation learning robotic domains. We introduce a new regularization loss component together with a learning algorithm that improves the stability of the learned autonomous system, by forcing the eigenvalues of the internal state updates of an LDS to be negative reals. We evaluate our approach on a series of real-life and simulated robotic experiments, in comparison to linear and nonlinear Recurrent Neural Network (RNN) architectures. Our results show that our stabilizing method significantly improves test performance of LDS, enabling such linear models to match the performance of contemporary nonlinear RNN architectures. A video of the obstacle avoidance performance of our method on a mobile robot, in unseen environments, compared to other methods can be viewed at https://youtu.be/mhEsCoNao5E. AU - Lechner, Mathias AU - Hasani, Ramin AU - Rus, Daniela AU - Grosu, Radu ID - 8704 SN - 10504729 T2 - Proceedings - IEEE International Conference on Robotics and Automation TI - Gershgorin loss stabilizes the recurrent neural network compartment of an end-to-end robot learning scheme ER - TY - CONF AB - Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle systems with uncertain parameters and inputs, where the uncertainties are bound to given intervals. The method is evaluated on the plant model of an experimental electro-mechanical braking system with periodic controller. In this model, the fast-switching controller dynamics requires simulation time scales of the order of nanoseconds. Accurate set-based computations for relatively large time horizons are known to be expensive. However, by appropriately decoupling the time variable with respect to the spatial variables, and enclosing the uncertain parameters using interval matrix maps acting on zonotopes, we show that the computation time can be lowered to 5000 times faster with respect to previous works. This is a step forward in formal verification of hybrid systems because reduced run-times allow engineers to introduce more expressiveness in their models with a relatively inexpensive computational cost. AU - Forets, Marcelo AU - Freire, Daniel AU - Schilling, Christian ID - 8750 SN - 9781728191485 T2 - 18th ACM-IEEE International Conference on Formal Methods and Models for System Design TI - Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions ER - TY - CONF AB - Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks. AU - Bogomolov, Sergiy AU - Forets, Marcelo AU - Frehse, Goran AU - Potomkin, Kostiantyn AU - Schilling, Christian ID - 8287 KW - reachability KW - hybrid systems KW - decomposition T2 - Proceedings of the International Conference on Embedded Software TI - Reachability analysis of linear hybrid systems via block decomposition ER -