Learning Probabilistic Termination Proofs

We present the first machine learning approach to the termination analysis of probabilistic programs. Ranking supermartingales (RSMs) prove that probabilistic programs halt, in expectation, within a finite number of steps. While previously RSMs were directly synthesised from source code, our method learns them from sampled execution traces. We introduce the neural ranking supermartingale: we let a neural network fit an RSM over execution traces and then we verify it over the source code using satisfiability modulo theories (SMT); if the latter step produces a counterexample, we generate from it new sample traces and repeat learning in a counterexample-guided inductive synthesis loop, until the SMT solver confirms the validity of the RSM. The result is thus a sound witness of probabilistic termination. Our learning strategy is agnostic to the source code and its verification counterpart supports the widest range of probabilistic single-loop programs that any existing tool can handle to date. We demonstrate the efficacy of our method over a range of benchmarks that include linear and polynomial programs with discrete, continuous, state-dependent, multi-variate, hierarchical distributions, and distributions with undefined moments

On the Trade-off Between Efficiency and Precision of Neural Abstraction

Neural abstractions have been recently introduced as formal approximations of complex, nonlinear dynamical models. They comprise a neural ODE and a certified upper bound on the error between the abstract neural network and the concrete dynamical model. So far neural abstractions have exclusively been obtained as neural networks consisting entirely of $ReLU$ activation functions, resulting in neural ODE models that have piecewise affine dynamics, and which can be equivalently interpreted as linear hybrid automata. In this work, we observe that the utility of an abstraction depends on its use: some scenarios might require coarse abstractions that are easier to analyse, whereas others might require more complex, refined abstractions. We therefore consider neural abstractions of alternative shapes, namely either piecewise constant or nonlinear non-polynomial (specifically, obtained via sigmoidal activations). We employ formal inductive synthesis procedures to generate neural abstractions that result in dynamical models with these semantics. Empirically, we demonstrate the trade-off that these different neural abstraction templates have vis-a-vis their precision and synthesis time, as well as the time required for their safety verification (done via reachability computation). We improve existing synthesis techniques to enable abstraction of higher-dimensional models, and additionally discuss the abstraction of complex neural ODEs to improve the efficiency of reachability analysis for these models.Comment: To appear at QEST 202

Formal Synthesis of Lyapunov Neural Networks

We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but lack of formal soundness. Symbolic computational methods for Lyapunov functions, which are in between, give formal guarantees but are typically semi-automatic because they rely on the user to provide appropriate function templates. We propose a method that finds Lyapunov functions fully automatically$-$using machine learning$-$while also providing formal guarantees$-$using satisfiability modulo theories (SMT). We employ a counterexample-guided approach where a numerical learner and a symbolic verifier interact to construct provably correct Lyapunov neural networks (LNNs). The learner trains a neural network that satisfies the Lyapunov criteria for asymptotic stability over a samples set; the verifier proves via SMT solving that the criteria are satisfied over the whole domain or augments the samples set with counterexamples. Our method supports neural networks with polynomial activation functions and multiple depth and width, which display wide learning capabilities. We demonstrate our method over several non-trivial benchmarks and compare it favourably against a numerical optimisation-based approach, a symbolic template-based approach, and a cognate LNN-based approach. Our method synthesises Lyapunov functions faster and over wider spatial domains than the alternatives, yet providing stronger or equal guarantees

Quantitative Verification with Neural Networks

We present a data-driven approach to the quantitative verification of probabilistic programs and stochastic dynamical models. Our approach leverages neural networks to compute tight and sound bounds for the probability that a stochastic process hits a target condition within finite time. This problem subsumes a variety of quantitative verification questions, from the reachability and safety analysis of discrete-time stochastic dynamical models, to the study of assertion-violation and termination analysis of probabilistic programs. We rely on neural networks to represent supermartingale certificates that yield such probability bounds, which we compute using a counterexample-guided inductive synthesis loop: we train the neural certificate while tightening the probability bound over samples of the state space using stochastic optimisation, and then we formally check the certificate's validity over every possible state using satisfiability modulo theories; if we receive a counterexample, we add it to our set of samples and repeat the loop until validity is confirmed. We demonstrate on a diverse set of benchmarks that, thanks to the expressive power of neural networks, our method yields smaller or comparable probability bounds than existing symbolic methods in all cases, and that our approach succeeds on models that are entirely beyond the reach of such alternative techniques.Comment: The conference version of this manuscript appeared at CONCUR 202

SIOUX project: a simultaneous multiband camera for exoplanet atmospheres studies

The exoplanet revolution is well underway. The last decade has seen order-of-magnitude increases in the number of known planets beyond the Solar system. Detailed characterization of exoplanetary atmospheres provide the best means for distinguishing the makeup of their outer layers, and the only hope for understanding the interplay between initial composition chemistry, temperature-pressure atmospheric profiles, dynamics and circulation. While pioneering work on the observational side has produced the first important detections of atmospheric molecules for the class of transiting exoplanets, important limitations are still present due to the lack of sys- tematic, repeated measurements with optimized instrumentation at both visible (VIS) and near-infrared (NIR) wavelengths. It is thus of fundamental importance to explore quantitatively possible avenues for improvements. In this paper we report initial results of a feasibility study for the prototype of a versatile multi-band imaging system for very high-precision differential photometry that exploits the choice of specifically selected narrow-band filters and novel ideas for the execution of simultaneous VIS and NIR measurements. Starting from the fundamental system requirements driven by the science case at hand, we describe a set of three opto-mechanical solutions for the instrument prototype: 1) a radial distribution of the optical flux using dichroic filters for the wavelength separation and narrow-band filters or liquid crystal filters for the observations; 2) a tree distribution of the optical flux (implying 2 separate foci), with the same technique used for the beam separation and filtering; 3) an exotic solution consisting of the study of a complete optical system (i.e. a brand new telescope) that exploits the chromatic errors of a reflecting surface for directing the different wavelengths at different foci

A low-mass planet candidate orbiting Proxima Centauri at a distance of 1.5 AU

Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).Our nearest neighbor, Proxima Centauri, hosts a temperate terrestrial planet. We detected in radial velocities evidence of a possible second planet with minimum mass m c sin i c = 5.8 ± 1.9 M ⊕ and orbital period P c = 5.21 - 0.22 + 0.26 years. The analysis of photometric data and spectro-scopic activity diagnostics does not explain the signal in terms of a stellar activity cycle, but follow-up is required in the coming years for confirming its planetary origin. We show that the existence of the planet can be ascertained, and its true mass can be determined with high accuracy, by combining Gaia astrometry and radial velocities. Proxima c could become a prime target for follow-up and characterization with next-generation direct imaging instrumentation due to the large maximum angular separation of ~1 arc second from the parent star. The candidate planet represents a challenge for the models of super-Earth formation and evolution.Peer reviewedFinal Published versio

New Variable Stars Discovered by the APACHE Survey. II. Results After the Second Observing Season

Routinely operating since July 2012, the APACHE survey has celebrated its second birthday. While the main goal of the Project is the detection of transiting planets around a large sample of bright, nearby M dwarfs in the northern hemisphere, the APACHE large photometric database for hundreds of different fields represents a relevant resource to search for and provide a first characterization of new variable stars. We celebrate here the conclusion of the second year of observations by reporting the discovery of 14 new variables.Comment: 25 pages, accepted for publication on The Journal of the American Association of Variable Star Observers (JAVVSO

Validation of an Automated System for the Extraction of a Wide Dataset for Clinical Studies Aimed at Improving the Early Diagnosis of Candidemia

: There is increasing interest in assessing whether machine learning (ML) techniques could further improve the early diagnosis of candidemia among patients with a consistent clinical picture. The objective of the present study is to validate the accuracy of a system for the automated extraction from a hospital laboratory software of a large number of features from candidemia and/or bacteremia episodes as the first phase of the AUTO-CAND project. The manual validation was performed on a representative and randomly extracted subset of episodes of candidemia and/or bacteremia. The manual validation of the random extraction of 381 episodes of candidemia and/or bacteremia, with automated organization in structured features of laboratory and microbiological data resulted in ≥99% correct extractions (with confidence interval < ±1%) for all variables. The final automatically extracted dataset consisted of 1338 episodes of candidemia (8%), 14,112 episodes of bacteremia (90%), and 302 episodes of mixed candidemia/bacteremia (2%). The final dataset will serve to assess the performance of different ML models for the early diagnosis of candidemia in the second phase of the AUTO-CAND project

Analysis of charmonium production at fixed-target experiments in the NRQCD approach

We present an analysis of the existing data on charmonium hadro-production based on non-relativistic QCD (NRQCD) calculations at the next-to-leading order (NLO). All the data on J/psi and psi' production in fixed-target experiments and on pp collisions at low energy are included. We find that the amount of color octet contribution needed to describe the data is about 1/10 of that found at the Tevatron