Robustness Verification of Support Vector Machines

We study the problem of formally verifying the robustness to adversarial examples of support vector machines (SVMs), a major machine learning model for classification and regression tasks. Following a recent stream of works on formal robustness verification of (deep) neural networks, our approach relies on a sound abstract version of a given SVM classifier to be used for checking its robustness. This methodology is parametric on a given numerical abstraction of real values and, analogously to the case of neural networks, needs neither abstract least upper bounds nor widening operators on this abstraction. The standard interval domain provides a simple instantiation of our abstraction technique, which is enhanced with the domain of reduced affine forms, which is an efficient abstraction of the zonotope abstract domain. This robustness verification technique has been fully implemented and experimentally evaluated on SVMs based on linear and nonlinear (polynomial and radial basis function) kernels, which have been trained on the popular MNIST dataset of images and on the recent and more challenging Fashion-MNIST dataset. The experimental results of our prototype SVM robustness verifier appear to be encouraging: this automated verification is fast, scalable and shows significantly high percentages of provable robustness on the test set of MNIST, in particular compared to the analogous provable robustness of neural networks

dtControl: Decision Tree Learning Algorithms for Controller Representation

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision trees are smaller and more explainable. We present dtControl, an easily extensible tool for representing memoryless controllers as decision trees. We give a comprehensive evaluation of various decision tree learning algorithms applied to 10 case studies arising out of correct-by-construction controller synthesis. These algorithms include two new techniques, one for using arbitrary linear binary classifiers in the decision tree learning, and one novel approach for determinizing controllers during the decision tree construction. In particular the latter turns out to be extremely efficient, yielding decision trees with a single-digit number of decision nodes on 5 of the case studies

On-the-fly synthesizer programming with rule learning

This manuscript explores automatic programming of sound synthesis algorithms within the context of the performative artistic practice known as live coding. Writing source code in an improvised way to create music or visuals became an instrument the moment affordable computers were able to perform real-time sound synthesis with languages that keep their interpreter running. Ever since, live coding has dealt with real time programming of synthesis algorithms. For that purpose, one possibility is an algorithm that automatically creates variations out of a few presets selected by the user. However, the need for real-time feedback and the small size of the data sets (which can even be collected mid-performance) are constraints that make existing automatic sound synthesizer programmers and learning algorithms unfeasible. Also, the design of such algorithms is not oriented to create variations of a sound but rather to find the synthesizer parameters that match a given one. Other approaches create representations of the space of possible sounds, allowing the user to explore it by means of interactive evolution. Even though these systems are exploratory-oriented, they require longer run-times. This thesis investigates inductive rule learning for on-the-fly synthesizer programming. This approach is conceptually different from those found in both synthesizer programming and live coding literature. Rule models offer interpretability and allow working with the parameter values of the synthesis algorithms (even with symbolic data), making preprocessing unnecessary. RuLer, the proposed learning algorithm, receives a dataset containing user labeled combinations of parameter values of a synthesis algorithm. Among those combinations sharing the same label, it analyses the patterns based on dissimilarity. These patterns are described as an IF-THEN rule model. The algorithm parameters provide control to define what is considered a pattern. As patterns are the base for inducting new parameter settings, the algorithm parameters control the degree of consistency of the inducted settings respect to the original input data. An algorithm (named FuzzyRuLer) able to extend IF-THEN rules to hyperrectangles, which in turn are used as the cores of membership functions, is presented. The resulting fuzzy rule model creates a map of the entire input feature space. For such a pursuit, the algorithm generalizes the logical rules solving the contradictions by following a maximum volume heuristics. Across the manuscript it is discussed how, when machine learning algorithms are used as creative tools, glitches, errors or inaccuracies produced by the resulting models are sometimes desirable as they might offer novel, unpredictable results. The evaluation of the algorithms follows two paths. The first focuses on user tests. The second responds to the fact that this work was carried out within the computer science department and is intended to provide a broader, nonspecific domain evaluation of the algorithms performance using extrinsic benchmarks (i.e not belonging to a synthesizer's domain) for cross validation and minority oversampling. In oversampling tasks, using imbalanced datasets, the algorithm yields state-of-the-art results. Moreover, the synthetic points produced are significantly different from those created by the other algorithms and perform (controlled) exploration of more distant regions. Finally, accompanying the research, various performances, concerts and an album were produced with the algorithms and examples of this thesis. The reviews received and collections where the album has been featured show a positive reception within the community. Together, these evaluations suggest that rule learning is both an effective method and a promising path for further research.Aquest manuscrit explora la programació automàtica d’algorismes de síntesi de so dins del context de la pràctica artística performativa coneguda com a live coding. L'escriptura improvisada de codi font per crear música o visuals es va convertir en un instrument en el moment en què els ordinadors van poder realitzar síntesis de so en temps real amb llenguatges que mantenien el seu intèrpret en funcionament. D'aleshores ençà, el live coding comporta la programació en temps real d’algorismes de síntesi de so. Per a aquest propòsit, una possibilitat és tenir un algorisme que creï automàticament variacions a partir d'alguns presets seleccionats. No obstant, la necessitat de retroalimentació en temps real i la petita mida dels conjunts de dades són restriccions que fan que els programadors automàtics de sintetitzadors de so i els algorismes d’aprenentatge no siguin factibles d’utilitzar. A més, el seu disseny no està orientat a crear variacions d'un so, sinó a trobar els paràmetres del sintetitzador que aplicats a l'algorisme de síntesi produeixen un so determinat (target). Altres enfocaments creen representacions de l'espai de sons possibles, per permetre a l'usuari explorar-lo mitjançant l'evolució interactiva, però requereixen temps més llargs. Aquesta tesi investiga l'aprenentatge inductiu de regles per a la programació on-the-fly de sintetitzadors. Aquest enfocament és conceptualment diferent dels que es troben a la literatura. Els models de regles ofereixen interpretabilitat i permeten treballar amb els valors dels paràmetres dels algorismes de síntesi, sense processament previ. RuLer, l'algorisme d'aprenentatge proposat, rep dades amb combinacions etiquetades per l'usuari dels valors dels paràmetres d'un algorisme de síntesi. A continuació, analitza els patrons, basats en la dissimilitud, entre les combinacions de cada etiqueta. Aquests patrons es descriuen com un model de regles IF-THEN. Els paràmetres de l'algorisme proporcionen control per definir el que es considera un patró. Llavors, controlen el grau de consistència dels nous paràmetres de síntesi induïts respecte a les dades d'entrada originals. A continuació, es presenta un algorisme (FuzzyRuLer) capaç d’estendre les regles IF-THEN a hiperrectangles, que al seu torn s’utilitzen com a nuclis de funcions de pertinença. El model de regles difuses resultant crea un mapa complet de l'espai de la funció d'entrada. Per això, l'algorisme generalitza les regles lògiques seguint una heurística de volum màxim. Al llarg del manuscrit es discuteix com, quan s’utilitzen algorismes d’aprenentatge automàtic com a eines creatives, de vegades són desitjables glitches, errors o imprecisions produïdes pels models resultants, ja que poden oferir nous resultats imprevisibles. L'avaluació dels algorismes segueix dos camins. El primer es centra en proves d'usuari. El segon, que respon al fet que aquest treball es va dur a terme dins del departament de ciències de la computació, pretén proporcionar una avaluació més àmplia, no específica d'un domini, del rendiment dels algorismes mitjançant benchmarks extrínsecs utilitzats per cross-validation i minority oversampling. En tasques d'oversampling, mitjançant imbalanced data sets, l'algorisme proporciona resultats equiparables als de l'estat de l'art. A més, els punts sintètics produïts són significativament diferents als creats pels altres algorismes i realitzen exploracions (controlades) de regions més llunyanesEste manuscrito explora la programación automática de algoritmos de síntesis de sonido dentro del contexto de la práctica artística performativa conocida como live coding. La escritura de código fuente de forma improvisada para crear música o imágenes, se convirtió en un instrumento en el momento en que las computadoras asequibles pudieron realizar síntesis de sonido en tiempo real con lenguajes que mantuvieron su interprete en funcionamiento. Desde entonces, el live coding ha implicado la programación en tiempo real de algoritmos de síntesis. Para ese propósito, una posibilidad es tener un algoritmo que cree automáticamente variaciones a partir de unos pocos presets seleccionados. Sin embargo, la necesidad de retroalimentación en tiempo real y el pequeño tamaño de los conjuntos de datos (que incluso pueden recopilarse durante la misma actuación), limitan el uso de los algoritmos existentes, tanto de programación automática de sintetizadores como de aprendizaje de máquina. Además, el diseño de dichos algoritmos no está orientado a crear variaciones de un sonido, sino a encontrar los parámetros del sintetizador que coincidan con un sonido dado. Otros enfoques crean representaciones del espacio de posibles sonidos, para permitir al usuario explorarlo mediante evolución interactiva. Aunque estos sistemas están orientados a la exploración, requieren tiempos más largos. Esta tesis investiga el aprendizaje inductivo de reglas para la programación de sintetizadores on-the-fly. Este enfoque es conceptualmente diferente de los que se encuentran en la literatura, tanto de programación de sintetizadores como de live coding. Los modelos de reglas ofrecen interpretabilidad y permiten trabajar con los valores de los parámetros de los algoritmos de síntesis (incluso con datos simbólicos), haciendo innecesario el preprocesamiento. RuLer, el algoritmo de aprendizaje propuesto, recibe un conjunto de datos que contiene combinaciones, etiquetadas por el usuario, de valores de parámetros de un algoritmo de síntesis. Luego, analiza los patrones, en función de la disimilitud, entre las combinaciones de cada etiqueta. Estos patrones se describen como un modelo de reglas lógicas IF-THEN. Los parámetros del algoritmo proporcionan el control para definir qué se considera un patrón. Como los patrones son la base para inducir nuevas configuraciones de parámetros, los parámetros del algoritmo controlan también el grado de consistencia de las configuraciones inducidas con respecto a los datos de entrada originales. Luego, se presenta un algoritmo (llamado FuzzyRuLer) capaz de extender las reglas lógicas tipo IF-THEN a hiperrectángulos, que a su vez se utilizan como núcleos de funciones de pertenencia. El modelo de reglas difusas resultante crea un mapa completo del espacio de las clases de entrada. Para tal fin, el algoritmo generaliza las reglas lógicas resolviendo las contradicciones utilizando una heurística de máximo volumen. A lo largo del manuscrito se analiza cómo, cuando los algoritmos de aprendizaje automático se utilizan como herramientas creativas, los glitches, errores o inexactitudes producidas por los modelos resultantes son a veces deseables, ya que pueden ofrecer resultados novedosos e impredecibles. La evaluación de los algoritmos sigue dos caminos. El primero se centra en pruebas de usuario. El segundo, responde al hecho de que este trabajo se llevó a cabo dentro del departamento de ciencias de la computación y está destinado a proporcionar una evaluación más amplia, no de dominio específica, del rendimiento de los algoritmos utilizando beanchmarks extrínsecos para cross-validation y oversampling. En estas últimas pruebas, utilizando conjuntos de datos no balanceados, el algoritmo produce resultados equiparables a los del estado del arte. Además, los puntos sintéticos producidos son significativamente diferentes de los creados por los otros algoritmos y realizan una exploración (controlada) de regiones más distantes. Finalmente, acompañando la investigación, realicé diversas presentaciones, conciertos y un ´álbum utilizando los algoritmos y ejemplos de esta tesis. Las críticas recibidas y las listas donde se ha presentado el álbum muestran una recepción positiva de la comunidad. En conjunto, estas evaluaciones sugieren que el aprendizaje de reglas es al mismo tiempo un método eficaz y un camino prometedor para futuras investigaciones.Postprint (published version

Using conditional restricted Boltzmann machines to generate timbral music composition systems

Machine-learning models have been successfully applied to musical composition in a variety of forms, including audio classification, recognition, and synthesis. The capability of algorithms to learn complex musical elements allows composers to more deeply investigate the development of their aesthetic. Coupled with the history of interdisciplinary solutions found in computer music and system aesthetics, this capability has led to an exploration of the integration of machine learning and music composition. Composition systems that take advantage of this integration have the opportunity to be connected with algorithms in theory, application, and art. In my systems, conditional restricted Boltzmann machines (CRBM) synthesize musical timbre by learning autoregressive connections between the current output, an abstracted non-linear hidden feature layer, and past out- puts. This provides a creative space where composers can synthesize audio spectra in collaboration with machines, defining novel creative systems that explore compositional material in an abstract, non-linear paradigm. By implementing CRBMs in timbral-synthesis composition systems, I provide concrete support that such an integration advances art through the exploration of machine learning. I demonstrate this in a variety of audio synthesis experiments validating the capabilities of two algorithmic structures to synthesize and control timbre: a single layer conditional restricted Boltzmann machine (CRBM) and a single layer factored conditional restricted Boltzmann machine (FCRBM). I start by accurately synthesizing specific instrumental timbres and different musical pitches, demonstrating the aural capabilities of directly using the algorithms. I then build from these experiments, creating a set of compositional utilities that provide the composer with a rich pallet to provoke aesthetic introspection. These compositional utilities are then implemented in two music composition systems that synthesize and control timbre in application, where the algorithms themselves are designed and manipulated as a means to realize artwork. Through the creation of music composition systems that are able to accurately synthesize and control musical timbre, I demonstrate these models have the capability of provoking the aesthetic introspection of composers. The resulting systems show the power and potential of integrating music composition and machine learning, endorsing an interdisciplinary approach to the development of art and technology

Scalable Synthesis and Verification: Towards Reliable Autonomy

We have seen the growing deployment of autonomous systems in our daily life, ranging from safety-critical self-driving cars to dialogue agents. While impactful and impressive, these systems do not often come with guarantees and are not rigorously evaluated for failure cases. This is in part due to the limited scalability of tools available for designing correct-by-construction systems, or verifying them posthoc. Another key limitation is the lack of availability of models for the complex environments with which autonomous systems often have to interact with. In the direction of overcoming these above mentioned bottlenecks to designing reliable autonomous systems, this thesis makes contributions along three fronts. First, we develop an approach for parallelized synthesis from linear-time temporal logic Specifications corresponding to the generalized reactivity (1) fragment. We begin by identifying a special case corresponding to singleton liveness goals that allows for a decomposition of the synthesis problem, which facilitates parallelized synthesis. Based on the intuition from this special case, we propose a more generalized approach for parallelized synthesis that relies on identifying equicontrollable states. Second, we consider learning-based approaches to enable verification at scale for complex systems, and for autonomous systems that interact with black-box environments. For the former, we propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. For the latter, we present a data-driven approach based on chance-constrained optimization that allows for a system to be evaluated for specification conformance without an accurate model of the environment. We demonstrate this approach on several tasks, including a lane-change scenario with real-world driving data. Lastly, we consider the problem of interpreting and verifying learning-based components such as neural networks. We introduce a new method based on Craig's interpolants for computing compact symbolic abstractions of pre-images for neural networks. Our approach relies on iteratively computing approximations that provably overapproximate and underapproximate the pre-images at all layers. Further, building on existing work for training neural networks for verifiability in the classification setting, we propose extensions that allow us to generalize the approach to more general architectures and temporal specifications.</p