Probabilistic data-driven methods for forecasting, identification and control

This dissertation presents contributions mainly in three different fields: system identification, probabilistic forecasting and stochastic control. Thanks to the concept of dissimilarity and by defining an appropriate dissimilarity function, it is shown that a family of predictors can be obtained. First, a predictor to compute nominal forecastings of a time-series or a dynamical system is presented. The effectiveness of the predictor is shown by means of a numerical example, where daily predictions of a stock index are computed. The obtained results turn out to be better than those obtained with popular machine learning techniques like Neural Networks. Similarly, the aforementioned dissimilarity function can be used to compute conditioned probability distributions. By means of the obtained distributions, interval predictions can be made by using the concept of quantiles. However, in order to do that, it is necessary to integrate the distribution for all the possible values of the output. As this numerical integration process is computationally expensive, an alternate method bypassing the computation of the probability distribution is also proposed. Not only is computationally cheaper but it also allows to compute prediction regions, which are the multivariate version of the interval predictions. Both methods present better results than other baseline approaches in a set of examples, including a stock forecasting example and the prediction of the Lorenz attractor. Furthermore, new methods to obtain models of nonlinear systems by means of input-output data are proposed. Two different model approaches are presented: a local data approach and a kernel-based approach. A kalman filter can be added to improve the quality of the predictions. It is shown that the forecasting performance of the proposed models is better than other machine learning methods in several examples, such as the forecasting of the sunspot number and the R¨ossler attractor. Also, as these models are suitable for Model Predictive Control (MPC), new MPC formulations are proposed. Thanks to the distinctive features of the proposed models, the nonlinear MPC problem can be posed as a simple quadratic programming problem. Finally, by means of a simulation example and a real experiment, it is shown that the controller performs adequately. On the other hand, in the field of stochastic control, several methods to bound the constraint violation rate of any controller under the presence of bounded or unbounded disturbances are presented. These can be used, for example, to tune some hyperparameters of the controller. Some simulation examples are proposed in order to show the functioning of the algorithms. One of these examples considers the management of a data center. Here, an energy-efficient MPC-inspired policy is developed in order to reduce the electricity consumption while keeping the quality of service at acceptable levels

Towards Revealing the Mystery behind Chain of Thought: a Theoretical Perspective

Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the capacity of LLMs with CoT in solving fundamental mathematical and decision-making problems. We start by giving an impossibility result showing that any bounded-depth Transformer cannot directly output correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of a constant size suffice to solve both tasks by generating CoT derivations using a commonly-used math language format. Moreover, we show LLMs with CoT are capable of solving a general class of decision-making problems known as Dynamic Programming, thus justifying its power in tackling complex real-world tasks. Finally, extensive experiments on four tasks show that, while Transformers always fail to predict the answers directly, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.Comment: 33 page

DynaProg for Scala

Dynamic programming is an algorithmic technique to solve problems that follow the Bellman’s principle: optimal solutions depends on optimal sub-problem solutions. The core idea behind dynamic programming is to memoize intermediate results into matrices to avoid multiple computations. Solving a dynamic programming problem consists of two phases: filling one or more matrices with intermediate solutions for sub-problems and recomposing how the final result was constructed (backtracking). In textbooks, problems are usually described in terms of recurrence relations between matrices elements. Expressing dynamic programming problems in terms of recursive formulae involving matrix indices might be difficult, if often error prone, and the notation does not capture the essence of the underlying problem (for example aligning two sequences). Moreover, writing correct and efficient parallel implementation requires different competencies and often a significant amount of time. In this project, we present DynaProg, a language embedded in Scala (DSL) to address dynamic programming problems on heterogeneous platforms. DynaProg allows the programmer to write concise programs based on ADP [1], using a pair of parsing grammar and algebra; these program can then be executed either on CPU or on GPU. We evaluate the performance of our implementation against existing work and our own hand-optimized baseline implementations for both the CPU and GPU versions. Experimental results show that plain Scala has a large overhead and is recommended to be used with small sequences (≤1024) whereas the generated GPU version is comparable with existing implementations: matrix chain multiplication has the same performance as our hand-optimized version (142% of the execution time of [2]) for a sequence of 4096 matrices, Smith-Waterman is twice slower than [3] on a pair of sequences of 6144 elements, and RNA folding is on par with [4] (95% running time) for sequences of 4096 elements. [1] Robert Giegerich and Carsten Meyer. Algebraic Dynamic Programming. [2] Chao-Chin Wu, Jenn-Yang Ke, Heshan Lin and Wu Chun Feng. Optimizing dynamic programming on graphics processing units via adaptive thread-level parallelism. [3] Edans Flavius de O. Sandes, Alba Cristina M. A. de Melo. Smith-Waterman alignment of huge sequences with GPU in linear space. [4] Guillaume Rizk and Dominique Lavenier. GPU accelerated RNA folding algorithm

Procedurally generated realistic virtual rural worlds

Manually creating virtual rural worlds is often a difficult and lengthy task for artists, as plant species selection, plant distributions and water networks must be deduced such that they realistically reflect the environment being modelled. As virtual worlds grow in size and complexity, climates vary on the terrain itself and a single ecosystem is no longer sufficient to realistically model all vegetation. Consequentially, the task is only becoming more difficult for these artists. Procedural methods are extensively used in computer graphics to partially or fully automate some tasks and take some of the burden off the user. Input parameters for these procedural algorithms are often unintuitive, however, and their impact on the final results, unclear. This thesis proposes, implements, and evaluates an approach to procedurally generate vegetation and water networks for realistic virtual rural worlds. Rather than placing these to reflect the environment being modelled, the work-flow is mirrored and the user models the environment directly by specifying the resources available. These intuitive input parameters are subsequently used to configure procedural algorithms and determine suitable vegetation, plant distributions and water networks. By design, the placeable plant species are configurable so any type of environment can be modelled at various levels of detail. The system has been tested by creating three ecosystems with little effort on the part of the user

Artificial Intelligence for Small Satellites Mission Autonomy

Space mission engineering has always been recognized as a very challenging and innovative branch of engineering: since the beginning of the space race, numerous milestones, key successes and failures, improvements, and connections with other engineering domains have been reached. Despite its relative young age, space engineering discipline has not gone through homogeneous times: alternation of leading nations, shifts in public and private interests, allocations of resources to different domains and goals are all examples of an intrinsic dynamism that characterized this discipline. The dynamism is even more striking in the last two decades, in which several factors contributed to the fervour of this period. Two of the most important ones were certainly the increased presence and push of the commercial and private sector and the overall intent of reducing the size of the spacecraft while maintaining comparable level of performances. A key example of the second driver is the introduction, in 1999, of a new category of space systems called CubeSats. Envisioned and designed to ease the access to space for universities, by standardizing the development of the spacecraft and by ensuring high probabilities of acceptance as piggyback customers in launches, the standard was quickly adopted not only by universities, but also by agencies and private companies. CubeSats turned out to be a disruptive innovation, and the space mission ecosystem was deeply changed by this. New mission concepts and architectures are being developed: CubeSats are now considered as secondary payloads of bigger missions, constellations are being deployed in Low Earth Orbit to perform observation missions to a performance level considered to be only achievable by traditional, fully-sized spacecraft. CubeSats, and more in general the small satellites technology, had to overcome important challenges in the last few years that were constraining and reducing the diffusion and adoption potential of smaller spacecraft for scientific and technology demonstration missions. Among these challenges were: the miniaturization of propulsion technologies, to enable concepts such as Rendezvous and Docking, or interplanetary missions; the improvement of telecommunication state of the art for small satellites, to enable the downlink to Earth of all the data acquired during the mission; and the miniaturization of scientific instruments, to be able to exploit CubeSats in more meaningful, scientific, ways. With the size reduction and with the consolidation of the technology, many aspects of a space mission are reduced in consequence: among these, costs, development and launch times can be cited. An important aspect that has not been demonstrated to scale accordingly is operations: even for small satellite missions, human operators and performant ground control centres are needed. In addition, with the possibility of having constellations or interplanetary distributed missions, a redesign of how operations are management is required, to cope with the innovation in space mission architectures. The present work has been carried out to address the issue of operations for small satellite missions. The thesis presents a research, carried out in several institutions (Politecnico di Torino, MIT, NASA JPL), aimed at improving the autonomy level of space missions, and in particular of small satellites. The key technology exploited in the research is Artificial Intelligence, a computer science branch that has gained extreme interest in research disciplines such as medicine, security, image recognition and language processing, and is currently making its way in space engineering as well. The thesis focuses on three topics, and three related applications have been developed and are here presented: autonomous operations by means of event detection algorithms, intelligent failure detection on small satellite actuator systems, and decision-making support thanks to intelligent tradespace exploration during the preliminary design of space missions. The Artificial Intelligent technologies explored are: Machine Learning, and in particular Neural Networks; Knowledge-based Systems, and in particular Fuzzy Logics; Evolutionary Algorithms, and in particular Genetic Algorithms. The thesis covers the domain (small satellites), the technology (Artificial Intelligence), the focus (mission autonomy) and presents three case studies, that demonstrate the feasibility of employing Artificial Intelligence to enhance how missions are currently operated and designed

Painting Pictures with Words - From Theory to System

A picture paints a thousand words, or so we are told. But how many words does it take to paint a picture? And how can words create pictures in the first place? In this thesis we examine a new theory of linguistic meaning -- where the meaning of words and sentences is determined by the scenes they evoke. We describe how descriptive text is parsed and semantically interpreted and how the semantic interpretation is then depicted as a rendered 3D scene. In doing so, we describe WordsEye, our text-to-scene system, and touch upon many fascinating issues of lexical semantics, knowledge representation, and what we call "graphical semantics." We introduce the notion of vignettes as a way to bridge between function and form, between the semantics of language and the grounded semantics of 3D scenes. And we describe how VigNet, our lexical semantic and graphical knowledge base, mediates the whole process. In the second part of this thesis, we describe four different ways WordsEye has been tested. We first discuss an evaluation of the system in an educational environment where WordsEye was shown to significantly improve literacy skills for sixth grade students versus a control group. We then compare WordsEye with Google Image Search on "realistic" and "imaginative" sentences in order to evaluate its performance on a sentence-by-sentence level and test its potential as a way to augment existing image search tools. Thirdly, we describe what we have learned in testing WordsEye as an online 3D authoring system where it has attracted 20,000 real-world users who have performed almost one million scene depictions. Finally, we describe tests of WordsEye as an elicitation tool for field linguists studying endangered languages. We then sum up by presenting a roadmap for enhancing the capabilities of the system and identifying key opportunities and issues to be addressed

Knowledge-enhanced neural grammar Induction

Natural language is usually presented as a word sequence, but the inherent structure of language is not necessarily sequential. Automatic grammar induction for natural language is a long-standing research topic in the field of computational linguistics and still remains an open problem today. From the perspective of cognitive science, the goal of a grammar induction system is to mimic children: learning a grammar that can generalize to infinitely many utterances by only consuming finite data. With regard to computational linguistics, an automatic grammar induction system could be beneficial for a wide variety of natural language processing (NLP) applications: providing syntactic analysis explicitly for a pipeline or a joint learning system; injecting structural bias implicitly into an end-to-end model. Typically, approaches to grammar induction only have access to raw text. Due to the huge search space of trees as well as data sparsity and ambiguity issues, grammar induction is a difficult problem. Thanks to the rapid development of neural networks and their capacity of over-parameterization and continuous representation learning, neural models have been recently introduced to grammar induction. Given its large capacity, introducing external knowledge into a neural system is an effective approach in practice, especially for an unsupervised problem. This thesis explores how to incorporate external knowledge into neural grammar induction models. We develop several approaches to combine different types of knowledge with neural grammar induction models on two grammar formalisms — constituency and dependency grammar. We first investigate how to inject symbolic knowledge, universal linguistic rules, into unsupervised dependency parsing. In contrast to previous state-of-the-art models that utilize time-consuming global inference, we propose a neural transition-based parser using variational inference. Our parser is able to employ rich features and supports inference in linear time for both training and testing. The core component in our parser is posterior regularization, where the posterior distribution of the dependency trees is constrained by the universal linguistic rules. The resulting parser outperforms previous unsupervised transition-based dependency parsers and achieves performance comparable to global inference-based models. Our parser also substantially increases parsing speed over global inference-based models. Recently, tree structures have been considered as latent variables that are learned through downstream NLP tasks, such as language modeling and natural language inference. More specifically, auxiliary syntax-aware components are embedded into the neural networks and are trained end-to-end on the downstream tasks. However, such latent tree models either struggle to produce linguistically plausible tree structures, or require an external biased parser to obtain good parsing performance. In the second part of this thesis, we focus on constituency structure and propose to use imitation learning to couple two heterogeneous latent tree models: we transfer the knowledge learned from a continuous latent tree model trained using language modeling to a discrete one, and further fine-tune the discrete model using a natural language inference objective. Through this two-stage training scheme, the discrete latent tree model achieves stateof-the-art unsupervised parsing performance. The transformer is a newly proposed neural model for NLP. Transformer-based pre-trained language models (PLMs) like BERT have achieved remarkable success on various NLP tasks by training on an enormous corpus using word prediction tasks. Recent studies show that PLMs can learn considerable syntactical knowledge in a syntaxagnostic manner. In the third part of this thesis, we leverage PLMs as a source of external knowledge. We propose a parameter-free approach to select syntax-sensitive self-attention heads from PLMs and perform chart-based unsupervised constituency parsing. In contrast to previous approaches, our head-selection approach only relies on raw text without any annotated development data. Experimental results on both English and eight other languages show that our approach achieves competitive performance

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Parallel CYK Membership Test on GPUs

Part 2: Parallel and Multi-Core TechnologiesInternational audienceNowadays general-purpose computing on graphics processing units (GPGPUs) performs computations what were formerly handled by the CPU using hundreds of cores on GPUs. It often improves the performance of sequential computation when the running program is well-structured and formulated for massive threading. The CYK algorithm is a well-known algorithm for the context-free language membership test and has been used in many applications including grammar inferences, compilers and natural language processing. We revisit the CYK algorithm and its structural properties suitable for parallelization. Based on the discovered properties, we then parallelize the algorithm using different combinations of memory types and data allocation schemes using a GPU. We evaluate the algorithm based on real-world data and herein demonstrate the performance improvement compared with CPU-based computations