Breaking the Curse of Dimensionality in Deep Neural Networks by Learning Invariant Representations

Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as natural language processing and computer vision, largely attributed to deep learning, a special class of machine learning models. Deep learning arguably surpasses traditional approaches by learning the relevant features from raw data through a series of computational layers. This thesis explores the theoretical foundations of deep learning by studying the relationship between the architecture of these models and the inherent structures found within the data they process. In particular, we ask What drives the efficacy of deep learning algorithms and allows them to beat the so-called curse of dimensionality-i.e. the difficulty of generally learning functions in high dimensions due to the exponentially increasing need for data points with increased dimensionality? Is it their ability to learn relevant representations of the data by exploiting their structure? How do different architectures exploit different data structures? In order to address these questions, we push forward the idea that the structure of the data can be effectively characterized by its invariances-i.e. aspects that are irrelevant for the task at hand. Our methodology takes an empirical approach to deep learning, combining experimental studies with physics-inspired toy models. These simplified models allow us to investigate and interpret the complex behaviors we observe in deep learning systems, offering insights into their inner workings, with the far-reaching goal of bridging the gap between theory and practice.Comment: PhD Thesis @ EPF

Linguistic Competence and New Empiricism in Philosophy and Science

The topic of this dissertation is the nature of linguistic competence, the capacity to understand and produce sentences of natural language. I defend the empiricist account of linguistic competence embedded in the connectionist cognitive science. This strand of cognitive science has been opposed to the traditional symbolic cognitive science, coupled with transformational-generative grammar, which was committed to nativism due to the view that human cognition, including language capacity, should be construed in terms of symbolic representations and hardwired rules. Similarly, linguistic competence in this framework was regarded as being innate, rule-governed, domain-specific, and fundamentally different from performance, i.e., idiosyncrasies and factors governing linguistic behavior. I analyze state-of-the-art connectionist, deep learning models of natural language processing, most notably large language models, to see what they can tell us about linguistic competence. Deep learning is a statistical technique for the classification of patterns through which artificial intelligence researchers train artificial neural networks containing multiple layers that crunch a gargantuan amount of textual and/or visual data. I argue that these models suggest that linguistic competence should be construed as stochastic, pattern-based, and stemming from domain-general mechanisms. Moreover, I distinguish syntactic from semantic competence, and I show for each the ramifications of the endorsement of a connectionist research program as opposed to the traditional symbolic cognitive science and transformational-generative grammar. I provide a unifying front, consisting of usage-based theories, a construction grammar approach, and an embodied approach to cognition to show that the more multimodal and diverse models are in terms of architectural features and training data, the stronger the case is for the connectionist linguistic competence. I also propose to discard the competence vs. performance distinction as theoretically inferior so that a novel and integrative account of linguistic competence originating in connectionism and empiricism that I propose and defend in the dissertation could be put forward in scientific and philosophical literature

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Pre-processing, classification and semantic querying of large-scale Earth observation spaceborne/airborne/terrestrial image databases: Process and product innovations.

By definition of Wikipedia, “big data is the term adopted for a collection of data sets so large and complex that it becomes difficult to process using on-hand database management tools or traditional data processing applications. The big data challenges typically include capture, curation, storage, search, sharing, transfer, analysis and visualization”. Proposed by the intergovernmental Group on Earth Observations (GEO), the visionary goal of the Global Earth Observation System of Systems (GEOSS) implementation plan for years 2005-2015 is systematic transformation of multisource Earth Observation (EO) “big data” into timely, comprehensive and operational EO value-adding products and services, submitted to the GEO Quality Assurance Framework for Earth Observation (QA4EO) calibration/validation (Cal/Val) requirements. To date the GEOSS mission cannot be considered fulfilled by the remote sensing (RS) community. This is tantamount to saying that past and existing EO image understanding systems (EO-IUSs) have been outpaced by the rate of collection of EO sensory big data, whose quality and quantity are ever-increasing. This true-fact is supported by several observations. For example, no European Space Agency (ESA) EO Level 2 product has ever been systematically generated at the ground segment. By definition, an ESA EO Level 2 product comprises a single-date multi-spectral (MS) image radiometrically calibrated into surface reflectance (SURF) values corrected for geometric, atmospheric, adjacency and topographic effects, stacked with its data-derived scene classification map (SCM), whose thematic legend is general-purpose, user- and application-independent and includes quality layers, such as cloud and cloud-shadow. Since no GEOSS exists to date, present EO content-based image retrieval (CBIR) systems lack EO image understanding capabilities. Hence, no semantic CBIR (SCBIR) system exists to date either, where semantic querying is synonym of semantics-enabled knowledge/information discovery in multi-source big image databases. In set theory, if set A is a strict superset of (or strictly includes) set B, then A B. This doctoral project moved from the working hypothesis that SCBIR computer vision (CV), where vision is synonym of scene-from-image reconstruction and understanding EO image understanding (EO-IU) in operating mode, synonym of GEOSS ESA EO Level 2 product human vision. Meaning that necessary not sufficient pre-condition for SCBIR is CV in operating mode, this working hypothesis has two corollaries. First, human visual perception, encompassing well-known visual illusions such as Mach bands illusion, acts as lower bound of CV within the multi-disciplinary domain of cognitive science, i.e., CV is conditioned to include a computational model of human vision. Second, a necessary not sufficient pre-condition for a yet-unfulfilled GEOSS development is systematic generation at the ground segment of ESA EO Level 2 product. Starting from this working hypothesis the overarching goal of this doctoral project was to contribute in research and technical development (R&D) toward filling an analytic and pragmatic information gap from EO big sensory data to EO value-adding information products and services. This R&D objective was conceived to be twofold. First, to develop an original EO-IUS in operating mode, synonym of GEOSS, capable of systematic ESA EO Level 2 product generation from multi-source EO imagery. EO imaging sources vary in terms of: (i) platform, either spaceborne, airborne or terrestrial, (ii) imaging sensor, either: (a) optical, encompassing radiometrically calibrated or uncalibrated images, panchromatic or color images, either true- or false color red-green-blue (RGB), multi-spectral (MS), super-spectral (SS) or hyper-spectral (HS) images, featuring spatial resolution from low (> 1km) to very high (< 1m), or (b) synthetic aperture radar (SAR), specifically, bi-temporal RGB SAR imagery. The second R&D objective was to design and develop a prototypical implementation of an integrated closed-loop EO-IU for semantic querying (EO-IU4SQ) system as a GEOSS proof-of-concept in support of SCBIR. The proposed closed-loop EO-IU4SQ system prototype consists of two subsystems for incremental learning. A primary (dominant, necessary not sufficient) hybrid (combined deductive/top-down/physical model-based and inductive/bottom-up/statistical model-based) feedback EO-IU subsystem in operating mode requires no human-machine interaction to automatically transform in linear time a single-date MS image into an ESA EO Level 2 product as initial condition. A secondary (dependent) hybrid feedback EO Semantic Querying (EO-SQ) subsystem is provided with a graphic user interface (GUI) to streamline human-machine interaction in support of spatiotemporal EO big data analytics and SCBIR operations. EO information products generated as output by the closed-loop EO-IU4SQ system monotonically increase their value-added with closed-loop iterations

Machine learning for improved detection and segmentation of building boundary

The first step in rescuing and mitigating the losses from natural or man-made disasters is to assess damaged assets, including services, utilities and infrastructure, such as buildings. However, manual visual analysis of the affected buildings can be time consuming and labour intensive. Automatic detection of buildings, on the other hand, has the potential to overcome the limitations of conventional approaches. This thesis reviews the existing methods for the automated detection of objects using multi-source geospatial data and presents two novel post processing techniques. Effective building segmentation and recognition techniques are also investigated. Artificial intelligence techniques have been used to identify building boundaries in automated building-detection applications. Compared with other neural network models, the convolutional neural network (CNN) architectures based on supervised and unsupervised approaches provide better results by looking at the image details as spatial information of the entity in the frame. This research incorporates the improved semantic detection ability of Region-based Convolutional Neural Network (Mask R-CNN) and the segmentation refining capability of the conditional random field (CRF)s. Mask R-CNN uses a pre-trained network to recognise the boundary boxes around buildings. It also provides contour key points around buildings that are masked in satellite images. This thesis proposes two novel post-processing techniques that operate by modifying and detecting the building’s relative orientation properties and combining the key points predicted by the two head neural networks to modify the predicted contour with the help of the proposed novel snap algorithms. The results show significant improvements in the accuracy of boundary detection compared with the state-ofthe-art techniques of 2.5%, 4.6% and 1% for F1-Score, Intersection over Union also known as Jacard coefficient (IoU), and overall pixel accuracy, respectively. CNNs have proven to be powerful tools for a wide range of image processing tasks where they can be used to automatically learn mid-level and high-level concepts from raw data, such as images. Finally, the results highlight the potential of further approaches to these applications, such as the planning of infrastructure