10,057 research outputs found

    Exploiting Structural Properties in the Analysis of High-dimensional Dynamical Systems

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    The physical and cyber domains with which we interact are filled with high-dimensional dynamical systems. In machine learning, for instance, the evolution of overparametrized neural networks can be seen as a dynamical system. In networked systems, numerous agents or nodes dynamically interact with each other. A deep understanding of these systems can enable us to predict their behavior, identify potential pitfalls, and devise effective solutions for optimal outcomes. In this dissertation, we will discuss two classes of high-dimensional dynamical systems with specific structural properties that aid in understanding their dynamic behavior. In the first scenario, we consider the training dynamics of multi-layer neural networks. The high dimensionality comes from overparametrization: a typical network has a large depth and hidden layer width. We are interested in the following question regarding convergence: Do network weights converge to an equilibrium point corresponding to a global minimum of our training loss, and how fast is the convergence rate? The key to those questions is the symmetry of the weights, a critical property induced by the multi-layer architecture. Such symmetry leads to a set of time-invariant quantities, called weight imbalance, that restrict the training trajectory to a low-dimensional manifold defined by the weight initialization. A tailored convergence analysis is developed over this low-dimensional manifold, showing improved rate bounds for several multi-layer network models studied in the literature, leading to novel characterizations of the effect of weight imbalance on the convergence rate. In the second scenario, we consider large-scale networked systems with multiple weakly-connected groups. Such a multi-cluster structure leads to a time-scale separation between the fast intra-group interaction due to high intra-group connectivity, and the slow inter-group oscillation, due to the weak inter-group connection. We develop a novel frequency-domain network coherence analysis that captures both the coherent behavior within each group, and the dynamical interaction between groups, leading to a structure-preserving model-reduction methodology for large-scale dynamic networks with multiple clusters under general node dynamics assumptions

    Interpreting Black-Box Models: A Review on Explainable Artificial Intelligence

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    Recent years have seen a tremendous growth in Artificial Intelligence (AI)-based methodological development in a broad range of domains. In this rapidly evolving field, large number of methods are being reported using machine learning (ML) and Deep Learning (DL) models. Majority of these models are inherently complex and lacks explanations of the decision making process causing these models to be termed as 'Black-Box'. One of the major bottlenecks to adopt such models in mission-critical application domains, such as banking, e-commerce, healthcare, and public services and safety, is the difficulty in interpreting them. Due to the rapid proleferation of these AI models, explaining their learning and decision making process are getting harder which require transparency and easy predictability. Aiming to collate the current state-of-the-art in interpreting the black-box models, this study provides a comprehensive analysis of the explainable AI (XAI) models. To reduce false negative and false positive outcomes of these back-box models, finding flaws in them is still difficult and inefficient. In this paper, the development of XAI is reviewed meticulously through careful selection and analysis of the current state-of-the-art of XAI research. It also provides a comprehensive and in-depth evaluation of the XAI frameworks and their efficacy to serve as a starting point of XAI for applied and theoretical researchers. Towards the end, it highlights emerging and critical issues pertaining to XAI research to showcase major, model-specific trends for better explanation, enhanced transparency, and improved prediction accuracy

    Rethinking data augmentation for adversarial robustness

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    Recent work has proposed novel data augmentation methods to improve the adversarial robustness of deep neural networks. In this paper, we re-evaluate such methods through the lens of different metrics that characterize the augmented manifold, finding contradictory evidence. Our extensive empirical analysis involving 5 data augmentation methods, all tested with an increasing probability of augmentation, shows that: (i) novel data augmentation methods proposed to improve adversarial robustness only improve it when combined with classical augmentations (like image flipping and rotation), and even worsen adversarial robustness if used in isolation; and (ii) adversarial robustness is significantly affected by the augmentation probability, conversely to what is claimed in recent work. We conclude by discussing how to rethink the development and evaluation of novel data augmentation methods for adversarial robustness. Our open-source code is available at https://github.com/eghbalz/rethink_da_for_a

    On the Generation of Realistic and Robust Counterfactual Explanations for Algorithmic Recourse

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    This recent widespread deployment of machine learning algorithms presents many new challenges. Machine learning algorithms are usually opaque and can be particularly difficult to interpret. When humans are involved, algorithmic and automated decisions can negatively impact people’s lives. Therefore, end users would like to be insured against potential harm. One popular way to achieve this is to provide end users access to algorithmic recourse, which gives end users negatively affected by algorithmic decisions the opportunity to reverse unfavorable decisions, e.g., from a loan denial to a loan acceptance. In this thesis, we design recourse algorithms to meet various end user needs. First, we propose methods for the generation of realistic recourses. We use generative models to suggest recourses likely to occur under the data distribution. To this end, we shift the recourse action from the input space to the generative model’s latent space, allowing to generate counterfactuals that lie in regions with data support. Second, we observe that small changes applied to the recourses prescribed to end users likely invalidate the suggested recourse after being nosily implemented in practice. Motivated by this observation, we design methods for the generation of robust recourses and for assessing the robustness of recourse algorithms to data deletion requests. Third, the lack of a commonly used code-base for counterfactual explanation and algorithmic recourse algorithms and the vast array of evaluation measures in literature make it difficult to compare the per formance of different algorithms. To solve this problem, we provide an open source benchmarking library that streamlines the evaluation process and can be used for benchmarking, rapidly developing new methods, and setting up new experiments. In summary, our work contributes to a more reliable interaction of end users and machine learned models by covering fundamental aspects of the recourse process and suggests new solutions towards generating realistic and robust counterfactual explanations for algorithmic recourse

    Contraction analysis of nonlinear systems and its application

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    The thesis addresses various issues concerning the convergence properties of switched systems and differential algebraic equation (DAE) systems. Specifically, we focus on contraction analysis problem, as well as tackling problems related to stabilization and synchronization. We consider the contraction analysis of switched systems and DAE systems. To address this, a transformation is employed to convert the contraction analysis problem into a stabilization analysis problem. This transformation involves the introduction of virtual systems, which exhibit a strong connection with the Jacobian matrix of the vector field. Analyzing these systems poses a significant challenge due to the distinctive structure of their Jacobian matrices. Regarding the switched systems, a time-dependent switching law is established to guarantee uniform global exponential stability (UGES). As for the DAE system, we begin by embedding it into an ODE system. Subsequently, the UGES property is ensured by analyzing its matrix measure. As our first application, we utilize our approach to stabilize time-invariant switched systems and time-invariant DAE systems, respectively. This involves designing control laws to achieve system contractivity, thereby ensuring that the trajectory set encompasses the equilibrium point. In oursecond application, we propose the design of a time-varying observer by treating the system’s output as an algebraic equation of the DAE system. In our study on synchronization problems, we investigate two types of synchronization issues: the trajectory tracking of switched oscillators and the pinning state synchronization. In the case of switched oscillators, we devise a time-dependent switching law to ensure that these oscillators effectively follow the trajectory of a time-varying system. As for the pinning synchronization problem, we define solvable conditions and, building upon these conditions, we utilize contraction theory to design dynamic controllers that guarantee synchronization is achieved among the agents

    Contraction analysis of nonlinear systems and its application

    Get PDF
    The thesis addresses various issues concerning the convergence properties of switched systems and differential algebraic equation (DAE) systems. Specifically, we focus on contraction analysis problem, as well as tackling problems related to stabilization and synchronization. We consider the contraction analysis of switched systems and DAE systems. To address this, a transformation is employed to convert the contraction analysis problem into a stabilization analysis problem. This transformation involves the introduction of virtual systems, which exhibit a strong connection with the Jacobian matrix of the vector field. Analyzing these systems poses a significant challenge due to the distinctive structure of their Jacobian matrices. Regarding the switched systems, a time-dependent switching law is established to guarantee uniform global exponential stability (UGES). As for the DAE system, we begin by embedding it into an ODE system. Subsequently, the UGES property is ensured by analyzing its matrix measure. As our first application, we utilize our approach to stabilize time-invariant switched systems and time-invariant DAE systems, respectively. This involves designing control laws to achieve system contractivity, thereby ensuring that the trajectory set encompasses the equilibrium point. In oursecond application, we propose the design of a time-varying observer by treating the system’s output as an algebraic equation of the DAE system. In our study on synchronization problems, we investigate two types of synchronization issues: the trajectory tracking of switched oscillators and the pinning state synchronization. In the case of switched oscillators, we devise a time-dependent switching law to ensure that these oscillators effectively follow the trajectory of a time-varying system. As for the pinning synchronization problem, we define solvable conditions and, building upon these conditions, we utilize contraction theory to design dynamic controllers that guarantee synchronization is achieved among the agents

    Enhancing traditional Chinese medicine diagnostics: Integrating ontological knowledge for multi-label symptom entity classification

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    In traditional Chinese medicine (TCM), artificial intelligence (AI)-assisted syndrome differentiation and disease diagnoses primarily confront the challenges of accurate symptom identification and classification. This study introduces a multi-label entity extraction model grounded in TCM symptom ontology, specifically designed to address the limitations of existing entity recognition models characterized by limited label spaces and an insufficient integration of domain knowledge. This model synergizes a knowledge graph with the TCM symptom ontology framework to facilitate a standardized symptom classification system and enrich it with domain-specific knowledge. It innovatively merges the conventional bidirectional encoder representations from transformers (BERT) + bidirectional long short-term memory (Bi-LSTM) + conditional random fields (CRF) entity recognition methodology with a multi-label classification strategy, thereby adeptly navigating the intricate label interdependencies in the textual data. Introducing a multi-associative feature fusion module is a significant advancement, thereby enabling the extraction of pivotal entity features while discerning the interrelations among diverse categorical labels. The experimental outcomes affirm the model's superior performance in multi-label symptom extraction and substantially elevates the efficiency and accuracy. This advancement robustly underpins research in TCM syndrome differentiation and disease diagnoses

    Deep Learning Techniques for Electroencephalography Analysis

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    In this thesis we design deep learning techniques for training deep neural networks on electroencephalography (EEG) data and in particular on two problems, namely EEG-based motor imagery decoding and EEG-based affect recognition, addressing challenges associated with them. Regarding the problem of motor imagery (MI) decoding, we first consider the various kinds of domain shifts in the EEG signals, caused by inter-individual differences (e.g. brain anatomy, personality and cognitive profile). These domain shifts render multi-subject training a challenging task and impede robust cross-subject generalization. We build a two-stage model ensemble architecture and propose two objectives to train it, combining the strengths of curriculum learning and collaborative training. Our subject-independent experiments on the large datasets of Physionet and OpenBMI, verify the effectiveness of our approach. Next, we explore the utilization of the spatial covariance of EEG signals through alignment techniques, with the goal of learning domain-invariant representations. We introduce a Riemannian framework that concurrently performs covariance-based signal alignment and data augmentation, while training a convolutional neural network (CNN) on EEG time-series. Experiments on the BCI IV-2a dataset show that our method performs superiorly over traditional alignment, by inducing regularization to the weights of the CNN. We also study the problem of EEG-based affect recognition, inspired by works suggesting that emotions can be expressed in relative terms, i.e. through ordinal comparisons between different affective state levels. We propose treating data samples in a pairwise manner to infer the ordinal relation between their corresponding affective state labels, as an auxiliary training objective. We incorporate our objective in a deep network architecture which we jointly train on the tasks of sample-wise classification and pairwise ordinal ranking. We evaluate our method on the affective datasets of DEAP and SEED and obtain performance improvements over deep networks trained without the additional ranking objective

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    Koopman Kernel Regression

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    Many machine learning approaches for decision making, such as reinforcement learning, rely on simulators or predictive models to forecast the time-evolution of quantities of interest, e.g., the state of an agent or the reward of a policy. Forecasts of such complex phenomena are commonly described by highly nonlinear dynamical systems, making their use in optimization-based decision-making challenging. Koopman operator theory offers a beneficial paradigm for addressing this problem by characterizing forecasts via linear time-invariant (LTI) ODEs, turning multi-step forecasts into sparse matrix multiplication. Though there exists a variety of learning approaches, they usually lack crucial learning-theoretic guarantees, making the behavior of the obtained models with increasing data and dimensionality unclear. We address the aforementioned by deriving a universal Koopman-invariant reproducing kernel Hilbert space (RKHS) that solely spans transformations into LTI dynamical systems. The resulting Koopman Kernel Regression (KKR) framework enables the use of statistical learning tools from function approximation for novel convergence results and generalization error bounds under weaker assumptions than existing work. Our experiments demonstrate superior forecasting performance compared to Koopman operator and sequential data predictors in RKHS.Comment: Accepted to the thirty-seventh Conference on Neural Information Processing Systems (NeurIPS 2023
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