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Model selection is an integral problem of model based optimization techniques such as Bayesian optimization (BO). Current approaches often treat model selection as an estimation problem, to be periodically updated with observations coming from the optimization iterations. In this paper, we propose an alternative way to achieve both efficiently. Specifically, we propose a novel way of integrating model selection and BO for the single goal of reaching the function optima faster. The algorithm moves back and forth between BO in the model space and BO in the function space, where the goodness of the recommended model is captured by a score function and fed back, capturing how well the model helped convergence in the function space. The score function is derived in such a way that it neutralizes the effect of the moving nature of the BO in the function space, thus keeping the model selection problem stationary. This back and forth leads to quick convergence for both model selection and BO in the function space. In addition to improved sample efficiency, the framework outputs information about the black-box function. Convergence is proved, and experimental results show significant improvement compared to standard BO.

The present study aims to explore the feasibility of language translation using quantum natural language processing algorithms on noisy intermediate-scale quantum (NISQ) devices. Classical methods in natural language processing (NLP) struggle with handling large-scale computations required for complex language tasks, but quantum NLP on NISQ devices holds promise in harnessing quantum parallelism and entanglement to efficiently process and analyze vast amounts of linguistic data, potentially revolutionizing NLP applications. Our research endeavors to pave the way for quantum neural machine translation, which could potentially offer advantages over classical methods in the future. We employ Shannon entropy to demonstrate the significant role of some appropriate angles of rotation gates in the performance of parametrized quantum circuits. In particular, we utilize these angles (parameters) as a means of communication between quantum circuits of different languages. To achieve our objective, we adopt the encoder-decoder model of classical neural networks and implement the translation task using long short-term memory (LSTM). Our experiments involved 160 samples comprising English sentences and their Persian translations. We trained the models with different optimisers implementing stochastic gradient descent (SGD) as primary and subsequently incorporating two additional optimizers in conjunction with SGD. Notably, we achieved optimal results-with mean absolute error of 0.03, mean squared error of 0.002, and 0.016 loss-by training the best model, consisting of two LSTM layers and using the Adam optimiser. Our small dataset, though consisting of simple synonymous sentences with word-to-word mappings, points to the utility of Shannon entropy as a figure of merit in more complex machine translation models for intricate sentence structures.

Whereas Laplacian and modularity based spectral clustering is apt to dense graphs, recent results show that for sparse ones, the non-backtracking spectrum is the best candidate to find assortative clusters of nodes. Here belief propagation in the sparse stochastic block model is derived with arbitrary given model parameters that results in a non-linear system of equations; with linear approximation, the spectrum of the non-backtracking matrix is able to specify the number $k$ of clusters. Then the model parameters themselves can be estimated by the EM algorithm. Bond percolation in the assortative model is considered in the following two senses: the within- and between-cluster edge probabilities decrease with the number of nodes and edges coming into existence in this way are retained with probability $\beta$. As a consequence, the optimal $k$ is the number of the structural real eigenvalues (greater than $\sqrt{c}$, where $c$ is the average degree) of the non-backtracking matrix of the graph. Assuming, these eigenvalues $\mu_1 >\dots > \mu_k$ are distinct, the multiple phase transitions obtained for $\beta$ are $\beta_i =\frac{c}{\mu_i^2}$; further, at $\beta_i$ the number of detectable clusters is $i$, for $i=1,\dots ,k$. Inflation-deflation techniques are also discussed to classify the nodes themselves, which can be the base of the sparse spectral clustering.

Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

Recommender system is one of the most important information services on today's Internet. Recently, graph neural networks have become the new state-of-the-art approach of recommender systems. In this survey, we conduct a comprehensive review of the literature in graph neural network-based recommender systems. We first introduce the background and the history of the development of both recommender systems and graph neural networks. For recommender systems, in general, there are four aspects for categorizing existing works: stage, scenario, objective, and application. For graph neural networks, the existing methods consist of two categories, spectral models and spatial ones. We then discuss the motivation of applying graph neural networks into recommender systems, mainly consisting of the high-order connectivity, the structural property of data, and the enhanced supervision signal. We then systematically analyze the challenges in graph construction, embedding propagation/aggregation, model optimization, and computation efficiency. Afterward and primarily, we provide a comprehensive overview of a multitude of existing works of graph neural network-based recommender systems, following the taxonomy above. Finally, we raise discussions on the open problems and promising future directions of this area. We summarize the representative papers along with their codes repositories in //github.com/tsinghua-fib-lab/GNN-Recommender-Systems.

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Graphs, which describe pairwise relations between objects, are essential representations of many real-world data such as social networks. In recent years, graph neural networks, which extend the neural network models to graph data, have attracted increasing attention. Graph neural networks have been applied to advance many different graph related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytical tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges, the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.