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A candidate explanation of the good empirical performance of deep neural networks is the implicit regularization effect of first order optimization methods. Inspired by this, we prove a convergence theorem for nonconvex composite optimization, and apply it to a general learning problem covering many machine learning applications, including supervised learning. We then present a deep multilayer perceptron model and prove that, when sufficiently wide, it $(i)$ leads to the convergence of gradient descent to a global optimum with a linear rate, $(ii)$ benefits from the implicit regularization effect of gradient descent, $(iii)$ is subject to novel bounds on the generalization error, $(iv)$ exhibits the lazy training phenomenon and $(v)$ enjoys learning rate transfer across different widths. The corresponding coefficients, such as the convergence rate, improve as width is further increased, and depend on the even order moments of the data generating distribution up to an order depending on the number of layers. The only non-mild assumption we make is the concentration of the smallest eigenvalue of the neural tangent kernel at initialization away from zero, which has been shown to hold for a number of less general models in contemporary works. We present empirical evidence supporting this assumption as well as our theoretical claims.

We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's widths increase, the network's learning trajectory is shown to be well captured by a meaningful and dynamically nonlinear limit (the \textit{mean field} limit), which is characterized by a system of ODEs. Our framework applies to a broad range of network architectures, learning dynamics and network initializations. Central to the framework is the new idea of a \textit{neuronal embedding}, which comprises of a non-evolving probability space that allows to embed neural networks of arbitrary widths. Using our framework, we prove several properties of large-width multilayer neural networks. Firstly we show that independent and identically distributed initializations cause strong degeneracy effects on the network's learning trajectory when the network's depth is at least four. Secondly we obtain several global convergence guarantees for feedforward multilayer networks under a number of different setups. These include two-layer and three-layer networks with independent and identically distributed initializations, and multilayer networks of arbitrary depths with a special type of correlated initializations that is motivated by the new concept of \textit{bidirectional diversity}. Unlike previous works that rely on convexity, our results admit non-convex losses and hinge on a certain universal approximation property, which is a distinctive feature of infinite-width neural networks and is shown to hold throughout the training process. Aside from being the first known results for global convergence of multilayer networks in the mean field regime, they demonstrate flexibility of our framework and incorporate several new ideas and insights that depart from the conventional convex optimization wisdom.

The applications of Artificial Intelligence (AI) methods especially machine learning techniques have increased in recent years. Classification algorithms have been successfully applied to different problems such as requirement classification. Although these algorithms have good performance, most of them cannot explain how they make a decision. Explainable Artificial Intelligence (XAI) is a set of new techniques that explain the predictions of machine learning algorithms. In this work, the applicability of XAI for software requirement classification is studied. An explainable software requirement classifier is presented using the LIME algorithm. The explainability of the proposed method is studied by applying it to the PROMISE software requirement dataset. The results show that XAI can help the analyst or requirement specifier to better understand why a specific requirement is classified as functional or non-functional. The important keywords for such decisions are identified and analyzed in detail. The experimental study shows that the XAI can be used to help analysts and requirement specifiers to better understand the predictions of the classifiers for categorizing software requirements. Also, the effect of the XAI on feature reduction is analyzed. The results showed that the XAI model has a positive role in feature analysis.

Interpretable machine learning offers insights into what factors drive a certain prediction of a black-box system. A large number of interpreting methods focus on identifying explanatory input features, which generally fall into two main categories: attribution and selection. A popular attribution-based approach is to exploit local neighborhoods for learning instance-specific explainers in an additive manner. The process is thus inefficient and susceptible to poorly-conditioned samples. Meanwhile, many selection-based methods directly optimize local feature distributions in an instance-wise training framework, thereby being capable of leveraging global information from other inputs. However, they can only interpret single-class predictions and many suffer from inconsistency across different settings, due to a strict reliance on a pre-defined number of features selected. This work exploits the strengths of both methods and proposes a framework for learning local explanations simultaneously for multiple target classes. Our model explainer significantly outperforms additive and instance-wise counterparts on faithfulness with more compact and comprehensible explanations. We also demonstrate the capacity to select stable and important features through extensive experiments on various data sets and black-box model architectures.

Neural Algorithmic Reasoning is an emerging area of machine learning which seeks to infuse algorithmic computation in neural networks, typically by training neural models to approximate steps of classical algorithms. In this context, much of the current work has focused on learning reachability and shortest path graph algorithms, showing that joint learning on similar algorithms is beneficial for generalisation. However, when targeting more complex problems, such similar algorithms become more difficult to find. Here, we propose to learn algorithms by exploiting duality of the underlying algorithmic problem. Many algorithms solve optimisation problems. We demonstrate that simultaneously learning the dual definition of these optimisation problems in algorithmic learning allows for better learning and qualitatively better solutions. Specifically, we exploit the max-flow min-cut theorem to simultaneously learn these two algorithms over synthetically generated graphs, demonstrating the effectiveness of the proposed approach. We then validate the real-world utility of our dual algorithmic reasoner by deploying it on a challenging brain vessel classification task, which likely depends on the vessels' flow properties. We demonstrate a clear performance gain when using our model within such a context, and empirically show that learning the max-flow and min-cut algorithms together is critical for achieving such a result.

Software is a great enabler for a number of projects that otherwise would be impossible to perform. Such projects include Space Exploration, Weather Modeling, Genome Projects, and many others. It is critical that software aiding these projects does what it is expected to do. In the terminology of software engineering, software that corresponds to requirements, that is does what it is expected to do is called correct. Checking the correctness of software has been the focus of a great deal of research in the area of software engineering. Practitioners in the field in which software is applied quite often do not assign much value to checking this correctness. Yet, as software systems become larger, potentially combined with distributed subsystems written by different authors, such verification becomes even more important. Concurrent, distributed systems are prone to dangerous errors due to different speeds of execution of their components such as deadlocks, race conditions, or violation of project-specific properties. This project describes an application of a static analysis method called model checking to verification of a distributed system for the Bioinformatics process. In it, we evaluate the efficiency of the model checking approach to the verification of combined processes with an increasing number of concurrently executed steps. We show that our experimental results correspond to analytically derived expectations. We also highlight the importance of static analysis to combined processes in the Bioinformatics field.

Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.

In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.

This paper proposes a method to modify traditional convolutional neural networks (CNNs) into interpretable CNNs, in order to clarify knowledge representations in high conv-layers of CNNs. In an interpretable CNN, each filter in a high conv-layer represents a certain object part. We do not need any annotations of object parts or textures to supervise the learning process. Instead, the interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. Our method can be applied to different types of CNNs with different structures. The clear knowledge representation in an interpretable CNN can help people understand the logics inside a CNN, i.e., based on which patterns the CNN makes the decision. Experiments showed that filters in an interpretable CNN were more semantically meaningful than those in traditional CNNs.

This paper reviews recent studies in understanding neural-network representations and learning neural networks with interpretable/disentangled middle-layer representations. Although deep neural networks have exhibited superior performance in various tasks, the interpretability is always the Achilles' heel of deep neural networks. At present, deep neural networks obtain high discrimination power at the cost of low interpretability of their black-box representations. We believe that high model interpretability may help people to break several bottlenecks of deep learning, e.g., learning from very few annotations, learning via human-computer communications at the semantic level, and semantically debugging network representations. We focus on convolutional neural networks (CNNs), and we revisit the visualization of CNN representations, methods of diagnosing representations of pre-trained CNNs, approaches for disentangling pre-trained CNN representations, learning of CNNs with disentangled representations, and middle-to-end learning based on model interpretability. Finally, we discuss prospective trends in explainable artificial intelligence.