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Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.

While deep learning strategies achieve outstanding results in computer vision tasks, one issue remains. The current strategies rely heavily on a huge amount of labeled data. In many real-world problems it is not feasible to create such an amount of labeled training data. Therefore, researchers try to incorporate unlabeled data into the training process to reach equal results with fewer labels. Due to a lot of concurrent research, it is difficult to keep track of recent developments. In this survey we provide an overview of often used techniques and methods in image classification with fewer labels. We compare 21 methods. In our analysis we identify three major trends. 1. State-of-the-art methods are scaleable to real world applications based on their accuracy. 2. The degree of supervision which is needed to achieve comparable results to the usage of all labels is decreasing. 3. All methods share common techniques while only few methods combine these techniques to achieve better performance. Based on all of these three trends we discover future research opportunities.

Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.