In the era of Internet of Things (IoT) and big data, collecting, processing and analyzing enormous data faces unprecedented challenges even when being stored in preprocessed form. Anomaly detection, statistically viewed as identifying outliers having low probabilities from the modelling of data distribution p(x), becomes more crucial. In this Master thesis, two (supervised and unsupervised) novel deep anomaly detection frameworks are presented which can achieve state-of-art performance on a range of datasets. Capsule net is an advanced artificial neural network, being able to encode intrinsic spatial relationship between parts and a whole. This property allows it to work as both a classifier and a deep autoencoder. Taking this advantage of CapsNet, a new anomaly detection technique named AnoCapsNet is proposed and three normality score functions are designed: prediction-probability-based (PP-based) normality score function, reconstruction-error-based (RE-based) normality score function, and a normality score function that combines prediction-probability-based and reconstruction-error-based together (named as PP+RE-based normality score function) for evaluating the "outlierness" of unseen images. The results on four datasets demonstrate that the PP-based method performs consistently well, while the RE-based approach is relatively sensitive to the similarity between labeled and unlabeled images. The PP+RE-based approach effectively takes advantages of both methods and achieves state-of-the-art results. In many situations, neither the domain of anomalous samples can be fully understood, nor the domain of the normal samples is straightforward. Thus deep generative models are more suitable than supervised methods in such cases. As a variant of variational autoencoder (VAE), beta-VAE is designed for automated discovery of interpretable factorised latent representations from raw image data in a completely unsupervised manner. The t-Distributed Stochastic Neighbor Embedding (t-SNE), an unsupervised non-linear technique primarily used for data exploration and visualizing high-dimensional data, has advantages at creating a single map that reveals local and important global structure at many different scales. Taking advantages of both disentangled representation learning (using beta-VAE as an implementation) and low-dimensional neighbor embedding (using t-SNE as an implementation), another novel anomaly detection approach named AnoDM (stands for Anomaly detection based on unsupervised Disentangled representation learning and Manifold learning) is presented. A new anomaly score function is defined by combining (1) beta-VAE's reconstruction error, and (2) latent representations' distances in the t-SNE space. This is a general framework, thus any disentangled representation learning and low-dimensional embedding techniques can be applied. AnoDM is evaluated on both image and time-series data and achieves better results than models that use just one of the two measures and other existing advanced deep learning methods.

We introduce Domain Aware Continual Zero-Shot Learning (DACZSL), the task of visually recognizing images of unseen categories in unseen domains sequentially. We created DACZSL on top of the DomainNet dataset by dividing it into a sequence of tasks, where classes are incrementally provided on seen domains during training and evaluation is conducted on unseen domains for both seen and unseen classes. We also proposed a novel Domain-Invariant CZSL Network (DIN), which outperforms state-of-the-art baseline models that we adapted to DACZSL setting. We adopt a structure-based approach to alleviate forgetting knowledge from previous tasks with a small per-task private network in addition to a global shared network. To encourage the private network to capture the domain and task-specific representation, we train our model with a novel adversarial knowledge disentanglement setting to make our global network task-invariant and domain-invariant over all the tasks. Our method also learns a class-wise learnable prompt to obtain better class-level text representation, which is used to represent side information to enable zero-shot prediction of future unseen classes. Our code and benchmarks are made available at https://zero-shot-learning.github.io/daczsl.

Deep Neural Networks have long been considered black box systems, where their interpretability is a concern when applied in safety critical systems. In this work, a novel approach of interpreting the decisions of DNNs is proposed. The approach depends on exploiting generative models and the interpretability of their latent space. Three methods for ranking features are explored, two of which depend on sensitivity analysis, and the third one depends on Random Forest model. The Random Forest model was the most successful to rank the features, given its accuracy and inherent interpretability.

Numerical methods, the collective name for numerical analysis and optimization techniques, have been widely used in the field of computer vision and deep learning. In this thesis, we investigate the algorithms of some numerical methods and their relevant applications in deep learning. These studied numerical techniques mainly include differentiable matrix power functions, differentiable eigendecomposition (ED), feasible orthogonal matrix constraints in optimization and latent semantics discovery, and physics-informed techniques for solving partial differential equations in disentangled and equivariant representation learning. We first propose two numerical solvers for the faster computation of matrix square root and its inverse. The proposed algorithms are demonstrated to have considerable speedup in practical computer vision tasks. Then we turn to resolve the main issues when integrating differentiable ED into deep learning -- backpropagation instability, slow decomposition for batched matrices, and ill-conditioned input throughout the training. Some approximation techniques are first leveraged to closely approximate the backward gradients while avoiding gradient explosion, which resolves the issue of backpropagation instability. To improve the computational efficiency of ED, we propose an efficient ED solver dedicated to small and medium batched matrices that are frequently encountered as input in deep learning. Some orthogonality techniques are also proposed to improve input conditioning. All of these techniques combine to mitigate the difficulty of applying differentiable ED in deep learning. In the last part of the thesis, we rethink some key concepts in disentangled representation learning. We first investigate the relation between disentanglement and orthogonality -- the generative models are enforced with different proposed orthogonality to show that the disentanglement performance is indeed improved. We also challenge the linear assumption of the latent traversal paths and propose to model the traversal process as dynamic spatiotemporal flows on the potential landscapes. Finally, we build probabilistic generative models of sequences that allow for novel understandings of equivariance and disentanglement. We expect our investigation could pave the way for more in-depth and impactful research at the intersection of numerical methods and deep learning.