Bayesian Neural Networks (BNNs) [37, 47] offer a probabilistic interpretation for deep learning models by imposing a prior distribution on the weight parameters and aim to obtain a posterior distribution instead of only point estimates. By marginalizing over this posterior for prediction, BNNs perform a procedure of ensemble learning. These principles facilitate the model to improve generalization, robustness and allow for uncertainty quantification. However, computing exactly the posterior of non-linear Bayesian networks is infeasible and approximate inference has been devised. The core challenge is how to construct an expressive approximation for the true posterior while maintaining computational efficiency and scalability, especially for modern deep learning architectures. Variational inference is a popular deterministic approximation approach to to deal with this challenge. The first practical methods are proposed in [15, 5, 28], in which, the approximate posterior is assumed to be a fully factorized distribution, also called mean-field variational inference. Generally, the mean-field approximation family encourages some advantages in inference including computational tractability and effective optimization with the stochastic gradient-based methods. However, it will ignore strong statistical dependencies among random weights of the neural networks, which leads to an inability to capture the complicated structure of the true posterior and to estimate true model uncertainty.

Modern machine learning models such as deep neural networks with high accuracy tend to be miscalibrated: The predicted top probability (confidence) does not reflect the actual accuracy of the model, and tends to be over-confident. For example, a WideResNet 32 on CIFAR100 has on average a predicted top probability of 87%, while the actual test accuracy is only 72% (Guo et al., 2017). As the confidence is often comprehended as an estimate of the true accuracy, such over-confidence could be dangerous, especially in risk-sensitive domains such as medical AI (Begoli et al., 2019), self-driving cars (Michelmore et al., 2018), and so on. To address this issue, there is a growing line of research on improving the calibration of models, by either performing recalibration of well-trained models to adjust the confidence scores (Platt et al., 1999; Zadrozny and Elkan; Naeini et al., 2015; Guo et al., 2017), or by averaging the predictions over multiple models to make the confidence scores more accurate (Lakshminarayanan et al., 2016; Gal and Ghahramani, 2016). These methods in general can reduce the over-confidence and improve the calibration of the model, while preserving (or even improving) the model's accuracy (Ovadia et al., 2019). Despite these progresses, the more fundamental question of why such over-confidence happens for vanillaly trained models remains not satisfactorily understood.

We consider some supervised binary classification tasks and a regression task, whereas SVM and Deep Learning, at present, exhibit the best generalization performances. We extend the work [3] on a generalized quadratic loss for learning problems that examines pattern correlations in order to concentrate the learning problem into input space regions where patterns are more densely distributed. From a shallow methods point of view (e.g.: SVM), since the following mathematical derivation of problem (9) in [3] is incorrect, we restart from problem (8) in [3] and we try to solve it with one procedure that iterates over the dual variables until the primal and dual objective functions converge. In addition we propose another algorithm that tries to solve the classification problem directly from the primal problem formulation. We make also use of Multiple Kernel Learning to improve generalization performances. Moreover, we introduce for the first time a custom loss that takes in consideration pattern correlation for a shallow and a Deep Learning task. We propose some pattern selection criteria and the results on 4 UCI data-sets for the SVM method. We also report the results on a larger binary classification data-set based on Twitter, again drawn from UCI, combined with shallow Learning Neural Networks, with and without the generalized quadratic loss. At last, we test our loss with a Deep Neural Network within a larger regression task taken from UCI. We compare the results of our optimizers with the well known solver SVMlight and with Keras Multi-Layers Neural Networks with standard losses and with a parameterized generalized quadratic loss, and we obtain comparable results.

We introduce an approach for training Variational Autoencoders (VAEs) that are certifiably robust to adversarial attack. Specifically, we first derive actionable bounds on the minimal size of an input perturbation required to change a VAE's reconstruction by more than an allowed amount, with these bounds depending on certain key parameters such as the Lipschitz constants of the encoder and decoder. We then show how these parameters can be controlled, thereby providing a mechanism to ensure a priori that a VAE will attain a desired level of robustness. Moreover, we extend this to a complete practical approach for training such VAEs to ensure our criteria are met. Critically, our method allows one to specify a desired level of robustness upfront and then train a VAE that is guaranteed to achieve this robustness. We further demonstrate that these Lipschitz--constrained VAEs are more robust to attack than standard VAEs in practice.

Natural-gradient descent on structured parameter spaces (e.g., low-rank covariances) is computationally challenging due to complicated inverse Fisher-matrix computations. We address this issue for optimization, inference, and search problems by using \emph{local-parameter coordinates}. Our method generalizes an existing evolutionary-strategy method, recovers Newton and Riemannian-gradient methods as special cases, and also yields new tractable natural-gradient algorithms for learning flexible covariance structures of Gaussian and Wishart-based distributions. We show results on a range of applications on deep learning, variational inference, and evolution strategies. Our work opens a new direction for scalable structured geometric methods via local parameterizations.

In this paper, we introduce the Layer-Peeled Model, a nonconvex yet analytically tractable optimization program, in a quest to better understand deep neural networks that are trained for a sufficiently long time. As the name suggests, this new model is derived by isolating the topmost layer from the remainder of the neural network, followed by imposing certain constraints separately on the two parts. We demonstrate that the Layer-Peeled Model, albeit simple, inherits many characteristics of well-trained neural networks, thereby offering an effective tool for explaining and predicting common empirical patterns of deep learning training. First, when working on class-balanced datasets, we prove that any solution to this model forms a simplex equiangular tight frame, which in part explains the recently discovered phenomenon of neural collapse in deep learning training [PHD20]. Moreover, when moving to the imbalanced case, our analysis of the Layer-Peeled Model reveals a hitherto unknown phenomenon that we term Minority Collapse, which fundamentally limits the performance of deep learning models on the minority classes. In addition, we use the Layer-Peeled Model to gain insights into how to mitigate Minority Collapse. Interestingly, this phenomenon is first predicted by the Layer-Peeled Model before its confirmation by our computational experiments.

In deformable registration, the geometric framework - large deformation diffeomorphic metric mapping or LDDMM, in short - has inspired numerous techniques for comparing, deforming, averaging and analyzing shapes or images. Grounded in flows, which are akin to the equations of motion used in fluid dynamics, LDDMM algorithms solve the flow equation in the space of plausible deformations, i.e. diffeomorphisms. In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. The central idea is to represent time-dependent velocity fields as fully connected ReLU neural networks (building blocks) and derive optimal weights by minimizing a regularized loss function. Computing minimizing paths between deformations, thus between shapes, turns to find optimal network parameters by back-propagating over the intermediate building blocks. Geometrically, at each time step, ResNet-LDDMM searches for an optimal partition of the space into multiple polytopes, and then computes optimal velocity vectors as affine transformations on each of these polytopes. As a result, different parts of the shape, even if they are close (such as two fingers of a hand), can be made to belong to different polytopes, and therefore be moved in different directions without costing too much energy. Importantly, we show how diffeomorphic transformations, or more precisely bilipshitz transformations, are predicted by our algorithm. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations. We thus provide essential foundations for more advanced shape variability analysis under a novel joint geometric-neural networks Riemannian-like framework, i.e. ResNet-LDDMM.

Graph Neural Networks (GNNs) have recently shown to be powerful tools for representing and analyzing graph data. So far GNNs is becoming an increasingly critical role in software engineering including program analysis, type inference, and code representation. In this paper, we introduce GraphGallery, a platform for fast benchmarking and easy development of GNNs based software. GraphGallery is an easy-to-use platform that allows developers to automatically deploy GNNs even with less domain-specific knowledge. It offers a set of implementations of common GNN models based on mainstream deep learning frameworks. In addition, existing GNNs toolboxes such as PyG and DGL can be easily incorporated into the platform. Experiments demonstrate the reliability of implementations and superiority in fast coding. The official source code of GraphGallery is available at https://github.com/EdisonLeeeee/GraphGallery and a demo video can be found at https://youtu.be/mv7Zs1YeaYo.

The success of deep learning in the computer vision and natural language processing communities can be attributed to training of very deep neural networks with millions or billions of parameters which can then be trained with massive amounts of data. However, similar trend has largely eluded training of deep reinforcement learning (RL) algorithms where larger networks do not lead to performance improvement. Previous work has shown that this is mostly due to instability during training of deep RL agents when using larger networks. In this paper, we make an attempt to understand and address training of larger networks for deep RL. We first show that naively increasing network capacity does not improve performance. Then, we propose a novel method that consists of 1) wider networks with DenseNet connection, 2) decoupling representation learning from training of RL, 3) a distributed training method to mitigate overfitting problems. Using this three-fold technique, we show that we can train very large networks that result in significant performance gains. We present several ablation studies to demonstrate the efficacy of the proposed method and some intuitive understanding of the reasons for performance gain. We show that our proposed method outperforms other baseline algorithms on several challenging locomotion tasks.

The training of deep residual neural networks (ResNets) with backpropagation has a memory cost that increases linearly with respect to the depth of the network. A simple way to circumvent this issue is to use reversible architectures. In this paper, we propose to change the forward rule of a ResNet by adding a momentum term. The resulting networks, momentum residual neural networks (MomentumNets), are invertible. Unlike previous invertible architectures, they can be used as a drop-in replacement for any existing ResNet block. We show that MomentumNets can be interpreted in the infinitesimal step size regime as second-order ordinary differential equations (ODEs) and exactly characterize how adding momentum progressively increases the representation capabilities of MomentumNets. Our analysis reveals that MomentumNets can learn any linear mapping up to a multiplicative factor, while ResNets cannot. In a learning to optimize setting, where convergence to a fixed point is required, we show theoretically and empirically that our method succeeds while existing invertible architectures fail. We show on CIFAR and ImageNet that MomentumNets have the same accuracy as ResNets, while having a much smaller memory footprint, and show that pre-trained MomentumNets are promising for fine-tuning models.