We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with layers capturing uncertainty over weights (Bayesian neural nets), pre-activation units (dropout), activations ("stochastic output layers"), and the function itself (Gaussian processes). With reversible layers, one can also propagate uncertainty from input to output such as for flow-based distributions and constant-memory backpropagation. Bayesian Layers are a drop-in replacement for other layers, maintaining core features that one typically desires for experimentation. As demonstration, we fit a 10-billion parameter "Bayesian Transformer" on 512 TPUv2 cores, which replaces attention layers with their Bayesian counterpart.

The application of stochastic variance reduction to optimization has shown remarkable recent theoretical and practical success. The applicability of these techniques to the hard non-convex optimization problems encountered during training of modern deep neural networks is an open problem. We show that naive application of the SVRG technique and related approaches fail, and explore why.

Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this study, we show that tensor networks can systematically partition structured data, e.g. color images, for distributed storage and communication in privacy-preserving manner. Leveraging the sea of big data and metadata privacy, empirical results show that neighbouring subtensors with implicit information stored in tensor network formats cannot be identified for data reconstruction. This technique complements the existing encryption and randomization techniques which store explicit data representation at one place and highly susceptible to adversarial attacks such as side-channel attacks and de-anonymization. Furthermore, we propose a theory for adversarial examples that mislead convolutional neural networks to misclassification using subspace analysis based on singular value decomposition (SVD). The theory is extended to analyze higher-order tensors using tensor-train SVD (TT-SVD); it helps to explain the level of susceptibility of different datasets to adversarial attacks, the structural similarity of different adversarial attacks including global and localized attacks, and the efficacy of different adversarial defenses based on input transformation. An efficient and adaptive algorithm based on robust TT-SVD is then developed to detect strong and static adversarial attacks.

Interactions such as double negation in sentences and scene interactions in images are common forms of complex dependencies captured by state-of-the-art machine learning models. We propose Mah\'e, a novel approach to provide Model-agnostic hierarchical \'explanations of how powerful machine learning models, such as deep neural networks, capture these interactions as either dependent on or free of the context of data instances. Specifically, Mah\'e provides context-dependent explanations by a novel local interpretation algorithm that effectively captures any-order interactions, and obtains context-free explanations through generalizing context-dependent interactions to explain global behaviors. Experimental results show that Mah\'e obtains improved local interaction interpretations over state-of-the-art methods and successfully explains interactions that are context-free.

It is important to detect and handle anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data commonly used by deep learning systems are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This approach enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments in vision and natural language processing settings, we find that Outlier Exposure significantly improves the detection performance. Our approach is even applicable to density estimation models and anomaly detectors for large-scale images. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.

We introduce a new normalization technique that exhibits the fast convergence properties of batch normalization using a transformation of layer weights instead of layer outputs. The proposed technique keeps the contribution of positive and negative weights to the layer output in equilibrium.

In our study, we demonstrate the synergy effect between convolutional neural networks and the multiplicity of SMILES. The model we propose, the so-called Convolutional Neural Fingerprint (CNF) model, reaches the accuracy of traditional descriptors such as Dragon (Mauri et al. [22]), RDKit (Landrum [18]), CDK2 (Willighagen et al. [43]) and PyDescriptor (Masand and Rastija [20]). Moreover the CNF model generally performs better than highly fine-tuned traditional descriptors, especially on small data sets, which is of great interest for the chemical field where data sets are generally small due to experimental costs, the availability of molecules or accessibility to private databases. We evaluate the CNF model along with SMILES augmentation during both training and testing. To the best of our knowledge, this is the first time that such a methodology is presented. We show that using the multiplicity of SMILES during training acts as a regulariser and therefore avoids overfitting and can be seen as ensemble learning when considered for testing.

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming (DP). Differently from the classical approximate DP approach, we first approximate the optimal policy by means of neural networks in the spirit of deep reinforcement learning, and then the value function by Monte Carlo regression. This is achieved in the DP recursion by performance or hybrid iteration, and regress now or later/quantization methods from numerical probabilities. We provide a theoretical justification of these algorithms. Consistency and rate of convergence for the control and value function estimates are analyzed and expressed in terms of the universal approximation error of the neural networks. Numerical results on various applications are presented in a companion paper [2] and illustrate the performance of our algorithms.

In this paper, we provide a theoretical understanding of word embedding and its dimensionality. Motivated by the unitary-invariance of word embedding, we propose the Pairwise Inner Product (PIP) loss, a novel metric on the dissimilarity between word embeddings. Using techniques from matrix perturbation theory, we reveal a fundamental bias-variance trade-off in dimensionality selection for word embeddings. This bias-variance trade-off sheds light on many empirical observations which were previously unexplained, for example the existence of an optimal dimensionality. Moreover, new insights and discoveries, like when and how word embeddings are robust to over-fitting, are revealed. By optimizing over the bias-variance trade-off of the PIP loss, we can explicitly answer the open question of dimensionality selection for word embedding.

We introduce a deep learning method to simulate the motion of particles trapped in a chaotic recirculating flame. The Lagrangian trajectories of particles, captured using a high-speed camera and subsequently reconstructed in 3-dimensional space, were used to train a variational autoencoder (VAE) which comprises multiple layers of convolutional neural networks. We show that the trajectories, which are statistically representative of those determined in experiments, can be generated using the VAE network. The performance of our model is evaluated with respect to the accuracy and generalization of the outputs.