We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed "DIRECT" approach has several advantages over its predecessors; (i) it can exactly compute ELBO gradients (i.e. unbiased, zero-variance gradient estimates), eliminating the need for high-variance stochastic gradient estimators and enabling the use of quasi-Newton optimization methods; (ii) its training complexity is independent of the number of training points, permitting inference on large datasets; and (iii) its posterior samples consist of sparse and low-precision quantized integers which permit fast inference on hardware limited devices. In addition, our DIRECT models can exactly compute statistical moments of the parameterized predictive posterior without relying on Monte Carlo sampling. The DIRECT approach is not practical for all likelihoods, however, we identify a popular model structure which is practical, and demonstrate accurate inference using latent variables discretized as extremely low-precision 4-bit quantized integers. While the ELBO computations considered in the numerical studies require over 10^2352 log-likelihood evaluations, we train on datasets with over two-million points in just seconds.

The growing importance of massive datasets with the advent of deep learning makes robustness to label noise a critical property for classifiers to have. Sources of label noise include automatic labeling for large datasets, non-expert labeling, and label corruption by data poisoning adversaries. In the latter case, corruptions may be arbitrarily bad, even so bad that a classifier predicts the wrong labels with high confidence. To protect against such sources of noise, we leverage the fact that a small set of clean labels is often easy to procure. We demonstrate that robustness to label noise up to severe strengths can be achieved by using a set of trusted data with clean labels, and propose a loss correction that utilizes trusted examples in a data-efficient manner to mitigate the effects of label noise on deep neural network classifiers. Across vision and natural language processing tasks, we experiment with various label noises at several strengths, and show that our method significantly outperforms existing methods.

Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian inference in Hilbert spaces. We investigate the link between QGMs and HSEs and show that the sum rule and Bayes rule for QGMs are equivalent to the kernel sum rule in HSEs and a special case of Nadaraya-Watson kernel regression, respectively. We show that these operations can be kernelized, and use these insights to propose a Hilbert Space Embedding of Hidden Quantum Markov Models (HSE-HQMM) to model dynamics. We present experimental results showing that HSE-HQMMs are competitive with state-of-the-art models like LSTMs and PSRNNs on several datasets, while also providing a nonparametric method for maintaining a probability distribution over continuous-valued features.

In this paper, we propose a new method called ProfWeight for transferring information from a pre-trained deep neural network that has a high test accuracy to a simpler interpretable model or a very shallow network of low complexity and a priori low test accuracy. We are motivated by applications in interpretability and model deployment in severely memory constrained environments (like sensors). Our method uses linear probes to generate confidence scores through flattened intermediate representations. Our transfer method involves a theoretically justified weighting of samples during the training of the simple model using confidence scores of these intermediate layers. The value of our method is first demonstrated on CIFAR-10, where our weighting method significantly improves (3-4\%) networks with only a fraction of the number of Resnet blocks of a complex Resnet model. We further demonstrate operationally significant results on a real manufacturing problem, where we dramatically increase the test accuracy of a CART model (the domain standard) by roughly $13\%$.

Flow-based generative models are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood and qualitative sample quality. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient synthesis of large and subjectively realistic-looking images.

Training of deep learning models depends on gradient descent and end-to-end differentiation. Under the slogan of differentiable programming, there is an increasing demand for efficient automatic gradient computation for emerging network architectures that incorporate dynamic control flow, especially in NLP. In this paper we propose an implementation of backpropagation using functions with callbacks, where the forward pass is executed as a sequence of function calls, and the backward pass as a corresponding sequence of function returns. A key realization is that this technique of chaining callbacks is well known in the programming languages community as continuation-passing style (CPS). Any program can be converted to this form using standard techniques, and hence, any program can be mechanically converted to compute gradients. Our approach achieves the same flexibility as other reverse-mode automatic differentiation (AD) techniques, but it can be implemented without any auxiliary data structures besides the function call stack, and it can easily be combined with graph construction and native code generation techniques through forms of multi-stage programming, leading to a highly efficient implementation that combines the performance benefits of define-then-run software frameworks such as TensorFlow with the expressiveness of define-by-run frameworks such as PyTorch.

Convolutional Neural Networks(CNNs) are both computation and memory intensive whichhindered their deployment in mobile devices. Inspired by the relevant concept in neural science literature, we propose Synaptic Pruning: a data-driven method to prune connections between input and output feature maps with a newly proposed class of parameters called Synaptic Strength. Synaptic Strength is designed tocapture the importance of a connection based on the amount of information it transports. Experiment results show the effectiveness of our approach. On CIFAR-10, we prune connections for various CNN models with up to 96%, which results in significant size reduction and computation saving. Further evaluation on ImageNet demonstrates that synaptic pruning is able to discover efficient models which is competitive to state-of-the-art compact CNNs such as MobileNet-V2 and NasNet-Mobile. Our contribution is summarized as following: (1) We introduce Synaptic Strength, a new class of parameters for CNNs to indicate the importance of each connections.

Recent work by Cohen et al. has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but from an implementation point of view is actually simpler. An unusual feature of the proposed architecture is that it uses the Clebsch--Gordan transform as its only source of nonlinearity, thus avoiding repeated forward and backward Fourier transforms. The underlying ideas of the paper generalize to constructing neural networks that are invariant to the action of other compact groups.

Training large-scale image recognition models is computationally expensive. This raises the question of whether there might be simple ways to improve the test performance of an already trained model without having to re-train or fine-tune it with new data. Here, we show that, surprisingly, this is indeed possible. The key observation we make is that the layers of a deep network close to the output layer contain independent, easily extractable class-relevant information that is not contained in the output layer itself. We propose to extract this extra class-relevant information using a simple key-value cache memory to improve the classification performance of the model at test time. Our cache memory is directly inspired by a similar cache model previously proposed for language modeling (Grave et al., 2017). This cache component does not require any training or fine-tuning; it can be applied to any pre-trained model and, by properly setting only two hyper-parameters, leads to significant improvements in its classification performance. Improvements are observed across several architectures and datasets. In the cache component, using features extracted from layers close to the output (but not from the output layer itself) as keys leads to the largest improvements. Concatenating features from multiple layers to form keys can further improve performance over using single-layer features as keys. The cache component also has a regularizing effect, a simple consequence of which is that it substantially increases the robustness of models against adversarial attacks.

For the task of generating complex outputs such as source code, editing existing outputs can be easier than generating complex outputs from scratch. With this motivation, we propose an approach that first retrieves a training example based on the input (e.g., natural language description) and then edits it to the desired output (e.g., code). Our contribution is a computationally efficient method for learning a retrieval model that embeds the input in a task-dependent way without relying on a hand-crafted metric or incurring the expense of jointly training the retriever with the editor. Our retrieve-and-edit framework can be applied on top of any base model. We show that on a new autocomplete task for GitHub Python code and the Hearthstone cards benchmark, retrieve-and-edit significantly boosts the performance of a vanilla sequence-to-sequence model on both tasks.