We present a mathematical model for geometric deep learning based upon a scattering transform defined over manifolds, which generalizes the wavelet scattering transform of Mallat. This geometric scattering transform is (locally) invariant to isometry group actions, and we conjecture that it is stable to actions of the diffeomorphism group.

Abstract--We propose a general framework for neural network compression that is motivated by the Minimum Description Length (MDL) principle. For that we first derive an expression forthe entropy of a neural network, which measures its complexity explicitly in terms of its bit-size. This objective generalizes many of the compression techniques proposed in the literature, in that pruning or reducing the cardinality of the weight elements of the network can be seen special cases of entropy-minimization techniques. Furthermore, we derive a continuous relaxation of the objective, which allows us to minimize it using gradient based optimization techniques. Finally, we show that we can reach stateof-the-art compressionresults on different network architectures and data sets, e.g. I. INTRODUCTION It is well established that deep neural networks excel on a wide range of machine learning tasks [1].

Deep neural network models used for medical image segmentation are large because they are trained with high-resolution three-dimensional (3D) images. Graphics processing units (GPUs) are widely used to accelerate the trainings. However, the memory on a GPU is not large enough to train the models. A popular approach to tackling this problem is patch-based method, which divides a large image into small patches and trains the models with these small patches. However, this method would degrade the segmentation quality if a target object spans multiple patches. In this paper, we propose a novel approach for 3D medical image segmentation that utilizes the data-swapping, which swaps out intermediate data from GPU memory to CPU memory to enlarge the effective GPU memory size, for training high-resolution 3D medical images without patching. We carefully tuned parameters in the data-swapping method to obtain the best training performance for 3D U-Net, a widely used deep neural network model for medical image segmentation. We applied our tuning to train 3D U-Net with full-size images of 192 x 192 x 192 voxels in brain tumor dataset. As a result, communication overhead, which is the most important issue, was reduced by 17.1%. Compared with the patch-based method for patches of 128 x 128 x 128 voxels, our training for full-size images achieved improvement on the mean Dice score by 4.48% and 5.32 % for detecting whole tumor sub-region and tumor core sub-region, respectively. The total training time was reduced from 164 hours to 47 hours, resulting in 3.53 times of acceleration.

We develop a novel probabilistic generative model based on the variational autoencoder approach. Notable aspects of our architecture are: a novel way of specifying the latent variables prior, and the introduction of an ordinality enforcing unit. We describe how to do supervised, unsupervised and semi-supervised learning, and nominal and ordinal classification, with the model. We analyze generative properties of the approach, and the classification effectiveness under nominal and ordinal classification, using two benchmark datasets. Our results show that our model can achieve comparable results with relevant baselines in both of the classification tasks.

In recent years, deep neural networks (DNNs) have been applied to various machine leaning tasks, including image recognition, speech recognition, and machine translation. However, large DNN models are needed to achieve state-of-the-art performance, exceeding the capabilities of edge devices. Model reduction is thus needed for practical use. In this paper, we point out that deep learning automatically induces group sparsity of weights, in which all weights connected to an output channel (node) are zero, when training DNNs under the following three conditions: (1) rectified-linear-unit (ReLU) activations, (2) an $L_2$-regularized objective function, and (3) the Adam optimizer. Next, we analyze this behavior both theoretically and experimentally, and propose a simple model reduction method: eliminate the zero weights after training the DNN. In experiments on MNIST and CIFAR-10 datasets, we demonstrate the sparsity with various training setups. Finally, we show that our method can efficiently reduce the model size and performs well relative to methods that use a sparsity-inducing regularizer.

The state-of-the-art hardware platforms for training Deep Neural Networks (DNNs) are moving from traditional single precision (32-bit) computations towards 16 bits of precision -- in large part due to the high energy efficiency and smaller bit storage associated with using reduced-precision representations. However, unlike inference, training with numbers represented with less than 16 bits has been challenging due to the need to maintain fidelity of the gradient computations during back-propagation. Here we demonstrate, for the first time, the successful training of DNNs using 8-bit floating point numbers while fully maintaining the accuracy on a spectrum of Deep Learning models and datasets. In addition to reducing the data and computation precision to 8 bits, we also successfully reduce the arithmetic precision for additions (used in partial product accumulation and weight updates) from 32 bits to 16 bits through the introduction of a number of key ideas including chunk-based accumulation and floating point stochastic rounding. The use of these novel techniques lays the foundation for a new generation of hardware training platforms with the potential for 2-4x improved throughput over today's systems.

Syndrome differentiation in Traditional Chinese Medicine (TCM) is the process of understanding and reasoning body condition, which is the essential step and premise of effective treatments. However, due to its complexity and lack of standardization, it is challenging to achieve. In this study, we consider each patient's record as a one-dimensional image and symptoms as pixels, in which missing and negative values are represented by zero pixels. The objective is to find relevant symptoms first and then map them to proper syndromes, that is similar to the object detection problem in computer vision. Inspired from it, we employ multi-instance multi-task learning combined with the convolutional neural network (MIMT-CNN) for syndrome differentiation, which takes region proposals as input and output image labels directly. The neural network consists of region proposals generation, convolutional layer, fully connected layer, and max pooling (multi-instance pooling) layer followed by the sigmoid function in each syndrome prediction task for image representation learning and final results generation. On the diabetes dataset, it performs better than all other baseline methods. Moreover, it shows stability and reliability to generate results, even on the dataset with small sample size, a large number of missing values and noises.

We study multiple rule-based and machine learning (ML) models for sepsis detection. We report the first neural network detection and prediction results on three categories of sepsis. We have used the retrospective Medical Information Mart for Intensive Care (MIMIC)-III dataset, restricted to intensive care unit (ICU) patients. Features for prediction were created from only common vital sign measurements. We show significant improvement of AUC score using neural network based ensemble model compared to single ML and rule-based models. For the detection of sepsis, severe sepsis, and septic shock, our model achieves an AUC of 0.94, 0.91 and 0.89, respectively. Four hours before the onset, it predicts the same three categories with an AUC of 0.80, 0.81 and 0.84 respectively. Further, we ranked the features and found that using six vital signs consistently provides higher detection and prediction AUC for all the models tested. Our novel ensemble model achieves highest AUC in detecting and predicting sepsis, severe sepsis, and septic shock in the MIMIC-III ICU patients, and is amenable to deployment in hospital settings.

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimation

In this paper, a robust visual tracking approach via mixed model based convolutional neural networks (SDT) is developed. In order to handle abrupt or fast motion, a prior map is generated to facilitate the localization of region of interest (ROI) before the deep tracker is performed. A top-down saliency model with nineteen shallow cues are employed to construct the prior map with online learnt combination weights. Moreover, apart from a holistic deep learner, four local networks are also trained to learn different components of the target. The generated four local heat maps will facilitate to rectify the holistic map by eliminating the distracters to avoid drifting. Furthermore, to guarantee the instance for online update of high quality, a prioritised update strategy is implemented by casting the problem into a label noise problem. The selection probability is designed by considering both confidence values and bio-inspired memory for temporal information integration. Experiments are conducted qualitatively and quantitatively on a set of challenging image sequences. Comparative study demonstrates that the proposed algorithm outperforms other state-of-the-art methods.