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In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a subset of the training data samples to optimize over this subspace. As with the Hessian Free (HF) method of [7], the Hessian matrix is never explicitly constructed, and is computed using a subset of data. In practice, as in HF, we typically use a positive definite substitute for the Hessian matrix such as the Gauss-Newton matrix. We investigate the effectiveness of our proposed method on deep neural networks, and compare its performance to widely used methods such as stochastic gradient descent, conjugate gradient descent and L-BFGS, and also to HF. Our method leads to faster convergence than either L-BFGS or HF, and generally performs better than either of them in cross-validation accuracy. It is also simpler and more general than HF, as it does not require a positive semi-definite approximation of the Hessian matrix to work well nor the setting of a damping parameter. The chief drawback versus HF is the need for memory to store a basis for the Krylov subspace.

In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a subset of the training data samples to optimize over this subspace. As with the Hessian Free (HF) method of [7], the Hessian matrix is never explicitly constructed, and is computed using a subset of data. In practice, as in HF, we typically use a positive definite substitute for the Hessian matrix such as the Gauss-Newton matrix. We investigate the effectiveness of our proposed method on deep neural networks, and compare its performance to widely used methods such as stochastic gradient descent, conjugate gradient descent and L-BFGS, and also to HF. Our method leads to faster convergence than either L-BFGS or HF, and generally performs better than either of them in cross-validation accuracy. It is also simpler and more general than HF, as it does not require a positive semi-definite approximation of the Hessian matrix to work well nor the setting of a damping parameter. The chief drawback versus HF is the need for memory to store a basis for the Krylov subspace.

More than eighty-five to ninety percentage of the diabetic patients are affected with diabetic retinopathy (DR) which is an eye disorder that leads to blindness. The computational techniques can support to detect the DR by using the retinal images. However, it is hard to measure the DR with the raw retinal image. This paper proposes an effective method for identification of DR from the retinal images. In this research work, initially the Weiner filter is used for preprocessing the raw retinal image. Then the preprocessed image is segmented using fuzzy c-mean technique. Then from the segmented image, the features are extracted using grey level co-occurrence matrix (GLCM). After extracting the fundus image, the feature selection is performed stochastic gradient descent, and least absolute shrinkage and selection operator (LASSO) for accurate identification during the classification process. Then the inception v3-convolutional neural network (IV3-CNN) model is used in the classification process to classify the image as DR image or non-DR image. By applying the proposed method, the classification performance of IV3-CNN model in identifying DR is studied. Using the proposed method, the DR is identified with the accuracy of about 95%, and the processed retinal image is identified as mild DR. 

This is the cover for the Roblox game Deep Descent by Polar Marine Exploration. Description: You have been forcefully recruited by the company to recover the remains of the previous research vessel, while descending you notice that you are not alone.. team up with others and survive the unfortunate and deadly journey. Explore the depths and regain your lost freedom.

Ultradeep stall descent and spin recovery characteristics of a 1/6 scale radio controlled model of the Piper PA38 Tomahawk aircraft was investigated. It was shown that the full scale PA38 is a suitable aircraft for conducting ultradeep stall research. Spin recovery was accomplished satisfactorily by entry to the ultradeep stall mode, followed by the exit from the ultradeep stall mode. It is concluded that since the PA38 has excellent spin recovery characteristics using normal recovery techniques (opposite rudder and forward control colum pressure), recovery using ultradeep stall would be beneficial only if the pilot suffered from disorientation.

Ultradeep stall descent and spin recovery characteristics of a 1/6 scale radio controlled model of the Piper PA38 Tomahawk aircraft was investigated. It was shown that the full scale PA38 is a suitable aircraft for conducting ultradeep stall research. Spin recovery was accomplished satisfactorily by entry to the ultradeep stall mode, followed by the exit from the ultradeep stall mode. It is concluded that since the PA38 has excellent spin recovery characteristics using normal recovery techniques (opposite rudder and forward control colum pressure), recovery using ultradeep stall would be beneficial only if the pilot suffered from disorientation.

SGD is the widely adopted method to train CNN. Conceptually it approximates the population with a randomly sampled batch; then it evenly trains batches by conducting a gradient update on every batch in an epoch. In this paper, we demonstrate Sampling Bias, Intrinsic Image Difference and Fixed Cycle Pseudo Random Sampling differentiate batches in training, which then affect learning speeds on them. Because of this, the unbiased treatment of batches involved in SGD creates improper load balancing. To address this issue, we present Inconsistent Stochastic Gradient Descent (ISGD) to dynamically vary training effort according to learning statuses on batches. Specifically ISGD leverages techniques in Statistical Process Control to identify a undertrained batch. Once a batch is undertrained, ISGD solves a new subproblem, a chasing logic plus a conservative constraint, to accelerate the training on the batch while avoid drastic parameter changes. Extensive experiments on a variety of datasets demonstrate ISGD converges faster than SGD. In training AlexNet, ISGD is 21.05\% faster than SGD to reach 56\% top1 accuracy under the exactly same experiment setup. We also extend ISGD to work on multiGPU or heterogeneous distributed system based on data parallelism, enabling the batch size to be the key to scalability. Then we present the study of ISGD batch size to the learning rate, parallelism, synchronization cost, system saturation and scalability. We conclude the optimal ISGD batch size is machine dependent. Various experiments on a multiGPU system validate our claim. In particular, ISGD trains AlexNet to 56.3% top1 and 80.1% top5 accuracy in 11.5 hours with 4 NVIDIA TITAN X at the batch size of 1536.

We design and implement a distributed multinode synchronous SGD algorithm, without altering hyper parameters, or compressing data, or altering algorithmic behavior. We perform a detailed analysis of scaling, and identify optimal design points for different networks. We demonstrate scaling of CNNs on 100s of nodes, and present what we believe to be record training throughputs. A 512 minibatch VGG-A CNN training run is scaled 90X on 128 nodes. Also 256 minibatch VGG-A and OverFeat-FAST networks are scaled 53X and 42X respectively on a 64 node cluster. We also demonstrate the generality of our approach via best-in-class 6.5X scaling for a 7-layer DNN on 16 nodes. Thereafter we attempt to democratize deep-learning by training on an Ethernet based AWS cluster and show ~14X scaling on 16 nodes.

We develop a fully discriminative learning approach for supervised Latent Dirichlet Allocation (LDA) model using Back Propagation (i.e., BP-sLDA), which maximizes the posterior probability of the prediction variable given the input document. Different from traditional variational learning or Gibbs sampling approaches, the proposed learning method applies (i) the mirror descent algorithm for maximum a posterior inference and (ii) back propagation over a deep architecture together with stochastic gradient/mirror descent for model parameter estimation, leading to scalable and end-to-end discriminative learning of the model. As a byproduct, we also apply this technique to develop a new learning method for the traditional unsupervised LDA model (i.e., BP-LDA). Experimental results on three real-world regression and classification tasks show that the proposed methods significantly outperform the previous supervised topic models, neural networks, and is on par with deep neural networks.

This is the in-game currency for the Roblox game Deep Descent by Polar Marine Exploration .

This is the showcase image for the Roblox game Deep Descent by Polar Marine Exploration. Description: You have been forcefully recruited by the company to recover the remains of the previous research vessel, while descending you notice that you are not alone.. team up with others and survive the unfortunate and deadly journey. Explore the depths and regain your lost freedom.

Aquanox is a 19 years old IP that is famous for its underwater action, also often quoted as being "The Wing Commander of sea fighting". Published first by BlueByte in 1996, now Aquanox is owned by Nordic Games and the 4th episode of the series is now handcrafted by the Serbian game development studio "Digital Arrow". Currently, they are currently running a Kickstarter campaign to get the ideas of the community and fans and form a game that will provide underwater action surpreme. AJ and Joerg talk to CEO, Producer, Designer and underwater expert Norbert Varga.

Aquanox is a 19 years old IP that is famous for its underwater action, also often quoted as being "The Wing Commander of sea fighting". Published first by BlueByte in 1996, now Aquanox is owned by Nordic Games and the 4th episode of the series is now handcrafted by the Serbian game development studio "Digital Arrow". Currently, they are currently running a Kickstarter campaign to get the ideas of the community and fans and form a game that will provide underwater action surpreme. AJ and Joerg talk to CEO, Producer, Designer and underwater expert Norbert Varga.

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Perma.cc archive of https://towardsdatascience.com/gradient-descent-algorithm-a-deep-dive-cf04e8115f21 created on 2022-08-13 07:53:24.446891+00:00.

Let R be an integral domain of finite type over Z and let f:X --> Spec R be a smooth projective morphism of relative dimension d >= 1. We investigate, for a vector bundle E on the total space X, under what arithmetical properties of a sequence (p_n, e_n)_{n \in \NN}, consisting of closed points p_n in Spec R and Frobenius descent data E_{p_n} \cong F^{e_n}^*(F) on the closed fibers X_{p_n}, the bundle E_0 on the generic fiber X_0 is semistable.