SVM: A Primal Form 2 Convex Optimization Review 3 The Lagrange Dual Problem of SVM 4 SVM with Kernels 5 Soft-Margin SVM 6 Sequential Minimal Optimization (SMO) Algorithm Feng Li (SDU) SVM December models (e.g., linear regression, linear SVM etc.) cannot reflect the nonlinear pattern in the data Kernels: Make linear model work in nonlinear settings By mapping data to higher dimensions where it exhibits very high dimensional space) Using the mapped representation could be inefficient too Thankfully, kernels help us avoid both these issues! The mapping does not have to be explicitly computed Computations

feature space is of considerable overhead). Fortunately, the concept of kernels helps us avoid all these issues! With the help of kernels, the mapping does not have to be explicitly computed, and computations + K2(x, z) • Scalar product: K(x, z) = αK1(x, z) • Direct product: K(x, z) = K1(x, z)K2(x, z) Kernels can be constructed by composing these rules. In SVM, Mercer’s condition can be translated to another K is positive semi-definite, K(·, ·) is a valid kernel function. Follows are some commonly used kernels: • Linear (trivial) Kernal: K(x, z) = xT z • Quadratic Kernel K(x, z) = (xT z)2 or (1 + xT z)2

convolutional layer which receives a 3-channel input. Each individual 3x3 matrix is a kernel. A column of 3 kernels represents a channel. As you might notice, with such structured sparsity we can obtain efficient drop unnecessary computation. In the case of this convolutional layer, we can drop rows, columns, kernels, and even whole channels. Libraries like XNNPACK3,4 can help accelerate networks on a variety of Tensorflow and PyTorch is pending as of the time of writing this book. Mainly what is lacking is kernels that can efficiently leverage the compressed weight matrices on hardware so that you can actually

regressions in 21.09 vs. 21.07: ‣ Up to 20% performance drop for Tacotron inference due to missing fused kernels in the scripted model. PyTorch RN-08516-001_v23.07 | 174 Chapter 27. PyTorch Release 21.08 regressions in 21.08 vs. 21.07: ‣ Up to 20% performance drop for Tacotron inference due to missing fused kernels in the scripted model. PyTorch RN-08516-001_v23.07 | 180 Chapter 28. PyTorch Release 21.07 Release 19.05 PyTorch RN-08516-001_v23.07 | 314 Known Issues ‣ Persistent batch normalization kernels are enabled by default in this build. This will provide a performance boost to many networks, but

input channels. Figure 4-20 demonstrates a regular convolution operation over this input using n kernels of dimensions (dk, dk, m) where dk is the spatial dimension of each kernel. The regular convolution performs two step convolution. In the first step, the input is convolved with m (dk, dk, 1) shaped kernels. The i-th channel of the input is convolved with the i-th kernel. It involves h x w x m x dk x dk m) shaped output. The second step performs a pointwise convolution using n (1, 1, m) dimensional kernels. It requires h x w x m x n operations. Hence, the total number of operations are h x w x m x (dk

卷积神经网络 主讲人：龙良曲 Convolution Moving window Several kernels Animation https://medium.freecodecamp.org/an-intuitive-guide-to-convolutional-neural- networks-260c2de0a050 Notation Input_channels: Kernel_channels: Kernel_channels: 2 ch Kernel_size: Stride: Padding: Multi-Kernels https://skymind.ai/wiki/convolutional-network x: [b, 3, 28, 28] one k: [3, 3, 3] multi-k: [16, 3, 3, 3] bias: [16] out: [b, 16

dom_kernels_and_connections.tif https://commons.wikimedia.org/wiki/Category:Machine_learning_algorithms#/media/File:Moving_From_unknown_to_known_feature_spaces_based_on_TS-ELM_with_random_kernels_and_connections

Artifacts: ringing, noise, etc. Remaining Challenges 81 Data from [Mosleh et al, 2014] inaccurate kernels inaccurate models unstable solvers information loss Efficient Network Structure U-Net or encoder-decoder

a network. The number of dense units, number of convolution channels or the size of convolution kernels can sometimes be 4 Jaderberg, Max, et al. "Population based training of neural networks." arXiv

https://storage.googleapis.com/tensorflow/keras-applications/resnet/resnet50_weights_tf_dim _ordering_tf_kernels_notop.h5 94773248/94765736 [==============================] - 1s 0us/step 94781440/94765736 [=