about PyTorch, including tutorials, documentation, and examples, see: ‣ PyTorch website ‣ PyTorch project This document provides information about the key features, software enhancements and improvements corresponds, see CUDA GPUs. For additional support details, see Deep Learning Frameworks Support Matrix. Key Features and Enhancements This PyTorch release includes the following key features and enhancements the NVIDIA containers for PyTorch. For earlier container versions, refer to the Frameworks Support Matrix. Container Version Ubuntu CUDA Toolkit PyTorch TensorRT 23.07 2.1.0a0+b5021ba 23.06 2.1.0a0+4136153

sparsify_smallest() and compress(). The sparsify_smallest() sets the absolute smallest weights in the input weight matrix to zero. The number of the absolute smallest weights is computed based on the sparsity_rate parameter Compress the weights matrix using gzip. compressed_w = gzip.compress(w.tobytes()) return compressed_w To demonstrate the effect of sparsity on compression, we create a sample 2D weight matrix with randomly compute the original weight matrix size, compressed weight matrix size, and compressed and sparsified weight matrix size. As shown in the output below, the sparsified compressed matrix is smaller than the regular

(at least in the pre deep learning era). Techniques like Principal Components Analysis, Low-Rank Matrix Factorization, etc. are popular tools for dimensionality reduction. We will explain these techniques your embeddings similar to Word2Vec, GloVe, and other embedding methods. How about we jump into a project now to demonstrate how embeddings can be used to achieve a high performing model while optimizing the recent literature. Using pre-trained embeddings to improve accuracy of a NLP task. In this project we will work with the DBPedia dataset, which has snippets of text from Wikipedia. Our goal is to

quantization section delves into the implementation details using code samples. We finish with a hands-on project that will walk you through the process of applying quantization in practical situations using popular function with an input and parameters such that . In the case of a fully-connected layer, is a 2-D matrix. Further, assume that we can train another network with far fewer parameters ( ) such that the labs/raw/main/pia23378-16.jpeg Solution: First, we will interpret the image in the form of a 2D matrix having values in [0.0, 1.0]. %matplotlib inline import matplotlib.pyplot as plt import matplotlib

environment while developing Python applications. Linux/Mac OS Linux or mac OS users, go to your project root directory and type the below command to create virtual environment, python3 -m venv kerasenv Keras 7 Quit virtual environment After finishing all your changes in your project, then simply run the below command to quit the environment: deactivate Anaconda Cloud We believe the utils module is as follows: HDF5Matrix It is used to represent the input data in HDF5 format. from keras.utils import HDF5Matrix data = HDF5Matrix('data.hdf5', 'data') to_categorical

s.t. gi(ω) ≤ 0, i = 1, · · · , k Aω − b = 0 f and gi (i = 1, · · · , k) are convex A is a l × n matrix, b ∈ Rl Feng Li (SDU) SVM December 28, 2021 26 / 82 Weak Duality V.s. Strong Duality Weak duality: Feng Li (SDU) SVM December 28, 2021 50 / 82 The Kernel Matrix For K to be a kernel function The kernel function K also defines the Kernel Matrix over the data (also denoted by K) Given m samples {x(1) example in the feature space F K: m × m matrix of pairwise similarities between samples in F space K is a symmetric matrix K is a positive semi-definite matrix Feng Li (SDU) SVM December 28, 2021 51

Mean vector µ ∈ Rn Covariance matrix Σ ∈ Rn×n Mahalanobis distance: r 2 = (x − µ)TΣ−1(x − µ) Σ is symmetric and positive semidefinite Σ = ΦΛΦT Φ is an orthonormal matrix, whose columns are eigenvectors eigenvectors of Σ Λ is a diagonal matrix with the diagonal elements being the eigenvalues Feng Li (SDU) GDA, NB and EM September 27, 2023 39 / 122 Multivariate Gaussian Distribution: A 2D Example From left to t. gi(x) = 0, i = 1, 2, · · · , m such that Rank(Dg(x∗)) = m < n where Rank(Dg(x∗)) denotes the matrix of partial derivatives � ∂gj ∂xi � . There exist unique Lagrange multipliers λ ∈ Rm such that

accelerate and smoothen the convergence Feng Li (SDU) Linear Regression September 13, 2023 23 / 31 Matrix Derivatives 1 A function f : Rm×n → R The derivative of f with respect to A is defined as ▽f (A) (A) = � �� ∂f ∂A11 · · · ∂f ∂An ... ... ... ∂f ∂Am1 · · · ∂f ∂Amn � �� For an n × n matrix, its trace is defined as trA = �n i=1 Aii trABCD = trDABC = trCDAB = trBCDA trA = trAT, tr(A + B) = trace derivative ▽AT trABATC = BTATC T + BATC 1Details can be found in “Properties of the Trace and Matrix Derivatives” by John Duchi Feng Li (SDU) Linear Regression September 13, 2023 24 / 31 Revisiting

of the data Examples: Discovering clusters Discovering latent factor Discovering graph structure Matrix completion Feng Li (SDU) Overview September 6, 2023 28 / 57 Unsupervised Learning: Discovering Learning: Matrix Completion Sometimes we have missing data, that is, variables whose values are unknown, such that the corresponding design matrix will then have “holes” in it The goal of matrix completion

CustomObjectScope [source] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 20.2 HDF5Matrix [source] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 20.3 Sequence visualization • Deep dream 3.3.18 如何在 Keras 中使用 HDF5 输入？ 你可以使用 keras.utils.io_utils 中的 HDF5Matrix 类。有关详细信息，请参阅 HDF5Matrix 文档。 你也可以直接使用 HDF5 数据集： import h5py with h5py.File('input/file.hdf5', 'r') as f: x_data 矩阵的初始化方法 (详见 initializers)。 • embeddings_regularizer: embeddings matrix 的正则化方法 (详见 regularizer)。 • embeddings_constraint: embeddings matrix 的约束函数 (详见 constraints)。 • mask_zero: 是否把 0 看作为一个应该被遮蔽的特殊的”padding”