configuration inside keras.json file. We can perform some pre-defined operations to know backend functions. 3. Keras ― Backend Configuration Keras 10 Theano Theano is an open source  Sum of input along with activation function represents neurons. Sum actually means computed value of all inputs and activation function represent a function, which modify the Sum value into 0, 1 Convolution layer: It is the primary building block and perform computational tasks based on convolution function.  Pooling layer: It is arranged next to convolution layer and is used to reduce the size of

can simply add a few additional layers (known as the prediction head), use the appropriate loss function, and train the model with the labeled data for the task at hand. We can keep the original model The resulting inputs and are passed through the ‘encoder network’ which is represented by the function and generates and , the respective hidden representations of the two inputs, as presented in figure the ‘projection head’ (represented by the function ) to first project the hidden representations into a lower dimensional space to obtain and . The loss function would then enforce agreement between and

defined by the constraints. The aim of the above optimiza- tion problem is to minimizing the objective function f(ω) subject to the inequal- ity constraints g1(ω), · · · , gk(ω) and the equality constraints h1(ω) and constraint functions. αi is the so-called Lagrange multiplier associated with gi(ω) ≤ 0, while β i is the one associated with hi(ω) = 0 3 We then define its Lagrange dual function G : Rk × Rl → R original constrained minimization problem); ii) G is an infimum of a set of affine functions and thus is a concave function regardless of the original problem; iii) G can be −∞ for some α and β Theorem 1

LLaMA-Factory 训练 Qwen 的最简单方法。欢迎通过查看官方仓库深入了解详细信息！ 1.13 Function Calling 在 Qwen-Agent 中，我们提供了一个专用封装器，旨在实现通过 dashscope API 与 OpenAI API 进行的函数调 用。 1.13. Function Calling 37 Qwen 1.13.1 使用示例 import json import import os from qwen_agent.llm import get_chat_model # Example dummy function hard coded to return the same weather # In production, this could be your backend API or an external API def get_current_weather(location 1: send the conversation and available functions to the model messages = [{ 'role': 'user', 'content': "What's the weather like in San Francisco?" }] functions = [{ (续下页) 38 Chapter 1. 文档 Qwen (接上页)

Event A is a subset of the sample space S P(A) is the probability that event A happens It is a function that maps the event A onto the interval [0, 1]. P(A) is also called the probability measure of A EM September 27, 2023 6 / 122 Conditional Probability (Contd.) Real valued random variable is a function of the outcome of a ran- domized experiment X : S → R Examples: Discrete random variables (S is (SDU) GDA, NB and EM September 27, 2023 7 / 122 Random Variables Real valued random variable is a function of the outcome of a ran- domized experiment X : S → R For continuous random variable X P(a < X

torch.nn: Models, Loss Functions ● torch.optim: Optimization ● Save/load models Prerequisites ● We assume you are already familiar with… 1. Python3 ■ if-else, loop, function, file IO, class, ... training deep neural networks Training Neural Networks Training Define Neural Network Loss Function Optimization Algorithm More info about the training process in last year's lecture video. Training mean() ● Addition z = x + y ● Subtraction z = x - y ● Power y = x.pow(2) Common arithmetic functions are supported, such as: Tensors – Common Operations Tensors – Common Operations ● Transpose:

code samples are provided to bridge the theory and practice gap. We have prepared a few helper functions: load_image(), show_image(), transform() and transform_and_show(), which will be used to transform package. Let’s start by loading the training and validation splits of the dataset. The make_dataset() function takes the name of the dataset and loads the training and the validation splits as follows. import the bottom (right after the input layer). We compile the model with a sparse cross entropy loss function (discussed in chapter 2) and the adam optimizer. from tensorflow.keras import applications as

· , l with variable ω ∈ Rn, domain D = �k i=1 domgi ∩�l j=1 domhj, optimal value p∗ Objective function f (ω) k inequality constraints gi(ω) ≤ 0, i = 1, · · · , k l equality constraints hj(ω) = 0, j = constraint functions αi is Lagrange multiplier associated with gi(ω) ≤ 0 β j is Lagrange multiplier associated with hj(ω) = 0 Feng Li (SDU) SVM December 28, 2021 18 / 82 Lagrange Dual Function The Lagrange Lagrange dual function G : Rk × Rl → R G(α, β ) = inf ω∈D L(ω, α, β ) = inf ω∈D � �f (ω) + k � i=1 αigi(ω) + l� j=1 β jhj(ω) � � G is concave, can be −∞ for some α, β Feng Li (SDU) SVM December

called feedforward neural networks or multilayer perceptrons (MLPs) • The goal is to approximate some function f ∗ • E.g., for a classifier, y = f ∗(x) maps an input x to a category y • A feedforward network and learns the value of the parameters θ that result in the best function approximations • f(x) is usually a highly non-linear function • Feedforward networks are of extreme importance to machine learning called activation function • Sigmoid: g(z) = 1/(1 + e−z) • ReLU: g(z) = max(z, 0) • Tanh: g(z) = (ez − e−z)/(ez + e−z) 4 / 19 Neuron (Contd.) • An example: logistic regression function g(x) = 1 1 +

"search" space because we are searching for a point in which minimizes (or maximizes) an Evaluation Function . Formally, we can define as Let's understand this using the earlier example for choosing quantization say that we are optimizing the validation loss, , for a given dataset on a model represented by a function with a set of hyperparameters . Further, assume that is a set of model parameters. HPO is attempting learning rate to run HPO. S = [ (5, .01), (10, .1), (20, .001), (50, .1), ] The create_model() function creates a single hidden layer model whose size is determined by the input size parameter. def create_model(size):