 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 learn by training and finally do to prediction. This step requires us to choose loss function and Optimizer. loss function and Optimizer are used in learning phase to find the error (deviation from actual

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

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

improve generalization. Let us consider an arbitrary neural network layer. We can abstract it using a function with an input and parameters such that . In the case of a fully-connected layer, is a 2-D matrix Thus, to find which bin the given x will go to, we simply do the following: . We need the floor function ( ) so that the floating point value is converted to an integer value. Now, if we plug in x = Although it is possible to work without it, you would have to introduce a for-loop either within the function, or outside it. This is crucial for deep learning applications which frequently operate on batches

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 initialized the dataset and created a model. Let’s continue and create a training function. Once we have the training function, we can kick-off the training process. The train() is simple. It takes the model

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 +

denoted by x 2 Rn, while y 2 R is the output variable. In linear regression models, the hypothesis function is defined by h✓(x) = ✓nxn + ✓n�1xn�1 + · · · + ✓1x1 + ✓0 Geometrically, when n = 1, h✓(x) is x1 1 3 777775 the hypothesis function h✓(x) can be re-written as h✓(x) = ✓T x (1) where ✓ 2 Rn+1 is a parameter vector. It is apparent that the hypothesis function is parameterized by ✓. Since our our goal is to make predictions according to the hypothesis function given a new test data, we need to find the optimal value of ✓ such that the resulting prediction is as accurate as possible. Such a procedure

吧。有的人可能会疑惑输出为什么不用在 forward 里面定义 Softmax 或者 Cross-Entropy，这是因为这些东西是在 NeuralNetwork 之外定义： #损 失 函 数 为 交 叉 熵 loss_function = nn . CrossEntropyLoss () # 学 习 率 learning_rate = 1e−3 # 优 化 器 为 随 机 梯 度 下 降 optimizer = torch model , loss_function , optimizer ) test_loop ( test_dataloader , model , loss_function ) print ( ”Done ! ” ) 然后就是训练和测试的程序，训练一轮的程序如下： def train_loop ( dataloader , model , loss_function , optimizer in enumerate ( dataloader ) : # Compute prediction and l o s s pred = model (X) l o s s = loss_function ( pred , y) # Backpropagation optimizer . zero_grad () #梯 度 归0w l o s s . backward () optimizer

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 Step 2: check if the model wanted to call a function last_response = messages[-1] if last_response.get('function_call', None): # Step 3: call the function # Note: the JSON response may not always be valid;

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) 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 as an infimum 1 of L with respect to ω, i.e., G(α, β ) = inf ω∈D L(ω, α, β ) = 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. Lower Bounds Property: