capable of natural language understanding, text generation, vision understanding, audio understanding, tool use, role play, playing as AI agent, etc. 最新版本 Qwen1.5 有以下特点： • 6 种模型规模，包括 0.5B、1.8B、4B、7B、14B 和 models or adapters. • --num_train_epochs: the number of training epochs. • --gradient_accumulation_steps: the number of gradient accumulation steps. • --per_device_train_batch_size: the batch size per GPU for training, and the total batch size is equalt to per_device_train_batch_size × number_of_gpus × gradient_accumulation_steps. • --learning_rate: the learning rate. • --warmup_steps: the number of warmup

be minimized. J(θ) = 1 2m m � i=1 (hθ(x(i)) − y(i))2 (2) One of the optimization approach is gradient descent algorithm. The algorithm is performed iteratively, and in each iteration, we update parameter y(i))x(i) j (3) where α is so-called “learning rate” based on which we can tune the convergence of the gradient descent. 1A training data is actually n-dimensional, i.e., x = [x1, x2, · · · , xn]. For each training There are m = 50 training examples, and you will use them to develop a linear regression model using gradient descent algorithm, based on which, we can predict the height given a new age value. In Matlab/Octave

been shifted up. These pixels need to be “filled” up. The deep learning frameworks provide several fill-up or interpolation algorithms to address the holes. Figure 3-6: Image Transformations. The source dataset has just 1020 samples. A large batch size, say 256, will result in a small number (5) of gradient updates per epoch. Finally, it calls the fit() method on the model object to start training. from WORD2VEC_LEN with zero values vector = np.zeros(shape=(len(text), MAX_SEQ_LEN, WORD2VEC_LEN)) # Fill up zero vector with the actual word vectors from the language model for tidx, doc in enumerate(nlp

然后从测试过的{ℒ}集合中挑出最好的ℒ∗，它所对应的?和?就可以近似作为最优?∗和?∗。 这种算法固然简单直接，但是面对大规模、高维度数据的优化问题时计算效率极低， 基本不可行。梯度下降算法(Gradient Descent)是神经网络训练中最常用的优化算法，配合 强大的图形处理芯片 GPU(Graphics Processing Unit)的并行加速计算能力，非常适合优化海 量数据的神经网络模型 )，黄色虚线为 d?(?) d? 。可以看出，函数导数(虚线)为 0 的点即为 ?(?)的驻点，函数的极大值和极小值点均出现在驻点中。 图 2.5 函数及其导数 函数的梯度(Gradient)定义为函数对各个自变量的偏导数(Partial Derivative)组成的向 量。考虑 3 维函数? = ?(?, ?)，函数对自变量?的偏导数记为 ?? ??，函数对自变量?的偏导数 ′ = ? − ? ?ℒ ?? ?′ = ? − ? ?ℒ ?? 方式循环更新参数?和?。 ② 图片来自 https://en.wikipedia.org/wiki/Gradient?oldid=747127712 预览版202112 第 2 章 回归问题 6 2.3 线性模型实战 在介绍了用于优化?和?的梯度下降算法后，现在来实战训练单输入神经元线性模型。

height_shift_range=0.0, brightness_range=None, shear_range=0.0, zoom_range=0.0, channel_shift_range=0.0, fill_mode='nearest', cval=0.0, horizontal_flip=False, vertical_flip=False, rescale=None, preprocessing_function=None upper]。随机缩放范围。如果是浮点数，[lower, upper] = [1-zoom_range, 1+zoom_range]。 • channel_shift_range: 浮点数。随机通道转换的范围。 • fill_mode: {“constant”, “nearest”, “reflect” or “wrap”} 之一。默认为 ‘nearest’。输入边界以外的 点根据给定的模式填充： – ‘constant’: – ‘reflect’: abcddcba|abcd|dcbaabcd – ‘wrap’: abcdabcd|abcd|abcdabcd • cval: 浮点数或整数。用于边界之外的点的值，当 fill_mode = "constant" 时。 • horizontal_flip: 布尔值。随机水平翻转。 • vertical_flip: 布尔值。随机垂直翻转。 • rescale: 重缩放因子。默认为

当我们获得了一些数据源及其表示、一个模型和一个合适的损失函数，接下来就需要一种算法，它能够搜索出 最佳参数，以最小化损失函数。深度学习中，大多流行的优化算法通常基于一种基本方法–梯度下降（gradient descent）。简而言之，在每个步骤中，梯度下降法都会检查每个参数，看看如果仅对该参数进行少量变动，训 练集损失会朝哪个方向移动。然后，它在可以减少损失的方向上优化参数。 1.2. 机器学习中的关键组件 表示，以下是等价的： ∂y ∂xi = ∂f ∂xi = fxi = fi = Dif = Dxif. (2.4.8) 2.4.3 梯度 我们可以连结一个多元函数对其所有变量的偏导数，以得到该函数的梯度（gradient）向量。具体而言，设 函数f : Rn → R的输入是一个n维向量x = [x1, x2, . . . , xn]⊤，并且输出是一个标量。函数f(x)相对于x的梯度 是一个包含n个偏导数的向量: 我们通常会试图计算一批训练样本中每个组成部分的损失函数的导数。这里，我们的目的不是计算微分矩阵， 而是单独计算批量中每个样本的偏导数之和。 # 对非标量调用backward需要传入一个gradient参数，该参数指定微分函数关于self的梯度。 # 本例只想求偏导数的和，所以传递一个1的梯度是合适的 x.grad.zero_() y = x * x # 等价于y.backward(torch

Supervised Learning: Regression and Classification 2 Linear Regression 3 Gradient Descent Algorithm 4 Stochastic Gradient Descent 5 Revisiting Least Square 6 A Probabilistic Interpretation to Linear = 1 2 m � i=1 (hθ(x(i)) − y(i))2 Feng Li (SDU) Linear Regression September 13, 2023 9 / 31 Gradient Definition Directional Derivative: The directional derivative of function f : Rn → R in the direction partial derivative of f (x) w.r.t. xi Feng Li (SDU) Linear Regression September 13, 2023 10 / 31 Gradient (Contd.) Theorem For any n-dimensional vector u, the directional derivative of f in the direction

distance from the (read) training data to the hyperplane is denoted by |✓T x(i) � y(i)|. 2 Gradient Descent Gradient Descent (GD) method is a first-order iterative optimization algorithm for finding the minimum one goes from ✓ in the direction of the negative gradient of J at ✓. Let rJ(✓) = [ @J @✓0 , @J @✓1 , · · · , @J @✓n ]T (2) denote the gradient of J(✓). In each iteration, we update ✓ according (4) The update is terminated when convergence is achieved. In our linear regression model, the gradient can be calculated as @J(✓) @✓j = @ @✓j 1 2 m X i=1 (✓T x(i) � y(i))2 = m X i=1 (✓T x(i)

neural network has invented; therefore, people refer to neural networks as a black box 8 / 19 Gradient Descent (GD) Algorithm • If the multi-variable cost (or loss) function L(θ) is differentiable in negative gradient of L at θ • Find a local minimum of a differentiable function using gradient descent θj ← θj − α∂L(θ) ∂θj , ∀j where α is so-called learning rate • Variations • Gradient ascent algorithm algorithm • Stochastic gradient descent/ascent • mini-batch gradient descent/ascent 9 / 19 Back-Propagation: Warm Up • w[l] jk is the weight from the k-th neuron in the (l − 1)-th layer to the j-th

Early Stop,Dropout 主讲人：龙良曲 Tricks ▪ Early Stopping ▪ Dropout ▪ Stochastic Gradient Descent Early Stopping ▪ Regularization How-To ▪ Validation set to select parameters ▪ Monitor validation performance Stochastic Gradient Descent ▪ Stochastic ▪ not random! ▪ Deterministic Gradient Descent https://towardsdatascience.com/difference-between-batch-gradient-descent-and- stochastic-gradient-descent-1187f1291aa1 87f1291aa1 Gradient Descent https://towardsdatascience.com/difference-between-batch-gradient-descent-and- stochastic-gradient-descent-1187f1291aa1 ?? ??? Stochastic Gradient Descent ▪ Not single usually