cross-entropy loss. We would refer you to the SimCLR paper for more details about the chosen loss functions and other alternatives considered. Once the desired test loss is achieved, the projection head optimizing non-convex functions, where multiple local minima might exist. Typical deep learning objective functions are non-convex too, and directly working with these functions might lead to the optimizer complexity you want to introduce in the training. Figure 6-12 shows multiple examples of pacing functions. The x-axis is the training iteration i.e. the variable described above, and the y-axis is the fraction

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 sub-classing Keras models. Core Modules Keras also provides a lot of built-in neural network related functions to properly create the Keras model and Keras layers. Some of the function are as follows:  many activation function like softmax, relu, etc.,  Loss module - Loss module provides loss functions like mean_squared_error, mean_absolute_error, poisson, etc.,  Optimizer module - Optimizer

jhj(ω) (12) In fact, L(ω, α, β ) can be treated as a weighted sum of the objective and constraint functions. αi is the so-called Lagrange multiplier associated with gi(ω) ≤ 0, while β i is the one associated supposed to the 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 Karush-Kuhn-Tucker (KKT) Conditions We assume that the objective function and the inequality constraint functions are differentiable. Again, let ω∗ and (α∗, β ∗) be any primal and dual optimal points, respectively

Testing Neural Networks in Pytorch ● Dataset & Dataloader ● Tensors ● torch.nn: Models, Loss Functions ● torch.optim: Optimization ● Save/load models Prerequisites ● We assume you are already familiar 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: official documentation for more information on data types. Tensors – PyTorch v.s. NumPy ● Many functions have the same names as well PyTorch NumPy x.reshape / x.view x.reshape x.squeeze() x.squeeze()

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) print('# Assistant Response 1:') responses = [] for responses in llm.chat(messages=messages, functions=functions, stream=True): print(responses) messages.extend(responses) # extend conversation with assistant's function # Note: the JSON response may not always be valid; be sure to handle errors available_functions = { 'get_current_weather': get_current_weather, } # only one function in this example, but you

y) P(a1 ≤ X ≤ b1, a2 ≤ Y ≤ b2) = � b1 a1 � b2 a2 f (x, y)dxdy Marginal probability density functions fX(x) = � ∞ −∞ f (x, y)dy for − ∞ < x < ∞ fY (x) = � ∞ −∞ f (x, y)dx for − ∞ < y < ∞ Extension f : Rn → R be the objective function, gj : Rn → R (with j = 1, · · · , m) be the m constraints functions, all of which have continuous fist derivatives. Let x∗ be an optimal solution to the following optimization �m i=1 1(y(i) = y) + 1 m + k Feng Li (SDU) GDA, NB and EM September 27, 2023 82 / 122 Convex Functions A set C is convex if the line segment between any two points in C lies in C, i.e., for ∀x1, x2

can change them during runtime. • It includes many layers as Torch. • It includes lot of loss functions. • It allows building networks whose structure is dependent on computation itself. • NLP: account like • TensorboardX (monitor training) • PyTorchViz (visualise computation graph) • Various other functions • loss (MSE,CE etc..) • optimizers Prepare Input Data •Load data •Iterate over examples Train other hyper-parameters as well!) and performs the updates Loss • Loss • Various predefined loss functions to choose from • L1, MSE, Cross Entropy …... Model • In PyTorch, a model is represented by a regular

为了说明，让我们向后退几步: print(loss.grad_fn) # MSELoss print(loss.grad_fn.next_functions[0][0]) # Linear print(loss.grad_fn.next_functions[0][0].next_functions[0][0]) # ReLU

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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 here as a Jupyter notebook for you to experiment. The following code snippet sets up the modules, functions and variables that will be used later on. It initializes the Natural Language Toolkit (NLTK) and aug_text.set_shape(text.shape) return aug_text, label return aug_text_fn Now that the augmentation functions are ready, prepare the training and the validation sets, and kick-off a run. tds = train500_ds

β ) = f (ω) + k � i=1 αigi(ω) + l� j=1 β jhj(ω) Weighted sum of objective and constraint functions αi is Lagrange multiplier associated with gi(ω) ≤ 0 β j is Lagrange multiplier associated with hj(ω) for all functions f that are “square integrable”, i.e., � ∞ −∞ f 2(x)dx < ∞ Feng Li (SDU) SVM December 28, 2021 49 / 82 Mercer’s Condition (Contd.) Let K1 and K2 be two kernel functions then the followings