this using the earlier example for choosing quantization and/or clustering techniques for model optimization. We have a search space which has two boolean valued parameters: quantization and clustering hyperparameters. Some of the commonly tuned hyperparameters are the learning rate and the momentum of the optimization algorithm and the training batch size. Other aspects of the training pipeline like data augmentation quality and footprint) that each string produces. Unlike the guitar which has a few knobs, the hyperparameter search space can be quite large. Moreover, unlike a guitar knob which is associated with a single

001之间，就会有更多的搜索资源可用，还有在0.001到0.01之间等等。 20 超参数调整的方法 Hyperparameter 1 Hyperparameter 2 Hyperparameter 1 Hyperparameter 2 21 由粗到细调整超参数 Hyperparameter 1 Hyperparameter 2 22 熊猫方式与鱼子酱方式 由计算资源决定 23 Batch Norm

最终，我们真正关心的是生成一个模型，它能够在从未见过的数据上表现良好。但“训练”模型只能将模型 与我们实际能看到的数据相拟合。因此，我们可以将拟合模型的任务分解为两个关键问题： • 优化（optimization）：用模型拟合观测数据的过程； 39 https://discuss.d2l.ai/t/1751 2.4. 微积分 63 • 泛化（generalization）：数学原理和实践者的 size）。η表示学习率（learning rate）。批量 大小和学习率的值通常是手动预先指定，而不是通过模型训练得到的。这些可以调整但不在训练过程中更新 的参数称为超参数（hyperparameter）。调参（hyperparameter tuning）是选择超参数的过程。超参数通常 88 3. 线性神经网络 是我们根据训练迭代结果来调整的，而训练迭代结果是在独立的验证数据集（validation dataset）上评估得 ∇2f）。这相当于根据半正定矩阵的定义，H ⪰ 0。 11.2.3 约束 凸优化的一个很好的特性是能够让我们有效地处理约束（constraints）。即它使我们能够解决以下形式的约 束优化（constrained optimization）问题： minimize x f(x) subject to ci(x) ≤ 0 for all i ∈ {1, . . . , N}. (11.2.16) 这里f是目标函数，ci是约束函数。例如第一个约束c1(x)

+ ? ≥ 1 Negative class: ?!? + ? ≤ −1 ? = 1 ? Figure 2: Hard-margin SVM. aim of the above optimization problem is to find a hyperplane (parameterized by ω and b) with margin γ = 1/∥ω∥ maximized, while training set. 2.2 Preliminary Knowledge of Convex Optimization 2.2.1 Optimization Problems and Lagrangian Duality We now consider the following optimization problem min ω f(ω) (9) s.t. gi(ω) ≤ 0, i = 1 gk(ω) and the equality constraints h1(ω), · · · , hl(ω). We construct the Lagrangian of the above optimization problem as L(ω, α, β ) = f(ω) + k � i=1 αigi(ω) + l � j=1 β jhj(ω) (12) In fact, L(ω, α

Outline 1 SVM: A Primal Form 2 Convex Optimization Review 3 The Lagrange Dual Problem of SVM 4 SVM with Kernels 5 Soft-Margin SVM 6 Sequential Minimal Optimization (SMO) Algorithm Feng Li (SDU) SVM December 28, 2021 15 / 82 Convex Optimization Review Optimization Problem Lagrangian Duality KKT Conditions Convex Optimization S. Boyd and L. Vandenberghe, 2004. Convex Optimization. Cambridge university press press. Feng Li (SDU) SVM December 28, 2021 16 / 82 Optimization Problems Considering the following optimization problem min ω f (ω) s.t. gi(ω) ≤ 0, i = 1, · · · , k hj(ω) = 0, j = 1, · · · , l with

Pytorch ● Dataset & Dataloader ● Tensors ● torch.nn: Models, Loss Functions ● torch.optim: Optimization ● Save/load models Prerequisites ● We assume you are already familiar with… 1. Python3 ■ 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 & Testing calculation. Training & Testing Neural Networks – in Pytorch Define Neural Network Loss Function Optimization Algorithm Training Validation Testing Step 2. torch.nn.Module Load Data torch.nn – Network

the input model and wraps the prunable blocks for sparse training using TFMOT (Tensorflow Model Optimization) library. In this case, we prune the 50% of the weights in each prunable block using magnitude-based UpdatePruningStep() works in conjunction with the TFMOT pruning wrappers to update the wrappers after each optimization step. update_pruning = tfmot.sparsity.keras.UpdatePruningStep() callbacks = [update_pruning] centroids_init = np.linspace(x_sorted[0], x_sorted[-1], num_clusters) # Construct the variables in this optimization problem. # We will not update 'x', and hence it is not trainable. x_var = tf.Variable(initial_value=x_sorted

requires large computational resources, so they have to be carefully used. Automated Hyper-Param Optimization (HPO) is one such technique that can be used to replace / supplement manual tweaking of hyper-parameters allocate resources to promising ranges of hyper-parameters like Bayesian Optimization (Figure 1-12 illustrates Bayesian Optimization). These algorithms construct ‘trials’ of hyper-parameters, where each trial across them is how future trials are constructed based on past results. Figure 1-12: Bayesian Optimization over two dimensions x1 and x2. Red contour lines denote a high loss value, and blue contour lines

Keras is an optimal choice for deep learning applications. Features Keras leverages various optimization techniques to make high level neural network API easier and more performant. It supports the Optimizer are used in learning phase to find the error (deviation from actual output) and do optimization so that the error will be minimized.  Fit the model: The actual learning process will optimize the layer (and the model) by dynamically applying the penalties on the weights during optimization process. To summarise, Keras layer requires below minimum details to create a complete layer

• 变量数目非常庞大 • 内存空间需求大 • 计算耗时 • 迭代的局部集束调整 • 大误差难以均匀扩散到整个序列 • 极易陷入局部最优 • 姿态图优化（Pose Graph Optimization） • 只优化相机之间的相对姿态，三维点都消元掉； • 是集束调整的一个近似，不是最优解。 基于自适应分段的集束调整 • 将长序列分成若干段短序列； • 每个短序列进行独立的Sf Recognition Pose Graph Optimization + Traditional BA Street序列结果比较 ENFT-SLAM ORB-SLAM Non-consecutive Track Matching Segment-based BA Bag-of-words Place Recognition Pose Graph Optimization + Traditional BA