represents dendrites.  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 layers, convolution layer, pooling layer, etc., Keras model and layer access Keras modules for activation function, loss function, regularization function, etc., Using Keras model, Keras Layer, and Keras from keras.models import Sequential from keras.layers import Dense, Activation model = Sequential() model.add(Dense(512, activation='relu', input_shape=(784,))) Where,  Line 1 imports Sequential

1 Dense [source] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.2.2 Activation [source] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2.3 Dropout [source] 的深度学习库 2 from keras.layers import Dense model.add(Dense(units=64, activation='relu', input_dim=100)) model.add(Dense(units=10, activation='softmax')) 在完成了模型的构建后, 可以使用 .compile() 来配置学习过程： model.compil import Sequential from keras.layers import Dense, Activation model = Sequential([ Dense(32, input_shape=(784,)), Activation('relu'), Dense(10), Activation('softmax'), ]) 也可以使用 .add() 方法将各层添加到模型中： model

8(a)的情况，接下来将扩大模型容量来解决这两个问 题。 3.5 非线性模型 既然线性模型不可行，那么可以给线性模型嵌套一个非线性函数，即可将其转换为非 线性模型。通常把这个非线性函数称为激活函数(Activation Function)，用?表示： = ?(?? + ?) 这里的?代表了某个具体的非线性激活函数，如 Sigmoid 函数(图 3.9(a))、ReLU 函数(图 3.9(b))。 称为感知机的净活性值(Net Activation)。 ?1 ?2 ? ?? ? ?1 ?2 ? ?? 输入? 输出 图 6.1 感知机模型 上式写成向量形式： ? = ?T? + ? 感知机是线性模型，并不能处理线性不可分问题。通过在线性模型后添加激活函数后得到 活性值(Activation) : = ?(?) = 在初始化时根据输入、输出节点数自动 生成并初始化。代码如下： class Layer: # 全连接网络层 def __init__(self, n_input, n_neurons, activation=None, weights=None, bias=None): 预览版202112 第 7 章 反向传播算法 24 """ :param

[ 0.05897928 -0.03343131 -0.041293 -0.57477116 0.79554345]] Now, apply the ReLU non-linear activation function, which can be implemented by invoking the np.maximum on y, such that it does element-wise implement this nonlinearity so easily as compared to other activation methods like tanh, sigmoid, etc. Print the output y of the activation function. This is the final output of our unquantized fully 2)) print(weights_diff) 0.003925407435722753 Now, we’ll calculate the final output after the activation function and evaluate the error between the two results. Notice that the error is very small.

preprocess_input(x)), core, layers.Flatten(), layers.Dropout(DROPOUT_RATE), layers.Dense(NUM_CLASSES, activation='softmax') ]) adam = optimizers.Adam(learning_rate=LEARNING_RATE) model.compile( optimizer=adam return_sequences=False)), layers.Dropout(0.5), layers.Dense(20, activation='relu'), layers.Flatten(), layers.Dense(1, activation='sigmoid'), ]) adam = optimizers.Adam(learning_rate=LEARNING_RATE) In this case, we use the ‘logits’ of the teacher model, which is the input to the final softmax activation layer, and divide the student model’s logits tensor by the temperature value (typically >= 1.0)

linearly separable. We can train a model with a single fully connected layer followed by a softmax activation, since it is a binary classification task. An important caveat is that the model quality naturally reduce each input to a single vector. The result is passed through a few dense layers and a softmax activation to generate an output tensor of size num_classes. This is similar to the Word2Vec example except axis=1) x = tf.keras.layers.Dense(512, activation='relu')(x) x = tf.keras.layers.Dense(128, activation='relu')(x) x = tf.keras.layers.Dense(num_classes, activation='softmax')(x) output = x model = tf.keras

between the input and a pattern θ exceeds some threshold b • y = g(θT x − b) • g(·) is called activation function • Sigmoid: g(z) = 1/(1 + e−z) • ReLU: g(z) = max(z, 0) • Tanh: g(z) = (ez − e−z)/(ez • E.g., we use a chain to represent f(x) = f3(f2(f1(x))) • If we take sigmod function as the activation function • z1 = w1x + b1 and a1 = σ(z1) • z2 = w2a1 + b2 and a2 = σ(z2) • z3 = w3a2 + b3 and a3 neuron in the l-th layer • b[l] j is the bias of the j-th neuron in the l-th layer • a[l] j is the activation of the j-th neuron in the l-th layer a[l] j = σ �� k w[l] jka[l−1] k + b[l] j � 10 / 19 Back-Propagation:

the last few years, some researchers have started to explore activation sparsity as well. Activation sparsity involves sparsifying activation maps to produce robust models. Rhu et al., through their work work on Compression DMA Engine12, observed that a non-trivial fraction of activation values for ReLU activation function are naturally sparse. Kurtz et al. leveraged this idea in their work13 to achieve exploiting activation sparsity for fast inference on deep neural networks." International Conference on Machine Learning. PMLR, 2020. 12 Rhu, Minsoo, et al. "Compressing DMA engine: Leveraging activation sparsity

output = tf.keras.layers.Dense(200, activation='relu')(output) output = tf.keras.layers.Dense(100, activation='relu')(output) output = tf.keras.layers.Dense(50, activation='relu')(output) output = tf.keras keras.layers.Dense(num_classes, activation=None)(output) output = tf.keras.layers.Activation('softmax')(output) bert_classifier = tf.keras.Model(bert_inputs, output) bert_classifier.compile( optimizer=tf trained for such a task will be of size (representing the logits) and followed by the softmax activation, which as you may know look as follows: denotes the model’s output probability associated with

return tf.keras.Sequential([ tf.keras.Input(shape=(5,5)), layers.Dense(size, activation='relu'), layers.Dense(5, activation='softmax') ]) Our model, input data and the hyperparameter trial set is ready Hence, they can be executed much more frequently than the blackbox. There are several choices for activation functions such as Probability of Improvement (PI), Expected Improvement (EI), Upper Confidence preprocess_input(x)), core, layers.Flatten(), layers.Dropout(dropout_rate), layers.Dense(NUM_CLASSES, activation='softmax') ]) adam = optimizers.Adam(learning_rate=learning_rate) model.compile( optimizer=adam