📅 最后修改于: 2020-12-10 04:56:01 🧑 作者: Mango
在本章中，我们将学习MXNet中称为符号的接口。
Apache MXNet的Symbol API是用于符号编程的接口。 Symbol API具有以下用途-
计算图
减少内存使用
使用前函数优化
下面给出的示例说明了如何使用MXNet的Symbol API创建简单的表达式-
通过使用来自常规Python列表的1-D和2-D’array’的NDArray-
import mxnet as mx
# Two placeholders namely x and y will be created with mx.sym.variable
x = mx.sym.Variable('x')
y = mx.sym.Variable('y')
# The symbol here is constructed using the plus ‘+’ operator.
z = x + y
输出
您将看到以下输出-
例
(x, y, z)
输出
输出如下-
(, , )
现在让我们详细讨论MXNet的ndarray API的类，函数和参数。
下表包含MXNet的Symbol API的类-
| Class | Definition |
|---|---|
| Symbol(handle) | This class namely symbol is the symbolic graph of the Apache MXNet. |
以下是mxnet.Symbol API涵盖的一些重要功能及其参数-
| Function and its Parameters | Definition |
|---|---|
| Activation([data, act_type, out, name]) | It applies an activation function element-wise to the input. It supports relu, sigmoid, tanh, softrelu, softsign activation functions. |
| BatchNorm([data, gamma, beta, moving_mean, …]) | It is used for batch normalization. This function normalizes a data batch by mean and variance. It applies a scale gamma and offset beta. |
| BilinearSampler([data, grid, cudnn_off, …]) | This function applies bilinear sampling to input feature map. Actually it is the key of “Spatial Transformer Networks”. If you are familiar with remap function in OpenCV, the usage of this function is quite similar to that. The only difference is that it has the backward pass. |
| BlockGrad([data, out, name]) | As name specifies, this function stops gradient computation. It basically stops the accumulated gradient of the inputs from flowing through this operator in backward direction. |
| cast([data, dtype, out, name]) | This function will cast all elements of the input to a new type. |
| This function will cast all elements of the input to a new type. | This function, as name specified, returns a new symbol of given shape and type, filled with zeros. |
| ones(shape[, dtype]) | This function, as name specified return a new symbol of given shape and type, filled with ones. |
| full(shape, val[, dtype]) | This function, as name specified returns a new array of given shape and type, filled with the given value val. |
| arange(start[, stop, step, repeat, …]) | It will return evenly spaced values within a given interval. The values are generated within half open interval [start, stop) which means that the interval includes start but excludes stop. |
| linspace(start, stop, num[, endpoint, name, …]) | It will return evenly spaced numbers within a specified interval. Similar to the function arrange(), the values are generated within half open interval [start, stop) which means that the interval includes start but excludes stop. |
| histogram(a[, bins, range]) | As name implies, this function will compute the histogram of the input data. |
| power(base, exp) | As name implies, this function will return element-wise result of base element raised to powers from exp element. Both inputs i.e. base and exp, can be either Symbol or scalar. Here note that broadcasting is not allowed. You can use broadcast_pow if you want to use the feature of broadcast. |
| SoftmaxActivation([data, mode, name, attr, out]) | This function applies softmax activation to input. It is intended for internal layers. It is actually deprecated, we can use softmax() instead. |
在下面的示例中，我们将使用函数power() ，该函数将把基础元素的逐元素结果返回为exp元素的幂：
import mxnet as mx
mx.sym.power(3, 5)
输出
您将看到以下输出-
243
例
x = mx.sym.Variable('x')
y = mx.sym.Variable('y')
z = mx.sym.power(x, 3)
z.eval(x=mx.nd.array([1,2]))[0].asnumpy()
输出
这产生以下输出-
array([1., 8.], dtype=float32)
例
z = mx.sym.power(4, y)
z.eval(y=mx.nd.array([2,3]))[0].asnumpy()
输出
当执行上述代码时，您应该看到以下输出-
array([16., 64.], dtype=float32)
例
z = mx.sym.power(x, y)
z.eval(x=mx.nd.array([4,5]), y=mx.nd.array([2,3]))[0].asnumpy()
输出
输出在下面提到-
array([ 16., 125.], dtype=float32)
在下面给出的示例中，我们将使用函数SoftmaxActivation()(或softmax()) ，该函数将应用于输入并用于内部层。
input_data = mx.nd.array([[2., 0.9, -0.5, 4., 8.], [4., -.7, 9., 2., 0.9]])
soft_max_act = mx.nd.softmax(input_data)
print (soft_max_act.asnumpy())
输出
您将看到以下输出-
[[2.4258138e-03 8.0748333e-04 1.9912292e-04 1.7924475e-02 9.7864312e-01]
[6.6843745e-03 6.0796250e-05 9.9204916e-01 9.0463174e-04 3.0112563e-04]]
Contrib NDArray API在symbol.contrib包中定义。它通常为新功能提供许多有用的实验性API。该API是社区可以尝试新功能的场所。功能提供者也将获得反馈。
以下是mxnet.symbol.contrib API涵盖的一些重要功能及其参数-
| Function and its Parameters | Definition |
|---|---|
| rand_zipfian(true_classes, num_sampled, …) | This function draws random samples from an approximately Zipfian distribution. The base distribution of this function is Zipfian distribution. This function randomly samples num_sampled candidates and the elements of sampled_candidates are drawn from the base distribution given above. |
| foreach(body, data, init_states) | As name implies, this function runs a loop with user-defined computation over NDArrays on dimension 0. This function simulates a for loop and body has the computation for an iteration of the for loop. |
| while_loop(cond, func, loop_vars[, …]) | As name implies, this function runs a while loop with user-defined computation and loop condition. This function simulates a while loop that literately does customized computation if the condition is satisfied. |
| cond(pred, then_func, else_func) | As name implies, this function run an if-then-else using user-defined condition and computation. This function simulates an if-like branch which chooses to do one of the two customized computations according to the specified condition. |
| getnnz([data, axis, out, name]) | This function gives us the number of stored values for a sparse tensor. It also includes explicit zeros. It only supports CSR matrix on CPU. |
| requantize([data, min_range, max_range, …]) | This function requantize the given data that is quantized in int32 and the corresponding thresholds, into int8 using min and max thresholds either calculated at runtime or from calibration. |
| index_copy([old_tensor, index_vector, …]) | This function copies the elements of a new_tensor into the old_tensor by selecting the indices in the order given in index. The output of this operator will be a new tensor that contains the rest elements of old tensor and the copied elements of new tensor. |
| interleaved_matmul_encdec_qk([queries, …]) | This operator compute the matrix multiplication between the projections of queries and keys in multi-head attention use as encoder-decoder. The condition is that the inputs should be a tensor of projections of queries that follows the layout: (seq_length, batch_size, num_heads*, head_dim). |
在下面的示例中，我们将使用rand_zipfian函数从近似Zipfian分布中绘制随机样本-
import mxnet as mx
true_cls = mx.sym.Variable('true_cls')
samples, exp_count_true, exp_count_sample = mx.sym.contrib.rand_zipfian(true_cls, 5, 6)
samples.eval(true_cls=mx.nd.array([3]))[0].asnumpy()
输出
您将看到以下输出-
array([4, 0, 2, 1, 5], dtype=int64)
例
exp_count_true.eval(true_cls=mx.nd.array([3]))[0].asnumpy()
输出
输出在下面提到-
array([0.57336551])
例
exp_count_sample.eval(true_cls=mx.nd.array([3]))[0].asnumpy()
输出
您将看到以下输出-
array([1.78103594, 0.46847373, 1.04183923, 0.57336551, 1.04183923])
在下面的示例中，我们将使用while_loop函数为用户定义的计算和循环条件运行while循环-
cond = lambda i, s: i <= 7
func = lambda i, s: ([i + s], [i + 1, s + i])
loop_vars = (mx.sym.var('i'), mx.sym.var('s'))
outputs, states = mx.sym.contrib.while_loop(cond, func, loop_vars, max_iterations=10)
print(outputs)
输出
输出如下：
[]
例
Print(States)
输出
这产生以下输出-
[, ]
在下面的示例中，我们将使用函数index_copy将new_tensor的元素复制到old_tensor中。
import mxnet as mx
a = mx.nd.zeros((6,3))
b = mx.nd.array([[1,2,3],[4,5,6],[7,8,9]])
index = mx.nd.array([0,4,2])
mx.nd.contrib.index_copy(a, index, b)
输出
当执行上述代码时，您应该看到以下输出-
[[1. 2. 3.]
[0. 0. 0.]
[7. 8. 9.]
[0. 0. 0.]
[4. 5. 6.]
[0. 0. 0.]]
Image Symbol API在symbol.image包中定义。顾名思义，它通常用于图像及其功能。
以下是mxnet.symbol.image API涵盖的一些重要功能及其参数-
| Function and its Parameters | Definition |
|---|---|
| adjust_lighting([data, alpha, out, name]) | As name implies, this function adjusts the lighting level of the input. It follows the AlexNet style. |
| crop([data, x, y, width, height, out, name]) | With the help of this function we can crop an image NDArray of shape (H x W x C) or (N x H x W x C) to the size given by user. |
| normalize([data, mean, std, out, name]) | It will normalize an tensor of shape (C x H x W) or (N x C x H x W) with mean and standard deviation(SD). |
| random_crop([data, xrange, yrange, width, …]) | Similar to crop(), it randomly crop an image NDArray of shape (H x W x C) or (N x H x W x C) to the size given by the user. It will upsample the result if src is smaller than the size. |
| random_lighting([data, alpha_std, out, name]) | As name implies, this function adds the PCA noise randomly. It also follows the AlexNet style. |
| random_resized_crop([data, xrange, yrange, …]) | It also crops an image randomly NDArray of shape (H x W x C) or (N x H x W x C) to the given size. It will upsample the result if src is smaller than the size. It will randomize the area and aspect ration as well. |
| resize([data, size, keep_ratio, interp, …]) | As name implies, this function will resize an image NDArray of shape (H x W x C) or (N x H x W x C) to the size given by user. |
| to_tensor([data, out, name]) | It converts an image NDArray of shape (H x W x C) or (N x H x W x C) with the values in the range [0, 255] to a tensor NDArray of shape (C x H x W) or (N x C x H x W) with the values in the range [0, 1]. |
在下面的示例中，我们将使用to_tensor函数将形状为(H xW x C)或(N xH xW x C)的图像NDArray转换为张量NDArray，该图像的大小为[0，255]形状(C xH x W)或(N x C x H x W)的形状，其值在[0，1]范围内。
import numpy as np
img = mx.sym.random.uniform(0, 255, (4, 2, 3)).astype(dtype=np.uint8)
mx.sym.image.to_tensor(img)
输出
输出说明如下-
例
img = mx.sym.random.uniform(0, 255, (2, 4, 2, 3)).astype(dtype=np.uint8)
mx.sym.image.to_tensor(img)
输出
输出如下所示：
在下面的示例中，我们将使用函数normalize()对具有平均值和标准偏差(SD)的形状(C xH x W)或(N x C x H x W)的张量进行规格化。
img = mx.sym.random.uniform(0, 1, (3, 4, 2))
mx.sym.image.normalize(img, mean=(0, 1, 2), std=(3, 2, 1))
输出
下面给出的是代码的输出-
例
img = mx.sym.random.uniform(0, 1, (2, 3, 4, 2))
mx.sym.image.normalize(img, mean=(0, 1, 2), std=(3, 2, 1))
输出
输出如下所示-
随机符号API在symbol.random包中定义。顾名思义，它是MXNet的随机分布生成器Symbol API。
以下是mxnet.symbol.random API涵盖的一些重要功能及其参数-
| Function and its Parameters | Definition |
|---|---|
| uniform([low, high, shape, dtype, ctx, out]) | It generates random samples from a uniform distribution. |
| normal([loc, scale, shape, dtype, ctx, out]) | It generates random samples from a normal (Gaussian) distribution. |
| randn(*shape, **kwargs) | It generates random samples from a normal (Gaussian) distribution. |
| poisson([lam, shape, dtype, ctx, out]) | It generates random samples from a Poisson distribution. |
| exponential([scale, shape, dtype, ctx, out]) | It generates samples from an exponential distribution. |
| gamma([alpha, beta, shape, dtype, ctx, out]) | It generates random samples from a gamma distribution. |
| multinomial(data[, shape, get_prob, out, dtype]) | It generates concurrent sampling from multiple multinomial distributions. |
| negative_binomial([k, p, shape, dtype, ctx, out]) | It generates random samples from a negative binomial distribution. |
| generalized_negative_binomial([mu, alpha, …]) | It generates random samples from a generalized negative binomial distribution. |
| shuffle(data, **kwargs) | It shuffles the elements randomly. |
| randint(low, high[, shape, dtype, ctx, out]) | It generates random samples from a discrete uniform distribution. |
| exponential_like([data, lam, out, name]) | It generates random samples from an exponential distribution according to the input array shape. |
| gamma_like([data, alpha, beta, out, name]) | It generates random samples from a gamma distribution according to the input array shape. |
| generalized_negative_binomial_like([data, …]) | It generates random samples from a generalized negative binomial distribution according to the input array shape. |
| negative_binomial_like([data, k, p, out, name]) | It generates random samples from a negative binomial distribution according to the input array shape. |
| normal_like([data, loc, scale, out, name]) | It generates random samples from a normal (Gaussian) distribution according to the input array shape. |
| poisson_like([data, lam, out, name]) | It generates random samples from a Poisson distribution according to the input array shape. |
| uniform_like([data, low, high, out, name]) | It generates random samples from a uniform distribution according to the input array shape. |
在下面的示例中，我们将使用shuffle()函数随机地对元素进行随机排序。它将沿第一个轴随机排列数组。
data = mx.nd.array([[0, 1, 2], [3, 4, 5], [6, 7, 8],[9,10,11]])
x = mx.sym.Variable('x')
y = mx.sym.random.shuffle(x)
y.eval(x=data)
输出
您将看到以下输出：
[
[[ 9. 10. 11.]
[ 0. 1. 2.]
[ 6. 7. 8.]
[ 3. 4. 5.]]
]
例
y.eval(x=data)
输出
当执行上述代码时，您应该看到以下输出-
[
[[ 6. 7. 8.]
[ 0. 1. 2.]
[ 3. 4. 5.]
[ 9. 10. 11.]]
]
在下面的示例中，我们将从广义负二项分布中抽取随机样本。为此，将使用函数generalized_negative_binomial() 。
mx.sym.random.generalized_negative_binomial(10, 0.1)
输出
输出如下-
稀疏符号API在mxnet.symbol.sparse包中定义。顾名思义，它在CPU上提供了稀疏的神经网络图和自动分化功能。
以下是一些重要功能(包括符号创建程序，符号操纵程序，数学函数，函数，双曲函数，Reduce函数，圆整，权力，神经网络)及其参数由mxnet.symbol.sparse API覆盖-
| Function and its Parameters | Definition |
|---|---|
| ElementWiseSum(*args, **kwargs) | This function will add all input arguments element wise. For example, 𝑎𝑑𝑑_𝑛(𝑎1,𝑎2,…𝑎𝑛=𝑎1+𝑎2+⋯+𝑎𝑛). Here, we can see that add_n is potentially more efficient than calling add by n times. |
| Embedding([data, weight, input_dim, …]) | It will map the integer indices to vector representations i.e. embeddings. It actually maps words to real-valued vectors in high-dimensional space which is called word embeddings. |
| LinearRegressionOutput([data, label, …]) | It computes and optimizes for squared loss during backward propagation giving just output data during forward propagation. |
| LogisticRegressionOutput([data, label, …]) | Applies a logistic function which is also called the sigmoid function to the input. The function is computed as 1/1+exp (−x). |
| MAERegressionOutput([data, label, …]) | This operator computes mean absolute error of the input. MAE is actually a risk metric corresponding to the expected value of absolute error. |
| abs([data, name, attr, out]) | As name implies, this function will return element-wise absolute value of the input. |
| adagrad_update([weight, grad, history, lr, …]) | It is an update function for AdaGrad optimizer. |
| adam_update([weight, grad, mean, var, lr, …]) | It is an update function for Adam optimizer. |
| add_n(*args, **kwargs) | As name implies it will adds all input arguments element-wise. |
| arccos([data, name, attr, out]) | This function will returns element-wise inverse cosine of the input array. |
| dot([lhs, rhs, transpose_a, transpose_b, …]) | As name implies, it will give the dot product of two arrays. It will depend upon the input array dimension: 1-D: inner product of vectors 2-D: matrix multiplication N-D: A sum product over the last axis of the first input and the first axis of the second input. |
| elemwise_add([lhs, rhs, name, attr, out]) | As name implies it will add arguments element wise. |
| elemwise_div([lhs, rhs, name, attr, out]) | As name implies it will divide arguments element wise. |
| elemwise_mul([lhs, rhs, name, attr, out]) | As name implies it will Multiply arguments element wise. |
| elemwise_sub([lhs, rhs, name, attr, out]) | As name implies it will Subtract arguments element wise. |
| exp([data, name, attr, out]) | This function will return element wise exponential value of the given input. |
| sgd_update([weight, grad, lr, wd, …]) | It acts as an update function for Stochastic Gradient Descent optimizer. |
| sigmoid([data, name, attr, out]) | As name implies it will compute sigmoid of x element wise. |
| sign([data, name, attr, out]) | It will return the element wise sign of the given input. |
| sin([data, name, attr, out]) | As name implies, this function will computes the element wise sine of the given input array. |
在下面的示例中，我们将使用ElementWiseSum()函数随机地随机排列元素。它将整数索引映射到矢量表示，即单词嵌入。
input_dim = 4
output_dim = 5
例
/* Here every row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
y = [[ 0., 1., 2., 3., 4.],
[ 5., 6., 7., 8., 9.],
[ 10., 11., 12., 13., 14.],
[ 15., 16., 17., 18., 19.]]
/* Here input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
x = [[ 1., 3.],
[ 0., 2.]]
/* Now, Mapped input x to its vector representation y.
Embedding(x, y, 4, 5) = [[[ 5., 6., 7., 8., 9.],
[ 15., 16., 17., 18., 19.]],
[[ 0., 1., 2., 3., 4.],
[ 10., 11., 12., 13., 14.]]]