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.DS_Store
.vscode
-*.pyc
-code/framework/data
-code/framework/output
+*.pyc
\ No newline at end of file
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+[submodule "code/framework"]
+ path = code/framework
+ url = https://github.com/vahidk/TensorflowFramework
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+# Effective TensorFlow 2 中文版
+
+目录
+=================
+## Part I: TensorFlow 2 基础
+1. [TensorFlow 2 基础](#basics)
+2. [广播](#broadcast)
+3. [利用重载OPs](#overloaded_ops)
+4. [控制流操作: 条件与循环](#control_flow)
+5. [原型核和使用Python OPs可视化](#python_ops)
+6. [TensorFlow中的数值稳定性](#stable)
+---
+
+_我们针对新发布的 TensorFlow 2.x API 更新了教程. 如果你想看 TensorFlow 1.x 的教程请移步 [v1 branch](https://github.com/vahidk/EffectiveTensorflow/tree/v1)._
+
+_安装 TensorFlow 2.0 (alpha) 请参照 [官方网站](https://www.tensorflow.org/install/pip):_
+```
+pip install tensorflow==2.0.0-alpha0
+```
+
+_我们致力于逐步扩展新的文章，并保持与Tensorflow API更新同步。如果你有任何建议请提出来。_
+
+# Part I: TensorFlow 2.0 基础
+
+
+## TensorFlow 基础
+
+重新设计的TensorFlow 2带来了更方便使用的API。如果你熟悉numpy，你用Tensorflow 2会很爽。不像完全静态图符号计算的Tensorflow 1，TF2隐藏静态图那部分，变得像个numpy。值得注意的是，虽然交互变化了，但是TF2仍然有静态图抽象的优势，TF1能做的TF2都能做。
+
+让我们从一个简单的例子开始吧，我们那俩随机矩阵乘起来。我们先看看Numpy怎么做这事先。
+```python
+import numpy as np
+
+x = np.random.normal(size=[10, 10])
+y = np.random.normal(size=[10, 10])
+z = np.dot(x, y)
+
+print(z)
+```
+
+现在看看用TensorFlow 2.0怎么办:
+```python
+import tensorflow as tf
+
+x = tf.random.normal([10, 10])
+y = tf.random.normal([10, 10])
+z = tf.matmul(x, y)
+
+print(z)
+```
+与NumPy差不多，TensorFlow 2也马上执行并返回结果。唯一的不同是TensorFlow用tf.Tensor类型存储结果，当然这种数据可以方便的转换为NumPy数据，调用tf.Tensor.numpy()成员函数就行:
+
+```python
+print(z.numpy())
+```
+
+为了理解符号计算的强大，让我们看看另一个例子。假设我们有从一个曲线(举个栗子 f(x) = 5x^2 + 3)上采集的样本点，并且我们要基于这些样本估计f(x)。我们建立了一个参数化函数g(x, w) = w0 x^2 + w1 x + w2，这个函数有输入x和隐藏参数w，我们的目标就是找出隐藏参数让g(x, w) ≈ f(x)。这个可以通过最小化以下的loss函数:L(w) = ∑ (f(x) - g(x, w))^2。虽然这个问题有解析解，但是我们更乐意用一个可以应用到任意可微分方程上的通用方法，嗯，SGD。我们仅需要计算L(w) 在不同样本点上关于w的平均提督，然后往梯度反方向调整就行。
+
+
+那么，怎么用TensorFlow实现呢:
+
+```python
+import numpy as np
+import tensorflow as tf
+
+# 假设我们知道我们期望的多项式方程是二阶方程，
+# 我们分配一个长3的向量并用随机噪声初始化。
+
+w = tf.Variable(tf.random.normal([3, 1]))
+
+# 用Adam优化器优化，初始学习率0.1
+opt = tf.optimizers.Adam(0.1)
+
+def model(x):
+ # 定义yhat为y的估计
+ f = tf.stack([tf.square(x), x, tf.ones_like(x)], 1)
+ yhat = tf.squeeze(tf.matmul(f, w), 1)
+ return yhat
+
+def compute_loss(y, yhat):
+ # loss用y和yhat之间的L2距离估计。
+ # 对w加了正则项保证w较小。
+ loss = tf.nn.l2_loss(yhat - y) + 0.1 * tf.nn.l2_loss(w)
+ return loss
+
+def generate_data():
+ # 根据真实函数生成一些训练样本
+ x = np.random.uniform(-10.0, 10.0, size=100).astype(np.float32)
+ y = 5 * np.square(x) + 3
+ return x, y
+
+def train_step():
+ x, y = generate_data()
+
+ def _loss_fn():
+ yhat = model(x)
+ loss = compute_loss(y, yhat)
+ return loss
+
+ opt.minimize(_loss_fn, [w])
+
+for _ in range(1000):
+ train_step()
+
+print(w.numpy())
+```
+运行这段代码你会看到近似下面这个的结果:
+```python
+[4.9924135, 0.00040895029, 3.4504161]
+```
+这和我们的参数很接近了.
+
+注意，上面的代码是交互式执行 (i.e. eager模式下ops直接执行)，这种操作并不高效. TensorFlow 2.0也提供静态图执行的法子，方便在GPUs和TPUs上快速并行执行。开启也很简单对于训练阶段函数用tf.function修饰就OK:
+
+```python
+@tf.function
+def train_step():
+ x, y = generate_data()
+
+ def _loss_fn():
+ yhat = model(x)
+ loss = compute_loss(y, yhat)
+ return loss
+
+ opt.minimize(_loss_fn, [w])
+```
+
+tf.function多牛逼，他也可以吧while、for之类函数转换进去。我们后面细说。
+
+这些只是TF能做的冰山一角。很多有几百万参数的复杂神经网络可以在TF用几行代码搞定。TF也可以在不同设备，不同线程上处理。
+
+## 广播操作
+
+TF支持广播元素操作。一般来说，如果你想执行加法或者乘法之类操作，你得确保相加或者相乘元素形状匹配，比如你不能把形状为[3, 2]的tensor加到形状为[3, 4]的tensor上。但是有个特例，就是当你把一个tensor和另一有维度长度是1的tensor是去加去乘，TF会把银行的把那个维扩展，让两个tensor可操作。（去看numpy的广播机制吧）
+
+```python
+import tensorflow as tf
+
+a = tf.constant([[1., 2.], [3., 4.]])
+b = tf.constant([[1.], [2.]])
+# c = a + tf.tile(b, [1, 2])
+c = a + b
+
+print(c)
+```
+
+广播可以让我们代码更短更高效。我们可以把不同长度的特征连接起来。比如用一些非线性操作复制特定维度，这在很多神经网络里经常用的到：
+
+
+```python
+a = tf.random.uniform([5, 3, 5])
+b = tf.random.uniform([5, 1, 6])
+
+# 连接a和b
+tiled_b = tf.tile(b, [1, 3, 1])
+c = tf.concat([a, tiled_b], 2)
+d = tf.keras.layers.Dense(10, activation=tf.nn.relu).apply(c)
+
+print(d)
+```
+
+但这个用了广播就更简单了，我们可以用f(m(x + y))等效f(mx + my)这个特性。然后隐含用广播来做连接。
+
+```python
+pa = tf.keras.layers.Dense(10).apply(a)
+pb = tf.keras.layers.Dense(10).apply(b)
+d = tf.nn.relu(pa + pb)
+
+print(d)
+```
+
+事实下面的代码在可以广播的场景下更好用。
+
+```python
+def merge(a, b, units, activation=None):
+ pa = tf.keras.layers.Dense(units).apply(a)
+ pb = tf.keras.layers.Dense(units).apply(b)
+ c = pa + pb
+ if activation is not None:
+ c = activation(c)
+ return c
+```
+
+所以，我们说了广播的好处，那么广播有啥坏处呢。隐含的广播可能导致debug麻烦。
+
+```python
+a = tf.constant([[1.], [2.]])
+b = tf.constant([1., 2.])
+c = tf.reduce_sum(a + b)
+
+print(c)
+```
+
+所以c的结果是啥？正确答案是12，当tensor形状不一样，TF自动的进行了广播。
+
+避免这个问题的法子就是尽量显式，比如reduce时候注明维度。
+
+```python
+a = tf.constant([[1.], [2.]])
+b = tf.constant([1., 2.])
+c = tf.reduce_sum(a + b, 0)
+
+print(c)
+```
+
+这里c得到[5, 7], 然后很容易发现问题。以后用reduce和tf.squeeze操作时最好注明维度。
+
+## 利用重载函数
+
+就像numpy，TF重载一些python操作来让graph构建更容易更可读。
+
+切片操作可以方便的索引tensor:
+```python
+z = x[begin:end] # z = tf.slice(x, [begin], [end-begin])
+```
+尽量不要用切片，因为这个效率很逊。为了理解这玩意效率到底有多逊，让我们康康一个例子。下面将做一个列方向上的reduce_sum。
+
+```python
+import tensorflow as tf
+import time
+
+x = tf.random.uniform([500, 10])
+
+z = tf.zeros([10])
+
+start = time.time()
+for i in range(500):
+ z += x[i]
+print("Took %f seconds." % (time.time() - start))
+```
+我的水果Pro上执行这段花了0.045秒，好逊。这是因为执行了500次切片，很慢的，更好的法子是矩阵分解。
+```python
+z = tf.zeros([10])
+for x_i in tf.unstack(x):
+ z += x_i
+```
+花了0.01秒，当然，最勇的法子是用tf.reduce_sum操作:
+```python
+z = tf.reduce_sum(x, axis=0)
+```
+这个操作用了0.0001秒, 比最初的方法快了100倍。
+
+TF也重载了一堆算数和逻辑操作
+```python
+z = -x # z = tf.negative(x)
+z = x + y # z = tf.add(x, y)
+z = x - y # z = tf.subtract(x, y)
+z = x * y # z = tf.mul(x, y)
+z = x / y # z = tf.div(x, y)
+z = x // y # z = tf.floordiv(x, y)
+z = x % y # z = tf.mod(x, y)
+z = x ** y # z = tf.pow(x, y)
+z = x @ y # z = tf.matmul(x, y)
+z = x > y # z = tf.greater(x, y)
+z = x >= y # z = tf.greater_equal(x, y)
+z = x < y # z = tf.less(x, y)
+z = x <= y # z = tf.less_equal(x, y)
+z = abs(x) # z = tf.abs(x)
+z = x & y # z = tf.logical_and(x, y)
+z = x | y # z = tf.logical_or(x, y)
+z = x ^ y # z = tf.logical_xor(x, y)
+z = ~x # z = tf.logical_not(x)
+```
+
+你也可以这些操作的扩展用法。 比如`x += y` 和 `x **= 2`。
+
+注意，py不允许and or not之类的重载。
+
+其他比如等于(==) 和不等(!=) 等被NumPy重载的操作并没有被TensorFlow实现，请用函数版本的 `tf.equal` 和 `tf.not_equal`。（less_equal,greater_equal之类也得用函数式）
+
+## 控制流，条件与循环
+
+当我们构建一个复杂的模型，比如递归神经网络，我们需要用条件或者循环来控制操作流。这一节里我们介绍一些常用的流控制操作。
+
+假设你想根据一个判断式来决定是否相乘或相加俩tensor。这个可以用py内置函数或者用tf.cond函数。
+
+```python
+a = tf.constant(1)
+b = tf.constant(2)
+
+p = tf.constant(True)
+
+# 或者:
+# x = tf.cond(p, lambda: a + b, lambda: a * b)
+x = a + b if p else a * b
+
+print(x.numpy())
+```
+由于判断式为真，因此输出相加结果，等于3。
+
+大多数时候你在TF里用很大的tensor，并且想把操作应用到batch上。用tf.where就能对一个batch得到满足判断式的成分进行操作。
+```python
+a = tf.constant([1, 1])
+b = tf.constant([2, 2])
+
+p = tf.constant([True, False])
+
+x = tf.where(p, a + b, a * b)
+
+print(x.numpy())
+```
+结果得到[3, 2].
+
+另一个常用的操作是tf.while_loop，他允许在TF里用动态循环处理可变长度序列。来个例子:
+
+```python
+@tf.function
+def fibonacci(n):
+ a = tf.constant(1)
+ b = tf.constant(1)
+
+ for i in range(2, n):
+ a, b = b, a + b
+
+ return b
+
+n = tf.constant(5)
+b = fibonacci(n)
+
+print(b.numpy())
+```
+输出5. 注意tf.function装饰器自动把python代码转换为tf.while_loop因此我们不用折腾TF API。
+
+现在想一下，我们想要保持完整的斐波那契数列的话，我们需要更新代码来保存历史值:
+```python
+@tf.function
+def fibonacci(n):
+ a = tf.constant(1)
+ b = tf.constant(1)
+ c = tf.constant([1, 1])
+
+ for i in range(2, n):
+ a, b = b, a + b
+ c = tf.concat([c, [b]], 0)
+
+ return c
+
+n = tf.constant(5)
+b = fibonacci(n)
+
+print(b.numpy())
+```
+
+如果你这么执行了，TF会反馈循环值发生变化。
+解决这个问题可以用 "shape invariants"，但是这个只能在底层tf.while_loop API里用。
+
+
+```python
+n = tf.constant(5)
+
+def cond(i, a, b, c):
+ return i < n
+
+def body(i, a, b, c):
+ a, b = b, a + b
+ c = tf.concat([c, [b]], 0)
+ return i + 1, a, b, c
+
+i, a, b, c = tf.while_loop(
+ cond, body, (2, 1, 1, tf.constant([1, 1])),
+ shape_invariants=(tf.TensorShape([]),
+ tf.TensorShape([]),
+ tf.TensorShape([]),
+ tf.TensorShape([None])))
+
+print(c.numpy())
+```
+这个又丑又慢。我们建立一堆没用的中间tensor。TF有更好的解决方法，用tf.TensorArray就行了:
+```python
+@tf.function
+def fibonacci(n):
+ a = tf.constant(1)
+ b = tf.constant(1)
+
+ c = tf.TensorArray(tf.int32, n)
+ c = c.write(0, a)
+ c = c.write(1, b)
+
+ for i in range(2, n):
+ a, b = b, a + b
+ c = c.write(i, b)
+
+ return c.stack()
+
+n = tf.constant(5)
+c = fibonacci(n)
+
+print(c.numpy())
+```
+TF while循环再建立负载递归神经网络时候很有用。这里有个实验，[beam search](https://en.wikipedia.org/wiki/Beam_search) 他用了tf.while_loops，你那么勇应该可以用tensor arrays实现的更高效吧。
+
+## 原型核和用Python OPs可视化
+
+TF里操作kernel使用Cpp实现来保证效率。但用Cpp写TensorFlow kernel很烦诶，所以你在实现自己的kernel前可以实验下自己想法是否奏效。用tf.py_function() 你可以把任何python操作编程tf操作。
+
+下面就是自己实现一个非线性的Relu:
+```python
+import numpy as np
+import tensorflow as tf
+import uuid
+
+def relu(inputs):
+ # Define the op in python
+ def _py_relu(x):
+ return np.maximum(x, 0.)
+
+ # Define the op's gradient in python
+ def _py_relu_grad(x):
+ return np.float32(x > 0)
+
+ @tf.custom_gradient
+ def _relu(x):
+ y = tf.py_function(_py_relu, [x], tf.float32)
+
+ def _relu_grad(dy):
+ return dy * tf.py_function(_py_relu_grad, [x], tf.float32)
+
+ return y, _relu_grad
+
+ return _relu(inputs)
+```
+为了验证梯度的正确性，你应该比较解析和数值梯度。
+```python
+# 计算解析梯度
+x = tf.random.normal([10], dtype=np.float32)
+with tf.GradientTape() as tape:
+ tape.watch(x)
+ y = relu(x)
+g = tape.gradient(y, x)
+print(g)
+
+# 计算数值梯度
+dx_n = 1e-5
+dy_n = relu(x + dx_n) - relu(x)
+g_n = dy_n / dx_n
+print(g_n)
+```
+这俩值应该很接近。
+
+注意这个实现很低效，因此只应该用在原型里，因为python代码超慢，后面你会想Cpp重新实现计算kernel的，大概。
+
+实际，我们通常用python操作来做可视化。比如你做图像分类，你在训练时想可视化你的模型预测，用Tensorboard看tf.summary.image()保存的结果吧:
+```python
+image = tf.placeholder(tf.float32)
+tf.summary.image("image", image)
+```
+但是你这只能可视化输入图，没法知道预测值，用tf的操作肯定嗝屁了，你可以用python操作:
+```python
+def visualize_labeled_images(images, labels, max_outputs=3, name="image"):
+ def _visualize_image(image, label):
+ # python里绘图
+ fig = plt.figure(figsize=(3, 3), dpi=80)
+ ax = fig.add_subplot(111)
+ ax.imshow(image[::-1,...])
+ ax.text(0, 0, str(label),
+ horizontalalignment="left",
+ verticalalignment="top")
+ fig.canvas.draw()
+
+ # 写入内存中
+ buf = io.BytesIO()
+ data = fig.savefig(buf, format="png")
+ buf.seek(0)
+
+ # Pillow解码图像
+ img = PIL.Image.open(buf)
+ return np.array(img.getdata()).reshape(img.size[0], img.size[1], -1)
+
+ def _visualize_images(images, labels):
+ # 只显示batch中部分图
+ outputs = []
+ for i in range(max_outputs):
+ output = _visualize_image(images[i], labels[i])
+ outputs.append(output)
+ return np.array(outputs, dtype=np.uint8)
+
+ # 、运行python op.
+ figs = tf.py_function(_visualize_images, [images, labels], tf.uint8)
+ return tf.summary.image(name, figs)
+```
+
+由于验证测试过一段时间测试一次，所以不用担心效率。
+
+## Numerical stability in TensorFlow
+
+用TF或者Numpy之类数学计算库的时候，既要考虑数学计算的正确性，也要注意数值计算的稳定性。
+
+举个例子，小学就教了x * y / y在y不等于0情况下等于x，但是实际:
+```python
+import numpy as np
+
+x = np.float32(1)
+
+y = np.float32(1e-50) # y 被当成0了
+z = x * y / y
+
+print(z) # prints nan
+```
+
+对于单精度浮点y太小了，直接被当成0了，当然y很大的时候也有问题:
+
+```python
+y = np.float32(1e39) # y 被当成无穷大
+z = x * y / y
+
+print(z) # prints nan
+```
+
+单精度浮点的最小值是1.4013e-45，任何比他小的值都被当成0，同样的任何大于3.40282e+38的,会被当成无穷大。
+
+```python
+print(np.nextafter(np.float32(0), np.float32(1))) # prints 1.4013e-45
+print(np.finfo(np.float32).max) # print 3.40282e+38
+```
+为了保证你计算的稳定，你必须避免过小值或者过大值。这个听起来理所当然，但是在TF进行梯度下降的时候可能很难debug。你在FP时候要保证稳定，在BP时候还要保证。
+
+让我们看一个例子，我们想要在一个logits向量上计算softmax，一个naive的实现就像：
+```python
+import tensorflow as tf
+
+def unstable_softmax(logits):
+ exp = tf.exp(logits)
+ return exp / tf.reduce_sum(exp)
+
+print(unstable_softmax([1000., 0.]).numpy()) # prints [ nan, 0.]
+```
+所以你logits的exp的值，即使logits很小会得到很大的值，说不定超过单精度的范围。最大的不溢出logit值是ln(3.40282e+38) = 88.7，比他大的就会导致nan。
+
+所以怎么让这玩意稳定，exp(x - c) / ∑ exp(x - c) = exp(x) / ∑ exp(x)就搞掂了。如果我们logits减去一个数，结果还是一样的，一般减去logits最大值。这样exp函数的输入被限定在[-inf, 0]，然后输出就是[0.0, 1.0]，就很棒:
+
+```python
+import tensorflow as tf
+
+def softmax(logits):
+ exp = tf.exp(logits - tf.reduce_max(logits))
+ return exp / tf.reduce_sum(exp)
+
+print(softmax([1000., 0.]).numpy()) # prints [ 1., 0.]
+```
+
+我们看一个更加复杂的情况，考虑一个分类问题，我们用softmax来得到logits的可能性，之后用交叉熵计算预测和真值。交叉熵这么算xe(p, q) = -∑ p_i log(q_i)。然后一个naive的实现如下:
+
+```python
+def unstable_softmax_cross_entropy(labels, logits):
+ logits = tf.math.log(softmax(logits))
+ return -tf.reduce_sum(labels * logits)
+
+labels = tf.constant([0.5, 0.5])
+logits = tf.constant([1000., 0.])
+
+xe = unstable_softmax_cross_entropy(labels, logits)
+
+print(xe.numpy()) # prints inf
+```
+
+由于softmax输出结果接近0，log的输出接近无限导致了计算的不稳定，我们扩展softmax并简化了计算交叉熵:
+
+```python
+def softmax_cross_entropy(labels, logits):
+ scaled_logits = logits - tf.reduce_max(logits)
+ normalized_logits = scaled_logits - tf.reduce_logsumexp(scaled_logits)
+ return -tf.reduce_sum(labels * normalized_logits)
+
+labels = tf.constant([0.5, 0.5])
+logits = tf.constant([1000., 0.])
+
+xe = softmax_cross_entropy(labels, logits)
+
+print(xe.numpy()) # prints 500.0
+```
+
+我们也证明了梯度计算的正确性:
+```python
+with tf.GradientTape() as tape:
+ tape.watch(logits)
+ xe = softmax_cross_entropy(labels, logits)
+
+g = tape.gradient(xe, logits)
+print(g.numpy()) # prints [0.5, -0.5]
+```
+这就对了。
+
+必须再次提醒，在做梯度相关操作时候必须注意保证每一层梯度都在有效范围内，exp和log操作由于可以把小数变得很大，因此可能让计算变得不稳定，所以使用exp和log操作必须十分谨慎。
diff --git a/README.md b/README.md
index 8fd4ceb..26fb625 100644
--- a/README.md
+++ b/README.md
@@ -1,25 +1,33 @@
-# Effective Tensorflow
+# Effective TensorFlow 2
Table of Contents
=================
-1. [Tensorflow Basics](#basics)
-2. [Understanding static and dynamic shapes](#shapes)
-3. [Broadcasting the good and the ugly](#broadcast)
-4. [Understanding order of execution and control dependencies](#control_deps)
-5. [Control flow operations: conditionals and loops](#control_flow)
-6. [Prototyping kernels and advanced visualization with Python ops](#python_ops)
-7. [Multi-GPU processing with data parallelism](#multi_gpu)
-8. [Building a neural network training framework with learn API](#tf_learn)
-9. [Tensorflow Cookbook](#cookbook)
- - [Beam search](#beam_search)
- - [Merge](#merge)
- - [Entropy](#entropy)
-
-## Tensorflow Basics
+## Part I: TensorFlow 2 Fundamentals
+1. [TensorFlow 2 Basics](#basics)
+2. [Broadcasting the good and the ugly](#broadcast)
+3. [Take advantage of the overloaded operators](#overloaded_ops)
+4. [Control flow operations: conditionals and loops](#control_flow)
+5. [Prototyping kernels and advanced visualization with Python ops](#python_ops)
+6. [Numerical stability in TensorFlow](#stable)
+---
+
+_We updated the guide to follow the newly released TensorFlow 2.x API. If you want the original guide for TensorFlow 1.x see the [v1 branch](https://github.com/vahidk/EffectiveTensorflow/tree/v1)._
+
+_To install TensorFlow 2.0 (alpha) follow the [instructions on the official website](https://www.tensorflow.org/install/pip):_
+```
+pip install tensorflow==2.0.0-alpha0
+```
+
+_We aim to gradually expand this series by adding new articles and keep the content up to date with the latest releases of TensorFlow API. If you have suggestions on how to improve this series or find the explanations ambiguous, feel free to create an issue, send patches, or reach out by email._
+
+# Part I: TensorFlow 2.0 Fundamentals
+
+
+## TensorFlow Basics
-The most striking difference between Tensorflow and other numerical computation libraries such as numpy is that operations in Tensorflow are symbolic. This is a powerful concept that allows Tensorflow to do all sort of things (e.g. automatic differentiation) that are not possible with imperative libraries such as numpy. But it also comes at the cost of making it harder to grasp. Our attempt here is demystify Tensorflow and provide some guidelines and best practices for more effective use of Tensorflow.
+TensorFlow 2 went under a massive redesign to make the API more accessible and easier to use. If you are familiar with numpy you will find yourself right at home when using TensorFlow 2. Unlike TensorFlow 1 which was purely symbolic, TensorFlow 2 hides its symbolic nature behind the hood to look like any other imperative library like NumPy. It's important to note the change is mostly an interface change, and TensorFlow 2 is still able to take advantage of its symbolic machinery to do everything that TensorFlow 1.x can do (e.g. automatic-differentiation and massively parallel computation on TPUs/GPUs).
-Let's start with a simple example, we want to multiply two random matrices. First we look at an implementation done in numpy:
+Let's start with a simple example, we want to multiply two random matrices. First we look at an implementation done in NumPy:
```python
import numpy as np
@@ -30,203 +38,147 @@ z = np.dot(x, y)
print(z)
```
-Now we perform the exact same computation this time in Tensorflow:
+Now we perform the exact same computation this time in TensorFlow 2.0:
```python
import tensorflow as tf
-x = tf.random_normal([10, 10])
-y = tf.random_normal([10, 10])
+x = tf.random.normal([10, 10])
+y = tf.random.normal([10, 10])
z = tf.matmul(x, y)
-sess = tf.Session()
-z_val = sess.run(z)
-
-print(z_val)
-```
-Unlike numpy that immediately performs the computation and copies the result to
-the output variable z, tensorflow only gives us a handle (of type Tensor) to a node in the graph that represents the result. If we try printing the value of z directly, we get something like this:
-```
-Tensor("MatMul:0", shape=(10, 10), dtype=float32)
+print(z)
```
-Since both the inputs have a fully defined shape, tensorflow is able to infer the shape of the tensor as well as its type. In order to compute the value of the tensor we need to create a session and evaluate it using Session.run() method.
+Similar to NumPy TensorFlow 2 also immediately performs the computation and produces the result. The only difference is that TensorFlow uses tf.Tensor type to store the results which can be easily converted to NumPy, by calling tf.Tensor.numpy() member function:
-***
-__Tip__: When using Jupyter notebook make sure to call tf.reset_default_graph() at the beginning to clear the symbolic graph before defining new nodes.
-***
+```python
+print(z.numpy())
+```
-To understand how powerful symbolic computation can be let's have a look at another example. Assume that we have samples from a curve (say f(x) = 5x^2 + 3) and we want to estimate f(x) without knowing its parameters. We define a parametric function g(x, w) = w0 x^2 + w1 x + w2, which is a function of the input x and latent parameters w, our goal is then to find the latent parameters such that g(x, w) ≈ f(x). This can be done by minimizing the following loss function: L(w) = (f(x) - g(x, w))^2. Although there's a closed form solution for this simple problem, we opt to use a more general approach that can be applied to any arbitrary differentiable function, and that is using stochastic gradient descent. We simply compute the average gradient of L(w) with respect to w over a set of sample points and move in the opposite direction.
+To understand how powerful symbolic computation can be let's have a look at another example. Assume that we have samples from a curve (say f(x) = 5x^2 + 3) and we want to estimate f(x) based on these samples. We define a parametric function g(x, w) = w0 x^2 + w1 x + w2, which is a function of the input x and latent parameters w, our goal is then to find the latent parameters such that g(x, w) ≈ f(x). This can be done by minimizing the following loss function: L(w) = ∑ (f(x) - g(x, w))^2. Although there's a closed form solution for this simple problem, we opt to use a more general approach that can be applied to any arbitrary differentiable function, and that is using stochastic gradient descent. We simply compute the average gradient of L(w) with respect to w over a set of sample points and move in the opposite direction.
-Here's how it can be done in Tensorflow:
+Here's how it can be done in TensorFlow:
```python
import numpy as np
import tensorflow as tf
-# Placeholders are used to feed values from python to Tensorflow ops. We define
-# two placeholders, one for input feature x, and one for output y.
-x = tf.placeholder(tf.float32)
-y = tf.placeholder(tf.float32)
-
# Assuming we know that the desired function is a polynomial of 2nd degree, we
-# allocate a vector of size 3 to hold the coefficients. The variable will be
-# automatically initialized with random noise.
-w = tf.get_variable("w", shape=[3, 1])
-
-# We define yhat to be our estimate of y.
-f = tf.stack([tf.square(x), x, tf.ones_like(x)], 1)
-yhat = tf.squeeze(tf.matmul(f, w), 1)
-
-# The loss is defined to be the l2 distance between our estimate of y and its
-# true value. We also added a shrinkage term, tp ensure the resulting weights
-# would be small.
-loss = tf.nn.l2_loss(yhat - y) + 0.1 * tf.nn.l2_loss(w)
+# allocate a vector of size 3 to hold the coefficients and initialize it with
+# random noise.
+w = tf.Variable(tf.random.normal([3, 1]))
# We use the Adam optimizer with learning rate set to 0.1 to minimize the loss.
-train_op = tf.train.AdamOptimizer(0.1).minimize(loss)
+opt = tf.optimizers.Adam(0.1)
-def generate_data():
- x_val = np.random.uniform(-10.0, 10.0, size=100)
- y_val = 5 * np.square(x_val) + 3
- return x_val, y_val
-
-sess = tf.Session()
-# Since we are using variables we first need to initialize them.
-sess.run(tf.global_variables_initializer())
-for _ in range(1000):
- x_val, y_val = generate_data()
- _, loss_val = sess.run([train_op, loss], {x: x_val, y: y_val})
- print(loss_val)
-print(sess.run([w]))
-```
-By running this piece of code you should see a result close to this:
-```
-[4.9924135, 0.00040895029, 3.4504161]
-```
-Which is a relatively close approximation to our parameters.
+def model(x):
+ # We define yhat to be our estimate of y.
+ f = tf.stack([tf.square(x), x, tf.ones_like(x)], 1)
+ yhat = tf.squeeze(tf.matmul(f, w), 1)
+ return yhat
-This is just tip of the iceberg for what Tensorflow can do. Many problems such a optimizing large neural networks with millions of parameters can be implemented efficiently in Tensorflow in just a few lines of code. Tensorflow takes care of scaling across multiple devices, and threads, and supports a variety of platforms.
+def compute_loss(y, yhat):
+ # The loss is defined to be the l2 distance between our estimate of y and its
+ # true value. We also added a shrinkage term, to ensure the resulting weights
+ # would be small.
+ loss = tf.nn.l2_loss(yhat - y) + 0.1 * tf.nn.l2_loss(w)
+ return loss
-## Understanding static and dynamic shapes
-
-Tensors in Tensorflow have a static shape attribute which is determined during graph construction. The static shape may be underspecified. For example we might define a float32 tensor of shape [None, 128]:
-```python
-import tensorflow as tf
+def generate_data():
+ # Generate some training data based on the true function
+ x = np.random.uniform(-10.0, 10.0, size=100).astype(np.float32)
+ y = 5 * np.square(x) + 3
+ return x, y
-a = tf.placeholder(tf.float32, [None, 128])
-```
-This means that the first dimension can be of any size and will be determined dynamically during Session.run(). You can query the static shape of a Tensor as follows:
+def train_step():
+ x, y = generate_data()
-```python
-static_shape = a.shape # returns TensorShape([Dimension(None), Dimension(128)])
-static_shape = a.shape.as_list() # returns [None, 128]
-```
+ def _loss_fn():
+ yhat = model(x)
+ loss = compute_loss(y, yhat)
+ return loss
+
+ opt.minimize(_loss_fn, [w])
-To get the dynamic shape of the tensor you can call tf.shape op, which returns a tensor representing the shape of the given tensor:
-```python
-dynamic_shape = tf.shape(a)
-```
+for _ in range(1000):
+ train_step()
-The static shape of a tensor can be set with Tensor.set_shape() method:
-```python
-a.set_shape([32, 128])
+print(w.numpy())
```
-Use this function only if you know what you are doing, in practice it's safer to do dynamic reshaping with tf.reshape() op:
-
+By running this piece of code you should see a result close to this:
```python
-a = tf.reshape(a, [32, 128])
+[4.9924135, 0.00040895029, 3.4504161]
```
+Which is a relatively close approximation to our parameters.
-If you feed 'a' with values that don't match the shape, you will get an InvalidArgumentError indicating that the
-number of values fed doesn't match the expected shape.
+Note that in the above code we are running Tensorflow in imperative mode (i.e. operations get instantly executed), which is not very efficient. TensorFlow 2.0 can also turn a given piece of python code into a graph which can then optimized and efficiently parallelized on GPUs and TPUs. To get all those benefits we simply need to decorate the train_step function with tf.function decorator:
-It can be convenient to have a function that returns the static shape when available and dynamic shape when it's not. The following utility function does just that:
```python
-def get_shape(tensor):
- static_shape = tensor.shape.as_list()
- dynamic_shape = tf.unstack(tf.shape(tensor))
- dims = [s[1] if s[0] is None else s[0]
- for s in zip(static_shape, dynamic_shape)]
- return dims
-```
+@tf.function
+def train_step():
+ x, y = generate_data()
-Now imagine we want to convert a Tensor of rank 3 to a tensor of rank 2 by collapsing the second and third dimensions into one. We can use our get_shape() function to do that:
-```python
-b = placeholder(tf.float32, [None, 10, 32])
-shape = get_shape(tensor)
-b = tf.reshape(b, [shape[0], shape[1] * shape[2]])
+ def _loss_fn():
+ yhat = model(x)
+ loss = compute_loss(y, yhat)
+ return loss
+
+ opt.minimize(_loss_fn, [w])
```
-Note that this works whether the shapes are statically specified or not.
-In fact we can write a general purpose reshape function to collapse any list of dimensions:
-```python
-import tensorflow as tf
-import numpy as np
+What's cool about tf.function is that it's also able to convert basic python statements like while, for and if into native TensorFlow functions. We will get to that later.
-def reshape(tensor, dims_list):
- shape = get_shape(tensor)
- dims_prod = []
- for dims in dims_list:
- if isinstance(dims, int):
- dims_prod.append(shape[dims])
- elif all([isinstance(shape[d], int) for d in dims]):
- dims_prod.append(np.prod([shape[d] for d in dims]))
- else:
- dims_prod.append(tf.prod([shape[d] for d in dims]))
- tensor = tf.reshape(tensor, dims_prod)
- return tensor
-```
-
-Then collapsing the second dimension becomes very easy:
-```python
-b = placeholder(tf.float32, [None, 10, 32])
-b = tf.reshape(b, [0, [1, 2]])
-```
+This is just tip of the iceberg for what TensorFlow can do. Many problems such as optimizing large neural networks with millions of parameters can be implemented efficiently in TensorFlow in just a few lines of code. TensorFlow takes care of scaling across multiple devices, and threads, and supports a variety of platforms.
## Broadcasting the good and the ugly
-Tensorflow supports broadcasting elementwise operations. Normally when you want to perform operations like addition and multiplication, you need to make sure that shapes of the operands match, e.g. you can’t add a tensor of shape [3, 2] to a tensor of shape [3, 4]. But there’s a special case and that’s when you have a singular dimension. Tensorflow implicitly tiles the tensor across its singular dimensions to match the shape of the other operand. So it’s valid to add a tensor of shape [3, 2] to a tensor of shape [3, 1]
+TensorFlow supports broadcasting elementwise operations. Normally when you want to perform operations like addition and multiplication, you need to make sure that shapes of the operands match, e.g. you can’t add a tensor of shape [3, 2] to a tensor of shape [3, 4]. But there’s a special case and that’s when you have a singular dimension. TensorFlow implicitly tiles the tensor across its singular dimensions to match the shape of the other operand. So it’s valid to add a tensor of shape [3, 2] to a tensor of shape [3, 1]
```python
import tensorflow as tf
a = tf.constant([[1., 2.], [3., 4.]])
b = tf.constant([[1.], [2.]])
-# c = a + tf.tile(a, [1, 2])
+# c = a + tf.tile(b, [1, 2])
c = a + b
+
+print(c)
```
Broadcasting allows us to perform implicit tiling which makes the code shorter, and more memory efficient, since we don’t need to store the result of the tiling operation. One neat place that this can be used is when combining features of varying length. In order to concatenate features of varying length we commonly tile the input tensors, concatenate the result and apply some nonlinearity. This is a common pattern across a variety of neural network architectures:
```python
-a = tf.random_uniform([5, 3, 5])
-b = tf.random_uniform([5, 1, 6])
+a = tf.random.uniform([5, 3, 5])
+b = tf.random.uniform([5, 1, 6])
# concat a and b and apply nonlinearity
tiled_b = tf.tile(b, [1, 3, 1])
c = tf.concat([a, tiled_b], 2)
-d = tf.layers.dense(c, 10, activation=tf.nn.relu)
+d = tf.keras.layers.Dense(10, activation=tf.nn.relu).apply(c)
+
+print(d)
```
But this can be done more efficiently with broadcasting. We use the fact that f(m(x + y)) is equal to f(mx + my). So we can do the linear operations separately and use broadcasting to do implicit concatenation:
```python
-pa = tf.layers.dense(a, 10, activation=None)
-pb = tf.layers.dense(b, 10, activation=None)
+pa = tf.keras.layers.Dense(10).apply(a)
+pb = tf.keras.layers.Dense(10).apply(b)
d = tf.nn.relu(pa + pb)
+
+print(d)
```
In fact this piece of code is pretty general and can be applied to tensors of arbitrary shape as long as broadcasting between tensors is possible:
```python
-def merge(a, b, units, activation=tf.nn.relu):
- pa = tf.layers.dense(a, units, activation=None)
- pb = tf.layers.dense(b, units, activation=None)
+def merge(a, b, units, activation=None):
+ pa = tf.keras.layers.Dense(units).apply(a)
+ pb = tf.keras.layers.Dense(units).apply(b)
c = pa + pb
if activation is not None:
c = activation(c)
return c
```
-A slightly more general form of this function is [included](#merge) in the cookbook.
So far we discussed the good part of broadcasting. But what’s the ugly part you may ask? Implicit assumptions almost always make debugging harder to do. Consider the following example:
@@ -234,9 +186,11 @@ So far we discussed the good part of broadcasting. But what’s the ugly part yo
a = tf.constant([[1.], [2.]])
b = tf.constant([1., 2.])
c = tf.reduce_sum(a + b)
+
+print(c)
```
-What do you think would the value of c would after evaluation? If you guessed 6, that’s wrong. It’s going to be 12. This is because when rank of two tensors don’t match, Tensorflow automatically expands the first dimension of the tensor with lower rank before the elementwise operation, so the result of addition would be [[2, 3], [3, 4]], and the reducing over all parameters would give us 12.
+What do you think the value of c would be after evaluation? If you guessed 6, that’s wrong. It’s going to be 12. This is because when rank of two tensors don’t match, TensorFlow automatically expands the first dimension of the tensor with lower rank before the elementwise operation, so the result of addition would be [[2, 3], [3, 4]], and the reducing over all parameters would give us 12.
The way to avoid this problem is to be as explicit as possible. Had we specified which dimension we would want to reduce across, catching this bug would have been much easier:
@@ -244,96 +198,94 @@ The way to avoid this problem is to be as explicit as possible. Had we specified
a = tf.constant([[1.], [2.]])
b = tf.constant([1., 2.])
c = tf.reduce_sum(a + b, 0)
+
+print(c)
```
Here the value of c would be [5, 7], and we immediately would guess based on the shape of the result that there’s something wrong. A general rule of thumb is to always specify the dimensions in reduction operations and when using tf.squeeze.
-## Understanding order of execution and control dependencies
-
-As we discussed in the first item, Tensorflow doesn't immediately run the operations that are defined but rather creates corresponding nodes in a graph that can be evaluated with Session.run() method. This also enables Tensorflow to do optimizations at run time to determine the optimal order of execution and possible trimming of unused nodes. If you only have tf.Tensors in your graph you don't need to worry about dependencies but you most probably have tf.Variables too, and tf.Variables make things much more difficult. My advice to is to only use Variables if Tensors don't do the job. This might not make a lot of sense to you now, so let's start with an example.
+## Take advantage of the overloaded operators
+
+Just like NumPy, TensorFlow overloads a number of python operators to make building graphs easier and the code more readable.
+The slicing op is one of the overloaded operators that can make indexing tensors very easy:
+```python
+z = x[begin:end] # z = tf.slice(x, [begin], [end-begin])
+```
+Be very careful when using this op though. The slicing op is very inefficient and often better avoided, especially when the number of slices is high. To understand how inefficient this op can be let's look at an example. We want to manually perform reduction across the rows of a matrix:
```python
import tensorflow as tf
+import time
-a = tf.constant(1)
-b = tf.constant(2)
-a = a + b
-
-tf.Session().run(a)
-```
+x = tf.random.uniform([500, 10])
-Evaluating "a" will return the value 3 as expected. Note that here we are creating 3 tensors, two constant tensors and another tensor that stores the result of the addition. Note that you can't overwrite the value of a tensor. If you want to modify it you have to create a new tensor. As we did here.
+z = tf.zeros([10])
-***
-__TIP__: If you don't define a new graph, Tensorflow automatically creates a graph for you by default. You can use tf.get_default_graph() to get a handle to the graph. You can then inspect the graph, for example by printing all its tensors:
+start = time.time()
+for i in range(500):
+ z += x[i]
+print("Took %f seconds." % (time.time() - start))
+```
+On my MacBook Pro, this took 0.045 seconds to run which is quite slow. The reason is that we are calling the slice op 500 times, which is going to be very slow to run. A better choice would have been to use tf.unstack op to slice the matrix into a list of vectors all at once:
```python
-print(tf.contrib.graph_editor.get_tensors(tf.get_default_graph()))
+z = tf.zeros([10])
+for x_i in tf.unstack(x):
+ z += x_i
```
-***
-
-Unlike tensors, variables can be updated. So let's see how we may use variables to do the same thing:
+This took 0.01 seconds. Of course, the right way to do this simple reduction is to use tf.reduce_sum op:
```python
-a = tf.Variable(1)
-b = tf.constant(2)
-assign = tf.assign(a, a + b)
-
-sess = tf.Session()
-sess.run(tf.global_variables_initializer())
-print(sess.run(assign))
+z = tf.reduce_sum(x, axis=0)
```
-Again, we get 3 as expected. Note that tf.assign returns a tensor representing the value of the assignment.
-So far everything seemed to be fine, but let's look at a slightly more complicated example:
+This took 0.0001 seconds, which is 100x faster than the original implementation.
+TensorFlow also overloads a range of arithmetic and logical operators:
```python
-a = tf.Variable(1)
-b = tf.constant(2)
-c = a + b
-
-assign = tf.assign(a, 5)
-
-sess = tf.Session()
-for i in range(10):
- sess.run(tf.global_variables_initializer())
- print(sess.run([assign, c]))
+z = -x # z = tf.negative(x)
+z = x + y # z = tf.add(x, y)
+z = x - y # z = tf.subtract(x, y)
+z = x * y # z = tf.mul(x, y)
+z = x / y # z = tf.div(x, y)
+z = x // y # z = tf.floordiv(x, y)
+z = x % y # z = tf.mod(x, y)
+z = x ** y # z = tf.pow(x, y)
+z = x @ y # z = tf.matmul(x, y)
+z = x > y # z = tf.greater(x, y)
+z = x >= y # z = tf.greater_equal(x, y)
+z = x < y # z = tf.less(x, y)
+z = x <= y # z = tf.less_equal(x, y)
+z = abs(x) # z = tf.abs(x)
+z = x & y # z = tf.logical_and(x, y)
+z = x | y # z = tf.logical_or(x, y)
+z = x ^ y # z = tf.logical_xor(x, y)
+z = ~x # z = tf.logical_not(x)
```
-Note that the tensor c here won't have a deterministic value. This value might be 3 or 7 depending on whether addition or assignment gets executed first.
-
-You should note that the order that you define ops in your code doesn't matter to Tensorflow runtime. The only thing that matters is the control dependencies. Control dependencies for tensors are straightforward. Every time you use a tensor in an operation that op will define an implicit dependency to that tensor. But things get complicated with variables because they can take many values.
-When dealing with variables, you may need to explicitly define dependencies using tf.control_dependencies() as follows:
-```python
-a = tf.Variable(1)
-b = tf.constant(2)
-c = a + b
+You can also use the augmented version of these ops. For example `x += y` and `x **= 2` are also valid.
-with tf.control_dependencies([c]):
- assign = tf.assign(a, 5)
+Note that Python doesn't allow overloading "and", "or", and "not" keywords.
-sess = tf.Session()
-for i in range(10):
- sess.run(tf.global_variables_initializer())
- print(sess.run([assign, c]))
-```
-This will make sure that the assign op will be called after the addition.
+Other operators that aren't supported are equal (==) and not equal (!=) operators which are overloaded in NumPy but not in TensorFlow. Use the function versions instead which are `tf.equal` and `tf.not_equal`.
## Control flow operations: conditionals and loops
When building complex models such as recurrent neural networks you may need to control the flow of operations through conditionals and loops. In this section we introduce a number of commonly used control flow ops.
-Let's assume you want to decide whether to multiply to or add two given tensors based on a predicate. This can be simply implemented with tf.cond which acts as a python "if" function:
+Let's assume you want to decide whether to multiply to or add two given tensors based on a predicate. This can be simply implemented with either python's built-in if statement or using tf.cond function:
```python
a = tf.constant(1)
b = tf.constant(2)
p = tf.constant(True)
-x = tf.cond(p, lambda: a + b, lambda: a * b)
+# Alternatively:
+# x = tf.cond(p, lambda: a + b, lambda: a * b)
+x = a + b if p else a * b
-print(tf.Session().run(x))
+print(x.numpy())
```
Since the predicate is True in this case, the output would be the result of the addition, which is 3.
-Most of the times when using Tensorflow you are using large tensors and want to perform operations in batch. A related conditional operation is tf.where, which like tf.cond takes a predicate, but selects the output based on the condition in batch.
+Most of the times when using TensorFlow you are using large tensors and want to perform operations in batch. A related conditional operation is tf.where, which like tf.cond takes a predicate, but selects the output based on the condition in batch.
```python
a = tf.constant([1, 1])
b = tf.constant([2, 2])
@@ -342,27 +294,54 @@ p = tf.constant([True, False])
x = tf.where(p, a + b, a * b)
-print(tf.Session().run(x))
+print(x.numpy())
```
This will return [3, 2].
-Another widely used control flow operation is tf.while_loop. It allows building dynamic loops in Tensorflow that operate on sequences of variable length. Let's see how we can generate Fibonacci sequence with tf.while_loops:
+Another widely used control flow operation is tf.while_loop. It allows building dynamic loops in TensorFlow that operate on sequences of variable length. Let's see how we can generate Fibonacci sequence with tf.while_loops:
+
```python
+@tf.function
+def fibonacci(n):
+ a = tf.constant(1)
+ b = tf.constant(1)
+
+ for i in range(2, n):
+ a, b = b, a + b
+
+ return b
+
n = tf.constant(5)
+b = fibonacci(n)
+
+print(b.numpy())
+```
+This will print 5. Note that tf.function automatically converts the given python code to use tf.while_loop so we don't need to directly interact with the TF API.
-def cond(i, a, b):
- return i < n
+Now imagine we want to keep the whole series of Fibonacci sequence. We may update our body to keep a record of the history of current values:
+```python
+@tf.function
+def fibonacci(n):
+ a = tf.constant(1)
+ b = tf.constant(1)
+ c = tf.constant([1, 1])
-def body(i, a, b):
- return i + 1, b, a + b
+ for i in range(2, n):
+ a, b = b, a + b
+ c = tf.concat([c, [b]], 0)
+
+ return c
+
+n = tf.constant(5)
+b = fibonacci(n)
+
+print(b.numpy())
+```
-i, a, b = tf.while_loop(cond, body, (2, 1, 1))
+Now if you try running this, TensorFlow will complain that the shape of the the one of the loop variables is changing.
+One way to fix this is is to use "shape invariants", but this functionality is only available when using the low-level tf.while_loop API:
-print(tf.Session().run(b))
-```
-This will print 5. tf.while_loops takes a condition function, and a loop body function, in addition to initial values for loop variables. These loop variables are then updated by multiple calls to the body function until the condition returns false.
-Now imagine we want to keep the whole series of Fibonacci sequence. We may update our body to keep a record of the history of current values:
```python
n = tf.constant(5)
@@ -370,49 +349,49 @@ def cond(i, a, b, c):
return i < n
def body(i, a, b, c):
- return i + 1, b, a + b, tf.concat([c, [a + b]], 0)
-
-i, a, b, c = tf.while_loop(cond, body, (2, 1, 1, tf.constant([1, 1])))
+ a, b = b, a + b
+ c = tf.concat([c, [b]], 0)
+ return i + 1, a, b, c
-print(tf.Session().run(c))
-```
-Now if you try running this, Tensorflow will complain that the shape of the the fourth loop variable is changing. So you must make that explicit that it's intentional:
-```
i, a, b, c = tf.while_loop(
cond, body, (2, 1, 1, tf.constant([1, 1])),
shape_invariants=(tf.TensorShape([]),
tf.TensorShape([]),
tf.TensorShape([]),
tf.TensorShape([None])))
-```
-This is not only getting ugly, but is also somewhat inefficient. Note that we are building a lot of intermediary tensors that we don't use. Tensorflow has a better solution for this kind of growing arrays. Meet tf.TensorArray. Let's do the same thing this time with tensor arrays:
-```python
-n = tf.constant(5)
-
-c = tf.TensorArray(tf.int32, n)
-c = c.write(0, 1)
-c = c.write(1, 1)
-def cond(i, a, b, c):
- return i < n
+print(c.numpy())
+```
-def body(i, a, b, c):
- c = c.write(i, a + b)
- return i + 1, b, a + b, c
+This is not only getting ugly, but is also pretty inefficient. Note that we are building a lot of intermediary tensors that we don't use. TensorFlow has a better solution for this kind of growing arrays. Meet tf.TensorArray. Let's do the same thing this time with tensor arrays:
+```python
+@tf.function
+def fibonacci(n):
+ a = tf.constant(1)
+ b = tf.constant(1)
-i, a, b, c = tf.while_loop(cond, body, (2, 1, 1, c))
+ c = tf.TensorArray(tf.int32, n)
+ c = c.write(0, a)
+ c = c.write(1, b)
-c = c.stack()
+ for i in range(2, n):
+ a, b = b, a + b
+ c = c.write(i, b)
+
+ return c.stack()
-print(tf.Session().run(c))
+n = tf.constant(5)
+c = fibonacci(n)
+
+print(c.numpy())
```
-Tensorflow while loops and tensor arrays are essential tools for building complex recurrent neural networks. As an exercise try writing a [beam search using](https://en.wikipedia.org/wiki/Beam_search) tf.while_loops. Can you make it more efficient with tensor arrays?
+TensorFlow while loops and tensor arrays are essential tools for building complex recurrent neural networks. As an exercise try implementing [beam search](https://en.wikipedia.org/wiki/Beam_search) using tf.while_loops. Can you make it more efficient with tensor arrays?
## Prototyping kernels and advanced visualization with Python ops
-Operation kernels in Tensorflow are entirely written in C++ for efficiency. But writing a Tensorflow kernel in C++ can be quite a pain. So, before spending hours implementing your kernel you may want to prototype something quickly, however inefficient. With tf.py_func() you can turn any piece of python code to a Tensorflow operation.
+Operation kernels in TensorFlow are entirely written in C++ for efficiency. But writing a TensorFlow kernel in C++ can be quite a pain. So, before spending hours implementing your kernel you may want to prototype something quickly, however inefficient. With tf.py_function() you can turn any piece of python code to a TensorFlow operation.
-For example this is how you can implement a simple ReLU nonlinearity kernel in Tensorflow as a python op:
+For example this is how you can implement a simple ReLU nonlinearity kernel in TensorFlow as a python op:
```python
import numpy as np
import tensorflow as tf
@@ -420,70 +399,66 @@ import uuid
def relu(inputs):
# Define the op in python
- def _relu(x):
+ def _py_relu(x):
return np.maximum(x, 0.)
# Define the op's gradient in python
- def _relu_grad(x):
+ def _py_relu_grad(x):
return np.float32(x > 0)
+
+ @tf.custom_gradient
+ def _relu(x):
+ y = tf.py_function(_py_relu, [x], tf.float32)
+
+ def _relu_grad(dy):
+ return dy * tf.py_function(_py_relu_grad, [x], tf.float32)
- # An adapter that defines a gradient op compatible with Tensorflow
- def _relu_grad_op(op, grad):
- x = op.inputs[0]
- x_grad = grad * tf.py_func(_relu_grad, [x], tf.float32)
- return x_grad
-
- # Register the gradient with a unique id
- grad_name = "MyReluGrad_" + str(uuid.uuid4())
- tf.RegisterGradient(grad_name)(_relu_grad_op)
+ return y, _relu_grad
- # Override the gradient of the custom op
- g = tf.get_default_graph()
- with g.gradient_override_map({"PyFunc": grad_name}):
- output = tf.py_func(_relu, [inputs], tf.float32)
- return output
+ return _relu(inputs)
```
-To verify that the gradients are correct you can use Tensorflow's gradient checker:
+To verify that the gradients are correct you can compare the numerical and analytical gradients and compare the vlaues.
```python
-x = tf.random_normal([10])
-y = relu(x * x)
+# Compute analytical gradient
+x = tf.random.normal([10], dtype=np.float32)
+with tf.GradientTape() as tape:
+ tape.watch(x)
+ y = relu(x)
+g = tape.gradient(y, x)
+print(g)
-with tf.Session():
- diff = tf.test.compute_gradient_error(x, [10], y, [10])
- print(diff)
+# Compute numerical gradient
+dx_n = 1e-5
+dy_n = relu(x + dx_n) - relu(x)
+g_n = dy_n / dx_n
+print(g_n)
```
-compute_gradient_error() computes the gradient numerically and returns the difference with the provided gradient. What we want is a very low difference.
+The numbers should be very close.
Note that this implementation is pretty inefficient, and is only useful for prototyping, since the python code is not parallelizable and won't run on GPU. Once you verified your idea, you definitely would want to write it as a C++ kernel.
-In practice we commonly use python ops to do visualization on Tensorboard. Consider the case that you are building an image classification model and want to visualize your model predictions during training. Tensorflow allows visualizing images with tf.summary.image() function:
+In practice we commonly use python ops to do visualization on Tensorboard. Consider the case that you are building an image classification model and want to visualize your model predictions during training. TensorFlow allows visualizing images with tf.summary.image() function:
```python
image = tf.placeholder(tf.float32)
tf.summary.image("image", image)
```
But this only visualizes the input image. In order to visualize the predictions you have to find a way to add annotations to the image which may be almost impossible with existing ops. An easier way to do this is to do the drawing in python, and wrap it in a python op:
```python
-import io
-import matplotlib.pyplot as plt
-import numpy as np
-import PIL
-import tensorflow as tf
-
-def visualize_labeled_images(images, labels, max_outputs=3, name='image'):
+def visualize_labeled_images(images, labels, max_outputs=3, name="image"):
def _visualize_image(image, label):
# Do the actual drawing in python
fig = plt.figure(figsize=(3, 3), dpi=80)
ax = fig.add_subplot(111)
ax.imshow(image[::-1,...])
ax.text(0, 0, str(label),
- horizontalalignment='left',
- verticalalignment='top')
+ horizontalalignment="left",
+ verticalalignment="top")
fig.canvas.draw()
# Write the plot as a memory file.
buf = io.BytesIO()
- data = fig.savefig(buf, format='png')
+ data = fig.savefig(buf, format="png")
buf.seek(0)
# Read the image and convert to numpy array
@@ -499,429 +474,111 @@ def visualize_labeled_images(images, labels, max_outputs=3, name='image'):
return np.array(outputs, dtype=np.uint8)
# Run the python op.
- figs = tf.py_func(_visualize_images, [images, labels], tf.uint8)
+ figs = tf.py_function(_visualize_images, [images, labels], tf.uint8)
return tf.summary.image(name, figs)
```
Note that since summaries are usually only evaluated once in a while (not per step), this implementation may be used in practice without worrying about efficiency.
-## Multi-GPU processing with data parallelism
-
- If you write your software in a language like C++ for a single cpu core, making it run on multiple GPUs in parallel would require rewriting the software from scratch. But this is not the case with Tensorflow. Because of its symbolic nature, tensorflow can hide all that complexity, making it effortless to scale your program across many CPUs and GPUs.
-
- Let's start with the simple example of adding two vectors on CPU:
- ```python
- import tensorflow as tf
+## Numerical stability in TensorFlow
+
+When using any numerical computation library such as NumPy or TensorFlow, it's important to note that writing mathematically correct code doesn't necessarily lead to correct results. You also need to make sure that the computations are stable.
-with tf.device(tf.DeviceSpec(device_type='CPU', device_index=0)):
- a = tf.random_uniform([1000, 100])
- b = tf.random_uniform([1000, 100])
- c = a + b
-
-tf.Session().run(c)
- ```
-
-The same thing can as simply be done on GPU:
-```python
-with tf.device(tf.DeviceSpec(device_type='GPU', device_index=0)):
- a = tf.random_uniform([1000, 100])
- b = tf.random_uniform([1000, 100])
- c = a + b
- ```
-
-But what if we have two GPUs and want to utilize both? To do that, we can split the data and use a separate GPU for processing each half:
-```python
-split_a = tf.split(a, 2)
-split_b = tf.split(b, 2)
-
-split_c = []
-for i in range(2):
- with tf.device(tf.DeviceSpec(device_type='GPU', device_index=i)):
- split_c.append(split_a[i] + split_b[i])
-
-c = tf.concat(split_c, axis=0)
- ```
-
-Let's rewrite this in a more general form so that we can replace addition with any other set of operations:
-```python
-def make_parallel(fn, num_gpus, **kwargs):
- in_splits = {}
- for k, v in kwargs.items():
- in_splits[k] = tf.split(v, num_gpus)
-
- out_split = []
- for i in range(num_gpus):
- with tf.device(tf.DeviceSpec(device_type='GPU', device_index=i)):
- with tf.variable_scope(tf.get_variable_scope(), reuse=i > 0):
- out_split.append(fn(**kwargs))
-
- return tf.concat(out_split, axis=0)
-
-
-def model(a, b):
- return a + b
-
-c = make_parallel(model, 2, a=a, b=b)
-```
-You can replace the model with any function that takes a set of tensors as input and returns a tensor as result with the condition that both the input and output are in batch. Note that we also added a variable scope and set the reuse to true. This makes sure that we use the same variables for processing both splits. This is something that will become handy in our next example.
-
-Let's look at a slightly more practical example. We want to train a neural network on multiple GPUs. During training we not only need to compute the forward pass but also need to compute the backward pass (the gradients). But how can we parallelize the gradient computation? This turns out to be pretty easy.
-
-Recall from the first item that we wanted to fit a second degree curve to a set of samples. We reorganized the code a bit to have the bulk of the operations in the model function:
+Let's start with a simple example. From primary school we know that x * y / y is equal to x for any non zero value of x. But let's see if that's always true in practice:
```python
import numpy as np
-import tensorflow as tf
-def model(x, y):
- w = tf.get_variable("w", shape=[3, 1])
+x = np.float32(1)
- f = tf.stack([tf.square(x), x, tf.ones_like(x)], 1)
- yhat = tf.squeeze(tf.matmul(f, w), 1)
-
- loss = tf.square(yhat - y)
- return loss
-
-x = tf.placeholder(tf.float32)
-y = tf.placeholder(tf.float32)
-
-loss = model(x, y)
-
-train_op = tf.train.AdamOptimizer(0.1).minimize(
- tf.reduce_mean(loss))
+y = np.float32(1e-50) # y would be stored as zero
+z = x * y / y
-def generate_data():
- x_val = np.random.uniform(-10.0, 10.0, size=100)
- y_val = 5 * np.square(x_val) + 3
- return x_val, y_val
-
-sess = tf.Session()
-sess.run(tf.global_variables_initializer())
-for _ in range(1000):
- x_val, y_val = generate_data()
- _, loss_val = sess.run([train_op, loss], {x: x_val, y: y_val})
-
-_, loss_val = sess.run([train_op, loss], {x: x_val, y: y_val})
-print(sess.run(tf.contrib.framework.get_variables_by_name("w")))
+print(z) # prints nan
```
-Now let's use make_parallel that we just wrote to parallelize this. We only need to change two lines of code from the above code:
-```python
-loss = make_parallel(model, 2, x=x, y=y)
+The reason for the incorrect result is that y is simply too small for float32 type. A similar problem occurs when y is too large:
-train_op = tf.train.AdamOptimizer(0.1).minimize(
- tf.reduce_mean(loss),
- colocate_gradients_with_ops=True)
-```
-
-The only thing that we need to change to parallelize backpropagation of gradients is to set the colocate_gradients_with_ops flag to true. This ensures that gradient ops run on the same device as the original op.
-
-## Building a neural network training framework with learn API
-
-For simplicity, in most of the examples here we manually create sessions and we don't care about saving and loading checkpoints but this is not how we usually do things in practice. You most probably want to use the learn API to take care of session management and logging. We provide a simple but practical framework in the [code/framework](https://github.com/vahidk/EffectiveTensorflow/tree/master/code/framework) directory for training neural networks using Tensorflow. In this item we explain how this framework works.
-
-When experimenting with neural network models you usually have a training/test split. You want to train your model on the training set, and once in a while evaluate it on test set and compute some metrics. You also need to store the model parameters as a checkpoint, and ideally you want to be able to stop and resume training. Tensorflow's learn API is designed to make this job easier, letting us focus on developing the actual model.
-
-The most basic way of using tf.learn API is to use tf.Estimator object directly. You need to define a model function that defines a loss function, a train op and one or a set of predictions:
-```python
-import tensorflow as tf
-
-def model_fn(features, labels, mode, params):
- predictions = ...
- loss = ...
- train_op = ...
- return tf.contrib.learn.ModelFnOps(
- mode=mode,
- predictions=predictions,
- loss=loss,
- train_op=train_op)
-
-params = ...
-run_config = tf.contrib.learn.RunConfig(model_dir=FLAGS.output_dir)
-estimator = tf.contrib.learn.Estimator(
- model_fn=model_fn, config=run_config, params=params)
-```
-
-To train the model you would then simply call Estimator.fit() function while providing an input function to read the data.
```python
-def input_fn():
- features = ...
- labels = ...
- return features, labels
+y = np.float32(1e39) # y would be stored as inf
+z = x * y / y
-estimator.fit(input_fn=input_fn, max_steps=...)
+print(z) # prints nan
```
-and to evaluate the model, call Estimator.evaluate(), providing a set of metrics:
-```
-metrics = { 'accuracy': tf.metrics.accuracy }
-estimator.evaluate(input_fn=input_fn, metrics=metrics)
-```
-
-Estimator object might be good enough for simple cases, but Tensorflow provides an even higher level object called Experiment which provides some additional useful functionality. Creating an experiment object is very easy:
+The smallest positive value that float32 type can represent is 1.4013e-45 and anything below that would be stored as zero. Also, any number beyond 3.40282e+38, would be stored as inf.
```python
-experiment = tf.contrib.learn.Experiment(
- estimator=estimator,
- train_input_fn=train_input_fn,
- eval_input_fn=eval_input_fn,
- eval_metrics=eval_metrics)
+print(np.nextafter(np.float32(0), np.float32(1))) # prints 1.4013e-45
+print(np.finfo(np.float32).max) # print 3.40282e+38
```
-Now we can call train_and_evaluate function to compute the metrics while training.
-```
-experiment.train_and_evaluate()
-```
+To make sure that your computations are stable, you want to avoid values with small or very large absolute value. This may sound very obvious, but these kind of problems can become extremely hard to debug especially when doing gradient descent in TensorFlow. This is because you not only need to make sure that all the values in the forward pass are within the valid range of your data types, but also you need to make sure of the same for the backward pass (during gradient computation).
-An even higher level way of running experiments is by using learn_runner.run() function. Here's how our main function looks like in the provided framework:
+Let's look at a real example. We want to compute the softmax over a vector of logits. A naive implementation would look something like this:
```python
import tensorflow as tf
-tf.flags.DEFINE_string('output_dir', '', 'Optional output dir.')
-tf.flags.DEFINE_string('schedule', 'train_and_evaluate', 'Schedule.')
-tf.flags.DEFINE_string('hparams', '', 'Hyper parameters.')
-
-FLAGS = tf.flags.FLAGS
-learn = tf.contrib.learn
-
-def experiment_fn(run_config, hparams):
- estimator = learn.Estimator(
- model_fn=make_model_fn(), config=run_config, params=hparams)
- return learn.Experiment(
- estimator=estimator,
- train_input_fn=make_input_fn(learn.ModeKeys.TRAIN, hparams),
- eval_input_fn=make_input_fn(learn.ModeKeys.EVAL, hparams),
- eval_metrics=eval_metrics_fn(hparams))
-
-def main(unused_argv):
- run_config = learn.RunConfig(model_dir=FLAGS.output_dir)
- hparams = tf.contrib.training.HParams()
- hparams.parse(FLAGS.hparams)
-
- estimator = learn.learn_runner.run(
- experiment_fn=experiment_fn,
- run_config=run_config,
- schedule=FLAGS.schedule,
- hparams=hparams)
+def unstable_softmax(logits):
+ exp = tf.exp(logits)
+ return exp / tf.reduce_sum(exp)
-if __name__ == '__main__':
- tf.app.run()
+print(unstable_softmax([1000., 0.]).numpy()) # prints [ nan, 0.]
```
-The schedule flag decides which member function of the Experiment object gets called. So, if you for example set schedule to 'train_and_evaluate', experiment.train_and_evaluate() would be called.
+Note that computing the exponential of logits for relatively small numbers results to gigantic results that are out of float32 range. The largest valid logit for our naive softmax implementation is ln(3.40282e+38) = 88.7, anything beyond that leads to a nan outcome.
-Now let's have a look at how we might actually write an input function. One way to do this is through python ops (See [this item](#python_ops) for more information on python ops).
-```python
-def input_fn():
- def _py_input_fn():
- # read a new example in python
- feature = ...
- label = ...
- return feature, label
-
- # Convert that to tensors
- feature, label = tf.py_func(_py_input_fn, [], (tf.string, tf.int64))
-
- feature_batch, label_batch = tf.train.shuffle_batch(
- [feature, label], batch_size=..., capacity=...,
- min_after_dequeue=...)
+But how can we make this more stable? The solution is rather simple. It's easy to see that exp(x - c) / ∑ exp(x - c) = exp(x) / ∑ exp(x). Therefore we can subtract any constant from the logits and the result would remain the same. We choose this constant to be the maximum of logits. This way the domain of the exponential function would be limited to [-inf, 0], and consequently its range would be [0.0, 1.0] which is desirable:
- return feature_batch, label_batch
-```
-
-An alternative way is to write your data as TFRecords format and use the multi-threaded TFRecordReader object to read the data:
```python
-def input_fn():
- features = {
- 'image': tf.FixedLenFeature([], tf.string),
- 'label': tf.FixedLenFeature([], tf.int64),
- }
- tensors = tf.contrib.learn.read_batch_features(
- file_pattern=...,
- batch_size=...,
- features=features,
- reader=tf.TFRecordReader)
-```
-See [mnist.py](https://github.com/vahidk/EffectiveTensorflow/blob/master/code/framework/dataset/mnist.py) for an example of how to convert your data to TFRecords format.
-
-The framework also comes with a simple convolutional network classifier in [convnet_classifier.py](https://github.com/vahidk/EffectiveTensorflow/blob/master/code/framework/model/convnet_classifier.py) that includes an example model and evaluation metric:
-
-```python
-def model_fn(features, labels, mode, params):
- images = features['image']
- labels = labels['label']
-
- predictions = ...
- loss = ...
+import tensorflow as tf
- return {'predictions': predictions}, loss
+def softmax(logits):
+ exp = tf.exp(logits - tf.reduce_max(logits))
+ return exp / tf.reduce_sum(exp)
-def eval_metrics_fn(params):
- return {
- 'accuracy': tf.contrib.learn.MetricSpec(tf.metrics.accuracy)
- }
-```
-MetricSpec connects our model to the given metric function (e.g. tf.metrics.accuracy). Since our label and predictions solely include a single tensor, everything automagically works. Although if your label/prediction includes multiple tensors, you need to explicitly specify which tensors you want to pass to the metric function:
-```python
-tf.contrib.learn.MetricSpec(
- tf.metrics.accuracy,
- label_key='label',
- prediction_key='predictions')
+print(softmax([1000., 0.]).numpy()) # prints [ 1., 0.]
```
-And that's it! This is all you need to get started with Tensorflow learn API. I recommend to have a look at the [source code](https://github.com/vahidk/EffectiveTensorflow/tree/master/code/framework) and see the official python API to learn more about the learn API.
-
-## Tensorflow Cookbook
-
-This section includes implementation of a set of common operations in Tensorflow.
+Let's look at a more complicated case. Consider we have a classification problem. We use the softmax function to produce probabilities from our logits. We then define our loss function to be the cross entropy between our predictions and the labels. Recall that cross entropy for a categorical distribution can be simply defined as xe(p, q) = -∑ p_i log(q_i). So a naive implementation of the cross entropy would look like this:
-### Beam Search
```python
-import tensorflow as tf
-
-def get_shape(tensor):
- """Returns static shape if available and dynamic shape otherwise."""
- static_shape = tensor.shape.as_list()
- dynamic_shape = tf.unstack(tf.shape(tensor))
- dims = [s[1] if s[0] is None else s[0]
- for s in zip(static_shape, dynamic_shape)]
- return dims
-
-def log_prob_from_logits(logits, axis=-1):
- """Normalize the log-probabilities so that probabilities sum to one."""
- return logits - tf.reduce_logsumexp(logits, axis=axis, keep_dims=True)
-
-def batch_gather(tensor, indices):
- """Gather in batch from a tensor of arbitrary size.
+def unstable_softmax_cross_entropy(labels, logits):
+ logits = tf.math.log(softmax(logits))
+ return -tf.reduce_sum(labels * logits)
- In pseduocode this module will produce the following:
- output[i] = tf.gather(tensor[i], indices[i])
+labels = tf.constant([0.5, 0.5])
+logits = tf.constant([1000., 0.])
- Args:
- tensor: Tensor of arbitrary size.
- indices: Vector of indices.
- Returns:
- output: A tensor of gathered values.
- """
- shape = get_shape(tensor)
- flat_first = tf.reshape(tensor, [shape[0] * shape[1]] + shape[2:])
- indices = tf.convert_to_tensor(indices)
- offset_shape = [shape[0]] + [1] * (indices.shape.ndims - 1)
- offset = tf.reshape(tf.range(shape[0]) * shape[1], offset_shape)
- output = tf.gather(flat_first, indices + offset)
- return output
+xe = unstable_softmax_cross_entropy(labels, logits)
-def rnn_beam_search(update_fn, initial_state, sequence_length, beam_width,
- begin_token_id, end_token_id, name='rnn'):
- """Beam-search decoder for recurrent models.
-
- Args:
- update_fn: Function to compute the next state and logits given the current
- state and ids.
- initial_state: Recurrent model states.
- sequence_length: Length of the generated sequence.
- beam_width: Beam width.
- begin_token_id: Begin token id.
- end_token_id: End token id.
- name: Scope of the variables.
- Returns:
- ids: Output indices.
- logprobs: Output log probabilities probabilities.
- """
- batch_size = initial_state.shape.as_list()[0]
-
- state = tf.tile(tf.expand_dims(initial_state, axis=1), [1, beam_width, 1])
-
- sel_sum_logprobs = tf.log([[1.] + [0.] * (beam_width - 1)])
-
- ids = tf.tile([[begin_token_id]], [batch_size, beam_width])
- sel_ids = tf.expand_dims(ids, axis=2)
-
- mask = tf.ones([batch_size, beam_width], dtype=tf.float32)
-
- for i in range(sequence_length):
- with tf.variable_scope(name, reuse=True if i > 0 else None):
-
- state, logits = update_fn(state, ids)
- logits = log_prob_from_logits(logits)
-
- sum_logprobs = (
- tf.expand_dims(sel_sum_logprobs, axis=2) +
- (logits * tf.expand_dims(mask, axis=2)))
-
- num_classes = logits.shape.as_list()[-1]
-
- sel_sum_logprobs, indices = tf.nn.top_k(
- tf.reshape(sum_logprobs, [batch_size, num_classes * beam_width]),
- k=beam_width)
-
- ids = indices % num_classes
-
- beam_ids = indices // num_classes
-
- state = batch_gather(state, beam_ids)
-
- sel_ids = tf.concat([batch_gather(sel_ids, beam_ids),
- tf.expand_dims(ids, axis=2)], axis=2)
-
- mask = (batch_gather(mask, beam_ids) *
- tf.to_float(tf.not_equal(ids, end_token_id)))
-
- return sel_ids, sel_sum_logprobs
+print(xe.numpy()) # prints inf
```
-## Merge
+Note that in this implementation as the softmax output approaches zero, the log's output approaches infinity which causes instability in our computation. We can rewrite this by expanding the softmax and doing some simplifications:
```python
-import tensorflow as tf
-
-def merge(tensors, units, activation=tf.nn.relu, name=None, **kwargs):
- """Merge features with broadcasting support.
+def softmax_cross_entropy(labels, logits):
+ scaled_logits = logits - tf.reduce_max(logits)
+ normalized_logits = scaled_logits - tf.reduce_logsumexp(scaled_logits)
+ return -tf.reduce_sum(labels * normalized_logits)
- This operation concatenates multiple features of varying length and applies
- non-linear transformation to the outcome.
+labels = tf.constant([0.5, 0.5])
+logits = tf.constant([1000., 0.])
- Example:
- a = tf.zeros([m, 1, d1])
- b = tf.zeros([1, n, d2])
- c = merge([a, b], d3) # shape of c would be [m, n, d3].
+xe = softmax_cross_entropy(labels, logits)
- Args:
- tensors: A list of tensor with the same rank.
- units: Number of units in the projection function.
- """
- with tf.variable_scope(name, default_name='merge'):
- # Apply linear projection to input tensors.
- projs = []
- for i, tensor in enumerate(tensors):
- proj = tf.layers.dense(
- tensor, units, activation=None,
- name='proj_%d' % i,
- **kwargs)
- projs.append(proj)
-
- # Compute sum of tensors.
- result = projs.pop()
- for proj in projs:
- result = result + proj
-
- # Apply nonlinearity.
- if activation:
- result = activation(result)
- return result
+print(xe.numpy()) # prints 500.0
```
-## Entropy
-
+We can also verify that the gradients are also computed correctly:
```python
-import tensorflow as tf
+with tf.GradientTape() as tape:
+ tape.watch(logits)
+ xe = softmax_cross_entropy(labels, logits)
+
+g = tape.gradient(xe, logits)
+print(g.numpy()) # prints [0.5, -0.5]
+```
+which is correct.
-def softmax(logits, dims=-1):
- """Compute softmax over specified dimensions."""
- exp = tf.exp(logits - tf.reduce_max(logits, dims, keep_dims=True))
- return exp / tf.reduce_sum(exp, dims, keep_dims=True)
+Let me remind again that extra care must be taken when doing gradient descent to make sure that the range of your functions as well as the gradients for each layer are within a valid range. Exponential and logarithmic functions when used naively are especially problematic because they can map small numbers to enormous ones and the other way around.
-def entropy(logits, dims=-1):
- """Compute entropy over specified dimensions."""
- probs = softmax(logits, dims)
- nplogp = probs * (tf.reduce_logsumexp(logits, dims, keep_dims=True) - logits)
- return tf.reduce_sum(nplogp, dims)
-```
diff --git a/code/framework b/code/framework
new file mode 160000
index 0000000..a9377d0
--- /dev/null
+++ b/code/framework
@@ -0,0 +1 @@
+Subproject commit a9377d0dd8f5ac93e810876fbe8987990e3c728f
diff --git a/code/framework/README.md b/code/framework/README.md
deleted file mode 100644
index a0de0ef..0000000
--- a/code/framework/README.md
+++ /dev/null
@@ -1,31 +0,0 @@
-# Tensorflow training framework
-
-Follow the example in dataset/mnist.py and model/convnet_classifier.py for
-examples of how to define custom datasets and models.
-
-## Install dependencies
-```
-pip install tensorflow numpy pillow matplotlib six
-```
-
-## Mnist
-To download the mnist dataset run:
-```
-python -m dataset.mnist convert
-```
-
-Run the following to visualize an example:
-```
-python -m dataset.mnist visualize
-```
-
-## Usage
-To train an mnist classification model run:
-```
-python -m main --model=convnet_classifier --dataset=mnist
-```
-
-To visualize the training logs in Tensorboard run:
-```
-tensorboard --logdir=output
-```
diff --git a/code/framework/__init__.py b/code/framework/__init__.py
deleted file mode 100644
index e69de29..0000000
diff --git a/code/framework/common/__init__.py b/code/framework/common/__init__.py
deleted file mode 100644
index e69de29..0000000
diff --git a/code/framework/common/ops.py b/code/framework/common/ops.py
deleted file mode 100644
index e29dd1c..0000000
--- a/code/framework/common/ops.py
+++ /dev/null
@@ -1,97 +0,0 @@
-from __future__ import absolute_import
-from __future__ import division
-from __future__ import print_function
-
-import numpy as np
-import tensorflow as tf
-
-
-def get_shape(tensor):
- """Returns static shape if available and dynamic shape otherwise."""
- static_shape = tensor.shape.as_list()
- dynamic_shape = tf.unstack(tf.shape(tensor))
- dims = [s[1] if s[0] is None else s[0]
- for s in zip(static_shape, dynamic_shape)]
- return dims
-
-
-def reshape(tensor, dims_list):
- """Reshape the given tensor by collapsing dimensions."""
- shape = get_shape(tensor)
- dims_prod = []
- for dims in dims_list:
- if isinstance(dims, int):
- dims_prod.append(shape[dims])
- elif all([isinstance(shape[d], int) for d in dims]):
- dims_prod.append(np.prod([shape[d] for d in dims]))
- else:
- dims_prod.append(tf.prod([shape[d] for d in dims]))
- tensor = tf.reshape(tensor, dims_prod)
- return tensor
-
-
-def dense_layers(tensor,
- sizes,
- activation=tf.nn.relu,
- linear_top_layer=False,
- drop_rate=0.0,
- name=None,
- **kwargs):
- """Builds a stack of fully connected layers with optional dropout."""
- with tf.variable_scope(name, default_name='dense_layers'):
- for i, size in enumerate(sizes):
- if i == len(sizes) - 1 and linear_top_layer:
- activation = None
- tensor = tf.layers.dropout(tensor, drop_rate)
- tensor = tf.layers.dense(
- tensor,
- size,
- name='dense_layer_%d' % i,
- activation=activation,
- **kwargs)
- return tensor
-
-
-def conv_layers(tensor,
- filters,
- kernels,
- pools,
- padding='same',
- activation=tf.nn.relu,
- drop_rate=0.0,
- **kwargs):
- for fs, ks, ps in zip(filters, kernels, pools):
- tensor = tf.layers.dropout(tensor, drop_rate)
- tensor = tf.layers.conv2d(
- tensor,
- filters=fs,
- kernel_size=ks,
- padding=padding,
- activation=activation,
- **kwargs)
- if ps and ps > 1:
- tensor = tf.layers.max_pooling2d(
- inputs=tensor, pool_size=ps, strides=ps, padding=padding)
- return tensor
-
-
-def create_optimizer(optimizer, learning_rate, decay_steps=None, **kwargs):
- global_step = tf.train.get_or_create_global_step()
-
- if decay_steps:
- learning_rate = tf.train.exponential_decay(
- learning_rate, global_step, decay_steps, 0.5, staircase=True)
- tf.summary.scalar('learning_rate', learning_rate)
-
- return tf.contrib.layers.OPTIMIZER_CLS_NAMES[optimizer](
- learning_rate, **kwargs)
-
-
-def average_gradients(tower_grads):
- average_grads = []
- for grad_and_vars in zip(*tower_grads):
- grads = [g for g, _ in grad_and_vars]
- grad = tf.reduce_mean(tf.stack(grads, axis=0), axis=0)
- v = grad_and_vars[0][1]
- average_grads.append((grad, v))
- return average_grads
diff --git a/code/framework/common/summary.py b/code/framework/common/summary.py
deleted file mode 100644
index a9cd6ed..0000000
--- a/code/framework/common/summary.py
+++ /dev/null
@@ -1,45 +0,0 @@
-"""Utility functions for visualization on tensorboard."""
-
-import io
-import matplotlib.pyplot as plt
-import numpy as np
-import PIL
-import tensorflow as tf
-
-
-def labeled_image(name, images, labels, max_outputs=3, flip_vertical=False,
- color='pink', font_size=15):
- def _visualize_image(image, label):
- # Do the actual drawing in python
- fig = plt.figure(figsize=(3, 3), dpi=80)
- ax = fig.add_subplot(111)
- if flip_vertical:
- image = image[::-1,...]
- ax.imshow(image.squeeze())
- ax.text(0, 0, str(label),
- horizontalalignment='left',
- verticalalignment='top',
- color=color,
- fontsize=font_size)
- fig.canvas.draw()
-
- # Write the plot as a memory file.
- buf = io.BytesIO()
- data = fig.savefig(buf, format='png')
- buf.seek(0)
-
- # Read the image and convert to numpy array
- img = PIL.Image.open(buf)
- return np.array(img.getdata()).reshape(img.size[0], img.size[1], -1)
-
- def _visualize_images(images, labels):
- # Only display the given number of examples in the batch
- outputs = []
- for i in range(max_outputs):
- output = _visualize_image(images[i], labels[i])
- outputs.append(output)
- return np.array(outputs, dtype=np.uint8)
-
- # Run the python op.
- figs = tf.py_func(_visualize_images, [images, labels], tf.uint8)
- return tf.summary.image(name, figs)
diff --git a/code/framework/common/utils.py b/code/framework/common/utils.py
deleted file mode 100644
index 263254a..0000000
--- a/code/framework/common/utils.py
+++ /dev/null
@@ -1,68 +0,0 @@
-from __future__ import absolute_import
-from __future__ import division
-from __future__ import print_function
-
-import io
-import numpy as np
-import PIL
-import multiprocessing as mp
-import tensorflow as tf
-
-
-def parallel_record_writer(iterator, create_example, path, num_threads=4):
- """Create a RecordIO file from data for efficient reading."""
-
- def _queue(inputs):
- for item in iterator:
- inputs.put(item)
- for _ in range(num_threads):
- inputs.put(None)
-
- def _map_fn(inputs, outputs):
- while True:
- item = inputs.get()
- if item is None:
- break
- example = create_example(item)
- outputs.put(example)
- outputs.put(None)
-
- # Read the inputs.
- inputs = mp.Queue()
- mp.Process(target=_queue, args=(inputs,)).start()
-
- # Convert to tf.Example
- outputs = mp.Queue()
- for _ in range(num_threads):
- mp.Process(target=_map_fn, args=(inputs, outputs)).start()
-
- # Write the output to file.
- writer = tf.python_io.TFRecordWriter(path)
- counter = 0
- while True:
- example = outputs.get()
- if example is None:
- counter += 1
- if counter == num_threads:
- break
- else:
- continue
- writer.write(example.SerializeToString())
- writer.close()
-
-
-def encode_image(data, format='png'):
- """Encodes a numpy array to string."""
- im = PIL.Image.fromarray(data)
- buf = io.BytesIO()
- data = im.save(buf, format=format)
- buf.seek(0)
- return buf.getvalue()
-
-
-def decode_image(data):
- """Decode the given image to a numpy array."""
- buf = io.BytesIO(data)
- im = PIL.Image.open(buf)
- data = np.array(im.getdata()).reshape([im.height, im.width, -1])
- return data
diff --git a/code/framework/dataset/__init__.py b/code/framework/dataset/__init__.py
deleted file mode 100644
index e69de29..0000000
diff --git a/code/framework/dataset/mnist.py b/code/framework/dataset/mnist.py
deleted file mode 100644
index 4222ed0..0000000
--- a/code/framework/dataset/mnist.py
+++ /dev/null
@@ -1,136 +0,0 @@
-from __future__ import absolute_import
-from __future__ import division
-from __future__ import print_function
-
-import gzip
-import matplotlib.pyplot as plt
-import numpy as np
-import os
-from six.moves import urllib
-import struct
-import sys
-import tensorflow as tf
-
-from common import utils
-
-REMOTE_URL = 'http://yann.lecun.com/exdb/mnist/'
-LOCAL_DIR = os.path.join('data/mnist/')
-TRAIN_IMAGE_URL = 'train-images-idx3-ubyte.gz'
-TRAIN_LABEL_URL = 'train-labels-idx1-ubyte.gz'
-TEST_IMAGE_URL = 't10k-images-idx3-ubyte.gz'
-TEST_LABEL_URL = 't10k-labels-idx1-ubyte.gz'
-
-IMAGE_SIZE = 28
-NUM_CLASSES = 10
-
-
-FEATURES = {
- 'image': tf.FixedLenFeature([], tf.string),
- 'label': tf.FixedLenFeature([], tf.int64),
-}
-
-HPARAMS = {
- 'image_size': IMAGE_SIZE,
- 'num_classes': NUM_CLASSES,
-}
-
-
-def get_split(split):
- output_data = os.path.join(LOCAL_DIR, 'data_%s.tfrecord' % split)
- return output_data
-
-
-def map_features(features):
- def _decode_image(image):
- image = tf.to_float(tf.image.decode_image(image, channels=1)) / 255.0
- image = tf.reshape(image, [IMAGE_SIZE, IMAGE_SIZE, 1])
- return image
-
- image = tf.map_fn(_decode_image, features['image'], tf.float32)
- label = features['label']
- return {'image': image}, {'label': label}
-
-
-def _download_data():
- if not os.path.exists(LOCAL_DIR):
- os.makedirs(LOCAL_DIR)
- for name in [
- TRAIN_IMAGE_URL,
- TRAIN_LABEL_URL,
- TEST_IMAGE_URL,
- TEST_LABEL_URL]:
- if not os.path.exists(LOCAL_DIR + name):
- urllib.request.urlretrieve(REMOTE_URL + name, LOCAL_DIR + name)
-
-
-def _image_iterator(split):
- image_urls = {
- tf.estimator.ModeKeys.TRAIN: TRAIN_IMAGE_URL,
- tf.estimator.ModeKeys.EVAL: TEST_IMAGE_URL
- }[split]
- label_urls = {
- tf.estimator.ModeKeys.TRAIN: TRAIN_LABEL_URL,
- tf.estimator.ModeKeys.EVAL: TEST_LABEL_URL
- }[split]
-
- with gzip.open(LOCAL_DIR + image_urls, 'rb') as f:
- magic, num, rows, cols = struct.unpack(">IIII", f.read(16))
- images = np.frombuffer(f.read(num * rows * cols), dtype=np.uint8)
- images = np.reshape(images, [num, rows, cols])
- print('Loaded %d images of size [%d, %d].' % (num, rows, cols))
-
- with gzip.open(LOCAL_DIR + label_urls, 'rb') as f:
- magic, num = struct.unpack(">II", f.read(8))
- labels = np.frombuffer(f.read(num), dtype=np.int8)
- print('Loaded %d labels.' % num)
-
- for i in range(num):
- yield utils.encode_image(images[i]), labels[i]
-
-
-def _convert_data(split):
- def _create_example(item):
- image, label = item
- example = tf.train.Example(features=tf.train.Features(
- feature={
- 'image': tf.train.Feature(
- bytes_list=tf.train.BytesList(value=[image])),
- 'label': tf.train.Feature(
- int64_list=tf.train.Int64List(value=[label.astype(np.int64)]))
- }))
- return example
-
- utils.parallel_record_writer(
- _image_iterator(split), _create_example, get_split(split))
-
-
-def _visulize_data(split=tf.estimator.ModeKeys.TRAIN):
- path = get_split(split)
- iterator = tf.python_io.tf_record_iterator(path)
- item = next(iterator)
-
- example = tf.train.Example()
- example.ParseFromString(item)
-
- image = utils.decode_image(
- example.features.feature['image'].bytes_list.value[0])
- label = example.features.feature['label'].int64_list.value[0]
-
- plt.imshow(image.squeeze())
- plt.title('Label: %d' % label)
- plt.show()
-
-
-if __name__ == '__main__':
- if len(sys.argv) != 2:
- print('Usage: python dataset.mnist ')
- sys.exit(1)
-
- if sys.argv[1] == 'convert':
- _download_data()
- _convert_data(tf.estimator.ModeKeys.TRAIN)
- _convert_data(tf.estimator.ModeKeys.EVAL)
- elif sys.argv[1] == 'visualize':
- _visulize_data()
- else:
- print('Unknown command', sys.argv[1])
diff --git a/code/framework/main.py b/code/framework/main.py
deleted file mode 100644
index b42300b..0000000
--- a/code/framework/main.py
+++ /dev/null
@@ -1,174 +0,0 @@
-from __future__ import absolute_import
-from __future__ import division
-from __future__ import print_function
-
-import collections
-import tensorflow as tf
-
-from common import ops
-import dataset.mnist
-import model.convnet_classifier
-
-tf.logging.set_verbosity(tf.logging.INFO)
-
-tf.flags.DEFINE_string('model', 'convnet_classifier', 'Model name.')
-tf.flags.DEFINE_string('dataset', 'mnist', 'Dataset name.')
-tf.flags.DEFINE_string('output_dir', '', 'Optional output dir.')
-tf.flags.DEFINE_string('schedule', 'train_and_evaluate', 'Schedule.')
-tf.flags.DEFINE_string('hparams', '', 'Hyper parameters.')
-tf.flags.DEFINE_integer('save_summary_steps', 10, 'Summary steps.')
-tf.flags.DEFINE_integer('save_checkpoints_steps', 10, 'Checkpoint steps.')
-tf.flags.DEFINE_integer('eval_steps', None, 'Number of eval steps.')
-tf.flags.DEFINE_integer('eval_frequency', 10, 'Eval frequency.')
-tf.flags.DEFINE_integer('num_gpus', 0, 'Numner of gpus.')
-
-FLAGS = tf.flags.FLAGS
-learn = tf.contrib.learn
-
-MODELS = {
- 'convnet_classifier': model.convnet_classifier
-}
-
-DATASETS = {
- 'mnist': dataset.mnist
-}
-
-HPARAMS = {
- 'optimizer': 'Adam',
- 'learning_rate': 0.001,
- 'decay_steps': 10000,
- 'batch_size': 128
-}
-
-def get_hparams():
- hparams = HPARAMS
- hparams.update(DATASETS[FLAGS.dataset].HPARAMS)
- hparams.update(MODELS[FLAGS.model].HPARAMS)
-
- hparams = tf.contrib.training.HParams(**hparams)
- hparams.parse(FLAGS.hparams)
-
- return hparams
-
-
-def make_input_fn(mode, params):
- def _input_fn():
- with tf.device(tf.DeviceSpec(device_type='CPU', device_index=0)):
- dataset = DATASETS[FLAGS.dataset]
- tensors = learn.read_batch_features(
- file_pattern=dataset.get_split(mode),
- batch_size=params.batch_size,
- features=dataset.FEATURES,
- reader=tf.TFRecordReader,
- randomize_input=True if mode == learn.ModeKeys.TRAIN else False,
- num_epochs=None if mode == learn.ModeKeys.TRAIN else 1,
- queue_capacity=params.batch_size*3,
- feature_queue_capacity=params.batch_size*2,
- reader_num_threads=8 if mode == learn.ModeKeys.TRAIN else 1)
- features, labels = dataset.map_features(tensors)
- return features, labels
- return _input_fn
-
-
-def make_model_fn():
- def _model_fn(features, labels, mode, params):
- model_fn = MODELS[FLAGS.model].model_fn
-
- global_step = tf.train.get_or_create_global_step()
-
- if FLAGS.num_gpus > 0 and mode == learn.ModeKeys.TRAIN:
- split_features = {k: tf.split(v, FLAGS.num_gpus)
- for k, v in features.iteritems()}
- split_labels = {k: tf.split(v, FLAGS.num_gpus)
- for k, v in labels.iteritems()}
- grads = []
- predictions = collections.defaultdict(list)
- losses = []
-
- opt = ops.create_optimizer(
- params.optimizer, params.learning_rate, params.decay_steps)
-
- for i in range(FLAGS.num_gpus):
- with tf.device(tf.DeviceSpec(device_type='GPU', device_index=i)):
- with tf.name_scope('tower_%d' % i):
- with tf.variable_scope(tf.get_variable_scope(), reuse=i > 0):
- device_features = {k: v[i] for k, v in split_features.iteritems()}
- device_labels = {k: v[i] for k, v in split_labels.iteritems()}
-
- device_predictions, device_loss = model_fn(
- device_features, device_labels, mode, params)
-
- for k, v in device_predictions.iteritems():
- predictions[k].append(v)
-
- if device_loss is not None:
- losses.append(device_loss)
-
- device_grads = opt.compute_gradients(device_loss)
- grads.append(device_grads)
-
- grads = ops.average_gradients(grads)
- train_op = opt.apply_gradients(grads, global_step=global_step)
-
- for k, v in predictions.iteritems():
- predictions[k] = tf.concat(v, axis=0)
-
- loss = tf.add_n(losses) if losses else None
- else:
- with tf.device(tf.DeviceSpec(device_type='GPU', device_index=0)):
- predictions, loss = model_fn(features, labels, mode, params)
-
- train_op = None
- if mode == learn.ModeKeys.TRAIN:
- opt = ops.create_optimizer(
- params.optimizer, params.learning_rate, params.decay_steps)
- train_op = opt.minimize(loss, global_step=global_step)
-
- tf.summary.scalar('loss/loss', loss)
-
- return tf.contrib.learn.ModelFnOps(
- mode=mode,
- predictions=predictions,
- loss=loss,
- train_op=train_op)
-
- return _model_fn
-
-
-def experiment_fn(run_config, hparams):
- estimator = learn.Estimator(
- model_fn=make_model_fn(), config=run_config, params=hparams)
- eval_metrics = MODELS[FLAGS.model].eval_metrics_fn(hparams)
- return learn.Experiment(
- estimator=estimator,
- train_input_fn=make_input_fn(learn.ModeKeys.TRAIN, hparams),
- eval_input_fn=make_input_fn(learn.ModeKeys.EVAL, hparams),
- eval_metrics=eval_metrics,
- eval_steps=FLAGS.eval_steps,
- min_eval_frequency=FLAGS.eval_frequency)
-
-
-def main(unused_argv):
- if FLAGS.output_dir:
- model_dir = FLAGS.output_dir
- else:
- model_dir = 'output/%s_%s' % (FLAGS.model, FLAGS.dataset)
- session_config = tf.ConfigProto()
- session_config.allow_soft_placement = True
- session_config.gpu_options.allow_growth = True
- run_config = learn.RunConfig(
- model_dir=model_dir,
- save_summary_steps=FLAGS.save_summary_steps,
- save_checkpoints_steps=FLAGS.save_checkpoints_steps,
- save_checkpoints_secs=None,
- session_config=session_config)
-
- estimator = learn.learn_runner.run(
- experiment_fn=experiment_fn,
- run_config=run_config,
- schedule=FLAGS.schedule,
- hparams=get_hparams())
-
-
-if __name__ == '__main__':
- tf.app.run()
diff --git a/code/framework/model/__init__.py b/code/framework/model/__init__.py
deleted file mode 100644
index e69de29..0000000
diff --git a/code/framework/model/convnet_classifier.py b/code/framework/model/convnet_classifier.py
deleted file mode 100644
index 1885e94..0000000
--- a/code/framework/model/convnet_classifier.py
+++ /dev/null
@@ -1,51 +0,0 @@
-from __future__ import absolute_import
-from __future__ import division
-from __future__ import print_function
-
-import numpy as np
-import tensorflow as tf
-
-from common import ops
-from common import summary
-
-FLAGS = tf.flags.FLAGS
-
-HPARAMS = {
- 'drop_rate': 0.5,
- 'crop_margin': 8,
-}
-
-
-def model_fn(features, labels, mode, params):
- images = features['image']
- labels = labels['label']
-
- drop_rate = params.drop_rate if mode == tf.estimator.ModeKeys.TRAIN else 0.0
-
- features = ops.conv_layers(
- images,
- filters=[32, 64, 128],
- kernels=[3, 3, 3],
- pools=[2, 2, 2])
-
- features = tf.contrib.layers.flatten(features)
-
- logits = ops.dense_layers(
- features, [512, params.num_classes],
- drop_rate=drop_rate,
- linear_top_layer=True)
-
- predictions = tf.argmax(logits, axis=1)
-
- loss = tf.losses.sparse_softmax_cross_entropy(
- labels=labels, logits=logits)
-
- summary.labeled_image("images", images, predictions)
-
- return {'predictions': predictions}, loss
-
-
-def eval_metrics_fn(params):
- metrics_dict = {}
- metrics_dict['accuracy'] = tf.contrib.learn.MetricSpec(tf.metrics.accuracy)
- return metrics_dict