Linear Classifier 02

In [1]:

import numpy as np
import tensorflow as tf
import time
np.random.seed(101)

2022-10-12 17:13:46.461742: I tensorflow/core/util/util.cc:169] oneDNN custom operations are on. You may see slightly different numerical results due to floating-point round-off errors from different computation orders. To turn them off, set the environment variable `TF_ENABLE_ONEDNN_OPTS=0`.

build your own data¶

x_train: [12, 4]
y_train: [12, ]
x_test: [4, 4]
y_test: [4, ]

[1, 0, 0, 0] --> 0
[0, 1, 0, 0] --> 0
[0, 0, 1, 0] --> 1
[0, 0, 0, 1] --> 1

In [2]:

x_train = np.zeros(shape=[12, 4], dtype=np.float32)
y_train = np.random.randint(0, 4, [12, ])

print(x_train)
print(y_train)

[[0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]]
[3 3 1 2 3 3 1 3 3 1 1 0]

In [3]:

x_train[np.arange(0, 12), y_train] = 1
print(x_train)

[[0. 0. 0. 1.]
 [0. 0. 0. 1.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]
 [0. 0. 0. 1.]
 [0. 1. 0. 0.]
 [0. 0. 0. 1.]
 [0. 0. 0. 1.]
 [0. 1. 0. 0.]
 [0. 1. 0. 0.]
 [1. 0. 0. 0.]]

In [4]:

y_test = np.int32(np.arange(0, 4))
x_test = np.zeros(shape=[4, 4], dtype=np.float32)
x_test[np.arange(0, 4), y_test] = 1

y_train[y_train == 1] = 0
y_train[y_train > 0] = 1
y_test[y_test == 1] = 0
y_test[y_test > 0] = 1

print(x_test)
print(y_test)

[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]
[0 0 1 1]

Linear Classifier¶

$ f = W^T X + b $

In [5]:

class Linear:
    def __init__(self, w_shape=[4, 2]):
        self.w = np.random.random(size=w_shape)
        self.w = np.float32(self.w)
        self.b = np.random.random(size=[w_shape[1]])
        self.b = np.float32(self.b)
        self.w, self.b = tf.Variable(self.w), tf.Variable(self.b)
    
    def forward(self, x):
        z = tf.matmul(x, self.w)+self.b # z = w*x+b
        return z

In [6]:

lin = Linear()
print(lin.w.shape)
print(lin.b.shape)

(4, 2)
(2,)

2022-10-12 17:13:48.138135: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 AVX512F AVX512_VNNI FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2022-10-12 17:13:48.628304: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1532] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 22077 MB memory:  -> device: 0, name: NVIDIA GeForce RTX 3090, pci bus id: 0000:65:00.0, compute capability: 8.6

In [7]:

z = lin.forward(x_train)
print(z.shape)
print(z)

(12, 2)
tf.Tensor(
[[1.1473757  1.0179554 ]
 [1.1473757  1.0179554 ]
 [1.6870271  0.4222926 ]
 [1.5197108  0.58448565]
 [1.1473757  1.0179554 ]
 [1.1473757  1.0179554 ]
 [1.6870271  0.4222926 ]
 [1.1473757  1.0179554 ]
 [1.1473757  1.0179554 ]
 [1.6870271  0.4222926 ]
 [1.6870271  0.4222926 ]
 [1.2724495  1.1259668 ]], shape=(12, 2), dtype=float32)

2022-10-12 17:13:49.799117: I tensorflow/stream_executor/cuda/cuda_blas.cc:1786] TensorFloat-32 will be used for the matrix multiplication. This will only be logged once.

In [8]:

class Loss:
    def __init__(self):
        pass
    
    def forward(self, x, y):
        """
        x's shape = [N,2]
        y's shape = [N,]
        """
        
        # step-1: choose the true class score
        #       inputs: x [N,2], (y), outputs: x_true [N,]
        #       find: dx, upstream: dx_true
        N = tf.shape(x)[0]
        row_idx = tf.range(0, N)
        row_col_idx = tf.transpose(tf.stack([row_idx, y]))
        x_true = tf.gather_nd(x, indices=row_col_idx)

        # step-2: find the score difference
        #       inputs: x [N,2], x_true [N,], outputs: diff [N,2]
        #       find: dx [N,2], dx_true [N,], upstream: ddiff [N,2]
        diff = x-tf.expand_dims(x_true, axis=1)+1 #[N,2]

        # step-3: clip the difference
        #       inputs: diff [N,2],   outputs: clip_diff [N,2]
        #       find: ddiff [N,2],   upstream: dclip_diff [N,2]
        clip_diff = tf.where(diff<0.0, 0.0, diff) #[N,2]

        # step-4: sum along the col axis
        #       inputs: clip_diff [N,2],    outputs: diff_sum [N,]
        #       find: dclip_diff,           upstream: ddiff_sum [N,]
        diff_sum = tf.reduce_sum(clip_diff, axis=1) #[N,]

        # step-5: find mean_loss
        #       inputs: diff_sum [N,]       outputs: loss [1]
        #       find: ddiff_sum [N,]        upstream: 1.0
        loss = tf.reduce_mean(diff_sum) # 1
        return loss

In [9]:

class Classifier:
    def __init__(self, input_dim=4, n_class=2):
        self.trainable_vars = []
        # initialize all the layers
        self.linear = Linear(w_shape=[input_dim, n_class])
        # self.linear2 = Linear(~~) # !!! for Midterm-HW
        self.trainable_vars.extend([self.linear.w, self.linear.b])
        self.loss = Loss()

    def forward(self, x, y):
        # h = self.l1.f() # !!! for Midterm-HW
        score = self.linear.forward(x)
        loss = self.loss.forward(score, y)
        return score, loss

    #@tf.function
    def update(self, x, y, step_size):
        # step-1: update gradient
        with tf.GradientTape() as tape:
            score, loss = self.forward(x, y)
        # step-2: find gradient
        grads = tape.gradient(loss, self.trainable_vars)
        # step-3: update variables
        for i, vars in enumerate(self.trainable_vars):
            self.trainable_vars[i].assign_sub(grads[i]*step_size)
        return score, loss

    def train(self, epoch=100, batch_size=4, step_size=0.1):
        for ep in range(epoch):
            # sample the batch from training data
            idx = np.random.permutation(len(y_train))
            batch_idx = np.arange(0, batch_size)
            x = x_train[batch_idx]
            y = y_train[batch_idx]
            
            start = time.perf_counter()
            score, loss = c.update(x, y, step_size)
            print("elapsed time:", time.perf_counter()-start)

            test_score, test_loss = c.forward(x_test, y_test)
            print(ep, loss, test_loss)

In [10]:

c = Classifier()
score, loss = c.forward(x_test, y_test)
print(score)
print(loss)

tf.Tensor(
[[0.27052885 1.5978663 ]
 [0.9159602  1.2705567 ]
 [0.87227374 1.5121853 ]
 [0.23545197 1.1321871 ]], shape=(4, 2), dtype=float32)
tf.Tensor(2.0363219, shape=(), dtype=float32)

In [11]:

c.backward()
print(c.linear.dw)
print(c.linear.db)

print()
print(c.linear.w)
print(c.linear.b)

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 c.backward()
      2 print(c.linear.dw)
      3 print(c.linear.db)

AttributeError: 'Classifier' object has no attribute 'backward'

In [12]:

c = Classifier()
c.train()

print()
print(c.linear.w)
print(c.linear.b)

elapsed time: 0.018572985994978808
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elapsed time: 0.003910679995897226
99 tf.Tensor(1.0, shape=(), dtype=float32) tf.Tensor(1.3122199, shape=(), dtype=float32)

<tf.Variable 'Variable:0' shape=(4, 2) dtype=float32, numpy=
array([[ 0.5206654 ,  0.57878953],
       [ 1.2598186 ,  0.01696173],
       [ 0.4381539 ,  1.2829198 ],
       [-0.04700221,  0.80722445]], dtype=float32)>
<tf.Variable 'Variable:0' shape=(2,) dtype=float32, numpy=array([0.55287653, 0.7436317 ], dtype=float32)>