gradient_centralization.md

Gradient Centralization for Better Training Performance

Author: Rishit Dagli
Date created: 06/18/21
Last modified: 07/25/23
Description: Implement Gradient Centralization to improve training performance of DNNs.

View in Colab • GitHub source

---

Introduction

This example implements Gradient Centralization, a new optimization technique for Deep Neural Networks by Yong et al., and demonstrates it on Laurence Moroney's Horses or Humans Dataset. Gradient Centralization can both speedup training process and improve the final generalization performance of DNNs. It operates directly on gradients by centralizing the gradient vectors to have zero mean. Gradient Centralization morever improves the Lipschitzness of the loss function and its gradient so that the training process becomes more efficient and stable.

This example requires tensorflow_datasets which can be installed with this command:

pip install tensorflow-datasets

---

Setup

from time import time

import keras
from keras import layers
from keras.optimizers import RMSprop
from keras import ops

from tensorflow import data as tf_data
import tensorflow_datasets as tfds

---

Prepare the data

For this example, we will be using the Horses or Humans dataset.

num_classes = 2
input_shape = (300, 300, 3)
dataset_name = "horses_or_humans"
batch_size = 128
AUTOTUNE = tf_data.AUTOTUNE

(train_ds, test_ds), metadata = tfds.load(
    name=dataset_name,
    split=[tfds.Split.TRAIN, tfds.Split.TEST],
    with_info=True,
    as_supervised=True,
)

print(f"Image shape: {metadata.features['image'].shape}")
print(f"Training images: {metadata.splits['train'].num_examples}")
print(f"Test images: {metadata.splits['test'].num_examples}")

``` Image shape: (300, 300, 3) Training images: 1027 Test images: 256

</div>
---
## Use Data Augmentation

We will rescale the data to `[0, 1]` and perform simple augmentations to our data.


```python
rescale = layers.Rescaling(1.0 / 255)

data_augmentation = [
    layers.RandomFlip("horizontal_and_vertical"),
    layers.RandomRotation(0.3),
    layers.RandomZoom(0.2),
]


# Helper to apply augmentation
def apply_aug(x):
    for aug in data_augmentation:
        x = aug(x)
    return x


def prepare(ds, shuffle=False, augment=False):
    # Rescale dataset
    ds = ds.map(lambda x, y: (rescale(x), y), num_parallel_calls=AUTOTUNE)

    if shuffle:
        ds = ds.shuffle(1024)

    # Batch dataset
    ds = ds.batch(batch_size)

    # Use data augmentation only on the training set
    if augment:
        ds = ds.map(
            lambda x, y: (apply_aug(x), y),
            num_parallel_calls=AUTOTUNE,
        )

    # Use buffered prefecting
    return ds.prefetch(buffer_size=AUTOTUNE)

Rescale and augment the data

train_ds = prepare(train_ds, shuffle=True, augment=True)
test_ds = prepare(test_ds)

---

Define a model

In this section we will define a Convolutional neural network.

model = keras.Sequential(
    [
        layers.Input(shape=input_shape),
        layers.Conv2D(16, (3, 3), activation="relu"),
        layers.MaxPooling2D(2, 2),
        layers.Conv2D(32, (3, 3), activation="relu"),
        layers.Dropout(0.5),
        layers.MaxPooling2D(2, 2),
        layers.Conv2D(64, (3, 3), activation="relu"),
        layers.Dropout(0.5),
        layers.MaxPooling2D(2, 2),
        layers.Conv2D(64, (3, 3), activation="relu"),
        layers.MaxPooling2D(2, 2),
        layers.Conv2D(64, (3, 3), activation="relu"),
        layers.MaxPooling2D(2, 2),
        layers.Flatten(),
        layers.Dropout(0.5),
        layers.Dense(512, activation="relu"),
        layers.Dense(1, activation="sigmoid"),
    ]
)

---

Implement Gradient Centralization

We will now subclass the RMSProp optimizer class modifying the keras.optimizers.Optimizer.get_gradients() method where we now implement Gradient Centralization. On a high level the idea is that let us say we obtain our gradients through back propagation for a Dense or Convolution layer we then compute the mean of the column vectors of the weight matrix, and then remove the mean from each column vector.

The experiments in this paper on various applications, including general image classification, fine-grained image classification, detection and segmentation and Person ReID demonstrate that GC can consistently improve the performance of DNN learning.

Also, for simplicity at the moment we are not implementing gradient cliiping functionality, however this quite easy to implement.

At the moment we are just creating a subclass for the RMSProp optimizer however you could easily reproduce this for any other optimizer or on a custom optimizer in the same way. We will be using this class in the later section when we train a model with Gradient Centralization.

class GCRMSprop(RMSprop):
    def get_gradients(self, loss, params):
        # We here just provide a modified get_gradients() function since we are
        # trying to just compute the centralized gradients.

        grads = []
        gradients = super().get_gradients()
        for grad in gradients:
            grad_len = len(grad.shape)
            if grad_len > 1:
                axis = list(range(grad_len - 1))
                grad -= ops.mean(grad, axis=axis, keep_dims=True)
            grads.append(grad)

        return grads


optimizer = GCRMSprop(learning_rate=1e-4)

---

Training utilities

We will also create a callback which allows us to easily measure the total training time and the time taken for each epoch since we are interested in comparing the effect of Gradient Centralization on the model we built above.

class TimeHistory(keras.callbacks.Callback):
    def on_train_begin(self, logs={}):
        self.times = []

    def on_epoch_begin(self, batch, logs={}):
        self.epoch_time_start = time()

    def on_epoch_end(self, batch, logs={}):
        self.times.append(time() - self.epoch_time_start)

---

Train the model without GC

We now train the model we built earlier without Gradient Centralization which we can compare to the training performance of the model trained with Gradient Centralization.

time_callback_no_gc = TimeHistory()
model.compile(
    loss="binary_crossentropy",
    optimizer=RMSprop(learning_rate=1e-4),
    metrics=["accuracy"],
)

model.summary()

Model: "sequential"

┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Layer (type)                    ┃ Output Shape              ┃    Param # ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ conv2d (Conv2D)                 │ (None, 298, 298, 16)      │        448 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d (MaxPooling2D)    │ (None, 149, 149, 16)      │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_1 (Conv2D)               │ (None, 147, 147, 32)      │      4,640 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dropout (Dropout)               │ (None, 147, 147, 32)      │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_1 (MaxPooling2D)  │ (None, 73, 73, 32)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_2 (Conv2D)               │ (None, 71, 71, 64)        │     18,496 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dropout_1 (Dropout)             │ (None, 71, 71, 64)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_2 (MaxPooling2D)  │ (None, 35, 35, 64)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_3 (Conv2D)               │ (None, 33, 33, 64)        │     36,928 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_3 (MaxPooling2D)  │ (None, 16, 16, 64)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_4 (Conv2D)               │ (None, 14, 14, 64)        │     36,928 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_4 (MaxPooling2D)  │ (None, 7, 7, 64)          │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ flatten (Flatten)               │ (None, 3136)              │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dropout_2 (Dropout)             │ (None, 3136)              │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dense (Dense)                   │ (None, 512)               │  1,606,144 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dense_1 (Dense)                 │ (None, 1)                 │        513 │
└─────────────────────────────────┴───────────────────────────┴────────────┘

 Total params: 1,704,097 (6.50 MB)

 Trainable params: 1,704,097 (6.50 MB)

 Non-trainable params: 0 (0.00 B)

We also save the history since we later want to compare our model trained with and not trained with Gradient Centralization

history_no_gc = model.fit(
    train_ds, epochs=10, verbose=1, callbacks=[time_callback_no_gc]
)

``` Epoch 1/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 24s 778ms/step - accuracy: 0.4772 - loss: 0.7405 Epoch 2/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 597ms/step - accuracy: 0.5434 - loss: 0.6861 Epoch 3/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 700ms/step - accuracy: 0.5402 - loss: 0.6911 Epoch 4/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 9s 586ms/step - accuracy: 0.5884 - loss: 0.6788 Epoch 5/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 9s 588ms/step - accuracy: 0.6570 - loss: 0.6564 Epoch 6/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 591ms/step - accuracy: 0.6671 - loss: 0.6395 Epoch 7/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 594ms/step - accuracy: 0.7010 - loss: 0.6161 Epoch 8/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 9s 593ms/step - accuracy: 0.6946 - loss: 0.6129 Epoch 9/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 699ms/step - accuracy: 0.6972 - loss: 0.5987 Epoch 10/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 11s 623ms/step - accuracy: 0.6839 - loss: 0.6197

</div>
---
## Train the model with GC

We will now train the same model, this time using Gradient Centralization,
notice our optimizer is the one using Gradient Centralization this time.


```python
time_callback_gc = TimeHistory()
model.compile(loss="binary_crossentropy", optimizer=optimizer, metrics=["accuracy"])

model.summary()

history_gc = model.fit(train_ds, epochs=10, verbose=1, callbacks=[time_callback_gc])

Model: "sequential"

┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Layer (type)                    ┃ Output Shape              ┃    Param # ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ conv2d (Conv2D)                 │ (None, 298, 298, 16)      │        448 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d (MaxPooling2D)    │ (None, 149, 149, 16)      │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_1 (Conv2D)               │ (None, 147, 147, 32)      │      4,640 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dropout (Dropout)               │ (None, 147, 147, 32)      │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_1 (MaxPooling2D)  │ (None, 73, 73, 32)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_2 (Conv2D)               │ (None, 71, 71, 64)        │     18,496 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dropout_1 (Dropout)             │ (None, 71, 71, 64)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_2 (MaxPooling2D)  │ (None, 35, 35, 64)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_3 (Conv2D)               │ (None, 33, 33, 64)        │     36,928 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_3 (MaxPooling2D)  │ (None, 16, 16, 64)        │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ conv2d_4 (Conv2D)               │ (None, 14, 14, 64)        │     36,928 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ max_pooling2d_4 (MaxPooling2D)  │ (None, 7, 7, 64)          │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ flatten (Flatten)               │ (None, 3136)              │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dropout_2 (Dropout)             │ (None, 3136)              │          0 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dense (Dense)                   │ (None, 512)               │  1,606,144 │
├─────────────────────────────────┼───────────────────────────┼────────────┤
│ dense_1 (Dense)                 │ (None, 1)                 │        513 │
└─────────────────────────────────┴───────────────────────────┴────────────┘

 Total params: 1,704,097 (6.50 MB)

 Trainable params: 1,704,097 (6.50 MB)

 Non-trainable params: 0 (0.00 B)

``` Epoch 1/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 12s 649ms/step - accuracy: 0.7118 - loss: 0.5594 Epoch 2/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 592ms/step - accuracy: 0.7249 - loss: 0.5817 Epoch 3/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 9s 587ms/step - accuracy: 0.8060 - loss: 0.4448 Epoch 4/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 693ms/step - accuracy: 0.8472 - loss: 0.4051 Epoch 5/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 594ms/step - accuracy: 0.8386 - loss: 0.3978 Epoch 6/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 593ms/step - accuracy: 0.8442 - loss: 0.3976 Epoch 7/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 9s 585ms/step - accuracy: 0.7409 - loss: 0.6626 Epoch 8/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 587ms/step - accuracy: 0.8191 - loss: 0.4357 Epoch 9/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 9s 587ms/step - accuracy: 0.8248 - loss: 0.3974 Epoch 10/10 9/9 ━━━━━━━━━━━━━━━━━━━━ 10s 646ms/step - accuracy: 0.8022 - loss: 0.4589

</div>
---
## Comparing performance


```python
print("Not using Gradient Centralization")
print(f"Loss: {history_no_gc.history['loss'][-1]}")
print(f"Accuracy: {history_no_gc.history['accuracy'][-1]}")
print(f"Training Time: {sum(time_callback_no_gc.times)}")

print("Using Gradient Centralization")
print(f"Loss: {history_gc.history['loss'][-1]}")
print(f"Accuracy: {history_gc.history['accuracy'][-1]}")
print(f"Training Time: {sum(time_callback_gc.times)}")

``` Not using Gradient Centralization Loss: 0.5345584154129028 Accuracy: 0.7604166865348816 Training Time: 112.48799777030945 Using Gradient Centralization Loss: 0.4014038145542145 Accuracy: 0.8153935074806213 Training Time: 98.31573963165283

</div>
Readers are encouraged to try out Gradient Centralization on different datasets from
different domains and experiment with it's effect. You are strongly advised to check out
the [original paper](https://arxiv.org/abs/2004.01461) as well - the authors present
several studies on Gradient Centralization showing how it can improve general
performance, generalization, training time as well as more efficient.

Many thanks to [Ali Mustufa Shaikh](https://github.com/ialimustufa) for reviewing this
implementation.