Sparsity and cluster preserving quantization aware training (PCQAT) Keras example

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This is an end to end example showing the usage of the sparsity and cluster preserving quantization aware training (PCQAT) API, part of the TensorFlow Model Optimization Toolkit's collaborative optimization pipeline.

Other pages

For an introduction to the pipeline and other available techniques, see the collaborative optimization overview page.


In the tutorial, you will:

  1. Train a keras model for the MNIST dataset from scratch.
  2. Fine-tune the model with pruning and see the accuracy and observe that the model was successfully pruned.
  3. Apply sparsity preserving clustering on the pruned model and observe that the sparsity applied earlier has been preserved.
  4. Apply QAT and observe the loss of sparsity and clusters.
  5. Apply PCQAT and observe that both sparsity and clustering applied earlier have been preserved.
  6. Generate a TFLite model and observe the effects of applying PCQAT on it.
  7. Compare the sizes of the different models to observe the compression benefits of applying sparsity followed by the collaborative optimization techniques of sparsity preserving clustering and PCQAT.
  8. Compare the accurracy of the fully optimized model with the un-optimized baseline model accuracy.


You can run this Jupyter Notebook in your local virtualenv or colab. For details of setting up dependencies, please refer to the installation guide.

 pip install -q tensorflow-model-optimization
import tensorflow as tf
import tf_keras as keras

import numpy as np
import tempfile
import zipfile
import os

Train a keras model for MNIST to be pruned and clustered

# Load MNIST dataset
mnist = keras.datasets.mnist
(train_images, train_labels), (test_images, test_labels) = mnist.load_data()

# Normalize the input image so that each pixel value is between 0 to 1.
train_images = train_images / 255.0
test_images  = test_images / 255.0

model = keras.Sequential([
  keras.layers.InputLayer(input_shape=(28, 28)),
  keras.layers.Reshape(target_shape=(28, 28, 1)),
  keras.layers.Conv2D(filters=12, kernel_size=(3, 3),
  keras.layers.MaxPooling2D(pool_size=(2, 2)),

opt = keras.optimizers.Adam(learning_rate=1e-3)

# Train the digit classification model
2024-03-09 12:49:28.954689: E external/local_xla/xla/stream_executor/cuda/] failed call to cuInit: CUDA_ERROR_NO_DEVICE: no CUDA-capable device is detected
Epoch 1/10
1688/1688 [==============================] - 21s 4ms/step - loss: 0.3037 - accuracy: 0.9146 - val_loss: 0.1153 - val_accuracy: 0.9682
Epoch 2/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.1133 - accuracy: 0.9680 - val_loss: 0.0895 - val_accuracy: 0.9762
Epoch 3/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0792 - accuracy: 0.9768 - val_loss: 0.0652 - val_accuracy: 0.9825
Epoch 4/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0662 - accuracy: 0.9803 - val_loss: 0.0633 - val_accuracy: 0.9823
Epoch 5/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0570 - accuracy: 0.9833 - val_loss: 0.0649 - val_accuracy: 0.9825
Epoch 6/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0498 - accuracy: 0.9853 - val_loss: 0.0571 - val_accuracy: 0.9842
Epoch 7/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0448 - accuracy: 0.9867 - val_loss: 0.0586 - val_accuracy: 0.9840
Epoch 8/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0405 - accuracy: 0.9873 - val_loss: 0.0586 - val_accuracy: 0.9848
Epoch 9/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0370 - accuracy: 0.9885 - val_loss: 0.0624 - val_accuracy: 0.9828
Epoch 10/10
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0332 - accuracy: 0.9902 - val_loss: 0.0554 - val_accuracy: 0.9848
<tf_keras.src.callbacks.History at 0x7f615076beb0>

Evaluate the baseline model and save it for later usage

_, baseline_model_accuracy = model.evaluate(
    test_images, test_labels, verbose=0)

print('Baseline test accuracy:', baseline_model_accuracy)

_, keras_file = tempfile.mkstemp('.h5')
print('Saving model to: ', keras_file)
keras.models.save_model(model, keras_file, include_optimizer=False)
Baseline test accuracy: 0.9835000038146973
Saving model to:  /tmpfs/tmp/tmpf70eijr3.h5
/tmpfs/tmp/ipykernel_41361/ UserWarning: You are saving your model as an HDF5 file via ``. This file format is considered legacy. We recommend using instead the native TF-Keras format, e.g. `'my_model.keras')`.
  keras.models.save_model(model, keras_file, include_optimizer=False)

Prune and fine-tune the model to 50% sparsity

Apply the prune_low_magnitude() API to achieve the pruned model that is to be clustered in the next step. Refer to the pruning comprehensive guide for more information on the pruning API.

Define the model and apply the sparsity API

Note that the pre-trained model is used.

import tensorflow_model_optimization as tfmot

prune_low_magnitude = tfmot.sparsity.keras.prune_low_magnitude

pruning_params = {
      'pruning_schedule': tfmot.sparsity.keras.ConstantSparsity(0.5, begin_step=0, frequency=100)

callbacks = [

pruned_model = prune_low_magnitude(model, **pruning_params)

# Use smaller learning rate for fine-tuning
opt = keras.optimizers.Adam(learning_rate=1e-5)


Fine-tune the model, check sparsity, and evaluate the accuracy against baseline

Fine-tune the model with pruning for 3 epochs.

# Fine-tune model
Epoch 1/3
1688/1688 [==============================] - 10s 4ms/step - loss: 0.0851 - accuracy: 0.9707 - val_loss: 0.0801 - val_accuracy: 0.9768
Epoch 2/3
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0591 - accuracy: 0.9801 - val_loss: 0.0672 - val_accuracy: 0.9808
Epoch 3/3
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0493 - accuracy: 0.9852 - val_loss: 0.0626 - val_accuracy: 0.9837
<tf_keras.src.callbacks.History at 0x7f60c8593ee0>

Define helper functions to calculate and print the sparsity and clusters of the model.

def print_model_weights_sparsity(model):
    for layer in model.layers:
        if isinstance(layer, keras.layers.Wrapper):
            weights = layer.trainable_weights
            weights = layer.weights
        for weight in weights:
            if "kernel" not in or "centroid" in
            weight_size = weight.numpy().size
            zero_num = np.count_nonzero(weight == 0)
                f"{}: {zero_num/weight_size:.2%} sparsity ",

def print_model_weight_clusters(model):
    for layer in model.layers:
        if isinstance(layer, keras.layers.Wrapper):
            weights = layer.trainable_weights
            weights = layer.weights
        for weight in weights:
            # ignore auxiliary quantization weights
            if "quantize_layer" in
            if "kernel" in
                unique_count = len(np.unique(weight))
                    f"{}/{}: {unique_count} clusters "

Let's strip the pruning wrapper first, then check that the model kernels were correctly pruned.

stripped_pruned_model = tfmot.sparsity.keras.strip_pruning(pruned_model)

conv2d/kernel:0: 50.00% sparsity  (54/108)
dense/kernel:0: 50.00% sparsity  (10140/20280)

Apply sparsity preserving clustering and check its effect on model sparsity in both cases

Next, apply sparsity preserving clustering on the pruned model and observe the number of clusters and check that the sparsity is preserved.

import tensorflow_model_optimization as tfmot
from tensorflow_model_optimization.python.core.clustering.keras.experimental import (

cluster_weights = tfmot.clustering.keras.cluster_weights
CentroidInitialization = tfmot.clustering.keras.CentroidInitialization

cluster_weights = cluster.cluster_weights

clustering_params = {
  'number_of_clusters': 8,
  'cluster_centroids_init': CentroidInitialization.KMEANS_PLUS_PLUS,
  'preserve_sparsity': True

sparsity_clustered_model = cluster_weights(stripped_pruned_model, **clustering_params)


print('Train sparsity preserving clustering model:'), train_labels,epochs=3, validation_split=0.1)
Train sparsity preserving clustering model:
Epoch 1/3
1688/1688 [==============================] - 9s 5ms/step - loss: 0.0422 - accuracy: 0.9869 - val_loss: 0.0712 - val_accuracy: 0.9818
Epoch 2/3
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0398 - accuracy: 0.9878 - val_loss: 0.0627 - val_accuracy: 0.9848
Epoch 3/3
1688/1688 [==============================] - 7s 4ms/step - loss: 0.0403 - accuracy: 0.9865 - val_loss: 0.0597 - val_accuracy: 0.9830
<tf_keras.src.callbacks.History at 0x7f6080153790>

Strip the clustering wrapper first, then check that the model is correctly pruned and clustered.

stripped_clustered_model = tfmot.clustering.keras.strip_clustering(sparsity_clustered_model)

print("Model sparsity:\n")

print("\nModel clusters:\n")
Model sparsity:

kernel:0: 50.93% sparsity  (55/108)
kernel:0: 58.12% sparsity  (11787/20280)

Model clusters:

conv2d/kernel:0: 8 clusters 
dense/kernel:0: 8 clusters

Apply QAT and PCQAT and check effect on model clusters and sparsity

Next, apply both QAT and PCQAT on the sparse clustered model and observe that PCQAT preserves weight sparsity and clusters in your model. Note that the stripped model is passed to the QAT and PCQAT API.

qat_model = tfmot.quantization.keras.quantize_model(stripped_clustered_model)

print('Train qat model:'), train_labels, batch_size=128, epochs=1, validation_split=0.1)

quant_aware_annotate_model = tfmot.quantization.keras.quantize_annotate_model(
pcqat_model = tfmot.quantization.keras.quantize_apply(

print('Train pcqat model:'), train_labels, batch_size=128, epochs=1, validation_split=0.1)
Train qat model:
422/422 [==============================] - 4s 7ms/step - loss: 0.0298 - accuracy: 0.9911 - val_loss: 0.0587 - val_accuracy: 0.9853
Train pcqat model:
WARNING:tensorflow:Gradients do not exist for variables ['conv2d/kernel:0', 'dense/kernel:0'] when minimizing the loss. If you're using `model.compile()`, did you forget to provide a `loss` argument?
WARNING:tensorflow:Gradients do not exist for variables ['conv2d/kernel:0', 'dense/kernel:0'] when minimizing the loss. If you're using `model.compile()`, did you forget to provide a `loss` argument?
WARNING:tensorflow:Gradients do not exist for variables ['conv2d/kernel:0', 'dense/kernel:0'] when minimizing the loss. If you're using `model.compile()`, did you forget to provide a `loss` argument?
WARNING:tensorflow:Gradients do not exist for variables ['conv2d/kernel:0', 'dense/kernel:0'] when minimizing the loss. If you're using `model.compile()`, did you forget to provide a `loss` argument?
422/422 [==============================] - 5s 7ms/step - loss: 0.0315 - accuracy: 0.9904 - val_loss: 0.0563 - val_accuracy: 0.9842
<tf_keras.src.callbacks.History at 0x7f6050606e80>
print("QAT Model clusters:")
print("\nQAT Model sparsity:")
print("\nPCQAT Model clusters:")
print("\nPCQAT Model sparsity:")
QAT Model clusters:
quant_conv2d/conv2d/kernel:0: 100 clusters 
quant_dense/dense/kernel:0: 18251 clusters 

QAT Model sparsity:
conv2d/kernel:0: 8.33% sparsity  (9/108)
dense/kernel:0: 7.52% sparsity  (1525/20280)

PCQAT Model clusters:
quant_conv2d/conv2d/kernel:0: 8 clusters 
quant_dense/dense/kernel:0: 8 clusters 

PCQAT Model sparsity:
conv2d/kernel:0: 50.93% sparsity  (55/108)
dense/kernel:0: 58.16% sparsity  (11794/20280)

See compression benefits of PCQAT model

Define helper function to get zipped model file.

def get_gzipped_model_size(file):
  # It returns the size of the gzipped model in kilobytes.

  _, zipped_file = tempfile.mkstemp('.zip')
  with zipfile.ZipFile(zipped_file, 'w', compression=zipfile.ZIP_DEFLATED) as f:

  return os.path.getsize(zipped_file)/1000

Observe that applying sparsity, clustering and PCQAT to a model yields significant compression benefits.

# QAT model
converter = tf.lite.TFLiteConverter.from_keras_model(qat_model)
converter.optimizations = [tf.lite.Optimize.DEFAULT]
qat_tflite_model = converter.convert()
qat_model_file = 'qat_model.tflite'
# Save the model.
with open(qat_model_file, 'wb') as f:

# PCQAT model
converter = tf.lite.TFLiteConverter.from_keras_model(pcqat_model)
converter.optimizations = [tf.lite.Optimize.DEFAULT]
pcqat_tflite_model = converter.convert()
pcqat_model_file = 'pcqat_model.tflite'
# Save the model.
with open(pcqat_model_file, 'wb') as f:

print("QAT model size: ", get_gzipped_model_size(qat_model_file), ' KB')
print("PCQAT model size: ", get_gzipped_model_size(pcqat_model_file), ' KB')
INFO:tensorflow:Assets written to: /tmpfs/tmp/tmpbd29dk98/assets
INFO:tensorflow:Assets written to: /tmpfs/tmp/tmpbd29dk98/assets
/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/tensorflow/lite/python/ UserWarning: Statistics for quantized inputs were expected, but not specified; continuing anyway.
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
W0000 00:00:1709988717.237025   41361] Ignored output_format.
W0000 00:00:1709988717.237075   41361] Ignored drop_control_dependency.
INFO:tensorflow:Assets written to: /tmpfs/tmp/tmpy4q5o_1n/assets
INFO:tensorflow:Assets written to: /tmpfs/tmp/tmpy4q5o_1n/assets
/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/tensorflow/lite/python/ UserWarning: Statistics for quantized inputs were expected, but not specified; continuing anyway.
W0000 00:00:1709988720.060897   41361] Ignored output_format.
W0000 00:00:1709988720.060927   41361] Ignored drop_control_dependency.
QAT model size:  13.958  KB
PCQAT model size:  7.876  KB

See the persistence of accuracy from TF to TFLite

Define a helper function to evaluate the TFLite model on the test dataset.

def eval_model(interpreter):
  input_index = interpreter.get_input_details()[0]["index"]
  output_index = interpreter.get_output_details()[0]["index"]

  # Run predictions on every image in the "test" dataset.
  prediction_digits = []
  for i, test_image in enumerate(test_images):
    if i % 1000 == 0:
      print(f"Evaluated on {i} results so far.")
    # Pre-processing: add batch dimension and convert to float32 to match with
    # the model's input data format.
    test_image = np.expand_dims(test_image, axis=0).astype(np.float32)
    interpreter.set_tensor(input_index, test_image)

    # Run inference.

    # Post-processing: remove batch dimension and find the digit with highest
    # probability.
    output = interpreter.tensor(output_index)
    digit = np.argmax(output()[0])

  # Compare prediction results with ground truth labels to calculate accuracy.
  prediction_digits = np.array(prediction_digits)
  accuracy = (prediction_digits == test_labels).mean()
  return accuracy

Evaluate the model, which has been pruned, clustered and quantized, and then see that the accuracy from TensorFlow persists in the TFLite backend.

interpreter = tf.lite.Interpreter(pcqat_model_file)

pcqat_test_accuracy = eval_model(interpreter)

print('Pruned, clustered and quantized TFLite test_accuracy:', pcqat_test_accuracy)
print('Baseline TF test accuracy:', baseline_model_accuracy)
Evaluated on 0 results so far.
Evaluated on 1000 results so far.
Evaluated on 2000 results so far.
INFO: Created TensorFlow Lite XNNPACK delegate for CPU.
WARNING: Attempting to use a delegate that only supports static-sized tensors with a graph that has dynamic-sized tensors (tensor#12 is a dynamic-sized tensor).
Evaluated on 3000 results so far.
Evaluated on 4000 results so far.
Evaluated on 5000 results so far.
Evaluated on 6000 results so far.
Evaluated on 7000 results so far.
Evaluated on 8000 results so far.
Evaluated on 9000 results so far.

Pruned, clustered and quantized TFLite test_accuracy: 0.9806
Baseline TF test accuracy: 0.9835000038146973


In this tutorial, you learned how to create a model, prune it using the prune_low_magnitude() API, and apply sparsity preserving clustering using the cluster_weights() API to preserve sparsity while clustering the weights.

Next, sparsity and cluster preserving quantization aware training (PCQAT) was applied to preserve model sparsity and clusters while using QAT. The final PCQAT model was compared to the QAT one to show that sparsity and clusters are preserved in the former and lost in the latter.

Next, the models were converted to TFLite to show the compression benefits of chaining sparsity, clustering, and PCQAT model optimization techniques and the TFLite model was evaluated to ensure that the accuracy persists in the TFLite backend.

Finally, the PCQAT TFLite model accuracy was compared to the pre-optimization baseline model accuracy to show that collaborative optimization techniques managed to achieve the compression benefits while maintaining a similar accuracy compared to the original model.