# Post-training quantization

Post-training quantization is a conversion technique that can reduce model size
while also improving CPU and hardware accelerator latency, with little
degradation in model accuracy. You can quantize an already-trained float
TensorFlow model when you convert it to TensorFlow Lite format using the
[TensorFlow Lite Converter](../convert/).

Note: The procedures on this page require TensorFlow 1.15 or higher.

### Optimization Methods

There are several post-training quantization options to choose from. Here is a
summary table of the choices and the benefits they provide:

| Technique            | Benefits                  | Hardware         |
| -------------------- | ------------------------- | ---------------- |
| Dynamic range        | 4x smaller, 2x-3x speedup | CPU              |
: quantization         :                           :                  :
| Full integer         | 4x smaller, 3x+ speedup   | CPU, Edge TPU,   |
: quantization         :                           : Microcontrollers :
| Float16 quantization | 2x smaller, GPU           | CPU, GPU         |
:                      : acceleration              :                  :

The following decision tree can help determine which post-training quantization
method is best for your use case:

![post-training optimization options](images/optimization.jpg)

### Dynamic range quantization

The simplest form of post-training quantization statically quantizes only the
weights from floating point to integer, which has 8-bits of precision:

<pre>
import tensorflow as tf
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
<b>converter.optimizations = [tf.lite.Optimize.DEFAULT]</b>
tflite_quant_model = converter.convert()
</pre>

At inference, weights are converted from 8-bits of precision to floating point
and computed using floating-point kernels. This conversion is done once and
cached to reduce latency.

To further improve latency, "dynamic-range" operators dynamically quantize
activations based on their range to 8-bits and perform computations with 8-bit
weights and activations. This optimization provides latencies close to fully
fixed-point inference. However, the outputs are still stored using floating
point so that the speedup with dynamic-range ops is less than a full fixed-point
computation.

### Full integer quantization

You can get further latency improvements, reductions in peak memory usage, and
compatibility with integer only hardware devices or accelerators by making sure
all model math is integer quantized.

For full integer quantization, you need to calibrate or estimate the range, i.e,
(min, max) of all floating-point tensors in the model. Unlike constant tensors
such as weights and biases, variable tensors such as model input, activations
(outputs of intermediate layers) and model output cannot be calibrated unless we
run a few inference cycles. As a result, the converter requires a representative
dataset to calibrate them. This dataset can be a small subset (around ~100-500
samples) of the training or validation data. Refer to the
`representative_dataset()` function below.

<pre>
def representative_dataset():
  for data in tf.data.Dataset.from_tensor_slices((images)).batch(1).take(100):
    yield [tf.dtypes.cast(data, tf.float32)]
</pre>

For testing purposes, you can use a dummy dataset as follows:

<pre>
def representative_dataset():
    for _ in range(100):
      data = np.random.rand(1, 244, 244, 3)
      yield [data.astype(np.float32)]
 </pre>

#### Integer with float fallback (using default float input/output)

In order to fully integer quantize a model, but use float operators when they
don't have an integer implementation (to ensure conversion occurs smoothly), use
the following steps:

<pre>
import tensorflow as tf
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
<b>converter.optimizations = [tf.lite.Optimize.DEFAULT]
converter.representative_dataset = representative_dataset</b>
tflite_quant_model = converter.convert()
</pre>

Note: This `tflite_quant_model` won't be compatible with integer only devices
(such as 8-bit microcontrollers) and accelerators (such as the Coral Edge TPU)
because the input and output still remain float in order to have the same
interface as the original float only model.

#### Integer only

*Creating integer only models is a common use case for
[TensorFlow Lite for Microcontrollers](https://www.tensorflow.org/lite/microcontrollers)
and [Coral Edge TPUs](https://coral.ai/).*

Note: Starting TensorFlow 2.3.0, we support the `inference_input_type` and
`inference_output_type` attributes.

Additionally, to ensure compatibility with integer only devices (such as 8-bit
microcontrollers) and accelerators (such as the Coral Edge TPU), you can enforce
full integer quantization for all ops including the input and output, by using
the following steps:

<pre>
import tensorflow as tf
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
converter.optimizations = [tf.lite.Optimize.DEFAULT]
converter.representative_dataset = representative_dataset
<b>converter.target_spec.supported_ops = [tf.lite.OpsSet.TFLITE_BUILTINS_INT8]</b>
<b>converter.inference_input_type = tf.int8</b>  # or tf.uint8
<b>converter.inference_output_type = tf.int8</b>  # or tf.uint8
tflite_quant_model = converter.convert()
</pre>

Note: The converter will throw an error if it encounters an operation it cannot
currently quantize.

### Float16 quantization

You can reduce the size of a floating point model by quantizing the weights to
float16, the IEEE standard for 16-bit floating point numbers. To enable float16
quantization of weights, use the following steps:

<pre>
import tensorflow as tf
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
<b>converter.optimizations = [tf.lite.Optimize.DEFAULT]
converter.target_spec.supported_types = [tf.float16]</b>
tflite_quant_model = converter.convert()
</pre>

The advantages of float16 quantization are as follows:

*   It reduces model size by up to half (since all weights become half of their
    original size).
*   It causes minimal loss in accuracy.
*   It supports some delegates (e.g. the GPU delegate) which can operate
    directly on float16 data, resulting in faster execution than float32
    computations.

The disadvantages of float16 quantization are as follows:

*   It does not reduce latency as much as a quantization to fixed point math.
*   By default, a float16 quantized model will "dequantize" the weights values
    to float32 when run on the CPU. (Note that the GPU delegate will not perform
    this dequantization, since it can operate on float16 data.)

### Integer only: 16-bit activations with 8-bit weights (experimental)

This is an experimental quantization scheme. It is similar to the "integer only"
scheme, but activations are quantized based on their range to 16-bits, weights
are quantized in 8-bit integer and bias is quantized into 64-bit integer. This
is referred to as 16x8 quantization further.

The main advantage of this quantization is that it can improve accuracy
significantly, but only slightly increase model size.

<pre>
import tensorflow as tf
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
converter.representative_dataset = representative_dataset
<b>converter.optimizations = [tf.lite.Optimize.DEFAULT]
converter.target_spec.supported_ops = [tf.lite.OpsSet.EXPERIMENTAL_TFLITE_BUILTINS_ACTIVATIONS_INT16_WEIGHTS_INT8]</b>
tflite_quant_model = converter.convert()
</pre>

If 16x8 quantization is not supported for some operators in the model,
then the model still can be quantized, but unsupported operators kept in float.
The following option should be added to the target_spec to allow this.
<pre>
import tensorflow as tf
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
converter.representative_dataset = representative_dataset
converter.optimizations = [tf.lite.Optimize.DEFAULT]
converter.target_spec.supported_ops = [tf.lite.OpsSet.EXPERIMENTAL_TFLITE_BUILTINS_ACTIVATIONS_INT16_WEIGHTS_INT8,
<b>tf.lite.OpsSet.TFLITE_BUILTINS</b>]
tflite_quant_model = converter.convert()
</pre>

Examples of the use cases where accuracy improvements provided by this
quantization scheme include: * super-resolution, * audio signal processing such
as noise cancelling and beamforming, * image de-noising, * HDR reconstruction
from a single image.

The disadvantage of this quantization is:

*   Currently inference is noticeably slower than 8-bit full integer due to the
    lack of optimized kernel implementation.
*   Currently it is incompatible with the existing hardware accelerated TFLite
    delegates.

Note: This is an experimental feature.

A tutorial for this quantization mode can be found
[here](post_training_integer_quant_16x8.ipynb).

### Model accuracy

Since weights are quantized post training, there could be an accuracy loss,
particularly for smaller networks. Pre-trained fully quantized models are
provided for specific networks in the
[TensorFlow Lite model repository](../models/). It is important to check the
accuracy of the quantized model to verify that any degradation in accuracy is
within acceptable limits. There are tools to evaluate
[TensorFlow Lite model accuracy](https://github.com/tensorflow/tensorflow/tree/master/tensorflow/lite/tools/evaluation/tasks){:.external}.


Alternatively, if the accuracy drop is too high, consider using
[quantization aware training](https://www.tensorflow.org/model_optimization/guide/quantization/training)
. However, doing so requires modifications during model training to add fake
quantization nodes, whereas the post-training quantization techniques on this
page use an existing pre-trained model.

### Representation for quantized tensors

8-bit quantization approximates floating point values using the following
formula.

$$real\_value = (int8\_value - zero\_point) \times scale$$

The representation has two main parts:

*   Per-axis (aka per-channel) or per-tensor weights represented by int8 two’s
    complement values in the range [-127, 127] with zero-point equal to 0.

*   Per-tensor activations/inputs represented by int8 two’s complement values in
    the range [-128, 127], with a zero-point in range [-128, 127].

For a detailed view of our quantization scheme, please see our
[quantization spec](./quantization_spec.md). Hardware vendors who want to plug
into TensorFlow Lite's delegate interface are encouraged to implement the
quantization scheme described there.
