# 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.

### 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 quantization 4x smaller, 2x-3x speedup CPU
Full integer quantization 4x smaller, 3x+ speedup CPU, Edge TPU, Microcontrollers
Float16 quantization 2x smaller, GPU acceleration CPU, GPU

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

### 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:

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


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.

def representative_dataset():
for data in tf.data.Dataset.from_tensor_slices((images)).batch(1).take(100):
yield [data.astype(tf.float32)]


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

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


#### 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:

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
tflite_quant_model = converter.convert()


#### Integer only

Creating integer only models is a common use case for TensorFlow Lite for Microcontrollers and Coral Edge TPUs.

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:

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
converter.target_spec.supported_ops = [tf.lite.OpsSet.TFLITE_BUILTINS_INT8]
converter.inference_input_type = tf.int8  # or tf.uint8
converter.inference_output_type = tf.int8  # or tf.uint8
tflite_quant_model = converter.convert()


### 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:

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


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.

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]
tflite_quant_model = converter.convert()


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.

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,
tf.lite.OpsSet.TFLITE_BUILTINS]
tflite_quant_model = converter.convert()


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.

A tutorial for this quantization mode can be found here.

### 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. 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.

Alternatively, if the accuracy drop is too high, consider using quantization aware 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. Hardware vendors who want to plug into TensorFlow Lite's delegate interface are encouraged to implement the quantization scheme described there.