Post-training quantization includes general techniques to reduce model size while also improving CPU and hardware accelerator latency with little degradation in model accuracy. These techniques can be performed on an already-trained float TensorFlow model and applied during TensorFlow Lite conversion.

### Optimization options

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 |
---|---|---|

Post training "hybrid" | 4x smaller, 2-3x speedup, accuracy | CPU |

Post training integer | 4x smaller, More speedup | CPU, Edge TPU, etc. |

Post training fp16 | 2x smaller, Potential GPU acceleration | CPU/GPU |

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

### Quantizing weights

The simplest form of post-training quantization quantizes weights from floating point to 8-bits of precision. This technique is enabled as an option in the TensorFlow Lite converter:

```
import tensorflow as tf
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
converter.optimizations = [tf.lite.Optimize.OPTIMIZE_FOR_SIZE]
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, hybrid operators dynamically quantize activations 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 hybrid ops is less than a full fixed-point computation. Hybrid ops are available for the most compute-intensive operators in a network:

- tf.contrib.layers.fully_connected
- tf.nn.conv2d
- tf.nn.embedding_lookup
- BasicRNN
- tf.nn.bidirectional_dynamic_rnn for BasicRNNCell type
- tf.nn.dynamic_rnn for LSTM and BasicRNN Cell types

### Full integer quantization of weights and activations

We can get further latency improvements, reductions in peak memory usage, and access to integer only hardware accelerators by making sure all model math is quantized. To do this, we need to measure the dynamic range of activations and inputs with a representative data set. You can simply create an input data generator and provide it to our converter.

```
import tensorflow as tf
def representative_dataset_gen():
for _ in range(num_calibration_steps):
# Get sample input data as a numpy array in a method of your choosing.
yield [input]
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
converter.optimizations = [tf.lite.Optimize.DEFAULT]
converter.representative_dataset = representative_dataset_gen
tflite_quant_model = converter.convert()
```

The resulting model will be fully quantized but still take float input and output for convenience.

Ops that do not have quantized implementations will automatically be left in floating point. This allows conversion to occur smoothly but may restrict deployment to accelerators that support float. To require the converter to only output integer operations, one can specify:

```
converter.target_spec.supported_ops = [tf.lite.OpsSet.TFLITE_BUILTINS_INT8]
```

This makes the converter throw an error if it encounters an operation it cannot currently quantize.

### Float16 quantization of weights

We can reduce the size of a floating point model by quantizing the weights to float16, the IEEE standard for 16 bit floating point numbers. The advantages of this quantization are as follows:

- reduce model size by up to half (since all weights are now half the original size)
- minimal loss in accuracy
- some delegates (e.g. the GPU delegate) can operate directly on float16 data, which results in faster execution than float32 computations.

This quantization may not be a good choice if you need maximum performance (a quantization to fixed point math would be better in that case). To enable float16 quantization of weights, specify "DEFAULT" optimization as above and then specify that float16 is in supported types for the target_spec:

```
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.lite.constants.FLOAT16]
tflite_quant_model = converter.convert()
```

By default, a float16 quantized model will "dequantize" the weights values to float32 when run on the CPU. The GPU delegate will not perform this dequantization, since it can operate on float16 data.

### 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 is a tool to evaluate TensorFlow Lite model accuracy.

If the accuracy drop is too high, consider using quantization aware training.

### Representation for quantized tensors

8-bit quantization approximates floating point values using the following
formula. `real_value = (int8_value - zero_point) * 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.