Optimum Quanto

🤗 Optimum Quanto is a python quantization backend for optimum that provides several features that are either not supported or limited by the base pytorch quantization tools:

• all features are available in eager mode (works with non-traceable models),
• quantized models can be placed on any device (including CUDA and MPS),
• automatically inserts quantization and dequantization stubs,
• automatically inserts quantized functional operations,
• automatically inserts quantized modules (see below the list of supported modules),
• provides a seamless workflow from a float model to a dynamic to a static quantized model,
• serialization compatible with pytorch weight_only and 🤗 safetensors,
• accelerated matrix multiplications on CUDA devices (int8-int8, fp16-int4),
• supports int2, int4, int8 and float8 weights,
• supports int8 and float8 activations.

Features yet to be implemented:

• dynamic activations smoothing,
• kernels for all mixed matrix multiplications on all devices,
• compatibility with torch compiler (aka dynamo).

Quantized modules

Thanks to a seamless propagation mechanism through quantized tensors, only a few modules working as quantized tensors insertion points are actually required.

The following modules can be quantized:

• Linear (QLinear). Weights are always quantized, and biases are not quantized. Inputs and outputs can be quantized.
• Conv2d (QConv2D). Weights are always quantized, and biases are not quantized. Inputs and outputs can be quantized.
• LayerNorm, Weights and biases are not quantized. Outputs can be quantized.

Limitations and design choices

Tensors

At the heart of quanto is a Tensor subclass that corresponds to:

• the projection of a source Tensor into the optimal range for a given destination type,
• the mapping of projected values to the destination type.

For floating-point destination types, the mapping is done by the native pytorch cast (i.e. Tensor.to()).

For integer destination types, the mapping is a simple rounding operation (i.e. torch.round()).

The goal of the projection is to increase the accuracy of the conversion by minimizing the number of:

• saturated values (i.e. mapped to the destination type min/max),
• zeroed values (because they are below the smallest number that can be represented by the destination type)

The projection is symmetric (affine), i.e. it does not use a zero-point. This makes quantized Tensors compatible with many operations.

One of the benefits of using a lower-bitwidth representation is that you will be able to take advantage of accelerated operations for the destination type, which is typically faster than their higher precision equivalents.

The current implementation however falls back to float32 operations for a lot of operations because of a lack of dedicated kernels (only int8 matrix multiplication is available).

Note: integer operations cannot be performed in float16 as a fallback because this format is very bad at representing integer and will likely lead to overflows in intermediate calculations.

Quanto does not support the conversion of a Tensor using mixed destination types.

Modules

Quanto provides a generic mechanism to replace torch modules by optimum-quanto modules that are able to process quanto tensors.

optimum-quanto modules dynamically convert their weights until a model is frozen, which slows down inference a bit but is required if the model needs to be tuned.

Biases are not converted because to preserve the accuracy of a typical addmm operation, they must be converted with a scale that is equal to the product of the input and weight scales, which leads to a ridiculously small scale, and conversely requires a very high bitwidth to avoid clipping. Typically, with int8 inputs and weights, biases would need to be quantized with at least 12 bits, i.e. in int16. Since most biases are today float16, this is a waste of time.

Activations are dynamically quantized using static scales (defaults to the range [-1, 1]). The model needs to be calibrated to evaluate the best activation scales (using a momentum).

Performances

In a nutshell:

• accuracy: models compiled with int8/float8 weights and float8 activations are very close to the 16-bit models,
• latency: all models but those using int4 weights are at least 2x slower than the 16-bit models due to the lack of optimized kernels (for now).
• device memory: approximately divided by float bits / integer bits.

The paragraph below is just an example. Please refer to the bench folder for detailed results per use-case of model.

meta-llama/Meta-Llama-3-8B

Installation

Optimum Quanto is available as a pip package.

pip install optimum-quanto

Quantization workflow

Quanto does not make a clear distinction between dynamic and static quantization: models are always dynamically quantized, but their weights can later be "frozen" to integer values.

A typical quantization workflow would consist of the following steps:

1. Quantize

The first step converts a standard float model into a dynamically quantized model.

from optimum.quanto import qint8

quantize(model, weights=qint8, activations=qint8)

At this stage, only the inference of the model is modified to dynamically quantize the weights.

2. Calibrate (optional if activations are not quantized)

Quanto supports a calibration mode that allows to record the activation ranges while passing representative samples through the quantized model.

with calibration(momentum=0.9):
    model(samples)

This automatically activates the quantization of the activations in the quantized modules.

3. Tune, aka Quantization-Aware-Training (optional)

If the performance of the model degrades too much, one can tune it for a few epochs to recover the float model performance.

model.train()
for batch_idx, (data, target) in enumerate(train_loader):
    data, target = data.to(device), target.to(device)
    optimizer.zero_grad()
    output = model(data).dequantize()
    loss = torch.nn.functional.nll_loss(output, target)
    loss.backward()
    optimizer.step()

4. Freeze integer weights

When freezing a model, its float weights are replaced by quantized integer weights.

freeze(model)

Please refer to the examples for instantiations of that workflow.

Per-axis versus per-tensor

Activations are always quantized per-tensor because most linear algebra operations in a model graph are not compatible with per-axis inputs: you simply cannot add numbers that are not expressed in the same base (you cannot add apples and oranges).

Weights involved in matrix multiplications are, on the contrary, always quantized along their first axis, because all output features are evaluated independently from one another.

The outputs of a quantized matrix multiplication will anyway always be dequantized, even if activations are quantized, because:

• the resulting integer values are expressed with a much higher bitwidth (typically int32) than the activation bitwidth (typically int8),
• they might be combined with a float bias.

Quantizing activations per-tensor to int8 can lead to serious quantization errors if the corresponding tensors contain large outlier values. Typically, this will lead to quantized tensors with most values set to zero (except the outliers).

A possible solution to work around that issue is to 'smooth' the activations statically as illustrated by SmoothQuant. You can find a script to smooth some model architectures under external/smoothquant.

A better option is to represent activations using float8.