# larq.quantizers¶

A Quantizer defines the way of transforming a full precision input to a quantized output and the pseudo-gradient method used for the backwards pass.

## ste_sign¶

ste_sign(x)


Sign binarization function. $q(x) = \begin{cases} -1 & x < 0 \\ 1 & x \geq 0 \end{cases}$

The gradient is estimated using the Straight-Through Estimator (essentially the binarization is replaced by a clipped identity on the backward pass). $\frac{\partial q(x)}{\partial x} = \begin{cases} 1 & \left|x\right| \leq 1 \\ 0 & \left|x\right| > 1 \end{cases}$

Arguments

• x: Input tensor.

Returns

Binarized tensor.

References

## approx_sign¶

approx_sign(x)


Sign binarization function. $q(x) = \begin{cases} -1 & x < 0 \\ 1 & x \geq 0 \end{cases}$

The gradient is estimated using the ApproxSign method. $\frac{\partial q(x)}{\partial x} = \begin{cases} (2 - 2 \left|x\right|) & \left|x\right| \leq 1 \\ 0 & \left|x\right| > 1 \end{cases}$

Arguments

• x: Input tensor.

Returns

Binarized tensor.

References

## magnitude_aware_sign¶

magnitude_aware_sign(x)


Magnitude-aware sign for Bi-Real Net.

Arguments

• x: Input tensor

Returns

Scaled binarized tensor (with values in $\{-a, a\}$, where $a$ is a float).

References

## SteTern¶

SteTern(threshold_value=0.1, ternary_weight_networks=False)


Ternarization function. $q(x) = \begin{cases} +1 & x > \Delta \\ 0 & |x| > \Delta \\ -1 & x < \Delta \end{cases}$

where $\Delta$ is defined as the threshold and can be passed as an argument, or can be calculated as per the Ternary Weight Networks original paper, such that

$\Delta = \frac{0.7}{n} \sum_{i=1}^{n} |W_i|$ where we assume that $W_i$ is generated from a normal distribution.

The gradient is estimated using the Straight-Through Estimator (essentially the Ternarization is replaced by a clipped identity on the backward pass). $\frac{\partial q(x)}{\partial x} = \begin{cases} 1 & \left|x\right| \leq 1 \\ 0 & \left|x\right| > 1 \end{cases}$

Arguments

• x: Input tensor.
• threshold value: The value for the threshold, $\Delta$.
• ternary_weight_networks: Boolean of whether to use the Ternary Weight Networks threshold calculation.

Returns

Ternarized tensor.

References