What is the mathematics behind the “smoothing” parameter in TensorBoard's scalar graphs?

Question

I presume it is some kind of moving average, but the valid range is between 0 and 1.

Answer 1

It is called exponential moving average, below is a code explanation how it is created.

Assuming all the real scalar values are in a list called scalars the smoothing is applied as follows:

def smooth(scalars: List[float], weight: float) -> List[float]:  # Weight between 0 and 1
    last = scalars[0]  # First value in the plot (first timestep)
    smoothed = list()
    for point in scalars:
        smoothed_val = last * weight + (1 - weight) * point  # Calculate smoothed value
        smoothed.append(smoothed_val)                        # Save it
        last = smoothed_val                                  # Anchor the last smoothed value

    return smoothed