Currently, I find if I use a smooth window then I’ll get a better result than tensorflow smooth function. So I deep into the smooth function of tensorboard.

Tensorboard smooth function is explained here and used here.

It’s source code as follows

private resmoothDataset(dataset: Plottable.Dataset) {
  let data = dataset.data();
  const smoothingWeight = this.smoothingWeight;
  let last = data.length > 0 ? data[0].scalar : NaN;
  data.forEach((d) => {
    if (!_.isFinite(last)) {
      d.smoothed = d.scalar;
    } else {
      // 1st-order IIR low-pass filter to attenuate the higher-
      // frequency components of the time-series.
      d.smoothed = last * smoothingWeight + (1 - smoothingWeight) * d.scalar;
    }
    last = d.smoothed;
  });
}

which can be rewrote in python as follows:

def smooth(scalars, weight):  # 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

It’s a recursive function and we summarized its formula below,

$$\left\{\begin{matrix} f(0) &=& data[0] \\ f(t) &=& f(t-1)*w + (1-w)*data[t] \end{matrix}\right.$$

where $data$ is our original data, $t$ is the iteration steps, and $w$ is the smooth weigths which is shown as a scroll widgets in tensorboard.