def METHOD_NAME(self, x_1x, scales):
    """
    Hierarchical attention, primarily used for getting best inference
    results.
    We use attention at multiple scales, giving priority to the lower
    resolutions. For example, if we have 4 scales {0.5, 1.0, 1.5, 2.0},
    then evaluation is done as follows:
          p_joint = attn_1.5 * p_1.5 + (1 - attn_1.5) * down(p_2.0)
          p_joint = attn_1.0 * p_1.0 + (1 - attn_1.0) * down(p_joint)
          p_joint = up(attn_0.5 * p_0.5) * (1 - up(attn_0.5)) * p_joint
    The target scale is always 1.0, and 1.0 is expected to be part of the
    list of scales. When predictions are done at greater than 1.0 scale,
    the predictions are downsampled before combining with the next lower
    scale.
    x_1x:
      scales - a list of scales to evaluate
      x_1x - dict containing 'images', the x_1x, and 'gts', the ground
               truth mask
    Output:
      If training, return loss, else return prediction + attention
    """
    assert 1.0 in scales, 'expected 1.0 to be the target scale'
    # Lower resolution provides attention for higher rez predictions,
    # so we evaluate in order: high to low
    scales = sorted(scales, reverse=True)
    pred = None
    for s in scales:
        x = nn.functional.interpolate(
            x_1x,
            scale_factor=s,
            align_corners=self.align_corners,
            mode='bilinear')
        outs = self.single_scale_forward(x)
        cls_out = outs['cls_out']
        attn_out = outs['logit_attn']
        if pred is None:
            pred = cls_out
        elif s >= 1.0:
            # downscale previous
            pred = scale_as(pred, cls_out, self.align_corners)
            pred = cls_out * attn_out + pred * (1 - attn_out)
        else:
            # s < 1.0: upscale current
            cls_out = cls_out * attn_out
            cls_out = scale_as(cls_out, pred, self.align_corners)
            attn_out = scale_as(attn_out, pred, self.align_corners)
            pred = cls_out + pred * (1 - attn_out)
    return [pred]