The Same Activation, Two Different Outputs

One neuron in a deep network is followed by a Batch Normalization layer whose learned parameters are

$\gamma = 3.0, \qquad \beta = -0.5$

Entering this training step, the layer is carrying the running estimates

$\mu_{\text{run}} = 6.0, \qquad \sigma^{2}_{\text{run}} = 13.0$

1. The training step. A mini-batch of $m = 4$ examples reaches this neuron with pre-normalization activations

$\mathbf{x} = [\,1.0,\; 7.0,\; 9.0,\; 15.0\,]$

In training mode the layer standardizes with the mini-batch's own statistics:

$\mu_B = \frac{1}{m}\sum_{i=1}^{m} x_i, \qquad \sigma_B^{2} = \frac{1}{m}\sum_{i=1}^{m}\left(x_i - \mu_B\right)^{2}$

$\hat{x} = \frac{x - \mu_B}{\sqrt{\sigma_B^{2} + \epsilon}}, \qquad y = \gamma\,\hat{x} + \beta$

Take $\epsilon = 0$ throughout.

2. The running-statistics update. Once the batch statistics are computed, the layer refreshes both running estimates with momentum $\alpha = 0.25$:

$\mu_{\text{run}} \leftarrow (1-\alpha)\,\mu_{\text{run}} + \alpha\,\mu_B, \qquad \sigma^{2}_{\text{run}} \leftarrow (1-\alpha)\,\sigma^{2}_{\text{run}} + \alpha\,\sigma_B^{2}$

3. The evaluation step. Training then stops and the model is switched to evaluation mode. An input arrives that produces the same pre-normalization activation at this neuron, $x = 15.0$. In evaluation mode the layer substitutes its running estimates for the batch statistics; $\gamma$ and $\beta$ are unchanged.

Let $y_{\text{train}}$ be this layer's output for $x = 15.0$ during the training step, and $y_{\text{eval}}$ its output for $x = 15.0$ in evaluation mode.

What is $y_{\text{eval}} - y_{\text{train}}$?

Round your answer to 3 decimal places.