Normalize a sequence of batches while maintaining running per-feature extrema. Initialize each running minimum to $+\infty$ and each running maximum to $-\infty$. For every incoming batch, update both arrays before normalizing that batch:

Here, $m_j$ and $M_j$ are the updated running minimum and maximum for feature $j$, and $\varepsilon$ is eps. Return normalized_batches as a list of NumPy arrays and the final min and max arrays in a dictionary.