Production Engineering: Mini-Batch Training

Implement:

def train_linear_regression_production(
    input: np.ndarray,
    target: np.ndarray,
    lr: float,
    epochs: int,
    batch_size: int,
    seed: int | None = None,
) -> tuple[np.ndarray, np.ndarray]:
    """
    Mini-batch gradient descent, reusing mse_gradient / gd_step per batch
    instead of once per epoch over the full dataset.
    """

Your function should:

1. Shuffle the sample order at the start of every epoch (a different shuffle each epoch, this is what keeps mini-batch gradients from being biased by data order).
2. Split the shuffled data into batches of batch_size (the last batch may be smaller if n_samples doesn't divide evenly, must not crash or silently drop it).
3. Take one gradient step per batch, not per epoch.
4. Never materialize more than one batch's worth of input at a time inside the per-batch step (no operation should touch the full input array once batching starts).
5. Accept an optional seed: when given, two calls with the same seed (and the same everything else) must return exactly the same weight, bias, including across epochs, not just within the first one. When seed is None, training is genuinely random run to run.
6. weight/bias follow 01-hypothesis-function's convention: weight shape (1, in_features), bias shape (1,), never squeezed.