Implement **global norm gradient clipping**, a common trick in optimization to prevent exploding gradients during training. Given a list of gradient vectors, you’ll scale them down only if their combined (global) L2 norm is too large.

The clipping rule is:
$$
\text{scale} = \min\left(1,\ \frac{\text{max\_norm}}{\sqrt{\sum_i \|g_i\|_2^2}}\right),\quad g_i' = \text{scale}\cdot g_i
$$

## Requirements

Implement the function
```python
import numpy as np

def clip_gradients(grads, max_norm):
    \"""
    Applies global norm gradient clipping.

    Args:
        grads (list[np.ndarray]): A list of gradient vectors (each is a 1D np.ndarray).
        max_norm (float): The maximum allowed global L2 norm.

    Returns:
        list[np.ndarray]: Clipped gradients, same nested-list structure as `grads`.
    \"""
    # Your solution below
```

**Rules:**
- Compute the **global L2 norm** across all gradients in `grads` (treat all entries as one long vector).
- If the global norm is `<= max_norm`, return gradients unchanged (numerically, same values).
- Otherwise, multiply every value in every gradient vector by a single shared `scale`.
- Use NumPy for the math; don’t use any deep learning framework utilities.
- Keep the output as a list of **NumPy arrays**.

## Example

```python
grads = [
    np.array([3.0, 4.0]),   # norm = 5
    np.array([0.0, 12.0])   # norm = 12
]
max_norm = 10.0

clip_gradients(grads, max_norm)
```

Output:
```python
[
    array([2.3077, 3.0769]),
    array([0.0, 9.2308])
]
```

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L1 and L2 norms

Gradient clipping

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1293. Gradient clipping

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Constraints

Similar Questions

Argument	Type
grads	list
max_norm	float