Implement **sinusoidal positional encoding** so you can add position information to token embeddings in an NLP model. You’ll generate a matrix where each position has a deterministic encoding based on sine and cosine waves.

The encoding is defined as:
$$
\text{PE}(pos, 2i)=\sin\left(\frac{pos}{10000^{\frac{2i}{d}}}\right),\quad
\text{PE}(pos, 2i+1)=\cos\left(\frac{pos}{10000^{\frac{2i}{d}}}\right)
$$
where $pos$ is the token index (starting at 0), $i$ is the dimension index, and $d$ is the model dimension.

## Requirements

Implement the function
```python
import numpy as np

def positional_encoding(seq_len, d_model):
    \"""
    Builds a sinusoidal positional encoding table.

    Args:
        seq_len (int): Number of token positions in the sequence.
        d_model (int): Embedding dimension (number of features per token).

    Returns:
        np.ndarray: Positional encoding matrix of shape (seq_len, d_model),
        where row `pos` is the encoding for that token position.
    \"""
    # Your solution below
```

**Rules:**
- Use the sinusoidal formula above with positions `pos = 0..seq_len-1`.
- Even dimensions use `sin`, odd dimensions use `cos`.
- Return the result as a **NumPy array**.
- Use only NumPy and Python built-in libraries (no PyTorch/TensorFlow).
- Aim for a vectorized NumPy implementation (avoid deeply nested loops if you can).

## Example

```python
seq_len = 3
d_model = 4

positional_encoding(seq_len, d_model)
```

Output:
```python
array([
  [0.0, 1.0, 0.0, 1.0],
  [0.84147, 0.54030, 0.0099998, 0.99995],
  [0.90930, -0.41615, 0.0199987, 0.99980]
])
```

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Positional encoding

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318. Positional encoding

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Similar Questions

Argument	Type
d_model	int
seq_len	int