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42. Positional embeddings for images
GeneralPositional embeddings help a vision model keep track of where each patch/token came from in an image, so spatial layout isn’t lost when you flatten patches into a sequence. In this task, you’ll generate 2D sinusoidal positional embeddings for an image grid, similar to what’s used in Vision Transformers.
The 2D sinusoidal embedding is formed by concatenating 1D embeddings for row and column positions:
where each 1D embedding uses
Requirements
Implement the function
Rules:
- Use 2D embeddings by concatenating row and column sinusoidal embeddings, each of size
d_model/2. - Return a NumPy array of shape
(height * width, d_model). - Use row-major order: index
idx = y * width + xcorresponds to position(y, x). - Do not call any prebuilt positional embedding utilities (e.g., from transformers).
- Use NumPy for vectorized computation.
Example
Output:
| Argument | Type |
|---|---|
| width | int |
| height | int |
| d_model | int |
| Return Name | Type |
|---|---|
| value | np.ndarray |
Constraints
Return NumPy array.
Output shape (height*width, d_model)
d_model must be even; half uses sin/cos
Hint 1
Split d_model into two halves: half = d_model//2 for rows and columns, and ensure d_model is even.
Hint 2
Implement a reusable 1D sinusoidal embedding builder: precompute denom = 10000 ** (2*i/half) for i=0..half/2-1, then fill even indices with sin(pos/denom) and odd with cos(pos/denom).
Hint 3
Precompute row_emb for all y and col_emb for all x. Use repeat or tile to create grids, then concat and reshape.
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Python Editor