208. Backprop: Embedding lookup

Hand-derive the gradient of L = sum(W[indices]) w.r.t. the embedding table W.

Forward: y = W[indices] — gather rows of W according to the integer index array indices. L = sum(y).

Implement:

• embedding_forward(W, indices) -> y of shape indices.shape + (embed_dim,)
• embedding_backward(W, indices) -> dL/dW of shape (vocab_size, embed_dim)

The trick: indices may repeat. If token i appears k times in indices, then W[i] contributes k copies to the sum, so dL/dW[i] = k * ones(embed_dim). Indices that don't appear get zero rows.

This is also called scatter-add in autograd land — the backward of a gather is a scatter that accumulates duplicates.