Implement multi-head self-attention correctly

Implement multi-head self-attention from scratch in PyTorch or NumPy. Given input X with shape (batch_size, seq_len, d_model), implement linear projections for Q, K, and V; split into h heads (d_k = d_model / h); compute scaled dot-product attention with optional padding and causal masks; then concatenate heads and apply an output projection. Ensure all tensor shapes and transpositions are correct. Provide the forward pass, explain the shape of each intermediate tensor, analyze time and memory complexity, and discuss numerical stability considerations (e.g., softmax scaling and mixed precision).