The shape tracking is where things get slippery.
Start by clarifying the requirements: input shape, number of heads, masking, and whether to use NumPy or PyTorch. Then outline the steps: linear projections, reshaping for multi-head, scaled dot-product attention with optional mask, concatenation, and final projection. Implement efficiently with vectorized operations, and discuss trade-offs like memory vs. speed.
Pro tip: Mention that you would use `torch.nn.Linear` for projections and `torch.matmul` for batched matrix multiplication, and that you'd verify the implementation against a reference like `torch.nn.MultiheadAttention` to ensure correctness.
Confirm input dimensions, number of heads, masking type (e.g., padding or causal), and framework. Initialize weight matrices for Q, K, V, and output projections.
Apply linear layers to input to get Q, K, V. Reshape from (batch, seq_len, hidden_dim) to (batch, num_heads, seq_len, head_dim) by splitting hidden_dim into num_heads * head_dim.
Compute attention scores as Q @ K^T / sqrt(head_dim). Apply optional mask (e.g., set masked positions to -inf before softmax). Compute softmax and multiply by V.
Reshape attention output back to (batch, seq_len, hidden_dim) by concatenating heads, then apply final linear projection.
Test with a small example, compare with a reference implementation, and discuss computational complexity, memory usage, and potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the SwiGLU architecture and the parallel gate/value projections, then outline the forward pass step-by-step, emphasizing the elementwise multiplication after Swish activation. Discuss implementation details like matrix shapes, activation function, and potential optimizations, and finally mention trade-offs and use cases.
Pro tip: Highlight that SwiGLU often uses a smaller hidden dimension (e.g., 2/3 of the standard 4x) to keep parameter count comparable, and mention that the parallel projections can be fused into a single matrix multiplication for efficiency.
Explain that SwiGLU consists of two parallel linear projections (gate and value) from the input, followed by Swish activation on the gate, elementwise multiplication, and a final output projection.
Describe the computation: given input x, compute gate = Swish(xW_g + b_g) and value = xW_v + b_v, then multiply elementwise, and finally project with W_o + b_o.
Mention matrix dimensions, initialization, and how to implement Swish (x * sigmoid(beta * x), often beta=1). Note that the two projections can be combined into one matrix multiplication for efficiency.
Talk about parameter count, computational cost, and how SwiGLU compares to ReLU/GELU. Mention that the hidden dimension is often reduced (e.g., 2/3 of 4d) to maintain similar parameter count.
If appropriate, sketch a concise PyTorch implementation to demonstrate clarity and correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by outlining the Transformer block architecture: multi-head attention followed by feed-forward network, each wrapped with residual connections and layer normalization. Then, discuss the order of operations (pre-norm vs post-norm) and how to ensure the output shape matches the input. Finally, mention any implementation details like dropout and activation functions.
Pro tip: Emphasize that pre-norm (LayerNorm before sublayer) is more stable for training deep Transformers, but post-norm (original) can work with careful initialization. Also, note that the residual connection requires the sublayer output to have the same dimension as the input, which is typically ensured by projecting to the model dimension.
Describe the multi-head attention and feed-forward network sublayers, including their internal operations and output dimensions.
Explain how to add the input of each sublayer to its output, ensuring shapes match, and discuss why this helps with gradient flow.
Specify where to apply layer normalization (pre-norm or post-norm) and how it normalizes across the feature dimension.
Show the full forward pass: input -> (LayerNorm -> Attention -> Dropout -> Residual) -> (LayerNorm -> FFN -> Dropout -> Residual) -> output, or the post-norm variant.
Confirm that the output shape equals the input shape, typically (batch_size, sequence_length, model_dim), and mention any necessary projections.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by defining the notation and then derive the time and memory complexity for multi-head attention, breaking it down into per-head and aggregated costs. Then explain masking as a per-head operation that applies the same mask to each head's attention scores before softmax, and discuss how it affects complexity. Finally, connect the concepts to practical implications like scalability and implementation.
Pro tip: Emphasize that masking does not change the asymptotic complexity but is crucial for correctness in autoregressive and padded scenarios. Mention that efficient implementations often fuse masking with softmax to avoid extra memory overhead.
Clearly state the dimensions: sequence length n, model dimension d, number of heads h, and per-head dimension d_k = d/h. Assume input and output dimensions are d.
Compute the cost of linear projections (O(n d^2)), attention scores (O(n^2 d)), and output projection (O(n d^2)). Sum and simplify to O(n^2 d + n d^2).
Account for storing inputs, outputs, and intermediate attention matrices. The dominant term is O(n^2 h) for attention scores per head, which simplifies to O(n^2 d) when aggregated.
Describe how masks (e.g., causal or padding) are applied to the attention scores before softmax, independently for each head. The same mask is broadcast across heads.
Note that masking does not alter asymptotic complexity but adds a constant factor. Mention that memory can be reduced by not materializing the full attention matrix if using efficient kernels.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.