This is where I spent most of my mental energy.
Start by defining the input tensors and their shapes, then walk through the linear projections to obtain Q, K, and V. Compute the scaled dot-product scores, apply optional masking, normalize with softmax, and finally multiply by V to get the output. Emphasize the scaling factor and mask handling as critical details.
Pro tip: Mention that the scaling factor 1/sqrt(d_k) prevents the dot products from growing too large, which would push softmax into regions with tiny gradients. Also, note that masking is typically done by adding a large negative value (e.g., -1e9) to the scores before softmax, and that this is essential for autoregressive decoding and padding.
Specify the input tensor X of shape (batch_size, seq_len, d_model) and the projection weight matrices W_Q, W_K, W_V each of shape (d_model, d_k).
Perform linear projections: Q = X @ W_Q, K = X @ W_K, V = X @ W_V, resulting in tensors of shape (batch_size, seq_len, d_k).
Calculate attention scores as S = (Q @ K^T) / sqrt(d_k), giving shape (batch_size, seq_len, seq_len).
If a mask is provided (e.g., for padding or causal attention), add a large negative value to masked positions in S to zero out their softmax probabilities.
Compute attention weights A = softmax(S, dim=-1), then output O = A @ V, resulting in shape (batch_size, seq_len, d_k).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the input shapes and label formats, then outline the mathematical steps: compute logits, apply log-softmax for numerical stability, gather the correct class log-probabilities, and average the negative log-likelihood. Write clean pseudocode that handles both class indices and one-hot labels, and mention edge cases like ignoring padding or class weights.
Pro tip: Emphasize numerical stability by using log-softmax instead of separate softmax and log operations, and explicitly state that you would use a gather operation for index labels to avoid unnecessary one-hot expansion. This shows you understand both correctness and efficiency in production ML code.
Confirm that logits have shape (batch_size, num_classes), labels can be either class indices (batch_size,) or one-hot (batch_size, num_classes), and the output is a scalar mean loss.
Use the log-softmax trick: subtract the max logit per example for numerical stability, then compute log_sum_exp and subtract it from each logit.
If labels are indices, gather the log-probability at the true class index for each example. If labels are one-hot, compute the dot product between log-probabilities and labels.
Take the negative of the extracted log-probabilities to get per-example losses, then return the mean over the batch as a scalar.
Mention ignoring padding indices (e.g., -100), applying class weights if needed, and using efficient operations like gather instead of one-hot expansion for index labels.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I gave the textbook answer about attention mixing information across positions while the FFN applies a nonlinear transformation independently at each position.
Start by clearly defining the FFN's role as a position-wise transformation that adds non-linear capacity and feature mixing after attention aggregates context. Then explain why attention alone is insufficient: it's a weighted sum (linear) and lacks per-token non-linearity and channel-wise interactions. Finally, connect to practical benefits like increased model capacity, better representation learning, and efficiency via parameter sharing across positions.
Pro tip: Emphasize that the FFN operates independently on each position, which is crucial for parallelization and efficiency, and mention that the expansion factor (e.g., 4x) is a key hyperparameter that balances capacity and compute. This shows you understand both theory and practical trade-offs.
Describe the FFN as two linear layers with a non-linear activation (e.g., ReLU, GELU) applied identically to each position. Mention the typical expansion factor (e.g., 4x) and that it's position-wise (shared weights across positions).
State that it introduces non-linearity and enables channel-wise interactions, transforming each token's representation independently. It acts as a key-value memory or feature enhancer after attention.
Highlight that attention is a linear weighted sum that mixes information across positions but lacks non-linear transformations. Without FFN, the model would be limited to linear combinations of value vectors, reducing expressive power.
Explain that the FFN adds model capacity and depth, allowing the network to learn complex functions. It also provides a bottleneck that can compress and expand representations, improving generalization.
Mention that the FFN is computationally efficient due to parallelization across positions and that its design (e.g., expansion factor) is a trade-off between performance and resource usage, relevant for large-scale systems like TikTok.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by explaining that dividing by sqrt(d_k) prevents the dot products from growing too large in magnitude, which would push softmax into regions with tiny gradients. Then connect this to training stability and the mathematical reasoning behind the scaling factor, emphasizing its role in maintaining well-behaved attention distributions.
Pro tip: Mention that without scaling, the softmax saturates and gradients vanish, making training unstable—this shows you understand the practical implications beyond just the formula. Also, note that the scaling factor is derived from the variance of the dot product under the assumption of independent components, demonstrating deeper mathematical insight.
Explain that attention scores are computed as dot products between queries and keys, and that as the dimension d_k grows, the variance of these dot products increases.
Describe how large magnitude scores cause the softmax to saturate, leading to extremely small gradients and hindering learning.
State that dividing by sqrt(d_k) normalizes the variance to approximately 1, keeping the scores in a range where softmax gradients are healthy.
Emphasize that this scaling is crucial for stable and efficient training of Transformer models, preventing vanishing gradients and allowing deeper architectures.
Note that this is a standard practice in Transformer implementations and that understanding it is key for debugging and optimizing attention mechanisms.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.