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I got through the mechanics fine: compute Q, K, V projections, dot Q with K-transpose, scale, softmax, multiply by V.
Start by defining the inputs (Q, K, V) and their dimensions, then outline the steps: compute attention scores via dot product, scale by sqrt(d_k), apply softmax, and compute weighted sum with V. Write clear pseudocode with matrix operations, and mention masking for decoder self-attention if relevant.
Pro tip: Mention that scaling by sqrt(d_k) prevents softmax saturation and vanishing gradients, and note that efficient implementations use optimized matrix multiplication libraries or fused kernels like FlashAttention.
Specify queries (Q), keys (K), values (V) with shapes (batch_size, seq_len, d_k) and (batch_size, seq_len, d_v). Mention that d_k is the dimension of queries and keys.
Compute the dot product between Q and K^T to get raw attention scores of shape (batch_size, seq_len, seq_len).
Divide the scores by sqrt(d_k) to stabilize gradients and prevent softmax saturation.
Apply softmax over the last dimension to get attention weights. If needed (e.g., decoder self-attention), apply a mask before softmax to prevent attending to future positions.
Multiply the attention weights by V to produce the final output of shape (batch_size, seq_len, d_v).
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Start by clarifying the scope: cross-entropy loss for binary vs. multi-class classification, and whether logits or probabilities are given. Then outline the mathematical formula and translate it into clear pseudocode, handling numerical stability (e.g., log-sum-exp trick) and edge cases.
Pro tip: Mention that in practice, frameworks like PyTorch combine softmax and cross-entropy for numerical stability, so pseudocode should reflect that by taking logits directly. Also, discuss how to handle class imbalance or label smoothing if relevant.
Ask whether the question refers to binary or multi-class cross-entropy, and whether inputs are probabilities or logits. This determines the formula and implementation details.
For multi-class: L = -sum(y_i * log(p_i)). For binary: L = -(y*log(p) + (1-y)*log(1-p)). Explain that y is the true label (one-hot) and p is predicted probability.
Define function signature, input shapes, and steps: compute softmax if logits, then compute log probabilities, then gather the log probability of the true class, then average over batch.
Use the log-sum-exp trick: log_softmax = logits - max(logits) - log(sum(exp(logits - max(logits)))). This avoids overflow/underflow.
Write clear pseudocode with comments, then walk through a small example (e.g., 3 classes, batch size 2) to verify correctness.
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Start by defining the position-wise feed-forward network (FFN) as a two-layer MLP applied independently to each position, then explain its role in transforming and enriching token representations. Emphasize how it complements self-attention by introducing non-linearity and increasing model capacity, and discuss trade-offs like parameter count and computational cost.
Pro tip: Highlight that the FFN is where most of the model's parameters reside, and relate its design to practical considerations like model scaling and inference latency—showing you understand both theory and engineering trade-offs.
Describe the FFN as a position-wise two-layer MLP with a non-linear activation (e.g., ReLU, GELU) applied identically to each token independently.
Explain that it transforms each token's representation, adding non-linearity and enabling the model to learn complex features beyond what attention can capture.
Contrast the FFN with self-attention: attention mixes information across positions, while the FFN processes each position separately, providing a complementary form of computation.
Discuss trade-offs: the FFN holds most parameters, impacting memory and compute; its expansion ratio (e.g., 4x) balances capacity and efficiency.
Connect to system design: the FFN's size affects model parallelism, inference latency, and hardware utilization, which are critical for deployment at scale.
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Start by explaining the purpose of scaling in dot-product attention: to prevent the softmax from saturating due to large dot products. Then derive the variance of the dot product under the assumption of independent components, showing that it grows with the key dimension, and explain how dividing by the square root of that dimension stabilizes the variance to 1. Conclude by discussing the practical benefits: improved gradient flow, faster convergence, and numerical stability.
Pro tip: Mention that while the scaling factor is standard, some variants use learned scaling or different normalizations; showing awareness of such alternatives demonstrates depth and practical experience.
Explain that attention scores are computed as dot products between queries and keys, and that these scores are passed through a softmax to obtain attention weights.
Assume query and key components are independent with zero mean and unit variance. Show that the dot product has variance equal to the key dimension, so its standard deviation is the square root of that dimension.
Describe how large dot products cause the softmax to produce near-one-hot distributions, leading to vanishing gradients and poor learning.
Show that dividing by the square root of the key dimension normalizes the variance back to 1, keeping the softmax in a well-behaved region.
Highlight that this scaling improves gradient flow, accelerates convergence, and enhances numerical stability, which is crucial for training deep transformers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.