Apple·Software Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Apple SWE interview that went deep into transformer internals. One question, but it had a lot of layers to it and I definitely underestimated how much they'd want on the complexity and numerical stability side.

Questions Asked (1)

Implement multi-head self-attention from scratch in PyTorch or NumPy. Given an input tensor of shape (batch_size, seq_len, d_model), write the full forward pass including linear projections for Q, K, V; splitting into h heads; scaled dot-product attention with optional padding and causal masks; head concatenation; and the output projection. Walk through the shape of every intermediate tensor, analyze time and memory complexity, and explain numerical stability concerns like softmax scaling and mixed precision.

System DesignTechnical Trade-offsAlgorithms & Data Structures

Author's notes

I got through the core implementation fine but stumbled when they pushed on shapes during the head-split step.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by outlining the overall architecture and tensor shapes, then implement each component step-by-step with clear comments on shape transformations. Emphasize the mathematical operations and complexity, and discuss practical considerations like masking and numerical stability.

Pro tip: Demonstrate awareness of production concerns by mentioning memory-efficient attention variants (e.g., FlashAttention) and how mixed precision affects softmax stability, showing you think beyond the basic implementation.

1. Clarify requirements and outline architecture

Restate the problem: implement multi-head self-attention with optional masks. Sketch the high-level flow: linear projections, head splitting, attention, concatenation, output projection.

2. Implement linear projections and head splitting

Write code for Q, K, V linear layers. Reshape and transpose to split into h heads. Track shapes: (batch, seq, d_model) -> (batch, seq, h, d_k) -> (batch, h, seq, d_k).

3. Implement scaled dot-product attention with masks

Compute scores = Q @ K^T / sqrt(d_k), apply padding and causal masks, softmax, then weighted sum with V. Handle mask broadcasting and numerical stability.

4. Concatenate heads and apply output projection

Transpose and reshape heads back to (batch, seq, d_model), then apply final linear layer. Verify shapes match input.

5. Analyze complexity and numerical stability

Discuss time O(n^2 d) and memory O(n^2 + n d) complexity. Explain softmax scaling, mask handling, and mixed precision concerns (e.g., using float32 for softmax).

Key Points to Mention

Tensor shape transformations at each step, especially head splitting and merging.
Scaling factor 1/sqrt(d_k) to prevent softmax saturation.
Masking techniques: additive masks with -inf for padding and causal masks.
Time and memory complexity: O(n^2 d) time, O(n^2) memory for attention matrix.
Numerical stability: subtract max before softmax, use float32 for softmax in mixed precision.
Potential optimizations: memory-efficient attention, kernel fusion, and use of einsum for clarity.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.