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Implement and analyze custom attention | Anthropic Interview Question

Quick Overview

This question evaluates implementation and analysis skills for scaled dot-product attention, testing competencies in efficient tensorized PyTorch coding, numerical stability and mixed-precision handling, masking semantics (causal and padding), multi-head shape correctness, and unit-test validation including gradient and edge-case behavior.

Implement Scaled Dot-Product Attention in PyTorch (from scratch)

Context

You will implement a numerically stable, vectorized scaled dot-product attention module in PyTorch and validate it with unit tests. Assume Q, K, V can have different sequence lengths (Lq vs Lk) and optionally multiple heads.

Requirements

Implementation
- Create a PyTorch module that computes scaled dot-product attention:
  - Inputs: Q ∈ R^{B×H×Lq×d_k}, K ∈ R^{B×H×Lk×d_k}, V ∈ R^{B×H×Lk×d_v} (allow H=1 when working without heads; also accept 3D by treating it as H=1).
  - Compute scores S = Q K^T, apply scaling by 1/sqrt(d_k) (unless a custom scale is provided).
  - Support masking:
    - Causal mask (upper-triangular).
    - Padding/attention masks (broadcastable to B×H×Lq×Lk). Boolean masks should treat True as "masked out"; additive masks should be added to scores (e.g., 0 for keep, -inf for disallow).
  - Apply numerically stable softmax to get attention weights; apply optional dropout on weights.
  - Return both attention output (B×H×Lq×d_v) and attention weights (B×H×Lq×Lk).
  - Ensure fp16/bf16 inputs are handled by upcasting to float32 for the softmax and downcasting afterward.
  - Ensure rows that are fully masked produce zero attention weights and zero outputs (no NaNs).
Tests
- Shape correctness: multiple heads, different Lq and Lk, different d_k and d_v.
- Gradient flow: backprop from a scalar loss; gradients are finite and nonzero for Q, K, V.
- Numerical stability: very large-magnitude Q/K should not produce NaNs/Inf; rows fully masked should produce zero weights/output.
- Masking correctness: padding mask and causal mask both behave as expected.
Explanations
- Explain why scaling by 1/sqrt(d_k) is used (variance control, softmax non-saturation) with a short derivation/intuition.
- Clarify when and why you apply normalization:
  - Softmax for attention weights (across keys for each query).
  - LayerNorm (or RMSNorm) around the attention block for training stability, not as a replacement for softmax.
- Analyze time and memory complexity.
- Propose optimizations for long sequences.

Quick Overview

Requirements

Implementation

Create a PyTorch module that computes scaled dot-product attention:
- Inputs: Q ∈ R^{B×H×Lq×d_k}, K ∈ R^{B×H×Lk×d_k}, V ∈ R^{B×H×Lk×d_v} (allow H=1 when working without heads; also accept 3D by treating it as H=1).
- Compute scores S = Q K^T, apply scaling by 1/sqrt(d_k) (unless a custom scale is provided).
- Support masking:
  - Causal mask (upper-triangular).
  - Padding/attention masks (broadcastable to B×H×Lq×Lk). Boolean masks should treat True as "masked out"; additive masks should be added to scores (e.g., 0 for keep, -inf for disallow).
- Apply numerically stable softmax to get attention weights; apply optional dropout on weights.
- Return both attention output (B×H×Lq×d_v) and attention weights (B×H×Lq×Lk).
- Ensure fp16/bf16 inputs are handled by upcasting to float32 for the softmax and downcasting afterward.
- Ensure rows that are fully masked produce zero attention weights and zero outputs (no NaNs).

Tests

Shape correctness: multiple heads, different Lq and Lk, different d_k and d_v.
Gradient flow: backprop from a scalar loss; gradients are finite and nonzero for Q, K, V.
Numerical stability: very large-magnitude Q/K should not produce NaNs/Inf; rows fully masked should produce zero weights/output.
Masking correctness: padding mask and causal mask both behave as expected.

Explanations

Explain why scaling by 1/sqrt(d_k) is used (variance control, softmax non-saturation) with a short derivation/intuition.
Clarify when and why you apply normalization:
- Softmax for attention weights (across keys for each query).
- LayerNorm (or RMSNorm) around the attention block for training stability, not as a replacement for softmax.
Analyze time and memory complexity.
Propose optimizations for long sequences.

Implement and analyze custom attention

Quick Overview

Implement and analyze custom attention

Implement Scaled Dot-Product Attention in PyTorch (from scratch)

Context

Requirements

Write your answer

Implement and analyze custom attention

Quick Overview

Implement and analyze custom attention

Implement Scaled Dot-Product Attention in PyTorch (from scratch)

Context

Requirements

Write your answer