Applied intuition·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Applied Intuition ML engineer interview, technical phone screen focused entirely on Transformer internals. One meaty question about positional encodings that took up basically the whole session.

Questions Asked (1)

Implement positional encodings for a Transformer language model. Walk through sinusoidal vs learned approaches, write PyTorch code to compute and add them to token embeddings, explain the math and tensor shapes, integrate into the full model, and describe what breaks if you skip positional info entirely and how you'd verify the fix.

System DesignTechnical Trade-offsAlgorithms & Data Structures

Author's notes

This was a lot to unpack in one question.

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AI HintsAI Generated

Suggested Approach

Start by contrasting sinusoidal and learned positional encodings, then implement sinusoidal encoding in PyTorch, add it to token embeddings, and integrate into a Transformer model. Explain the math and tensor shapes, and discuss the consequences of omitting positional information and how to verify the fix.

Pro tip: Mention that sinusoidal encodings can extrapolate to longer sequences than seen during training, which is crucial for deployment, and that learned embeddings are simpler but require fixed maximum length.

1. Compare sinusoidal vs learned positional encodings

Discuss the trade-offs: sinusoidal are fixed, parameter-free, and allow extrapolation; learned are trainable, flexible, but limited to seen lengths and add parameters.

2. Implement sinusoidal positional encoding in PyTorch

Write a function that computes the sinusoidal encoding matrix using sine and cosine functions with different frequencies, and returns a tensor of shape (max_len, d_model).

3. Add positional encodings to token embeddings

In the model's forward pass, slice the positional encoding to the sequence length and add it to the token embeddings, ensuring shapes match: (batch_size, seq_len, d_model).

4. Integrate into the full Transformer model

Show how to incorporate the positional encoding into the embedding layer of a Transformer, either by precomputing and adding or by using a buffer that is not a parameter.

5. Explain what breaks without positional info and how to verify

Without positional encodings, the model treats sequences as bags of words, losing order information; verify by testing on tasks requiring order (e.g., sequence reversal) and checking that the model fails without and succeeds with positional encodings.

Key Points to Mention

Sinusoidal encodings use sine and cosine functions of different frequencies: PE(pos, 2i) = sin(pos / 10000^(2i/d_model)), PE(pos, 2i+1) = cos(pos / 10000^(2i/d_model)).
Learned positional embeddings are typically implemented as an nn.Embedding layer with a fixed maximum sequence length.
Tensor shapes: token embeddings are (batch_size, seq_len, d_model); positional encodings are (seq_len, d_model) and broadcast to batch.
Without positional encodings, the self-attention mechanism is permutation equivariant, so the model cannot distinguish word order.
Verification: train a small Transformer on a toy task like sequence reversal or sorting; without positional encodings, it will fail to learn, but with them, it will succeed.
Sinusoidal encodings can be precomputed and stored as a buffer, not a parameter, to avoid updating during training.

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