Dandy·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

Technical screen for an ML Engineer role at Dandy. One question, pretty deep on neural network fundamentals. Left feeling like I either nailed it or completely missed what they were actually probing for.

Questions Asked (1)

If you replace every activation function in a deep neural network with the identity function y = x, what happens to the network's expressive power? Walk through why depth stops mattering, why non-linear functions become unrepresentable, and when you'd actually want identity activations on purpose.

Technical Trade-offsAlgorithms & Data Structures

Author's notes

I knew the core answer: stacking linear layers just collapses to a single linear transformation because composing affine maps gives you another affine map.

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AI HintsAI Generated

Suggested Approach

Start by explaining that replacing all activation functions with the identity collapses the network into a single linear transformation, regardless of depth. Then discuss how this eliminates non-linear expressiveness, making the network equivalent to a linear model. Finally, mention scenarios where identity activations are intentionally used, such as in linear bottlenecks or residual connections.

Pro tip: Emphasize that the composition of linear functions is still linear, so depth becomes irrelevant. Also, note that identity activations can be useful in specific architectures like ResNets or when implementing linear autoencoders.

1. Define the identity activation

Clarify that the identity function returns the input unchanged, so each neuron's output is a linear combination of its inputs.

2. Show that composition of linear functions is linear

Explain that multiplying weight matrices across layers yields a single linear transformation, so depth adds no expressive power.

3. Discuss loss of non-linear expressiveness

Highlight that without non-linear activations, the network cannot approximate non-linear functions, limiting it to linear decision boundaries.

4. Identify when identity activations are useful

Mention cases like linear autoencoders, residual connections, or when a layer is intended to be a linear projection.

Key Points to Mention

Composition of linear functions is linear: W2(W1x) = (W2W1)x
Depth becomes irrelevant because the network reduces to a single linear layer
Non-linear functions (e.g., XOR, circles) become unrepresentable
Identity activations are used in linear bottlenecks, residual connections, and linear autoencoders
The universal approximation theorem requires non-linear activations
Practical implications: training such a network is equivalent to training a linear model

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