LinkedIn·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

LinkedIn ML Engineer interview that went deep on optimization theory. One question on Adam took up a big chunk of time and I wasn't fully prepared for how far they'd push on the intuition behind it.

Questions Asked (1)

Walk through how Adam works, including its first and second moment estimates, the bias correction step, and the per-parameter update rule. Then explain why dividing by the square root of the second moment adapts the learning rate per parameter, how that connects to RMSProp, and what it means for sparse or unevenly scaled gradients.

Technical Trade-offsAlgorithms & Data Structures

Author's notes

I got the mechanics down fine, m_t and v_t, bias correction, the update formula.

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AI HintsAI Generated

Suggested Approach

Start by defining Adam's core components: first and second moment estimates, bias correction, and the update rule. Then explain how the second moment enables per-parameter adaptive learning rates, drawing parallels to RMSProp and highlighting benefits for sparse or unevenly scaled gradients. Use clear notation and emphasize the intuition behind each step.

Pro tip: Connect Adam's design to practical scenarios like NLP with sparse features or recommendation systems with uneven gradients, showing you understand both theory and real-world impact. Mention that while Adam often works well out-of-the-box, its adaptive nature can sometimes lead to suboptimal convergence, so knowing when to switch to SGD with momentum is valuable.

1. Define the moment estimates

Explain that Adam maintains exponential moving averages of the gradient (first moment, m_t) and its square (second moment, v_t), with decay rates β1 and β2. Provide the update equations: m_t = β1*m_{t-1} + (1-β1)*g_t and v_t = β2*v_{t-1} + (1-β2)*g_t^2.

2. Describe bias correction

Explain that because m_t and v_t are initialized at zero, they are biased toward zero, especially early in training. Introduce bias-corrected estimates: m_hat_t = m_t / (1 - β1^t) and v_hat_t = v_t / (1 - β2^t), which counteract this initialization bias.

3. State the per-parameter update rule

Present the update: θ_t = θ_{t-1} - α * m_hat_t / (sqrt(v_hat_t) + ε), where α is the step size and ε is a small constant for numerical stability. Emphasize that this is applied element-wise to each parameter.

4. Explain adaptive learning rates and RMSProp connection

Discuss how dividing by sqrt(v_hat_t) scales the learning rate inversely to the gradient's recent magnitude. Connect this to RMSProp, which uses a similar denominator but without bias correction and without the first moment. Adam can be seen as RMSProp with momentum and bias correction.

5. Discuss implications for sparse and uneven gradients

Explain that parameters with infrequent or small gradients get larger effective learning rates because their v_t is small, while those with frequent or large gradients get smaller updates. This makes Adam effective for sparse data (e.g., embeddings) and problems with unevenly scaled gradients.

Key Points to Mention

First moment (m_t) is the mean of gradients, providing momentum.
Second moment (v_t) is the uncentered variance of gradients, used for scaling.
Bias correction is crucial for early training steps when estimates are biased toward zero.
The update rule uses m_hat_t / (sqrt(v_hat_t) + ε) to adapt per-parameter learning rates.
RMSProp is a precursor to Adam; Adam adds momentum and bias correction.
Adaptive learning rates help with sparse gradients (e.g., in NLP) and uneven scaling (e.g., different feature frequencies).

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