numpy

A recurring ML-coding screen. The loop itself is easy; what interviewers watch for is k-means++ init, a genuine convergence criterion, and awareness of the failure modes. Here is the compact implementation plus the follow-ups interviewers reliably ask.

A deceptively easy ML-coding ask. Writing exp/sum is trivial; the signal is the max-subtraction trick and the log-sum-exp form that stop it overflowing. Here is the stable implementation and the reason the naive version breaks.

The from-scratch implementation that frontier labs and NVIDIA really do ask. Writing it shows you grasp shapes, the scale factor, the causal mask, and how heads split and recombine. Here is a correct, readable implementation plus the follow-ups.

A from-scratch ML-coding staple that tests whether you really know the math you rely on. The signal is the clean gradient (it reduces to Xᵀ(ŷ - y)/n), numerical stability, and vectorization. Here is the implementation and the details interviewers push on.

The core operation beneath every embedding/RAG retrieval, posed as a coding exercise. The signal is vectorizing the similarity, normalizing correctly, and using a partial selection (argpartition) rather than a full sort. Here is the efficient implementation and the scaling follow-up.

A common ML-coding check that confirms you actually understand the metrics you quote. The signal is getting TP/FP/FN/TN right and knowing macro vs micro averaging for multiclass, not reaching for sklearn.

k-NN is quick to code and a solid check of vectorization and the lazy-learner tradeoff. Interviewers look for a tidy vectorized distance calculation plus knowing why naive prediction is O(n) and how to accelerate it. The implementation follows.

Coding conv2d shows you understand what a CNN layer really computes rather than just being able to name it. Interviewers watch for correct output-shape math, tidy stride and padding handling, and awareness of the im2col trick frameworks actually rely on.

LayerNorm appears in every transformer, and coding it verifies you know what it normalizes over and why. Interviewers look for normalization across the feature dimension per token, the learnable scale and shift, and the RMSNorm simplification modern LLMs took up.

Coding BatchNorm verifies you know the train/inference difference, the part everyone forgets. Interviewers look for normalizing over the batch with running stats kept for inference. The implementation follows.

Single-head attention shows up often; multi-head layers on the split-into-heads, attend-per-head, concatenate pattern. What gets scored is the reshape into heads plus a sharp explanation of why several heads help. Here is the implementation.

Dropout takes five lines, yet most candidates fumble two of them: turning it off at inference and rescaling the survivors so the expected activation holds constant. Inverted dropout is the convention they want to see.

Plain multi-head attention is rarely the whole exercise: the usual extension is to chain it into KV-cached decoding and GQA in one sitting. The locked answer walks the NumPy implementation, the equivalence check that proves your cache is correct, and the reshape bugs that silently corrupt attention.

A from-scratch classic that checks recursion plus the split criterion math. The signal is computing impurity correctly, picking the best threshold by information gain, and knowing the stopping rules. Here is a clean recursive implementation.

A from-scratch staple that checks whether you grasp the conditional-independence assumption and why you work in log space. The signal is fitting per-class means and variances, summing log-likelihoods, and adding the log prior. Here is the implementation.

A from-scratch favorite that probes linear algebra fluency. The signal is centering first, using SVD instead of forming the covariance matrix, and reading variance off the singular values. Here is the implementation and the details interviewers push on.

A build-it-yourself check on the EM algorithm and soft clustering. What matters is the pair of alternating steps (responsibilities, then weighted re-estimation), log-sum-exp for numerical stability, and seeing how GMM extends k-means. The code follows.

A build-it-yourself check on the least-squares closed form and the numerical traps hiding in it. What matters is deriving the normal equations, understanding why you never invert explicitly, and reaching for lstsq or the SVD instead. The code follows.

A build-it-yourself check on recurrent forward passes and backprop through time. What matters is the shared-weight recurrence, summing gradients over timesteps, and articulating the vanishing-gradient problem. The code follows.

A build-it-yourself check on gated recurrence. What matters is wiring the forget/input/output gates and candidate correctly, keeping cell state distinct from hidden state, and explaining why the additive cell path cures vanishing gradients. The code follows.

A build-it-yourself check on modern optimizers. What matters is the moment estimates, bias correction, and the single change that counts: AdamW decouples weight decay from the gradient rather than folding it into the loss. The code follows, plus why it wins.

A build-it-yourself check on how learning-rate schedules are actually computed. What matters is correct closed-form formulas, knowing when each schedule shines, and why decaying the rate aids convergence. Below is the implementation of the common ones.