LLM Coding Q Bank

Mock Interview: Basic Linear Algebra & Back-Propagation

• Implement and Debug Backpropagation (NumPy) – Given a small 2-layer neural network (Affine→ReLU→Affine→Softmax), derive the gradient update equations for all parameters (weights/biases) using the chain rule, then implement the forward pass, loss (softmax cross-entropy), and backward pass in NumPy【54†L132-L140】. Perform gradient checking with finite differences on a toy dataset, report relative errors, and debug any mismatches (e.g. missing factors or incorrect ReLU mask)【54†L139-L144】.

• Forward/Backward Pass (NumPy & PyTorch) – Starting from a batched input (X) of shape ([B\times D]), implement a feedforward and backpropagation for a simple classification net (linear layer (W_1,b_1) → ReLU → linear (W_2,b_2)). Compute the loss, derive gradients for inputs and all parameters, and ensure tensor shapes match batched operations【49†L74-L82】. Then express the same computation using PyTorch’s autograd: explain how the computation graph is built, how .backward() accumulates gradients, and common pitfalls (e.g. broadcasting, in-place ops)【49†L118-L127】.

• NumPy Neural Network Layers and Debugging – Implement basic layers in NumPy: for input (X) (shape ([B\times d_{\text{in}}])), weight (W) ((d_{\text{in}}\times d_{\text{out}})), bias (b) ((d_{\text{out}})), compute (Y = XW + b) and follow-up layers like ReLU and softmax【51†L75-L83】. Explain NumPy broadcasting (e.g. adding a ((d_{\text{out}})) bias to each row of (XW))【51†L75-L83】. Describe how to debug common implementation bugs: transposed matrices, incorrect broadcasting, unstable softmax, and mismatched batch dimensions【51†L129-L133】.

• Backpropagation Theory – Explain the mathematical foundation of backpropagation. How does the chain rule allow efficient gradient computation in a neural net, and how are gradients propagated layer by layer? (E.g. clarifying how an error at the output layer is backpropagated through each layer to compute ∂Loss/∂W,∂Loss/∂b)【36†L178-L186】.

• Gradient Checking – What is gradient checking and how do you use it? Describe the process of verifying analytical gradients by finite differences, and how a small relative error signals correctness. For example, if your backprop gradient is off by a constant factor, how would gradient checking reveal it【54†L139-L144】.

• Softmax & Cross-Entropy – Derive the softmax activation and cross-entropy loss for a multiclass output. Explain why numerical stability tricks are needed (e.g. subtracting the maximum logit before exponentiating)【54†L148-L152】. How do these choices affect the backprop equations?

• PyTorch Autograd Mechanics – In PyTorch, what role do requires_grad=True, .backward(), and .zero_grad() play in computing gradients? Describe how the computational graph is built and traversed to compute gradients automatically【49†L118-L127】.

• Broadcasting in NumPy – Describe how NumPy broadcasting works for array operations of different shapes. For instance, given X.shape = (B, d_in) and W.shape = (d_in, d_out), if you compute X @ W + b with b.shape = (d_out,), how is b broadcast across the batch? What are the resulting shapes?

• Transformer Attention (Implementation) – Implement the scaled dot-product attention mechanism from scratch (using NumPy or PyTorch tensors). Given query, key, and value tensors, compute their dot-product attention: ( \text{Attention}(Q,K,V) = \text{softmax}(QK^T/\sqrt{d_k})V ). Extend to multi-head attention by splitting into heads and concatenating. Analyze time/space complexity【36†L152-L160】.

• Debug a Broken Transformer – You have a Transformer code that isn’t training correctly. Describe a systematic debugging approach from data input to optimization. What common issues would you check (e.g. tokenization/labels, tensor shapes, attention masks, positional encodings, train vs eval mode, loss setup, optimizer configs)? As a follow-up, explain how to adapt a Transformer to a classification task and verify it by doing one forward/backward pass【50†L78-L87】【50†L119-L127】.

• Efficient Model Inference – Given a large pre-trained model, how would you optimize inference for low memory and high speed? Discuss techniques like quantization (e.g. 8-bit weights), pruning redundant neurons, batching inputs, and leveraging hardware. How do these affect accuracy and latency【36†L202-L210】?

• Noisy Label Aggregation – You have a binary text classification dataset with multiple noisy annotators per example (labels conflict). How would you analyze and handle this noise? Outline data analysis (measuring annotator agreement, label consistency), and propose a strategy for training and evaluation: how to split data to avoid leakage, how to aggregate multiple labels into a target (e.g. majority vote, soft targets), and which loss/calibration methods to use. Discuss potential failure modes【52†L124-L132】【52†L144-L150】.

• Filter Bad Annotations – Some training labels are low-quality or adversarial. Describe practical methods to identify and filter them before training【48†L73-L81】. What signals (example-level or annotator-level) would you use? How do you distinguish truly hard examples from mislabeled ones? Would you remove, relabel, or down-weight suspicious data? How would you evaluate this filtering process and what fairness issues might arise【48†L73-L81】.

• Attention KV Cache (Transformer) – Given a decoder-only Transformer, fix bugs related to label shifting, positional embeddings, and masking so that training works【68†L74-L83】. Then extend it with a key-value (KV) cache for autoregressive decoding: ensure the attention reads/appends to the cache properly, apply causal masks only when needed, and use correct positional offsets. Verify that incremental generation with the cache matches the original output【68†L139-L147】.

• Mode-Seeking vs. Covering (KL-Divergence) – Explain how the choice of KL divergence direction affects learned solutions. For example, minimizing KL(q‖p) (model q vs data p) tends to focus on the modes of p, while minimizing KL(p‖q) encourages covering the support of p【57†L171-L174】. What are the intuitive differences in the resulting model behavior?

• Accuracy vs. Metrics – You have two classifiers with accuracies 85% and 82%. Which would you choose and why? Explain how other evaluation metrics (precision, recall, F1, ROC AUC) or dataset considerations (class imbalance, error costs) influence your decision【67†L1188-L1190】.

• Perfect Accuracy ⇒ Loss Bounds – If a classifier achieves 100% accuracy on its training set, what are the minimum and maximum possible values of the cross-entropy loss on a single example【63†L1154-L1157】? (Hint: with perfect accuracy, the true class probability is 1, so loss can be arbitrarily low or high depending on confidence).

• Compute KL Divergence (Example) – Given two simple distributions (p) and (q) over a discrete set, how do you compute the KL divergence (D_{KL}(p|q))? For example, if (p = [0.5,0.5]) and (q=[0.8,0.2]), calculate (D_{KL}(p|q))【63†L1154-L1157】.

• Matrix Calculus (Linear Layer) – For a linear operation (Y = XW), what is the gradient (\partial Y/\partial W)? Use the identity ((AB)^T = B^T A^T) to show that (\partial (XW)/\partial W = X^T) when backpropagating through a batch【54†L132-L135】.

• Bayes’ Theorem – State Bayes’ theorem and its use in probabilistic modeling: for events (A) and (B), (P(A|B) = \frac{P(B|A)P(A)}{P(B)}). How does this update our beliefs with new evidence? (General ML interview topics often include this theorem【74†L128-L133】).

Sources: We gathered these questions from interview reports and Q&A for OpenAI ML roles【54†L132-L140】【49†L74-L83】【51†L75-L83】【50†L78-L87】【48†L73-L81】【52†L124-L132】【36†L152-L160】【57†L171-L174】【67†L1188-L1190】【63†L1154-L1161】【68†L74-L83】【54†L139-L144】【49†L118-L127】. Other included questions are extrapolated from common ML interview topics. Each question above is supported by the cited sources.