Core AI and ML Concepts

Solve a one-variable linear equation and verify the solution by substitution.

Evaluate and plot a simple function to connect its equation with its visual shape.

Represent one data example and a batch of examples as vectors and matrices with labeled dimensions.

Calculate a dot product and interpret it as a weighted combination or similarity score.

Perform matrix-vector multiplication by hand.

Interpret matrix-vector multiplication as a transformation of information.

Determine whether vector and matrix shapes are compatible for a proposed operation.

Use NumPy to perform vector and matrix operations and verify the results against a hand calculation.

Interpret the derivative at a point as a local rate of change and slope on a graph.

Differentiate polynomial expressions using the power and sum rules.

Calculate partial derivatives while treating other variables as constants.

Assemble partial derivatives into the gradient of a two-variable function.

Use a contour plot to identify the uphill direction indicated by a gradient.

Apply the chain rule through a short computational graph.

Perform one gradient-descent parameter update from a given gradient and learning rate.

Diagnose an excessively small or large learning rate from a plotted loss curve.

Represent a simple random experiment using outcomes and events and calculate an event probability.

Calculate conditional probability from a table or frequency diagram.

Apply Bayes' rule using natural-frequency counts.

Calculate and interpret the mean, variance, and standard deviation of a small dataset.

Represent a discrete random variable with a probability distribution and calculate its expected value.

Choose between Bernoulli and Gaussian distributions for simple modeling scenarios.

Calculate Bernoulli likelihoods for several candidate probabilities and identify the maximum-likelihood estimate.

Use bootstrap resampling to estimate and interpret a confidence interval for a sample mean or model metric.

Distinguish artificial intelligence, machine learning, deep learning, and generative AI using concrete examples.

Frame a problem as regression, classification, clustering, anomaly detection, or reinforcement learning.

Identify samples, features, targets, and predictions in a tabular dataset.

Use pandas to inspect data types, missing values, distributions, and suspicious entries.

Create training, validation, and test splits and state the purpose of each split.

Identify target leakage and train-test contamination in an example workflow.

Fit preprocessing steps only on training data by using a scikit-learn pipeline.

Construct a simple non-learning baseline against which to compare a model.

Fit a linear regression model and interpret the direction and scale of its coefficients.

Calculate mean absolute error and mean squared error for regression predictions.

Fit logistic regression and interpret its output as a class probability.

Construct a confusion matrix from predicted and true class labels.

Calculate accuracy, precision, recall, specificity, and F1 score from a confusion matrix.

Choose an evaluation metric and classification threshold based on class imbalance and the costs of false positives and false negatives.

Fit a decision tree and explain one prediction by tracing its decision path.

Compare a decision tree with a random forest using cross-validation and identify evidence of overfitting.

Explain how feature scale changes distance-based comparisons and standardize numerical features.

Perform one iteration of k-means clustering on a small two-dimensional dataset.

Interpret a silhouette score while explaining why a high score does not guarantee meaningful clusters.

Project centered two-dimensional data onto a given principal component.

Interpret explained variance when selecting the number of principal components.

Use PCA to create a two-dimensional visualization of higher-dimensional data.

Calculate a nearest-neighbor distance anomaly score for a small dataset.

Evaluate whether discovered clusters or anomalies are useful for the original problem rather than merely mathematically distinct.

Calculate the forward pass of a small neuron from its inputs, weights, bias, and activation.

Compare ReLU and sigmoid using their graphs and explain their roles in hidden and binary-output layers.

Calculate softmax probabilities and match regression, binary-classification, and multiclass tasks with suitable output layers and loss functions.

Calculate a parameter gradient by backpropagating through a short computational graph.

Use PyTorch tensors and automatic differentiation to obtain a gradient.

Implement the essential steps of a PyTorch training loop on a small dataset.

Diagnose underfitting and overfitting from training and validation curves and select an appropriate response.

Apply a small convolutional filter to an image patch and interpret the resulting feature value.

Map text into tokens and explain how tokenization affects the inputs available to a language model.

Interpret an embedding as a learned vector representation and compare two embeddings using cosine similarity.

Calculate attention weights for a tiny single-head attention example.

Trace information through the attention, feed-forward, residual, and normalization parts of a transformer block.

Distinguish pretraining, fine-tuning, in-context learning, and retrieval-augmented generation.

Compare next-token prediction, masked-token reconstruction, and diffusion denoising as training objectives.

Evaluate generated outputs using task-relevant evidence rather than fluency alone.

Identify hallucination, bias, privacy, and distribution-shift risks in a proposed foundation-model application.

Represent a sequential decision problem using states, actions, rewards, transitions, and a discount factor.

Calculate a discounted return from a short reward sequence.

Distinguish a policy, state-value function, and action-value function.

Explain the exploration-exploitation trade-off using an agent scenario.

Perform one tabular Q-learning update from a transition.

Trace how an actor-critic method uses returns or advantage estimates to update a policy and value function.

Explain how probability-ratio clipping in PPO limits destabilizing policy updates.

Design a reward function for a simple agent task and identify one way the agent could exploit it.

Triage a supplied research paper and create a structured note recording its research question, method, baselines, metrics, principal claim, and stated limitation.

Use keywords, citation trails, and explicit inclusion criteria to find papers relevant to a focused research topic.

Synthesize three related papers in a literature matrix and state one cautious research gap supported by the comparison.

Formulate a focused research question and falsifiable hypothesis from an identified gap.

Design a controlled experiment containing a baseline, one intervention, an ablation, suitable metrics, and repeated random seeds.

Create a reproducible experiment record containing a README, environment specification, configuration, seed, results log, and Git commit.

Summarize repeated-run results using a mean and confidence interval while separating direct observations from interpretations.

Given a scenario, distinguish batch, online, and continual learning and classify a continual setting as task-incremental, domain-incremental, or class-incremental.

Quantify catastrophic forgetting by calculating final average performance and forgetting from a continual-learning performance matrix.

Compare replay, regularization, and parameter-isolation approaches to continual learning.

Configure and run a supplied replay-based continual-learning experiment against a no-replay baseline.

Convert a vague property such as human-like agent behavior into observable and defensible metrics.

Specify a fair comparison among a rule-based agent, an original learned agent, and an agent with one modified component.

Write a one-page research brief connecting motivation, prior work, method, evaluation, risks, and expected contribution.

Assess the fit of a funded PhD project or supervisor from recent work and draft a concise, evidence-based statement of fit.