Four homework assignments, 10% each. Submit a runnable notebook/code, experiment results, and a 2-page report for each assignment. All deadlines are 11:59 p.m. Eastern Time.

Homework 1: Generative Modeling

Train a VAE and a flow-matching model on the same 2D toy dataset, such as a mixture of eight Gaussians.

• Implement the training objectives and sampling procedures using small networks.
• Generate 1,000 samples per model. Compare sample plots, mode coverage, and sampling time; define your coverage metric.
• Change one setting, such as the VAE KL weight or the number of flow sampling steps, and explain its effect.

Keep training budgets comparable and report model sizes. The goal is to understand how the methods work; a CPU-scale experiment is sufficient.

Homework 2: Prompting vs. Fine-tuning

Choose a small open language model and a classification or short-answer task. Compare zero-shot prompting, few-shot prompting, and LoRA supervised fine-tuning using the same base model.

• Use separate training, development, and test sets; include at least 50 test examples.
• Tune prompts and training settings on the development set, then evaluate all three methods on the same untouched test set.
• Report task accuracy or another appropriate metric, trainable parameter count, and training/inference time. Analyze five representative outputs.

Use a model that fits your available hardware. Explain when adaptation helps, when it fails, and what it costs. Relevant reading: LoRA.

Homework 3: Build and Evaluate an Agent

Build a small question-answering agent with two tools: a calculator and search over a fixed local document collection. Add persistent memory for information from earlier turns.

• Prepare 20 test cases: 10 single-turn tasks requiring tools and 10 multi-turn tasks requiring earlier information. Write reference answers before testing.
• Compare three configurations of the same model: no tools/memory, tools only, and tools plus memory. Use the same conversation histories and context budget; include facts outside the recent context so that persistent memory must retrieve them.
• Report success rate by task type, tool errors, and model/tool call counts. Inspect three failure cases, including a tool failure or misleading retrieved instruction.

Keep the document collection and maximum call budget fixed. Use a simple implementation; a specific agent framework is not required.