CS6362 Advanced Machine Learning

🧭 Description

This is a course on machine learning that studies different types of learning scenarios. A scenario is characterized by four choices:

1. The specification of our model. Is the model linear? A neural network? For most of the course we assume only that a model has parameters that can be learned, accepts something as input, and produces something as output. Model design returns in Module V, where systems constraints begin to shape it.
2. The input provided for learning. How many data items, and how many of them are labeled? The answer ranges from a modest labeled dataset in Modules I and II, to no labels at all in Module IV, to internet-scale corpora in Module V.
3. The output of the model. Are we making predictions about a given data item, or generating novel data? If predicting, regression or classification?
4. What we expect from the learning method. Are we seeking the best model, or a set of good models? Module I pursues the first, Module II the second.

The course is about algorithms for learning across these axes.

We begin with optimization: gradient descent and its stochastic variants, and how they converge. Then we take up the harder question of which solution they converge to, and why a model with enough capacity to fit random labels nonetheless generalizes.

From there we ask what we are entitled to believe about a fitted model, and how uncertain we should be. This is inference: the Bayesian view, together with the approximations that make it tractable.

With those foundations in place, we turn to models that produce samples rather than predictions, then to learning without labels at all, then to what changes when scale and post-training dominate, and finally to understanding and evaluating the systems that result.

The ELBO you derive in Module II is the VAE objective in Module III. The self-supervised objectives in Module IV are what the scaling laws in Module V scale. By the end, the pieces of a modern foundation model should look like consequences of ideas you have derived yourself, rather than a list of architectures.

💡 The emphasis is on deriving these methods from first principles, so you can adapt and extend them, not only apply them.

🧱 Module Structure

The course is divided into six modules. Readings for each lecture are listed in the schedule.

Modules I and II treat the supervised setting: regression, Gaussian processes and Bayesian neural networks all predict a label from an input. Module III turns to models that produce samples rather than predictions, Module IV to learning without labels, Module V to training at scale, and Module VI to inspecting and evaluating the resulting systems.

Logistics

• Course Code: CS6362
• Term: Fall 2026
• Class Times: Mondays & Wednesdays 03:35 PM - 04:50 PM
• Location: Featheringill Hall 129
• Instructor: Hirak Sarkar — hirak.sarkar@vanderbilt.edu
• Teaching Assistant: Huy Tran — huy.tran@vanderbilt.edu
• Instructor Office Hours: Tuesdays 02:00 PM - 03:00 PM, Sony Building, Room A3015 — or by appointment

🎯 Learning Goals

By the end of this course, students will be able to:

• Analyze gradient descent and its stochastic variants — why they work, and their limitations
• Explain what solution SGD converges to: interpolation, double descent, implicit bias
• Formulate learning problems as Bayesian inference and reason about closed-form posteriors
• Derive and implement approximate inference — Laplace, variational inference, MCMC
• Build and critique generative models: VAEs, GANs, flows, score matching, diffusion
• Compare self-supervised objectives and explain what representations they encode
• Reason about scale: scaling laws, compute-optimal training, and post-training methods
• Interpret and evaluate deployed models — features, agent behavior, and benchmark validity
• Read and reconstruct results from current machine learning research literature

🏗️ Syllabus

This course is lecture-based, delivered primarily through slides with occasional whiteboard work. Slides will be posted to this page.

Assignments

Programming assignments run throughout the semester, in Python. We use NumPy for matrix computations — experience with multidimensional arrays, slicing, and broadcasting is expected — and where relevant JAX for automatic differentiation.

If specifically asked for implementing an assignment, you must build on provided boilerplate code. Where that is the case, you may not import additional Python libraries beyond those included with the assignment; doing so forfeits credit for the assignment. Include instructions for running your code, and submit as an archive.

There are three assignments. The first two cover optimization and inference respectively. The third is an open-ended scaling-laws assignment: you will train a family of small models across a range of sizes and compute budgets, fit a power law to the results, and use it to predict the loss of a larger model you then train to check. Everything runs on a laptop or a free Colab tier, and the Thanksgiving break falls inside the window to give you time for the sweeps.

Quizzes

Quizzes are either take-home or in-class, and are announced in advance — there are no pop quizzes. Each covers 1–2 questions on the current or previous lectures.

In-class quizzes are brief (15–20 minutes) and completed at the end of class: closed book, closed phone, closed any device — bring a pen or pencil. Take-home quizzes are completed outside class and submitted by the stated deadline.

Missing an in-class quiz, or arriving more than 25 minutes late on that day, means zero credit for that quiz; exceptions are case-by-case (e.g. medical absence). Your lowest quiz score is dropped.

Attendance

Attendance is taken in class and is the basis for the class-participation portion of your grade.

Project

The latter half of the semester is devoted to a research project in teams of 1–2. You will go in depth on a topic covered in class, situated in recent research — papers from roughly the last five years at ICML, NeurIPS, ICLR, and relevant venues in vision (CVPR, ICCV, ECCV) and NLP (ACL, EMNLP, NAACL-HLT).

• Proposal (~3 pages): basic information, brief description, hypotheses (the most important part), a literature survey of 4–5 papers, data (make sure it exists and is accessible), an evaluation plan, and a project plan. Also presented to the class.
• Midway report (~5 pages): refined aims and hypotheses, a fuller survey of 10–15 papers, methods, experimental design, and any refinement of the plan.
• Presentation to the class at the end of the semester.
• Final submission (8 pages excluding references), in the form of a research paper — introduction, related work, methods, experiments, discussion — plus all code and documentation.

Written portions use the NeurIPS LaTeX style, preprint mode. Standard ML libraries such as PyTorch or Flax are permitted, but projects that use publicly-available code for a paper are not allowed — the point is to gain experience implementing algorithms and evaluating them experimentally.

🗓️ Schedule

👥 Course Assessment (Tentative)

Late submission policy

One day late: 10% off  ·  two days late: 20% off  ·  past two days: no credit. The exception is class presentations — no credit is given if you do not present in your allotted time.

📋 Prerequisites

An introductory course in machine learning, plus sufficient background in linear algebra and probability and statistics. Relevant mathematical background will be covered over the semester, but what is covered in class should be treated as necessary rather than always sufficient — filling remaining gaps is your responsibility.

📚 Textbooks and Reference Material

The schedule draws on the following books and review articles, referenced by abbreviation.

Optimization

• MML — Deisenroth, Faisal & Ong, Mathematics for Machine Learning
• FML — Mohri, Rostamizadeh & Talwalkar, Foundations of Machine Learning
• LSML — Bottou et al., Optimization Methods for Large-Scale Machine Learning (free arXiv version)
• HCT — Garrigos et al., Handbook of Convergence Theorems for (Stochastic) Gradient Methods. Ch. 5 (Stochastic Gradient Descent) is assigned; Ch. 3 covers deterministic gradient descent

Inference

• PML-1 — Murphy, Probabilistic Machine Learning: An Introduction
• PML-2 — Murphy, Probabilistic Machine Learning: Advanced Topics
• GP — Rasmussen & Williams, Gaussian Processes for Machine Learning
• MCGE — Mohamed, Rosca, Figurnov & Mnih, Monte Carlo Gradient Estimation in Machine Learning

The readings listed in the schedule are intended to complement the lecture slides.

Reading list by module

Papers grouped by module, in the order covered. Per-lecture assignments are in the schedule.

Module I — Fundamentals of optimization

• Robbins & Monro (1951), A Stochastic Approximation Method — the origin of SGD
• Bottou et al., Optimization Methods for Large-Scale Machine Learning (LSML)
• Garrigos et al., Handbook of Convergence Theorems for (Stochastic) Gradient Methods (HCT) — Ch. 5 only
• Jacot et al., Neural Tangent Kernel
• Tancik et al., Fourier Features
• Zhang et al., Understanding Deep Learning Requires Rethinking Generalization
• Belkin et al., Reconciling Modern Machine Learning Practice and the Bias–Variance Trade-off — double descent
• Soudry et al., The Implicit Bias of Gradient Descent on Separable Data

Module II — Fundamentals of inference

Textbook readings: PML-1 Ch. 6, PML-2 Ch. 2–3, 5–7, 10–12, 15, 17, 19, and GP Ch. 2. One article:

• Mohamed et al., Monte Carlo Gradient Estimation in Machine Learning (MCGE)

Module III — Generative modeling

• Dempster et al. (1977), Maximum Likelihood from Incomplete Data via the EM Algorithm
• Kingma et al., Auto-Encoding Variational Bayes — the VAE
• van den Oord et al., Neural Discrete Representation Learning — VQ-VAE
• Goodfellow et al., Generative Adversarial Networks
• Arjovsky et al., Wasserstein GAN
• Rezende et al., Variational Inference with Normalizing Flows
• Hyvärinen et al., Estimation of Non-Normalized Statistical Models by Score Matching
• Song et al., Generative Modeling by Estimating Gradients of the Data Distribution
• Ho et al., Denoising Diffusion Probabilistic Models
• Lipman et al., Flow Matching for Generative Modeling

Module IV — Self-supervised learning

• Mikolov et al., Efficient Estimation of Word Representations in Vector Space — Word2Vec
• Chen et al., A Simple Framework for Contrastive Learning of Visual Representations — SimCLR
• Grill et al., Bootstrap Your Own Latent — BYOL
• Bardes et al., VICReg: Variance-Invariance-Covariance Regularization
• Vaswani et al., Attention Is All You Need

Module V — Scale and post-training

• How to Scale Your Model — online book on scaling model training and inference
• Kaplan et al., Scaling Laws for Neural Language Models
• Hoffmann et al., Training Compute-Optimal Large Language Models — Chinchilla
• Dao et al., FlashAttention
• Ouyang et al., Training Language Models to Follow Instructions with Human Feedback — InstructGPT
• Rafailov et al., Direct Preference Optimization
• DeepSeek-AI et al., DeepSeek-R1

Module VI — Interpretability and evaluation

• Elhage et al., Toy Models of Superposition
• Bricken et al., Towards Monosemanticity — sparse autoencoders
• Templeton et al., Scaling Monosemanticity
• Yao et al., ReAct: Synergizing Reasoning and Acting in Language Models
• Yang et al., SWE-agent
• Liang et al., Holistic Evaluation of Language Models — HELM
• Yao et al., τ-bench

⚖️ Policies

Academic honesty

Students should adhere to the Vanderbilt Honor System. Cheating and plagiarism will not be tolerated. Do not copy, in any way, another student’s work on assignments. See also Vanderbilt’s Academic Integrity policies.

Use of LLMs for completing assignments

Using large language models to complete assignments is acceptable provided you:

1. Acknowledge which specific LLM was used.
2. Distinguish your own work from what the LLM produced.
3. Provide the prompt given to the LLM.

Whether to use an LLM depends on what you want out of the course. The process of creation — working through a derivation, implementing an algorithm from scratch — is one of the best ways to learn. Having an LLM create for you will likely limit what you take away.

Privacy

Student data is protected under FERPA; see the Vanderbilt Student Privacy Statement. Please take care not to disclose private information during lectures or in submissions.

Nondiscrimination and anti-harassment

Vanderbilt is committed to an environment free of discrimination and harassment of any kind. If you feel you are being sexually harassed, please see Project Safe. If you feel unsafe, taken advantage of in any way, or mentally or emotionally unwell, please reach out to the Student Care Network.

Subject to change

Information in the course syllabus, other than the general assessment, may be subject to change with advance notice, at the discretion of the instructor.

🌎 Previous Offerings and Related Courses

• Vanderbilt — CS 6362, Fall 2024 (M. Berger)
• Stanford — CS 236: Deep Generative Models
• Berkeley — CS 294-158: Deep Unsupervised Learning
• CMU — 10-708: Probabilistic Graphical Models