# Course basics

## Logistics

• Time: Thursdays 12-14, Fridays 12-13
• Location of lectures: for now, online over zoom (passcode given via email)
• Location of interactive sessions: online over gather.town (only works with a computer, not with the phone) see schedule
• Lectures will also be recorded and posted online
• Instructor: Fanny Yang
• Teaching assistants:
• Konstantin Donhauser (konstantin.donhauser at inf.ethz.ch), Parnian Kassraie (parnian.kassraie at inf.ethz.ch)
• Office hours: online over zoom upon request via email
• Sign up on waitlist until March 7th
• De-register until March 17th
• E-mails will most likely not be responded to if it’s a logistical inquiry - please post privately on campuswire

### We will use the following platforms

• Please ask questions in campuswire, eternal gratitude from your peers is ensured ;). It will also be used for all announcements, discussion of homeworks and lectures, and parts of the assignments.
• gather.town for interactive sessions
• gradescope enroll with entry code 5VRB46 (homeworks)
• hackmd We will use this for some collaborative work. Please sign up so that you can start working on a joint sheet right away.

## Learning objectives

This course is designed to prepare Master students for successful research in ML, and prepare PhD students to find new research ideas related to ML theory. Content wise, the technical part will focus on generalization bounds using uniform convergence, and non-parametric regression.

By the end of the course

• both easily read and write theorems that provide generalization guarantees for machine learning algorithms
• find high-impact questions and theorems to prove and work on that you are highly passionate about

Learning objectives

1. acquire enough mathematical background to understand a good fraction of theory papers published in the typical ML venues. For this purpose, students will learn common mathematical techniques from statistics and optimization in the first part of the course and apply this knowledge in the project work

2. critically examine recently published work in terms of relevance and determine impactful (novel) research problems. This will be an integral part of the project work and involves experimental as well as theoretical questions

3. find and outline an approach (some subproblem) to prove a conjectured theorem. This will be practiced in lectures / exercise and homeworks and potentially in the final project.

4. effectively communicate and present the problem motivation, new insights and results to a technical audience. This will be primarily learned via the final presentation and report as well as during peer-grading of peer talks.

# Evaluation

• 10% HW, 50% oral midterm, 40% project
• Homework:
• some graded homework problems
• rest is self-graded with mandatory hand-in. The discrepancy between your own and our score for the selected problem will enter the final homework grade. This is to encourage you to go through the solutions carefully while self-grading.
• Project report and presentation: see project website
• Presence is mandatory in the last four weeks of classes during presentations

## Homework information

• Homeworks are designed to

• do some technical (“just algebra”) work that needs to be practiced individually
• learn how to read more material on the matter effectively (homework content will be part of the midterm exam!)
• No late homework

• Each homework write-up must be neatly typeset as a PDF document using TeX, LaTeX, or similar systems (for more details see below). This is for you to practice getting efficient at it. Ensure that the following appear on the first page of the write-up:

• your name,
• your Student ID, and
• the names and IDs of any students with whom you discussed the assignment.
• Submit your write-up, one page per question, as a single PDF file by 11:59 PM of the specified due date to gradescope. Follow the instructions and mark the pages that belong to the corresponding questions. See more details on the homework sheet.

• Some questions will be graded by the TAs. All questions will be self-graded by you.

• Discussions on campuswire

## Academic integrity for homeworks

As graduates students we expect you to take this class because you want to learn the material and how to do research. All assessments are designed to maximize the learning effect. Cheating will harm yourself and hence it is of your own interest to adhere to the following policy.

• All homework is submitted individually, and must be in your own words.

• You may discuss only at a high level with up to two classmates; please list their IDs on the first page of your homework. Everyone must still submit an individual write-up, and yours must be in your own words; indeed, your discussions with classmates should be too high level for it to be possible that they are not in your own words.

• We prefer you do not dig around for homework solutions; if you do rely upon external resources, cite them, and still write your solutions in your own words.

• When integrity violations are found, they will be submitted to the department’s evaluation board.

# Schedule & course content

• Subject to frequent changes, check back often!
• The slides are not shown as is during lecture, but they contain a superset of the content of each lecture
Date Topic Location Material Assignments
25.2 Logistics, Risk decomposition [Notes] Recording MW 1 HW 1
26.2 Concentration bounds and uniform convergence [Notes] Recording MW 2,3,4
4.3. Azuma-Hoeffding, McDiarmid, Uniform Law [Notes] Recording MW 2, 4 HW 1 due, HW 1 sol
5.3. Symmetrization and Rademacher complexity [Notes] Recording
11.3. VC bound, Rademacher contraction [Notes] Margin bound (ex) Recording Gather MW 4 HW 1 self-grade due
12.3. Margin bound proof Recording HW 2, Project sign-up
18.3. Structural risk minimization, metric entropy [Notes] Recording SS 7, 26, MW 5 Project proposal due
19.3. Chaining and Dudley’s integral[Notes] Recording MW 5
25.3. From features maps to kernels to RKHS [Notes] Recording MW 12
26.3. From RKHS to features, Mercer’s Theorem [Notes] Recording SC4, MW 12
1.4. Kernels in high dimensions (ex) Gather Paper HW 2 due, HW 2 sol
2.4. No class, holiday
7.-8.4. Holidays, enjoy! HW 3
15.4. Non-parametric regression and localized complexities [Notes] Recording MW 13
16.4. Risk bounds for kernel ridge regression (KRR) [Notes] Recording MW 13
22.4. Random design, Minimax lower bounds [Notes] Recording MW 14, MW 15
23.4. Minimax lower bounds [Notes] Recording MW 15
29.4. Minimax lower bounds [Notes - NTK vs. NN (ex) Recording HW 3 due, HW 3 sol, HW 2 self-grade due
30.4. NTK vs. NN Recording
6.5. Oral midterm
7.5. Oral midterm
13.5. No class, holiday
14.5. Interpolation and double descent Recording Mid-Project drafts due
20.5. Implicit bias [Notes Recording HW 3 self-grade due
21.5. Project feedback
27.5. Presentations 1, see full schedule
28.5. Presentations 2, see full schedule
3.6. Presentations 3, see full schedule
4.6. Presentation 4, see full schedule Peer-grading due
18.6. No class Project reports due

# References

## Course content

Links to books are online resources free from the ETH Zurich network

Learning Theory

Some more background reading for your general wisdom, knowledge and entertainment

## Typesetting

• For LaTeX, see 1, 2 or 3, 4
• For Pandoc Markdown by John McFarlane, refer to my git repo with sample instructions on how to use Pandoc for simple math notes and webpages

# Interactive sessions

We meet in gather.town. Please make sure before the start of the lecture that you can enter gather.town. Some people have had problems with the microphone and camera in the past. The problem sheet for the session are

The virtual interactive session will take place as follows:

1. Everyone goes into the gather.town main hall where the podium is and the chairs are.

2. There, the speaker briefly presents the problem and instructions. The problem is usually divided into 3-4 sub-problems. The problem sheet can be found on the website.

3. Each participant can choose which of the presented sub-problems he or she would like to solve.

4. For each sub-problem there are two rooms in our meeting room. The goal is for each room to independently solve the corresponding subproblem. Please spread out so that no more than 3-4 students work together in one room.

5. In each room: 25 minutes of

• discussion - you may use the prepared hackmd link or scribbletogether (on iPad/tablet use app) to collaborate (press x to open)

• representative prepares a 6 min presentation using hackmd or scribble

1. After 25 minutes: 20 minutes of short presentations
• One group per question (random choice) will be called to go on stage

• Introduce yourself and group members by names

• Present your results w/ screenshare (6 min.), take questions (1 min.)

• To ask questions please move onto the red carpet in the big hall

## Some notes on our setup in gather.town environment

• You can hear and see only your direct neighbors

• If you enter a public space (red carpet and the spot directly behind the podium), everyone can see and hear you

• You can move using the arrows on your keyboard

• We have created private spaces which you enter when you walk in one of the side rooms. Every group is assigned to one of these rooms where they can discuss and solve the assigned problems.

• In each room there are two white bards. If you stand right next to one of these whiteboards, you can click x to open the hackmd respectively scribbles, which you can use to interactively solve the problem

• One of the whiteboards contains a scribbles link which you can use as an interactive whiteboard. You can also join the board on your tablet using the 4-digit code (via browser or app, the latter is easier)

• The other whiteboard contains a link to a hackmd site where you can jointly write in markdown. For markdown syntax see e.g. this primer. For adding formulas use “” and latex syntax. You can also start standard latex environments such as ‘\begin{align}’

You can look here to familiarize yourself with the gather.town environment.

For completeness, the links for collaboration for each of the individual rooms are: