Extra Credit

Read one paper and come talk about it

Requirement Details
Reading One paper, selected by you and approved in advance
Scheduling At least 14 calendar days’ notice
Maximum award +2.0 percentage points

How it works

  1. Choose a paper. Find a research article or substantial preprint related to data science, scientific computing, numerical linear algebra, optimization, networks, probability, statistics, or machine learning.

  2. Request a meeting at least 14 calendar days in advance. Email abhijit.chowdhary@tufts.edu with the subject line “[MATH 123] Extra Credit”. Include:

    • the paper’s title, authors, and a link;
    • two or three sentences about why it interests you; and
    • several office-hour dates that work for you.

  3. Wait for confirmation. I will confirm that the paper is a reasonable fit and that we have a meeting time. If you are deciding between papers, you may include up to two candidates in your email.

  4. Prepare. You may bring the paper and your own notes. I do not expect anything like slides or a written report; indeed, don’t do that! I plan to sit across from you and chat about the paper. You should understand the big picture, the article organization, the main methodology and how it’s supported. Bring whatever you want for that purpose.

  5. Come talk. We will spend about 15 minutes discussing the problem, the paper’s approach, and what you made of it.

Tip

It is completely fine if some arguments or technical details remain beyond you. I once spent 1 month carefully tracing out all the proofs from a single paper. I’m not asking this of you! Choose something for which you can understand the motivating problem, trace at least one important idea, and interpret a main result. If you cannot tell whether a paper is appropriate, ask.

Credit schedule

The award depends on when the completed conversationtakes place. Earlier conversations earn more credit because I don’t want to get destroyed around final’s week.

Timing of completed conversation Extra credit earned
Before the October 22 +2.0 percentage points (full award)
After the October 22, through December 10 +1.0 percentage point

Credit is added to the numerical course grade after the grading formula in the syllabus is applied, up to a maximum course percentage of 100. For example, a successful conversation on October 20 adds 2.0 percentage points.

Because meeting space is limited, requesting a time 14 days ahead does not guarantee a particular date. Please, schedule early. If I need to move a confirmed meeting to a later credit window, you will keep the value of the original meeting date. If you request the change, the new meeting date determines the award.

What to be ready to discuss

This is not an oral exam. To earn the amount in the schedule above, the conversation should show that you read the paper and made a good-faith effort to understand it. You should be prepared to address most of the following in your own words:

  • What problem does the paper study, and why does that problem matter?
  • What is one central mathematical or computational idea in the paper, beyond what is stated in the abstract?
  • What assumptions does the method or theorem rely on, if any?
  • What is one main theoretical or experimental result, and what does it tell us?
  • What did you find surprising, unclear, or limited?
  • What question would you ask the authors?

I’m not expecting a polished summary of the entire paper. A focused, thoughtful explanation of one important thread is better than a rapid tour of every section.

NoteUsing outside resources

You may use textbooks, videos, software, sorcery, generative-AI tools, etc., to help unpack unfamiliar material, but they should support your understanding of the paper. During our conversation, you must be able to explain the ideas yourself and distinguish the paper’s claims from outside commentary.

If the conversation does not yet demonstrate that preparation, no partial award will be assigned for that meeting. You may try again in a later credit window, subject to the same 14-day scheduling rule.

Fine print

  • You may complete this project once during the semester.
  • The conversation is individual, though several students may independently choose the same paper.
  • The paper and meeting time must both be approved in advance.
  • The final day for a conversation is Thursday, December 10, 2026. A meeting on that date must therefore be requested no later than November 26.
  • If this oral format presents an access barrier, contact me so that we can arrange an equivalent way to demonstrate the same preparation.

Some paper recommendations

You do not need to choose from this list, but these are reasonable places to start. I have favored papers with a clear motivating question, a concrete method or application, and enough examples or experiments to support a good conversation. Every paper still requires advance approval.

For a long tutorial or survey, propose the particular sections or central idea you plan to follow in your approval email.

PCA, low rank, and matrix factorization

  • A Simpler Approach to Matrix Completion, Benjamin Recht (2011). Shows when a low-rank matrix can be reconstructed from a random sample of its entries by solving a nuclear-norm minimization problem.
  • The Optimal Hard Threshold for Singular Values is 4/√3, Matan Gavish and David Donoho (2014). Derives a principled cutoff for deciding which singular values to retain when estimating a low-rank matrix from noisy data, and compares it with common alternatives.
  • LoRA: Low-Rank Adaptation of Large Language Models, Edward Hu et al. (2021). Uses low-rank matrix factors to make the fine-tuning of very large language models much cheaper; focus on the low-rank idea and experiments rather than every detail of the underlying models.

Regression, classification, and generalization

  • Random Forests, Leo Breiman (2001). Combines randomized decision trees and studies why an ensemble can be more accurate and stable than its individual members.
  • Dropout: A Simple Way to Prevent Neural Networks from Overfitting, Nitish Srivastava et al. (2014). Randomly removes units during training to reduce overfitting, connecting a simple training procedure with the benefits of averaging many neural networks.
  • XGBoost: A Scalable Tree Boosting System, Tianqi Chen and Carlos Guestrin (2016). Develops a fast, scalable implementation of gradient-boosted trees and explains the algorithmic and systems ideas that make it work on large datasets.
  • Understanding Deep Learning Requires Rethinking Generalization, Chiyuan Zhang et al. (2017). Uses memorable experiments with random labels and random pixels to ask why highly over-parameterized models can generalize at all.
  • Attention Is All You Need, Ashish Vaswani et al. (2017). Introduces the Transformer, replacing recurrent computation with attention and showing how this permits substantially more parallel training.

Uncertainty quantification

Clustering, graphs, and networks

  • \(k\)-means++: The Advantages of Careful Seeding, David Arthur and Sergei Vassilvitskii (2007). Starts with a tiny change to the initialization of \(k\)-means and develops both an approximation guarantee and experiments.

  • Web-Scale \(k\)-Means Clustering, D. Sculley (2010). Introduces mini-batch \(k\)-means to reduce the computational cost of clustering massive, sparse datasets while retaining good solutions.

  • DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN, Erich Schubert, Jörg Sander, Martin Ester, Hans-Peter Kriegel, and Xiaowei Xu (2017). Reexamines DBSCAN’s complexity, the role of spatial indexes, practical parameter selection, and when density-based clustering remains competitive.

  • Clusterability: A Theoretical Study, Margareta Ackerman and Shai Ben-David (2009). Compares several ways to formalize whether a dataset has a strong clustering structure and finds that these apparently similar notions can disagree.

  • Visualizing Data Using t-SNE, Laurens van der Maaten and Geoffrey Hinton (2008). Develops one of the best-known methods for visualizing high-dimensional data and illustrates both its objective function and empirical behavior.

Randomness and scalable computation

Optimization