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Arnav Sirigere
DIMACS REU 2026 ↗

Arnav Sirigere

Mathematics & Computer Science @ UIUC

Hi! I'm a rising junior at the University of Illinois Urbana-Champaign studying Mathematics and Computer Science with interests in high-performance computing and machine learning. I'm particularly drawn to problems that combine mathematical rigor with practical computation, and I've also enjoyed topics such as algorithms, graph theory, optimization and stochastic processes.

Beyond academics and research, I enjoy activities that challenge both the mind and body. In my free time, I enjoy speedcubing, chess, dancing, exploring wildlife and nature, and playing sports such as cricket, tennis, and badminton.

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Research Project

My summer research

An overview of what I'm investigating, why it matters, and how I'm approaching it.

Who is Really Top-K? Quantifying Ranking Stability and Ambiguity under Model Multiplicity

Advised by Prof. Lesia Semenova · DIMACS REU 2026

Ranking systems (such as search engines, recommender systems, and LLM response rankers) often suffer from model multiplicity, where many different models achieve nearly identical performance while producing drastically different rankings for the top-k items. This creates a reliability challenge: is an item highly ranked because it is truly the best choice, or simply because of an arbitrary selection among equally accurate models? This project investigates the Rashomon Set, the collection of all models that achieve near-optimal loss. Rather than focusing on a single trained model, we study the entire set to identify stable rankings that persist across nearly all high-performing models and ambiguous rankings that vary substantially. Our work combines theoretical and empirical approaches, including rigorous mathematical analysis of ranking stability within the Rashomon Set and the development of interpretable diagnostics for quantifying uncertainty in ranked outputs. By understanding when rankings are robust and when they are inherently sensitive to model choice, we aim to improve the reliability and transparency of ranking systems used in high-stakes applications such as hiring algorithms and the ordering of fact-based responses in Large Language Models.

Lab Notebook

Weekly research log

A running record of what I'm working on, thinking about, and learning each week.

Week 1 · June 2026

Onboarding & First Look at the Problem

Landed at Newark Airport and Ubered straight to Buell Apartments. I was running late for the inaugural pizza dinner. I met up with Larry, who also handed me my room keys. I tossed all my stuff in my room and rushed out to make it to dinner. I met my roommates John, Ryan, and Herbert, along with everyone else from the cohort. Brought two boxes of leftovers back.


The next day I had some nice breakfast and attended the DIMACS program orientation. We also had a workshop that discussed creating our DIMACS website. Apparently, this is part of some contract that I signed without reading. Fortunately, I had a few spare Claude Credits lying around. I also attended two talks about Fair Resource Allocation and Quantum Algorithms. Oh and I also got paid this week.


Had my first meeting with Prof. Semenova, where we went over the project overview and motivation. We already had a general idea of the direction we wanted to pursue. She pointed me to several great resources to build background knowledge and become familiar with the key theory and setup. I have attached some resources I went over below.


📄 Rashomon Effect Overview

I developed a basic understanding of the Rashomon effect, learnt about important questions that need to be asked, and saw it in action. It talked about reasons for the Rashomon effect, like noisy data. It had results showing several ML models with different functional forms achieving similar accuracy on the FICO dataset, despite disagreeing on feature importance. Went over some really cool packing results about compelx and simple models within the Rashomon Set, and learnt about tools that exhaustively find the Rashomon Set, solving the interaction bottleneck for some speicifc simple models. I started wondering about how you would explore and sample from broader Rashomon Sets.


📄 Definitions & Ridge Regression Application

I went through the formal definitions and related notation for describing Rashomon Sets. I learnt how to measure the size of the Rashomon Set using the Rashomon Ratio, that measures the fraction of near-optimal models within the hypothesis space. It can be used to gain insight on the simplicity of the learning problem and predict existence of simple yet accurate models. As an exercise, I proved Theorem 10 from Appendix B using some simple linear algebra. We derived the Rashomon Parameter for ridge regression. This is a linear model trained using the squared error, but with an extra L2-Regularization penalty term to ensure that the weights don't blow up unnecessarily, thus obtaining a smooth and bounded Rashomon Set. We obtain a beautiful result, showing that the Rashomon Set is an ellipsoid centered at the optimal solution. A key takeaway is that the Rashomon Set is independent from the regression targets.

🗺️ Side Quests

We played some fun card games. I introduced them to Cabo, a game I have been addicted to recently. They did not seem to enjoy the complexities of the game :/. John introduced me and Ryan to Crew, a cooperative card game that I fell in love with. We reached Level 15 without a single failed attempt. We also played some frisbee late at night. It helped with learning everyone's names because you didn't want to throw it at someone without giving them a warning.

Week 2 · June 2026

Experimental Design & Further Reading

I started the week by working on my slide deck for student presentations. The first draft was a bit too technical for a 5 minute talk, so Prof. Semenova suggested tuning it down a little and focus on explaining the motivation behind the project. I also "borrowed" some slides from her own presentations she has given in the past. I really enjoyed everyone's presentations and was finally able to learn about all of the other interesting work that was about to happen this summer.


In my weekly meeting with Prof. Semenova, me and Nikhil brainstormed ideas for measuring ranking stability across model multiplicty. Basically, we wanted to come up with tools for studying how much the top-k candidates of each leaderboard produced by equally accurate models vary. We were able to come up with quite a few ideas: Fixing candidates and asking how many models agree on them being in or out of the Top-K, fixing two models and looking at the intersection of their individual Top-K and examining permutations of the leaderboard. We also thought about measuring the confidence against the distance between models. We further refined our ideas and decided to focus on three ideas. Firstly, looking at agreement of the Top-p (p < k) candidates across all models using the union of their top-p sets. Secondly, considering models pairwise and measuring the number of invariants, total variation distance of the mass function measuring confidence and the cosine distance. Lastly, we would examine candidates pairwsie as well, along with analyzing the Hamming distance across models.


I also went through the first 5 pages of this paper below:


📄 ElliCE: Algorithmic Recourse via the Rashomon Sets

In general, this paper talks about efficient and robust closed-form counterfactual example generation for algorithmic recourse, taking the Rashomon effect into consideration and exploiitng the geometry of the Rashomon set to reduce the problem to a convex optimization problem. I learnt that this work can be generalized to complicated models as well, as long as they can be parameterized as a vector. While going through papers previously, I always incorrectly assumed a vector parameterization of models only describes linear models with weights like ridge or logistic regression. This paper works with L2 regularized cross-entropy loss or logistic loss, but can be generalized to any convex loss function. The definition for conterfactual examples was pretty straight forward and I learn about the Gower's distance. Taking inspiration from the result previously derived for ridge regression, a 2-degree Taylor's series expansion can be used to approximate the Rashomon Set as an ellipsoid with similar form using the Hessian. It is important to note that the Hessian is positive definite since the logistic loss is convex and L-2 norm is strictly convex. I was able to correctly formulate the Quadratically Constrained Quadratic Program required to find the best counterfactual example and as an exercise, I proved Theorem 1 which provides a closed-form solution to the inner minimization problem of the constraint.

🗺️ Side Quests

We watched the NBA finals together. This my first time watching an NBA game, I am not a huge basketball fan. I was supporting the Knicks, because I was born in New York state and learnt it's been over half a decade since they've won. Game 2 was very close. Watched some of the India vs Afganistan Test Match, where India registered their biggest test victory ever. More games are scheduled, let's see how many all nighters I manage to pull to watch them. We also played badminton and table tennis over the weekend. I used to play both games a lot during middle school, but gradually lost interest. Felt good playing after a long time. Joshua destroyed us all. I also had my Amazon interview this week, which I failed. I could not have been more unlucky, but that's a story for another time.

Week 3 · June 2026

Claudemaxxing

This week I started coding experiments to analyze the Rashomon Set for random forests trained over different data sets like FICO and COMPAS. I started with the elementary task of getting it to work with one model. Train-Validation-Test split and the usual hyperparamter tuning, nothing special. Then, once the best hyperparamters were fixed, generated an entire set of random forest models that were each given a unique seed, which ocntrols the randomness, bootstrapping and feature selection. The idea was to filter out the best performing models based on a fixed tolerance, but all the models passed this threshold. I analyzed the individual losses of all models and noticed they were pretty close as well. I further analyzed the pairwise hamming distance between models which was also surprisingly small. I later discovered that I was using the wrong loss to evaluate the models. I had to use 0-1 loss, but initially thought it wss a better idea to use log loss since I figured eventually we will be using probability prediction / regression for scoring. This created a possibility of punishing models that predicted the labels correctly and all models that had individual trees with highly overfitted leaf nodes. Overall, we can capture a diverse set of equally performing models.


Attended an amazing talk by Neil Sloane, the creator of OEIS (The Online Encyclopedia of Integer Sequences). I knew him from numerous Numberphile videos. We talked about the Curling number and Runs, and even covered a nice proof showing that every positive integer appears in the EKG sequence. There was some sequence that involved an infinite spiral chess board and a knight moving. I hope to spend more time looking at that particular sequence and exploring the OEIS. Maybe even try some elementary proofs.

🗺️ Side Quests

The Knicks make the largest comeback ever in an NBA final, recovering from a 29 point deficit. Consistent and intentful play leads them to victory. I played a very good 93% accuracy chess game during a break from work as well. Some badminton as always.

Week 4 · June 2026

A Breakthrough - Proving a Result!!

After grasping enough content from important parts of the ElliCe paper, I was able to develop a theoretical framework to analyze leaderboard and ranking stability for linear models, establishing the exact geometric boundaries of the Rashomon Set using point-wise leverage scores. I found a sufficient and necessary condition for ranking stability, but it was inefficient for practical purposes. It would run in O(N^2) time, since it needed to compute the pairwise difference leverage score. Prof. Semenova shared a really interesting idea about focusing on the worst case deviation in the score for an individual item. After finding the clsoed form solution to the max deviation in terms of the leverage score, I was able to find a sufficiet condition that would guarantee ranking stability. This theorem compares the smallest score deviation between any two items with the highest individual score deviation in the worst case. This is also a very practical solution, as it can be checked in O(N) time.


Attended a talk by Thotsaporn Thanatipanoda, where we talked about Game Theory. He introduced John von Neumann's simplified version of a poker game, where there is an "infinite deck" ranging from 0 and 1. We then simplified the game down to 7 cards and tried to play the game ourselves, trying to find the optimal strategy. He further explained Nash Equilibrium and demonstrated the MiniMax Theorem. He then reduced finding the optimal solution to a lienar programming problem and we played around a with a solver for different number of cards and bet values. From my experience with solving Game Theory problems, I was under the impression that there is no real "correct" solution. But my understanding of Nash Equilbrium and seeing the solver in effect helped me appreciate the mathemtial elegance behind these games.

🗺️ Side Quests

I lost 150 ELO points this week on Chess.com. I was hoping to cross 1400 this week. I ended at 1200.

Life Beyond the Lab

Beyond research

Summer adventures, campus life, and memories made along the way.

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[ Featured Memory ]

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[ Campus Event ]

[e.g. "REU kickoff picnic on the Rutgers green."]

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[ Exploring NJ / NYC ]

[e.g. "Day trip to NYC with the cohort."]

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[e.g. "Late-night board games in the common room."]

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[ Seminar or Talk ]

[e.g. "Attending a guest lecture on cryptography."]

Acknowledgements

With gratitude

This research would not be possible without the support of many generous people and institutions.

🧑‍🔬

Research Mentor

Sincere thanks to Prof. Lesia Semenova for her patient guidance, thoughtful feedback, and enthusiasm for this problem. I've learned immensely from our weekly meetings.

🏛️

DIMACS & Rutgers University

Thank you to the DIMACS center and Rutgers University for hosting this REU program and providing an exceptional research environment.

💰

Funding & Support

This research is supported by the National Science Foundation under grant CCF-2447342.

👥

Fellow REU Participants

To my cohort — thank you for the late-night conversations, shared confusions, and collective celebrations. This summer would be far less rich without all of you.