About

Karthik Sridharan is an Associate Professor at the department of Computer Science at Cornell University. His primary area of research is theoretical machine learning. Prior to his current position, he was a postdoctoral research associate at the University of Pennsylvania, where he worked jointly with Alexander Rakhlin and Michael Kearns. He obtained his PhD from Toyota Technological Institute at Chicago under the supervision of Nathan Srebro.

Research topics

• Machine Learning
• Computer Science
• Artificial Intelligence
• Mathematical optimization
• Mathematics

Selected publications

• On the Robustness of Langevin Dynamics to Score Function Error

  ArXiv.org · 2026-03-11

  articleOpen access

  We consider the robustness of score-based generative modeling to errors in the estimate of the score function. In particular, we show that Langevin dynamics is not robust to the L^2 errors (more generally L^p errors) in the estimate of the score function. It is well-established that with small L^2 errors in the estimate of the score function, diffusion models can sample faithfully from the target distribution under fairly mild regularity assumptions in a polynomial time horizon. In contrast, our work shows that even for simple distributions in high dimensions, Langevin dynamics run for any polynomial time horizon will produce a distribution far from the target distribution in Total Variation (TV) distance, even when the L^2 error (more generally L^p) of the estimate of the score function is arbitrarily small. Considering such an error in the estimate of the score function is unavoidable in practice when learning the score function from data, our results provide further justification for diffusion models over Langevin dynamics and serve to caution against the use of Langevin dynamics with estimated scores.

  PublisherOA PDF

• On the Robustness of Langevin Dynamics to Score Function Error

  arXiv (Cornell University) · 2026-03-11

  preprintOpen access

  We consider the robustness of score-based generative modeling to errors in the estimate of the score function. In particular, we show that Langevin dynamics is not robust to the L^2 errors (more generally L^p errors) in the estimate of the score function. It is well-established that with small L^2 errors in the estimate of the score function, diffusion models can sample faithfully from the target distribution under fairly mild regularity assumptions in a polynomial time horizon. In contrast, our work shows that even for simple distributions in high dimensions, Langevin dynamics run for any polynomial time horizon will produce a distribution far from the target distribution in Total Variation (TV) distance, even when the L^2 error (more generally L^p) of the estimate of the score function is arbitrarily small. Considering such an error in the estimate of the score function is unavoidable in practice when learning the score function from data, our results provide further justification for diffusion models over Langevin dynamics and serve to caution against the use of Langevin dynamics with estimated scores.

  PublisherDOI

• Orlicz Space on Groupoids

  arXiv (Cornell University) · 2025-01-10

  preprintOpen access1st authorCorresponding

  Let $G$ be a locally compact second countable groupoid with a fixed Haar system $λ=\{λ^{u}\}_{u\in G^{0}}$ and $(Φ,Ψ)$ be a complementary pair of $N$-functions satisfying $Δ_{2}$-condition. In this article, we introduce the continuous field of Orlicz space $(L^Φ_{0},Δ_{1})$ and provide a sufficient condition for the space of continuous sections vanishing at infinity, denoted $E^Φ_{0}$, to be an algebra under a suitable convolution. The condition for a closed $C_{b}(G^{0})$-submodule $I$ of $E^Φ_{0}$ to be a left ideal is established. Further, we provide a groupoid analogue of the characterization of the space of convolutors of Morse-Transue space for locally compact groups.

  PublisherOA PDFDOI

• Pseudo-differential operators on compact groupoids

  Journal of Pseudo-Differential Operators and Applications · 2025-08-05

  article1st authorCorresponding
  PublisherDOI

• Efficiently Escaping Saddle Points under Generalized Smoothness via Self-Bounding Regularity

  ArXiv.org · 2025-03-06

  preprintOpen access

  We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods. Smoothness is a restrictive assumption in machine learning in both theory and practice, motivating significant recent work on finding first order stationary points of functions satisfying generalizations of smoothness with first order methods. We develop a novel framework that lets us systematically study the convergence of a large class of first-order optimization algorithms (which we call decrease procedures) under generalizations of smoothness. We instantiate our framework to analyze the convergence of first order optimization algorithms to first and \textit{second} order stationary points under generalizations of smoothness. As a consequence, we establish the first convergence guarantees for first order methods to second order stationary points under generalizations of smoothness. We demonstrate that several canonical examples fall under our framework, and highlight practical implications.

  PublisherOA PDFDOI

• System-Aware Unlearning Algorithms: Use Lesser, Forget Faster

  ArXiv.org · 2025-06-06

  preprintOpen accessSenior author

  Machine unlearning addresses the problem of updating a machine learning model/system trained on a dataset $S$ so that the influence of a set of deletion requests $U \subseteq S$ on the unlearned model is minimized. The gold standard definition of unlearning demands that the updated model, after deletion, be nearly identical to the model obtained by retraining. This definition is designed for a worst-case attacker (one who can recover not only the unlearned model but also the remaining data samples, i.e., $S \setminus U$). Such a stringent definition has made developing efficient unlearning algorithms challenging. However, such strong attackers are also unrealistic. In this work, we propose a new definition, system-aware unlearning, which aims to provide unlearning guarantees against an attacker that can at best only gain access to the data stored in the system for learning/unlearning requests and not all of $S\setminus U$. With this new definition, we use the simple intuition that if a system can store less to make its learning/unlearning updates, it can be more secure and update more efficiently against a system-aware attacker. Towards that end, we present an exact system-aware unlearning algorithm for linear classification using a selective sampling-based approach, and we generalize the method for classification with general function classes. We theoretically analyze the tradeoffs between deletion capacity, accuracy, memory, and computation time.

  PublisherOA PDFDOI

• Weak containment of representation on topological groupoids

  ArXiv.org · 2025-10-07

  preprintOpen access1st authorCorresponding

  Let $G$ be a second-countable, locally compact Hausdorff groupoid equipped with a Haar system. This paper investigates the weak containment of continuous unitary representations of groupoids. We show that both induction and inner tensor product of representations preserve weak containment. Additionally, we introduce the notion of a topological invariant mean on $G/H$ and explore its connection to amenability. With that, we establish a groupoid analogue of Greenleaf's theorem. Finally, we provide independent results concerning the restriction of induced representations for continuous unitary representations of relatively clopen wide subgroupoids $H\subseteq G$ with discrete unit space and closed transitive wide subgroupoids of compact transitive groupoids.

  PublisherOA PDFDOI

• Active Learning via Regression Beyond Realizability

  ArXiv.org · 2025-05-31

  preprintOpen accessSenior author

  We present a new active learning framework for multiclass classification based on surrogate risk minimization that operates beyond the standard realizability assumption. Existing surrogate-based active learning algorithms crucially rely on realizability$\unicode{x2014}$the assumption that the optimal surrogate predictor lies within the model class$\unicode{x2014}$limiting their applicability in practical, misspecified settings. In this work we show that under conditions significantly weaker than realizability, as long as the class of models considered is convex, one can still obtain a label and sample complexity comparable to prior work. Despite achieving similar rates, the algorithmic approaches from prior works can be shown to fail in non-realizable settings where our assumption is satisfied. Our epoch-based active learning algorithm departs from prior methods by fitting a model from the full class to the queried data in each epoch and returning an improper classifier obtained by aggregating these models.

  PublisherOA PDFDOI

• Induced Representation of Topological groupoids

  ArXiv.org · 2025-03-14

  preprintOpen access1st authorCorresponding

  Let $G$ be a locally compact second countable groupoid with a Haar system. In this article, we introduce the induced representation of $G$ from a continuous unitary representation of a closed wide subgroupoid $H$ with a Haarsystem provided there exists a full equivariant system of measures $μ=\{μ^{u}\}_{u\in G^{0}}$ on $G/H$. We prove some basic properties of induced representation and a theorem on induction in stages. A groupoid version of Mackey's tensor product theorem is also provided. We also prove a groupoid version of Frobenius Reciprocity theorem on compact transitive groupoids.

  PublisherOA PDFDOI

• Langevin Dynamics: A Unified Perspective on Optimization via Lyapunov Potentials

  arXiv (Cornell University) · 2024-07-05

  preprintOpen accessSenior author

  We study the problem of non-convex optimization using Stochastic Gradient Langevin Dynamics (SGLD). SGLD is a natural and popular variation of stochastic gradient descent where at each step, appropriately scaled Gaussian noise is added. To our knowledge, the only strategy for showing global convergence of SGLD on the loss function is to show that SGLD can sample from a stationary distribution which assigns larger mass when the function is small (the Gibbs measure), and then to convert these guarantees to optimization results. We employ a new strategy to analyze the convergence of SGLD to global minima, based on Lyapunov potentials and optimization. We convert the same mild conditions from previous works on SGLD into geometric properties based on Lyapunov potentials. This adapts well to the case with a stochastic gradient oracle, which is natural for machine learning applications where one wants to minimize population loss but only has access to stochastic gradients via minibatch training samples. Here we provide 1) improved rates in the setting of previous works studying SGLD for optimization, 2) the first finite gradient complexity guarantee for SGLD where the function is Lipschitz and the Gibbs measure defined by the function satisfies a Poincaré Inequality, and 3) prove if continuous-time Langevin Dynamics succeeds for optimization, then discrete-time SGLD succeeds under mild regularity assumptions.

  PublisherOA PDFDOI

Frequent coauthors

• Alexander Rakhlin

  73 shared

• Dylan J. Foster

  30 shared

• Ohad Shamir

  22 shared

• Ayush Sekhari

  22 shared

• Ambuj Tewari

  19 shared

• Nathan Srebro

  17 shared

• Mehryar Mohri

  13 shared

• Andrew Cotter

  10 shared

Labs

• Karthik Sridharan LabPI

Education

• Ph.D.

  Toyota Technological Institute at Chicago

• Other

  University of Pennsylvania