About Me

I am a 4th year PhD student in the Computer Science department at the University of California San Diego where I work with Prof. Sanjoy Dasgupta and Prof. Misha Belkin. I completed a BSc in Mathematics and Computer Science, followed by an MSc in Computer Science at Chennai Mathematical Institute (CMI, India). Previously, I have held positions as a research scientist intern/fellow at Adobe Research (San Jose, CA, USA), Max Planck Institute for Software Systems (Saarbrücken, Germany), and IBM Research (Bengaluru, IN).

I am broadly interested in advancing both the theoretical foundations and practical applications of machine learning. Specifically, my focus lies in statistical machine learning, algorithm design, interactive learning, optimization, and the theoretical aspects of deep learning. I am particularly enthusiastic about leveraging tools from probability theory, analysis, differential geometry, and statistics to rigorously study the computational and statistical efficiency of learning algorithms. My goal is to deepen our understanding of the principles underlying data-driven learning and the capabilities of machines to extract meaningful insights from complex datasets.

More recently, I’m interested in the following problems (feel free to drop an email if you have interesting ideas to discuss):

• Learning Distance Functions:
  Exploring the intersection of manifold learning, linear representation hypothesis, and classical distance learning.
  ArXiv 2024

• Kernel Machines:
  Investigating the statistical-computational gap in learning with fixed or adaptive kernels.
  ArXiv 2024, ArXiv 2021

• Emergent Behavior in Neural Models:
  Studying phenomena such as grokking and phase transitions in neural architectures.
  Work in progress

• Generalization with Non-Parametric Models:
  Addressing reliability and hallucination issues in models using simple yet interpretable classifiers like nearest neighbors.
  Manuscript on selective classification with Neareat neighbors available

Contact: (username id) akk002 at ucsd dot edu

I’m looking for a research/engineer position for a summer internship in 2025. Please request a CV via email.

Recent News

1. [Dec, 2024] Attended Unknown Futures of Generalization workshop at Simons Institute, UC Berkeley.
2. [Summer, 2023] I was a research scientist intern at Adobe Research (San Jose, CA).
3. [Aug, 2022] Attended the Deep learning theory workshop at Simons Institute, UC Berkeley.
4. [July, 2022] Attended a summer school on Discrete Mathematics at Charles University, Prague (CZK).

Publications and Preprints

1. Learning Smooth Distance Functions via Queries
   Akash Kumar, Sanjoy Dasgupta
   In submission to a conference.
   [ArXiv 2024]

2. Mirror Descent on Reproducing Kernel Banach Space (RKBS)
   Akash Kumar, Misha Belkin, Parthe Pandit
   In submission to a Journal.
   [ArXiv 2024]

3. Convergence of Nearest Neighbor Selective Classification
   Akash Kumar, Sanjoy Dasgupta
   Manuscript on request.

4. Robust Empirical Risk Minimization with Tolerance
   Robi Bhattacharjee, Kamalika Chaudhuri, Max Hopkins, Akash Kumar, Hantao Yu (alphabetical order)
   Accepted in The 34th International Conference on Algorithmic Learning Theory (ALT’23), 2023
   A preliminary version appeared in AdvML Frontiers @ ICML 2022
   [ArXiv 2023]

5. Teaching via Best-Case Counterexamples in the Learning-with-Equivalence-Queries Paradigm
   Akash Kumar, Yuxin Chen, Adish Singla.
   Accepted in The 35th Conference on Neural Information Processing Systems (NeurIPS’21), 2021
   [Proc 2021], [Openreview]
   

6. The Teaching Dimension of Kernel Perceptrons
   Akash Kumar, Hanqi Zhang, Adish Singla, Yuxin Chen.
   Accepted in The 24th International Conference on Artificial Intelligence and Statistics (AISTATS’21), 2021
   [ArXiv 2021], [Proc 2021]
   

7. Average-case Complexity of Teaching Convex Polytopes via Halfspace Queries
   Akash Kumar, Adish Singla, Yisong Yue, Yuxin Chen.
   [ArXiv 2020]
   Rejected from ICML 2021 with 6 reviews
   Rejected from NeurlPS 2020 with 4 reviews
   

8. Deletion to Induced Matching
   Akash Kumar, Mithilesh Kumar.
   [ArXiv 2020]

Recent talks

Feature Learning in Large Language Models (Adobe Research, San Jose)
Teaching via Best-case Counterexamples (UCSD AI Seminar)

Some notes

Improved Certified Adversarial Lower Bound Using Adaptive Relaxations
Ongoing project on adversarial deep learning.

Escaping Saddle Points and Tensor Decomposition
Master’s Thesis under the guidance of Dr. K V Subrahmanyam. [Slides]

Natural Proofs Vs Derandomization
Project report completed as part of the Advanced Complexity course at Chennai Mathematical Institute.