I defended my PhD in December 2024, advised by Dr. Ravi
Sundaram in the Theoretical Computer Science
Group at Northeastern
University. My thesis was on the use of a heterogeneous algorithmic
toolkit for problems involving a variety of graph parameters. Before
joining NEU, I completed my B.Tech. degree (2013-2017) in Information
and Communication Technology from DAIICT, Gandhinagar, India (see Bachelor Thesis). I also got a minor in
Computational Sciences and still have some lingering interest in areas
like High Performance Computing, Complex Networks, and Modelling and
Simulation.
2025-01-01:[Woah.. future magic.] I’ll
be joining Khoury College
of Computer Sciences as an Assistant Teaching Professor starting
January 2025 and will be teaching CS 3000 Algorithms in the Spring
semester.
2024-12-17: I successfully defended my
thesis.
2024-05-12: Links to explanations for
why computers think 0.1 + 0.2 = 0.30000000000000004.
2024-04-24: A very basic (but optimal)
Tic-Tac-Toe implementation in Elm
(ported from strategies originally implemented in Haskell).
2023-07-17: An animated version of one of my
favorite proofs (without words) of the Pythagoras theorem. Mathstodon
post providing some context.
2023-07-14: An animation
going over the simplest cases of the Master Theorem that I made to learn
to use the manim python library. Mathstodon
post providing some context.
Past Teaching
Algorithms courses: Instructor of Record – UG Fall 2024, UG 2023 Summer 2. Teaching
Assistant – UG Summer 1 2024, MS Fall 2022, MS Fall 2021, UG Spring
2021, MS Fall 2019, UG Fall 2017.
Teaching Assistant for Discrete Structures in Fall 2023 and for
Theory of Computation in Spring 2024.
To help with TAing, I made a LaTeX template for easily creating the
various handouts seen in such courses. You can find it on my repo of
various LaTeX templates; see the course-handout-usage-example.tex
file for an example of using the course-handouts-preamble.sty
style file.
In the past (Jul–Nov 2016) I have also been a Teaching Assistant for
an undergraduate High Performance Computing course offered to 3rd year
B.Tech students. Experiences in teaching this course, and the tools we
hacked up to help, lead to the development of a web-based platform to
aid HPC education and a journal paper. Details
below. ⤵
Research
I am interested in understanding the theoretical aspects of problems
arising in Computer Science. In particular problems related to:
Graph algorithms: specifically those dealing with either estimating
or leveraging various kinds of graph parameters and utilizing that to
solve problems; as well as various hardness results and lower bounds for
such problems. I am also interested in how a theoretician needs a
heterogeneous toolkit today including techniques generally sequestered
into subfields like approximation, randomized, sublinear or fixed
parameter tractable algorithms. I am also working on a problem that has
to resort to the (mostly heuristic) world of machine learning to solve
certain graph problems.
Machine learning: specifically those related to kernels and random
features, overparametrization, convergence and generalization in neural
networks.
My PhD thesis’ focus is on the heterogeneous toolkit including
approximation algorithms, randomized algorithms, fixed-parameter
tractable algorithms, sublinear time and constant time algorithms and
machine learning. These are used to solve problems involving graph
parameters given the prevalence of large data sets, highly specialized
graph subclasses, and problem scenarios that are less structured and
more complex.
Here are a list of my publications. The
symbol indicates alphabetical ordering of authors as is customary in
theoretical computer science.
Toward remote and secure
authentication: Disambiguation of magnetic microwire signatures using
neural networks Akshar Varma, Xiaoyu Zhang,
Brian Lejeune, Laura Cebada Almagro, Rafael P del Real, Pilar Marin,
Ogheneyunume Fitchorova, Laura H Lewis, Ravi Sundaram. MRS
Communications volume 13, pages 16–20 (February 2023). I presented a
poster on preliminary work at the MRS 2022 Spring Meeting (May 2022);
see slides below.
@article{VarmaDisambiguationUsingNNinMRS2023,
title={Toward remote and secure authentication: Disambiguation of magnetic microwire signatures using neural networks},
author={Varma, Akshar and Zhang, Xiaoyu and Lejeune, Brian and Almagro, Laura Cebada and del Real, Rafael P and Marin, Pilar and Fitchorova, Ogheneyunume and Lewis, Laura H and Sundaram, Ravi},
journal={MRS Communications},
volume={13},
number={1},
pages={16--20},
year={2023},
publisher={Springer}
}
Secure and high-throughput authentication systems require materials with
uniquely identifiable responses that can be remotely detected and
rapidly disambiguated. To this end, complex electromagnetic responses
from arrangements of amorphous ferromagnetic microwires were analyzed
using machine learning. These novel materials deliver maximal spectral
dispersion when the frequency of incident electromagnetic radiation
matches the microwire resonance. Utilizing data obtained from 225 unique
microwire arrangements, a neural network reproduced the response
distribution of unseen data to a confidence level of 90%, with a mean
square error less than 0.01. This favorable performance affirms the
potential of magnetic microwires for use in tags for secure article
surveillance systems.
Realization Problems
on Reachability Sequences
Matthew Dippel, Ravi Sundaram, Akshar Varma Theoretical
Computer Science, Volume 866, Pages 1-13 (April 2021). I presented a
preliminary version at the COCOON 2020 conference and it appeared in its
proceedings; see slides and video below.
@article{VarmaReachabilityRealizationinTCS2021,
title={Realization problems on reachability sequences},
author={Dippel, Matthew and Sundaram, Ravi and Varma, Akshar},
journal={Theoretical Computer Science},
volume={866},
pages={1--13},
year={2021},
publisher={Elsevier}
}
@inproceedings{VarmaReachabilityRealizationinCOCOON2020,
title={Realization Problems on Reachability Sequences},
author={Dippel, Matthew and Sundaram, Ravi and Varma, Akshar},
booktitle={Computing and Combinatorics: 26th International Conference, COCOON 2020, Atlanta, GA, USA, August 29--31, 2020, Proceedings},
pages={274--286},
year={2020},
organization={Springer}
}
The classical Erdos-Gallai theorem (1960) kicked off the study of graph
realizability by characterizing degree sequences. We extend this line of
research by investigating realizability of directed acyclic graphs
(DAGs) given a sequence of tuples each containing multiple node
properties including the degree, reachability value (number of nodes
reachable from a given node), depth and height of a node. The most
interesting problems are when the sequences contain both a local
constraint via degree values and a global constraint via reachability
values. We show that, without degree constraints, DAG reachability
realization is solvable in linear time, whereas it is strongly
NP-complete given upper bounds on in-degree or out-degree. After
defining a suitable notion of bicriteria approximation based on
consistency, we give two approximation algorithms achieving O(log
n)-reachability consistency and O(log n)-degree consistency; the first,
randomized, uses LP (Linear Program) rounding, while the second,
deterministic, employs a k-set packing heuristic. We end with some
future directions of research and a set of conjectures that we hope will
motivate further study of realizability with reachability constraints.
Attention improves
concentration when learning node embeddings
Matthew Dippel, Adam Kiezun, Tanay Mehta, Ravi Sundaram, Srikanth
Thirumalai, Akshar Varma. arXiv preprint (June 2020). In
Dec 2018, I gave a short talk (on preliminary work) at ICTSfun-fact during the TBML
discussion meeting; see slides and video below.
@article{VarmaAttentionImprovesConcentration2020,
title={Attention improves concentration when learning node embeddings},
author={Dippel, Matthew and Kiezun, Adam and Mehta, Tanay and Sundaram, Ravi and Thirumalai, Srikanth and Varma, Akshar},
journal={arXiv preprint arXiv:2006.06834},
year={2020}
}
We consider the problem of predicting edges in a graph from node
attributes in an e-commerce setting. Specifically, given nodes labelled
with search query text, we want to predict links to related queries that
share products. Experiments with a range of deep neural architectures
show that simple feedforward networks with an attention mechanism
perform best for learning embeddings. The simplicity of these models
allows us to explain the performance of attention. We propose an
analytically tractable model of query generation, AttEST, that views
both products and the query text as vectors embedded in a latent space.
We prove (and empirically validate) that the point-wise mutual
information (PMI) matrix of the AttEST query text embeddings displays a
low-rank behavior analogous to that observed in word embeddings. This
low-rank property allows us to derive a loss function that maximizes the
mutual information between related queries which is used to train an
attention network to learn query embeddings. This AttEST network beats
traditional memory-based LSTM architectures by over 20% on F-1 score. We
justify this out-performance by showing that the weights from the
attention mechanism correlate strongly with the weights of the best
linear unbiased estimator (BLUE) for the product vectors, and conclude
that attention plays an important role in variance reduction.
Let’s HPC: A web-based platform to
aid parallel, distributed and high performance computing
education Bhaskar Chaudhury, Akshar Varma,
Yashwant Keswani, Yashodhan Bhatnagar, Samarth Parikh Journal of
Parallel and Distributed Computing, Volume 118, Part 1, Pages 213-232
(August 2018).
@article{VarmaLetsHPCinJPDC2018,
title={Let’s hpc: A web-based platform to aid parallel, distributed and high performance computing education},
author={Chaudhury, Bhaskar and Varma, Akshar and Keswani, Yashwant and Bhatnagar, Yashodhan and Parikh, Samarth},
journal={Journal of Parallel and Distributed Computing},
volume={118},
pages={213--232},
year={2018},
publisher={Elsevier}
}
Let’s HPC (www.letshpc.org) is an
evolving open-access web-based platform to supplement conventional
classroom oriented High Performance Computing (HPC) and Parallel &
Distributed Computing (PDC) education. This platform has been developed
to allow users to learn, evaluate, teach and see the performance of
parallel algorithms from a system’s viewpoint. The Let’s HPC platform’s
motivation comes from the experiences of teaching HPC/PDC courses and it
is designed to help streamline the process of analyzing parallel
programs. At the heart of this platform is a database archiving
the performance and execution environment related data of standard
parallel algorithm implementations run on different computing
architectures using different programming environments. The online
plotting and analysis tools of our platform can be combined seamlessly
with the database to aid self-learning, teaching, evaluation and
discussion of different HPC related topics, with a particular focus on a
holistic system’s perspective. The user can quantitatively compare and
understand the importance of numerous deterministic as well as
non-deterministic factors of both the software and the hardware that
impact the performance of parallel programs. Instructors of HPC/PDC
related courses can use the platform’s tools to illustrate the
importance of proper data collection and analysis in understanding
factors impacting performance as well as to encourage peer learning
among students. Scripts are provided for automatically collecting
performance related data, which can then be analyzed using the
platform’s tools. The platform also allows students to prepare a
standard lab/project report aiding the instructor in uniform evaluation.
The platform’s modular design enables easy inclusion of performance
related data from contributors as well as addition of new features in
the future. This paper summarizes the background and motivation
behind the Let’s HPC project, the design philosophy of the platform, the
present capabilities of the platform, as well as the plans for future
developments.
Reachability Problems and
Space Bounds Akshar Varma; under guidance of Prof. Nutan Limaye, IIT
Bombay. Bachelor Thesis.
@Thesis{VarmaBachelorThesis2017,
title={Reachability Problems and Space Bounds}, author={Varma, Akshar},
type={bathesis}, institution={DA-IICT}, year={2017} }
Space complexity is an important field of study, to understand the
theoretical memory requirements to solve various problems. Such study is
necessary due to the increasing availability of large amounts of data,
and hence problem sizes, to know which questions can be answered within
feasible memory capabilities. This project studies certain graph
reachability problems within the classes NL, L, UL, coUL, etc.
Particularly, for 3D monotone grid graphs, the reachability or
st-connectivity problem is looked at, that is whether there is a path
from one vertex s to another vertex t. This particular problem is of
interest as variants of it span across the space complexity spectrum.
Bourke et al. show that the general variant is NL-Complete, hence
linking it to the L vs. NL question. We look at variants that are more
tractable, and show, using various reductions, that variants of the 3D
monotone grid graph reachability (3D-MGGR) problem have some interesting
properties. We show that the 3D-MGGR with O(1) 2D layers is in UL
coUL using logspace and AC0 reductions. We also relax one of
the monotonicity conditions within layers and show that problem to have
the same complexity. On the other hand, we prove that removing
monotonicity between layers makes the problem difficult, specifically we
show that the 3D-MGGR problem without monotonicity between layers is
NL-Complete even for the case of only 2 layers. To understand the nature
of other 3D-MGGR variants, we provide preliminary ideas on defining a
restricted class of graphs which would allow the monotonicity conditions
to be relaxed further. These results provide an insight into the
nature of complexity classes within NL, and also into how well these
problems can characterize these complexity classes. Our reductions show
that nuanced variants of 3D-MGGR can have significantly distinct
complexities and are worth studying.
Quite a long time ago, I had attended the NMI workshop on
Complexity Theory at IIT Gandhinagar in November 2016 and the Forum for
Information Retrieval Evaluation at DA-IICT, Gandhinagar in December
2015.
Some of my favorite built-in parts of Emacs include: Ido, Dired,
TRAMP, Keyboard Macros, Org+Agenda and most importantly the beautiful
self documentation.
Some packages of note I use from MELPA include: Magit, AUCTex, PDF
Tools, Notmuch.
Packages I use which improves the Emacs (editing) experience without
any significant learning curve. These tend to be among the top
downloaded MELPA packages.
Plug and play: aggresive-indent, beginend, highlight-numbers,
hungry-delete, anzu (just the basic stuff is sufficient), undo-tree,
which-key, browse-kill-ring, dired-rainbow, volatile-highlights.
10-15 minutes for basic usage: smartparens, expand-region,
move-text, wgrep, iedit.
Idea from: https://morganastra.me/tools-I-use.html,
which does have some nice tools listed in there. I use none of them,
although I do use Emacs (instead of Spacemacs), ripgrep/rg in Emacs (an
alternative to ag that is available as an Emacs package), Vimium (which
is similar to Vimperator). I only list Emacs since I spend most of my
time in there and don’t have particularly strong views about any other
tool.
My name, Akshar Varma, in various other scripts that might aid
pronunciation (and two audio snippets). Roughly in decreasing order of
confidence. (Note: I don’t actually speak all of these languages.)
I think that the first audio is slightly closer to a native speaker
of Hindi while the second audio is slightly closer to a native speaker
of Malayalam. Apart from that minor difference, both sound correct to
me.
A friend helped with this; they told me that since Arabic doesn’t
have a v sound this uses a f sound instead.
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Assistant Teaching Professor
Twitter
symbol indicates alphabetical ordering of authors as is customary in
theoretical computer science.
My Emacs config idea h/t, on EmacsWiki
