Research on Omanshu Thapliyal

So does your Car fail? (A Small Harness for Mathematical Exploration) - Part 3

Wed, 16 Sep 2026 12:02:49 -0400

Part 1:https://omanshuthapliyal.github.io/blog/hrt-conjecture/

Part 2: https://omanshuthapliyal.github.io/blog/hrt-conjecture-part-2/

In the (last couple) (of posts) I explained what the recently (dis-)proven HRT conjecture states, and what it implies. We looked at how a computer-assisted argument can turn a difficult mathematical question into a finite collection of things that can be checked. Here, we try the more mundane inverse problem: how do we set up a small AI harness such that an LLM can suggest where to look, while the things that matter are still checked deterministically? Here’s a speedy recap. The original HRT conjecture asked whether this could ever happen.¹ For a function $$g$$, define the time-frequency shift $$ \pi(a,b)g(x) = e^{2\pi i b x}g(x-a). $$ Given finitely many distinct points $$ \Lambda = \{(a_k,b_k)\}_{k=1}^{N} \subset \mathbb{R}^{2}, $$ HRT asked whether the collection $$\{\pi(a_k,b_k)g\}_{k=1}^{N}$$ is always linearly independent whenever $$g\neq 0$$. Equivalently, can we find nonzero coefficients $$c_k$$ such that $$ \sum_{k=1}^{N} c_k \pi(a_k,b_k)g = 0? $$

Reward is enough — when can we 'reinforce' the learning?

Wed, 13 Aug 2025 11:07:46 -0700

This blog post summarizes the papers Settling the Reward Hypothesis¹ and Utility Theory for Sequential Decision Making ².

The reward hypothesis is at the core of Reinforcement Learning (RL) in that whether sequential action problems can be posed as some sort of a reward maximization. One of the founders of modern RL, Richard S. Sutton, puts it as³:

“That all of what we mean by goals and purposes can be well thought of as maximization of the expected value of the cumulative sum of a received scalar signal (reward).”

Technology Readiness Levels of AI methods

Tue, 15 Oct 2024 11:07:46 -0700

Recent news of the SpaceX catching its Starship Super Heavy booster¹ is quite discussed and marveled upon in the media, and rightly so. Executing what was done can perhaps be explained as trying to catch a falling stick, then balancing it vertically, all while the stick is over 200 ft tall, weighs over 150 tonnes, spews fire, and costs over tens of millions of dollars. One cannot but feel a little giddy as a controls engineering enthusiast over this massive success. It makes me think why we are closer to automation in certain domains/problems than others? Why, for example, is your vacuum cleaning robot seemingly better at navigating in a cluttered environment than your possibly self-driving car? Why is the tremendous progress in machine learning & AI not permeating outside of our web lives as much as we expected in the early 2000’s?

Why I am studying this: Data Driven Safety

Wed, 16 Mar 2022 12:32:31 -0400

This is my attempt to try to motivate and justify why I am studying what I study, and to try to justify the title of my dissertation.

While most emphasis on safety has been provided from a model-driven perspective, data-driven approaches present a novel semi model-driven method by employing model-discovery. As data becomes more inexpensive, and system capabilities highly nonlinear, and often subject to parameter variations during mission, data-driven approaches are utilized more and more in controls engineering. Further, online and real-time applications increasingly require unknown models and nonlinear interactions to be learned for control synthesis. To this end, more established fields of system identification are increasingly utilizing data-driven models by using neural networks, autoregressive models, and other machine learning techniques. Due to the expressive nature of such machine learning techniques, they are utilized to learn models of unknown dynamical systems from observed data sequences. In such approaches, a `discovered model’ is arrived at using data, and employed to perform control design. Even though purely model-driven are slowly getting harder to apply to more recent, realistic, and complex scenarios, they provide a strong basis to study extensions of similar approaches to data-driven techniques for estimation and control. As a result, I attempt to utilize model-driven techniques and extend them to study safety and security properties of cyberphysical systems using data. Therefore, my primary aim is to study data-driven approaches to safety, and data-driven vulnerabilities against cyberattacks, of complex control systems.

Birds and Frogs in Science

Sun, 25 Aug 2019 20:20:44 +0530

One of my fellow grad students shared a paper with me that turned out to be a great read. It was Professor Freeman Dyson’s article titled Birds and Frogs, that was the invited Einstein lecture at the American Mathematical Society. Dyson talks about two categories of mathematicians (researchers) – birds, and frogs. While birds soar high, and get a view of the entire landscape, frogs tread tread deep, looking for details. Dyson argues how both kinds are equally important for mathematics in particular, and science in general. He does not make a case for either being superior to the other, merely pointing out the differences between the research approach of the two.