Published in Proceedings of the 2025 SIAM International Conference on Data Mining 2nd Workshop on Metacognitive Predictive of AI Behavior. 

Published in ACM Transactions on Probabilistic Machine Learning, wherein the empirical and formal properties of the Certainty and Competence framework for discriminative tasks are demonstrated, indicating SOTA Out-of-Distribution Detection over EnergyBased Methods.

Published in IEEE/CVF Winter Conference, wherein address the problem of detecting out-of-context (OOC) objects in a scene. We find that a pre-trained FM, such as GPT-4, provides a more nuanced notion of OOC and enables zero-shot OOC detection when coupled with other pre-trained FMs for caption generation such as BLIP-2, and image in-painting with Sta-ble Diffusion 2.0. Our approach does not need any dataset-specific training. We demonstrate the efficacy of our approach on two OOC object detection datasets, achieving 90.8% zero-shot accuracy on the MIT-OOC dataset and 87.26% on the IJCAI22-COCO-OOC dataset.

Published IEEE MILCOM. By combining certainty and competence scoring, derived from a recent post-hoc uncertainty quantification framework, and with the use of logic tensor networks (LTN), a form of neurosymbolic artificial intelligence, we examine and make improvements to the baseline xView2 neural network architecture developed for disaster damage assessment for aerial image data.

Poster in NeurIPS2024. In this paper, we present a dynamic semantic clustering approach inspired by the Chinese Restaurant Process, aimed at addressing uncertainty in the inference of Large Language Models (LLMs). We quantify uncertainty of an LLM on a given query by calculating entropy of the generated semantic clusters. 

Published in SPIE Proceedings Volume 13054, Assurance and Security for AI-Enabled Systems. Herein, we develop the theory of graph representation learning (GRL) to extend to Bayesian Graph Neural Networks and to incorporate various forms of uncertainty quantification to improve model development and application in the presence of adversarial attacks. 

Published IEEE MILCOM. n this paper, we propose combining neural foundation models (FMs) using symbolic programs that results in a more effective AI for adversarial conditions. Neuro-symbolic composition of FMs to solve complex tasks requires interactive and unambiguous specification of the intent, task decomposition into subtasks that can be solved by individual FMs, program synthesis for composing FMs, and neuro-symbolic inference that schedules inference of different FMs and combines their results. 

Pre-print wherein we introduce a novel approach for calibrating uncertainty quantification (UQ) tailored for multi-modal large language models (LLMs)

UIC PhD Dissertation, Published in 2022. Establishes minimal logical foundations for the definition and analysis of genetic functions whose image takes values over the Surreal number field, and introduces the notion of Veblen rank to bind the growth of complexity of said functions. 

Partially completed paper whose novel results appear in my dissertation; providing the motivation for the work that lead to Veblen rank.

Incomplete notes whose research program partially inspired my dissertation work; the topics extend from the summary of differentiation and attempts for integration of the surreals as well as exploring connections between Class sized models of set theory in which the Surreal numbers can be embedded and the automorphism between the surreal numbers in some ground model and the forcing extension.

A review document that I prepared for some of my perspicacious Calculus III students at UIC (this may be useful for other students studying Calculus III or interested in learning some of the fundamentals for Differential Geometry). 

A joint paper co-written by myself and two other graduate students for Lev Reyzin's Mathematics of Artificial Intelligence course - our principal result finds an example proving a conjecture of Alon et al that sign rank and dual sign rank do not agree. 

My dissertation for my MMath degree at the University of Waterloo; a broad historical survey of the subject of topos theory connecting the original motivations in algebraic geometry (the Weil conjectures), with recent developments in formal proof verification and functorial semantics.

Personal notes that informed a talk given in a course on Homotopy Type Theory at the University of Waterloo and Perimeter Institute in 2014.

Personal notes informing the content of two talks given at at the University of Waterloo's Graduate Seminar in Algebraic topology; a survey introducing the conceptual terms of category theory with the aim of motivating and defining derived functors.

A survey intended to provide an introductory overview for the formalisms found in introductory courses on quantum mechanics- chiefly the role played by Hilbert spaces.

A paper co-authored with 3 other students at Columbia's summer 2011 REU; we construct sequences of Apollonian group generators with infinite length to identify self-similar unbounded packings and connect such words with non-trivial residual points.