Combinatorics and Algorithms for Real Problems

Projects are listed by Type:

Algorithms, Machine Learning-AI

Algorithms Projects

TITLE: LAXMAN PROJECT

Mentor: Laxman Dhulipala

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TITLE: MOH PROJECT

Mentors: MohammadTaghi HajiAghayi

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TITLE: ERIN PROJECT

Mentors: Erin Molloy

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Machine Learning and AI Projects

TITLE: MING PROJECT

Mentors: Ming Lin

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TITLE: JORDAN PROJECT

Mentors: Jordan Boyd-Graber

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TITLE: Alternative Neural Nets for Navigating Games, Puzzles, and the Physical World

Mentor: Sarah Miller

THIS PROJECT IS TENTATIVE!!!!

Prereqisites Familiarity with machine learning, discrete math, algorithms, and programming; Candidates familiar with either formalization/proof development (i.e., Lean) or quantum computing may tackle respective aspects of the work, but neither is required.

Description

Project description: Building and training neural networks (NN) to reason both efficiently and flexibly in novel circumstances has been an enduring challenge. Using combinatorial game theory, we will build and train novel types of networks to solve puzzles and play games, aiming to capture increasingly general capabilities. We will test this framework on larger and more complex classes of puzzles and games towards ambiguous real-world predictions and decisions.

After testing this formal framework on interesting sums of puzzles and games, we can proceed with any of the following, depending on the students’ experience and inclination: (a) applications to physical systems, (b) formalization in a programming language, preferably Lean, or (c) exploring enhanced or accelerated computation using quantum resources. Option (a) does not require a physics prerequisite, and neither the formal methods of (b) nor the quantum computing of (c) will be necessary to make progress on this nascent approach to neural architectures and machine learning more generally.

We will compare these novel alternatives to more standard state-of-the-art methods, such as the latest innovations on transformer-based models andor popular reinforcement learning approaches that have been persistently plagued by hallucinations andor failures to transfer across complex environments.