Project Opportunities

Title: Relevance and Irrelevance: From Renormalization Group to Information Bottleneck and Back

Summary of opportunity:

This project explores the deep mathematical connections between renormalization group (RG) concepts of relevant and irrelevant variables in statistical physics and the notion of relevant and irrelevant information in information bottleneck (IB) theory. The candidate will develop a unified framework that transfers analytical and numerical techniques between these fields, using RG methods to solve information bottleneck problems and information-theoretic insights to generate new insights into renormalization group. This bidirectional approach will yield new solutions, perturbation theory, and computational methods that leverage the shared mathematical structure of coarse-graining in physics and optimal compression in information bottleneck theory.

Opportunity synopsis:

Renormalization group (RG) and the information bottleneck (IB) method share a fundamental goal: systematically identifying what variables and information are relevant at different scales while discarding irrelevant details. In RG, relevant variables persist under coarse-graining while irrelevant ones vanish; in IB, relevant information is preserved while irrelevant information is compressed away. Recent work has revealed that these parallels extend beyond analogy to precise mathematical correspondence, with direct implications for modern machine learning where neural networks must learn relevant representations from high-dimensional data.

This project will develop a comprehensive theoretical framework exploiting this correspondence in both directions. From RG to IB, we will adapt Wilson's momentum-shell integration, decimation procedures, and critical phenomena analysis to derive new solutions for optimal data compression in machine learning. From IB to RG, we will use information-theoretic measures to define novel RG flows and generate insights into universal behavior. The research will establish how deep neural networks implicitly perform information bottleneck optimization during training, connecting information compression to RG-like hierarchical feature extraction.

Key technical objectives include: (1) establishing mappings between RG flows and information bottleneck optimization trajectories in representation learning, (2) developing perturbative expansions using both analytical and numerical methods, (3) exploring normalizing flows as a method for solving IB optimization, and (4) investigating how formulating IB and RG with alternative information measures could lead to new insights into statistical physics and neural networks.

The project combines rigorous mathematical analysis with practical algorithmic development for modern AI systems. Applications include understanding how transformer models compress information across layers, designing principled pruning methods based on RG or IB-inspired relevance measures, and developing new representation learning algorithms that explicitly optimize for relevant information at multiple scales. Expected outcomes include new solutions for information compression, insights into phase transitions during neural network training, and computational methods that leverage physics-inspired coarse-graining for efficient representation learning. The candidate will work at the intersection of theoretical physics, information theory, and machine learning, developing expertise valuable for both fundamental research and practical applications in AI systems that must identify and preserve relevant information across different levels of abstraction.

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Project Opportunities

Title: Non-Reciprocal Active Matter in Bacterial Colonies

Summary of opportunity:

How do thousands of bacteria coordinate their movements to give rise to complex structures and collective behavior without any central control? Recent advances in high-precision experimental techniques have enabled experimentalists to simultaneously track thousands of individual bacteria. Understanding these systems requires developing new statistical physics frameworks for active matter guided by real experimental data. This project offers a unique opportunity to discover novel phase transitions and collective effects that are absent in equilibrium systems, collaborate with cutting-edge bacterial tracking datasets from international collaborators, inform future experiments, and develop a new lens through which to understand biological complexity. This work will contribute to the foundations of active matter theory, generating new insights that could inform future bioengineering applications.

Opportunity synopsis:

Recent breakthroughs in bacterial tracking technology now allow simultaneous observation of thousands of individual cells, revealing collective behaviors that cannot be readily explained by equilibrium statistical physics or traditional active matter theory. Bacterial colonies exhibit non-reciprocal interactions where cells respond asymmetrically to their neighbors, leading to phase transitions and pattern formation absent in equilibrium systems. The newly available experimental data offer an unprecedented opportunity to develop new theoretical frameworks grounded in biological reality.

This project will build statistical physics models directly from experimental observations, using maximum entropy methods and Bayesian inference to extract interaction rules from bacterial trajectory data. Working closely with international experimental collaborators, we will develop theories that capture salient collective phenomena in Myxococcus xanthus colonies, including non-reciprocal phase transitions and exceptional point dynamics.

Cultivating a collaboration with a leading experimental group is a key aspect of this project. Our theoretical models will not only explain existing observations but also predict new collective behaviors that can guide future experiments. This iterative process will establish a new paradigm for understanding biological active matter, contributing fundamental insights while informing strategies for controlling bacterial communities in biomedical and biotechnological applications.

DrWave Ngampruetikorn

LEARNING & TEACHING SUMMARy