PhD Thesis Defense: Charles Liu

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Meeting ID: 963 8964 6986
Passcode: 411695

"A Generalized Framework for the 'Core' Thalamocortical Circuit Computation"

Abstract

This thesis explores a biologically-inspired computational framework based on a common excitatory-inhibitory circuit in the superficial layers of the cortex. By varying the strength of local feedback inhibition, this single circuit gives rise to distinct unsupervised learning behaviors: strong inhibition leads to clustering and hierarchical clustering, while weak inhibition produces principal component-like representations. From this principle, we develop three algorithms: Lateral Inhibition Clustering (LI-C), Lateral Inhibition Hierarchical Clustering (LI-HC), and Antipodal Iterative Mean Estimation (AIME).

LI-C performs clustering without requiring a predefined number of clusters, using a competitive learning rule to extract dominant patterns from data. LI-HC extends this mechanism by incorporating biologically plausible masking and recursive inhibition, enabling multi-level structure discovery. To enhance interpretability, we introduce a suite of cluster engineering strategies that refine cluster outputs in a data-driven way.

AIME operates under low-inhibition dynamics and serves as an efficient, interpretable alternative to traditional Principal Component Analysis (PCA). It produces diverse, meaningful components that span the principal subspace and scales linearly with input dimension, making it suitable for high-dimensional settings. Empirical and theoretical results show that AIME not only recovers principal directions but also offers redundancy and robustness not available in standard PCA.

Together, these models uncover a surprising computational unification: clustering and PCA, often viewed as distinct, emerge from the same circuit under different inhibitory regimes. This research explores this relationship both conceptually and mathematically, highlighting its implications for unsupervised learning and neural computation.

Thesis Committee

• Richard Granger (chair)
• Peter Chin
• Simon Shepherd
• Lilianne Mujica-Parodi (Stony Brook U)

Contact

For more information, contact Thayer Registrar at thayer.registrar@dartmouth.edu.