Deep learning frameworks for modeling how neural circuits learn

Abstract

The brain's prowess in learning and adapting remains an enigma, particularly in its approach to the 'temporal credit assignment' problem. How do neural circuits determine which specific states and connections contribute to future outcomes, and subsequently adjust these for enhanced learning? My thesis addresses this by combining insights from the latest large-scale neuroscience data and recent deep learning theoretical tools. The first two projects introduce novel learning rules inspired by the Allen Institute's transcriptomics data, which revealed widespread and intricate cell-type-specific interactions among neuromodulatory molecules. This rule enables neurons to propagate credit information efficiently, enhancing learning performance beyond that of biologically plausible predecessors. Extensive computational experiments confirm the significant role of local neuromodulatory signals in learning, offering new perspectives on neural information processing. My third project assesses the generalization capabilities of bio-plausible learning rules through the lens of deep learning theory, particularly focusing on the curvature of the loss landscape via the loss’ Hessian eigenspectrum. Our findings reveal that these rules often settle in high-curvature regions of the loss landscape, indicating suboptimal generalization. This analysis led to a mathematical theorem linking synaptic weight update dynamics to landscape curvature, proposing neuromodulator-driven adjustments as a potential enhancement for learning rule performance. Given how initial conditions can greatly influence a system’s future trajectory, the fourth project delves into the impact of initial connectivity structures on learning dynamics in neural circuits. By examining various connectivity patterns derived from neuroscience data, including recent electron microscopy data, we analyze how these structures influence learning regimes, implicating metabolic costs and risks of catastrophic forgetting. Our findings suggest that high-rank initializations utilize pre-existing high-dimensional input expansion to facilitate input decoding, leading to minimal changes post-training and increasing the propensity for lazy learning. These specific initializations thus predispose networks toward certain learning behaviors, critically affecting their ability to adapt and generalize.