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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Neuro-Computational Model of Cortical Growth

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Dr. Rishabh Pathak

A neuro-computational model of cortical growth integrates principles from neuroscience and computational modeling to study the development of the cerebral cortex, the outer layer of the brain responsible for higher cognitive functions. Here are the key aspects of a neuro-computational model of cortical growth:


1. Biologically Realistic Representation: The model incorporates biologically realistic features of cortical development, such as neuronal migration, synaptogenesis, and dendritic arborization. By simulating these processes computationally, researchers can study how neural activity and connectivity influence cortical growth.


2. Neuroanatomical Constraints: The model considers neuroanatomical constraints, such as the presence of radial glial cells and the formation of cortical layers, to accurately represent the structural organization of the developing cortex. By incorporating these constraints, the model can capture the spatiotemporal dynamics of cortical growth.


3. Neuronal Connectivity: The model accounts for the establishment of neuronal connections within the cortex, including the formation of local circuits and long-range connections. By simulating the growth of axonal and dendritic arbors, researchers can study how connectivity patterns emerge during cortical development.


4. Activity-Dependent Plasticity: The model incorporates activity-dependent mechanisms of synaptic plasticity, such as Hebbian learning rules, to simulate how neural activity influences the refinement of cortical circuits. By considering the role of activity in shaping connectivity patterns, the model can elucidate the impact of sensory experience on cortical growth.


5. Computational Simulations: Neuro-computational models use computational simulations, such as neural network models or biologically detailed simulations, to study the dynamics of cortical growth. These simulations allow researchers to investigate how interactions between neurons, glial cells, and growth factors contribute to the development of the cortex.


6.  Plasticity and Learning: The model explores how plasticity mechanisms and learning algorithms influence the organization and function of the developing cortex. By simulating learning tasks or sensory experiences, researchers can study how cortical circuits adapt and reorganize in response to environmental stimuli.


7.   Validation and Comparison: Neuro-computational models are validated against experimental data, such as neuroimaging studies or electrophysiological recordings, to ensure their biological relevance and accuracy. By comparing model predictions with empirical observations, researchers can assess the model's ability to capture the dynamics of cortical growth.


8.  Insights into Neurodevelopmental Disorders: By simulating aberrant growth patterns or disruptions in cortical development, neuro-computational models can provide insights into the mechanisms underlying neurodevelopmental disorders, such as autism spectrum disorders or intellectual disabilities. These models help researchers understand how alterations in cortical growth processes may contribute to neurological conditions.


In summary, a neuro-computational model of cortical growth offers a powerful framework for studying the intricate processes involved in the development of the cerebral cortex. By combining neuroscience principles with computational modeling techniques, researchers can gain valuable insights into the mechanisms driving cortical growth, connectivity formation, and the emergence of functional circuits in the developing brain.

 

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