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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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Basal Ganglia (BG)

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Dr. Rishabh Pathak

The Basal Ganglia (BG) is a group of interconnected subcortical nuclei in the brain that play a crucial role in motor control, cognition, emotion, and behavior modulation. Here is a detailed explanation of the Basal Ganglia:


1.   Anatomy: The Basal Ganglia is a complex network of nuclei located deep within the brain, including structures such as the striatum (comprising the caudate nucleus and putamen), globus pallidus (external and internal segments), subthalamic nucleus, and substantia nigra (pars compacta and pars reticulata). These nuclei are interconnected with the cerebral cortex, thalamus, and brainstem regions, forming circuits that regulate motor and non-motor functions.

2.     Function:

o  Motor Control: The Basal Ganglia are involved in the planning, initiation, execution, and modulation of voluntary movements. They contribute to motor coordination, movement scaling, action selection, and the suppression of unwanted movements. Dysfunction in the Basal Ganglia can lead to movement disorders such as Parkinson's disease, Huntington's disease, and dystonia.

o   Cognition: Beyond motor functions, the Basal Ganglia also play a role in cognitive processes such as decision-making, reward processing, learning, and memory. They are implicated in action selection, habit formation, and the integration of motor and cognitive functions.

o  Emotion and Behavior: The Basal Ganglia influence emotional responses, motivation, and social behavior. They are involved in regulating mood, reward-seeking behavior, impulsivity, and the processing of emotional stimuli. Dysfunction in the Basal Ganglia circuits can contribute to psychiatric disorders like depression, addiction, and obsessive-compulsive disorder.

3. Neurotransmitters: The Basal Ganglia circuits primarily utilize the neurotransmitters dopamine, gamma-aminobutyric acid (GABA), and glutamate to transmit signals between different nuclei. Dopaminergic projections from the substantia nigra and ventral tegmental area play a critical role in modulating Basal Ganglia function and are particularly affected in Parkinson's disease and other movement disorders.


4.    Pathophysiology:

o   Parkinson's Disease: Degeneration of dopaminergic neurons in the substantia nigra leads to dopamine deficiency in the Basal Ganglia, resulting in motor symptoms like tremors, rigidity, bradykinesia, and postural instability. Treatment strategies for Parkinson's disease often involve dopaminergic medications, deep brain stimulation, and physical therapy.

o    Huntington's Disease: In Huntington's disease, a genetic disorder, degeneration of the striatum and other Basal Ganglia nuclei leads to involuntary movements, cognitive decline, and psychiatric symptoms. The disease is characterized by chorea, dystonia, and progressive neurodegeneration.

5.  Clinical Implications: Understanding the role of the Basal Ganglia in motor control, cognition, and emotion is essential for diagnosing and treating neurological and psychiatric disorders. Imaging techniques, electrophysiological studies, and computational models are used to investigate Basal Ganglia function and dysfunction in health and disease.

In summary, the Basal Ganglia is a complex brain structure involved in a wide range of functions, including motor control, cognition, emotion, and behavior modulation. Dysregulation of Basal Ganglia circuits can lead to movement disorders, cognitive impairments, and psychiatric symptoms, highlighting the importance of studying these nuclei in both health and disease.

 

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