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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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Neural Circuits and Computation

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Dr. Rishabh Pathak


 

Neural circuits and computation refer to the intricate networks of interconnected neurons in the brain that work together to process information and generate behaviors. Here is a brief explanation of neural circuits and computation:


1. Neural Circuits: Neural circuits are pathways formed by interconnected neurons that communicate with each other through synapses. These circuits are responsible for processing sensory information, generating motor commands, and mediating cognitive functions.

2. Computation in Neural Circuits: Neural circuits perform computations by integrating and processing incoming signals from sensory inputs or other neurons. This processing involves complex interactions between excitatory and inhibitory neurons, synaptic plasticity, and feedback mechanisms.

3. Behavioral Relevance: Neural circuits play a crucial role in mediating specific behaviors by translating sensory inputs into motor outputs. Different circuits are specialized for various functions, such as motor control, memory formation, and emotional processing.

4. Study Methods: Researchers study neural circuits using a combination of experimental techniques, including electrophysiology, optogenetics, and imaging methods. These approaches help unravel the dynamics of neural circuits and how they contribute to behavior.

5. Computational Models: Computational neuroscience employs mathematical models to simulate the behavior of neural circuits and understand how they process information. These models provide insights into the underlying principles governing neural computation.


Understanding neural circuits and computation is essential for unraveling the complexities of brain function and behavior. By studying how these circuits process information and generate behaviors, researchers can gain valuable insights into the mechanisms underlying cognition, perception, and decision-making

 

 

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