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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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Functional Brain Network

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Dr. Rishabh Pathak

Functional brain networks refer to the interconnected system of brain regions that exhibit synchronized neural activity and functional connectivity during specific cognitive tasks or at rest. 

1. Definition:

   - Functional brain networks are patterns of coordinated neural activity among different brain regions that work together to support specific cognitive functions, such as attention, memory, language, and emotion regulation [T5].

   - These networks are identified using techniques like functional magnetic resonance imaging (fMRI) and electroencephalography (EEG), which measure changes in blood flow or electrical activity to infer functional connections between brain regions.

 

2. Resting-State Networks (RSNs):

   - Resting-state networks (RSNs) are functional brain networks that exhibit synchronized activity even in the absence of a specific task, reflecting the intrinsic organization of the brain's functional architecture.

   - Common RSNs include the Default Mode Network (DMN), Frontoparietal Network (FPN), Salience Network (SAN), Limbic Network (LIM), Dorsal Attention Network (DAN), Somatomotor Network (SMN), and Visual Network (VIS).

 

3. Functional Connectivity:

   - Functional connectivity refers to the statistical correlation or coherence of neural activity between different brain regions, indicating the strength of communication and interaction within a functional brain network.

   - Measures of functional connectivity can reveal how information is processed and integrated across distributed brain regions during cognitive tasks or in resting states.

 

4. Task-Related Networks:

   - Task-related functional brain networks are activated when individuals engage in specific cognitive tasks or sensory-motor activities, reflecting the dynamic coordination of brain regions to support task performance.

   - These networks can be identified by analyzing changes in neural activity patterns or connectivity during task execution, providing insights into the neural mechanisms underlying cognitive processes.

 

5. Network Dynamics:

   - Functional brain networks exhibit dynamic changes in connectivity patterns and network configurations in response to external stimuli, cognitive demands, and internal states.

   - The flexibility and adaptability of brain networks allow for efficient information processing, cognitive flexibility, and the integration of sensory, motor, and cognitive functions.

 

In summary, functional brain networks represent the coordinated activity and connectivity patterns among brain regions that underlie cognitive processes and behaviors. By studying the organization and dynamics of these networks using advanced neuroimaging techniques, researchers can unravel the complex interactions within the brain and gain insights into normal brain function, cognitive disorders, and the effects of interventions on brain connectivity.



 

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