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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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What is Brain Stimulation and its applications in research world?

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Dr. Rishabh Pathak


 

Brain Stimulation is a field of neuroscience that involves the use of various techniques to modulate brain activity non-invasively. This can include methods such as transcranial magnetic stimulation (TMS), transcranial direct current stimulation (tDCS), and deep brain stimulation (DBS). These techniques are used to study brain function, investigate neurological disorders, and potentially treat conditions such as depression, chronic pain, and movement disorders. Brain stimulation has shown promise in enhancing cognitive abilities, promoting neuroplasticity, and modulating neural circuits.

 Here are some applications of brain stimulation in the research world:

1.     Neuroscientific Research: Brain stimulation techniques are widely used in neuroscience research to investigate brain function, neural circuits, and the underlying mechanisms of various cognitive processes. Researchers can manipulate brain activity in specific regions to study their role in perception, attention, memory, and motor control.

2.     Neuroplasticity: Brain stimulation has been shown to induce neuroplastic changes in the brain, leading to alterations in synaptic strength and connectivity. This is valuable for studying how the brain adapts to different stimuli and experiences, as well as for exploring potential treatments for neurological disorders.

3.     Clinical Applications: Brain stimulation techniques are used in clinical research to explore their therapeutic potential for various neurological and psychiatric conditions. For example, TMS is FDA-approved for the treatment of depression, and research is ongoing to investigate its efficacy in conditions such as chronic pain, schizophrenia, and stroke rehabilitation.

4.     Cognitive Enhancement: Brain stimulation has been explored as a tool for enhancing cognitive abilities such as memory, attention, and learning. By modulating brain activity in specific regions, researchers aim to improve cognitive function in healthy individuals and potentially aid in the treatment of cognitive deficits.

5.     Brain-Computer Interfaces: Brain stimulation techniques are integrated into brain-computer interface research, where neural signals are used to control external devices or communicate with computers. By modulating brain activity, researchers can enhance the efficiency and accuracy of brain-computer interfaces for various applications.


Overall, brain stimulation plays a crucial role in advancing our understanding of the brain, exploring new therapeutic interventions for neurological disorders, and enhancing cognitive function. Its applications in the research world continue to expand, offering promising avenues for both basic neuroscience and clinical practice.

 

 

Hussain, S. J., Claudino, L., Bönstrup, M., Norato, G., Cruciani, G., Thompson, R., ... Cohen, L. G. (2019). Sensorimotor oscillatory phase–power interaction gates resting human corticospinal output. Cerebral Cortex, 29(9), 3766–3777. https://doi.org/10.1093/cercor/bhy255.

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