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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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How does experience impact the development of the brain?

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Dr. Rishabh Pathak

Experience plays a crucial role in shaping the development of the brain across the lifespan. Here are some key ways in which experience impacts brain development:


1.  Sensitive Periods: Early experiences during sensitive periods in development have a profound impact on brain structure and function. These periods involve rapid and efficient learning, such as language acquisition, and experiences during this time can have long-lasting effects on neural pathways.


2. Synaptic Density: The decline in synaptic density after birth and in early childhood is influenced by experience. Greenough and colleagues proposed that experience shapes the developing brain through mechanisms like experience-expectant and experience-dependent processes. Lack of expected experiences or abnormal experiences can lead to non-normative neural patterns.


3. Synaptic Plasticity: Experience influences synaptic plasticity, the ability of synapses to strengthen or weaken over time in response to neural activity. Learning and exposure to new stimuli lead to the formation of new synaptic connections, contributing to the adaptability of the brain.


4.     Environmental Enrichment: Environments rich in sensory, cognitive, and social stimulation have been shown to promote brain development. Enriched environments can lead to increased synaptic connections, enhanced neuroplasticity, and improved cognitive abilities.


5.     Learning and Memory: Learning new skills, acquiring knowledge, and engaging in cognitive tasks stimulate neural networks and promote the formation of new connections in the brain. Memory formation and retrieval processes are also influenced by experiences and environmental factors.


6.     Neuroplasticity: The brain's ability to reorganize itself in response to experience is known as neuroplasticity. This adaptive capacity allows the brain to modify its structure and function based on learning, practice, and exposure to diverse stimuli throughout life.


Overall, experiences ranging from early childhood interactions to lifelong learning opportunities have a significant impact on brain development. The brain's plasticity and ability to adapt to environmental inputs underscore the dynamic nature of neural development and the continuous influence of experience on shaping cognitive abilities and behavior.

 

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