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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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De Constructing Smell

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Dr. Rishabh Pathak

Deconstructing smell involves understanding the complex process by which our olfactory system detects and interprets different odors. Here is a breakdown of the key components involved in the sense of smell:


1.    Odorants: Smell begins with the detection of odorants, which are volatile chemical compounds that emanate from substances in the environment. These odorants can be derived from a wide range of sources, such as food, flowers, or chemicals.


2. Olfactory Receptors: Olfactory receptors are specialized proteins located in the olfactory epithelium of the nasal cavity. These receptors are sensitive to specific odorant molecules and can detect a diverse array of smells. When an odorant binds to its corresponding olfactory receptor, it initiates a series of biochemical signals.


3.  Olfactory Bulb: The olfactory receptors send signals to the olfactory bulb, which is a structure located at the base of the brain. The olfactory bulb processes the incoming olfactory signals and helps to differentiate between different odors.


4.    Olfactory Cortex: From the olfactory bulb, the signals are relayed to the olfactory cortex, which is part of the brain's limbic system. The limbic system is involved in emotions, memory, and behavior, which is why smells can evoke strong emotional responses and trigger memories.


5. Perception: The brain integrates the information from the olfactory receptors, olfactory bulb, and olfactory cortex to create the perception of smell. Different odors activate specific patterns of neural activity in the brain, allowing us to distinguish between various smells and associate them with memories or emotions.


6. Behavioral Responses: Smell plays a crucial role in guiding behavior, such as identifying food, detecting danger, or recognizing familiar scents. The sense of smell can influence our preferences, mood, and even social interactions.


By deconstructing smell into its fundamental components and understanding how these components interact, researchers can gain insights into the mechanisms underlying olfaction and how the brain processes and interprets different odors. This knowledge can have implications for various fields, including neuroscience, psychology, and even product development (e.g., in the fragrance industry).

 

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