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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 are the downstream consequences of increased glutamate signaling in the NAc?

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Dr. Rishabh Pathak

Increased glutamate signaling in the nucleus accumbens (NAc) can have several downstream consequences that may influence behavior, particularly in the context of ethanol-preferring behavior in mice lacking type 1 equilibrative nucleoside transporter (ENT1). Here are some potential downstream effects of increased glutamate signaling in the NAc:


1. Altered Neurotransmission: Elevated glutamate levels can lead to increased excitatory neurotransmission in the NAc. This heightened excitatory activity may impact the overall balance of neurotransmitters in the brain, potentially influencing reward processing and addictive behaviors associated with ethanol consumption.


2.  Synaptic Plasticity: Glutamate is a key neurotransmitter involved in synaptic plasticity, the ability of synapses to strengthen or weaken over time in response to activity. Increased glutamate signaling in the NAc may contribute to alterations in synaptic plasticity, potentially affecting the formation and consolidation of reward-related memories and behaviors.


3.   Activation of NMDA Receptors: Glutamate acts on various receptors in the brain, including N-methyl-D-aspartate (NMDA) receptors. Activation of NMDA receptors in the NAc can trigger intracellular signaling cascades that modulate neuronal function and plasticity. Changes in NMDA receptor activity due to increased glutamate signaling may impact synaptic transmission and neuronal excitability in the NAc.


4. Behavioral Effects: Changes in glutamate signaling in the NAc can influence behavioral responses, including those related to reward processing, motivation, and addiction. Altered glutamatergic transmission in this brain region may contribute to the development and maintenance of ethanol-preferring behavior in mice, as observed in the context of ENT1 deficiency.


Overall, increased glutamate signaling in the NAc can have profound effects on neuronal function, synaptic plasticity, and behavior, potentially contributing to the modulation of ethanol-related behaviors in animal models. Understanding the downstream consequences of altered glutamatergic activity in the NAc is crucial for unraveling the neurobiological mechanisms underlying addiction and substance use disorders.

 

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