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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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Anticipatory Postural Adjustment (APA)

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Dr. Rishabh Pathak

Anticipatory Postural Adjustments (APAs) are preparatory muscle activities that occur before the initiation of voluntary movements to maintain postural stability and ensure effective execution of the intended movement. Here is a detailed explanation of Anticipatory Postural Adjustments:


1. Definition: APAs are a series of coordinated muscle contractions that occur in advance of a planned movement to stabilize the body and prepare the postural system for the upcoming action. These adjustments are essential for maintaining balance, preventing falls, and optimizing the efficiency of voluntary movements.


2.  Timing: APAs typically precede the onset of voluntary movements and are initiated in anticipation of the intended action. The timing and magnitude of APAs are finely tuned to the characteristics of the upcoming movement, such as its direction, velocity, and force requirements. By activating specific muscle groups in advance, APAs help counteract destabilizing forces and ensure a smooth transition into the movement phase.


3.Neural Control: The generation of APAs involves complex neural mechanisms that integrate sensory information, motor planning, and feedforward control. Brain regions such as the cerebellum, basal ganglia, and cortical motor areas play crucial roles in coordinating the timing and amplitude of APAs to facilitate coordinated motor performance and postural stability.


4.    Role in Gait: In the context of gait and locomotion, APAs are particularly important for coordinating the sequence of muscle activations to support the rhythmic pattern of walking and running. Disruptions in the timing or amplitude of APAs can lead to gait abnormalities, such as freezing of gait (FOG) in conditions like Parkinson's disease.


5. Interaction with Movement Disorders: Studies have shown that abnormalities in APAs can contribute to movement impairments in neurological disorders. For example, dysfunction in the integration of APAs with stepping movements involving brain regions like the pontomedullary reticular formation (pmRF) and pedunculopontine nucleus (PPN) may be implicated in the pathogenesis of freezing of gait in Parkinson's disease.


6. Research and Rehabilitation: Understanding the role of APAs in motor control and postural stability is essential for designing effective rehabilitation strategies for individuals with movement disorders or balance impairments. Therapeutic interventions that target the optimization of APAs can improve motor performance, reduce fall risk, and enhance overall functional mobility.


In summary, Anticipatory Postural Adjustments are pre-programmed muscle activities that play a crucial role in preparing the body for voluntary movements, maintaining postural stability, and ensuring efficient motor control. By studying APAs, researchers and clinicians can gain insights into the neural mechanisms underlying motor planning, coordination, and balance control in health and disease.

 

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