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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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Types of Delta Activities

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Dr. Rishabh Pathak

There are several types of delta activities observed in EEG recordings, each with distinct characteristics and clinical significance. Here are some common types of delta activities:


1.     Polymorphic Delta Activity (PDA):

oPolymorphic delta activity is characterized by the presence of slow delta waves of varying durations and amplitudes, resulting in an irregular and non-rhythmic EEG pattern.

oPDA can be normal in certain contexts, such as during non-rapid eye movement (NREM) sleep, or abnormal when asymmetric or showing other abnormal features indicating potential focal brain disturbances or lesions.

2.   Posterior Slow Waves of Youth (PSWY):

oPSWY are specific delta-wave patterns observed in wakefulness, characterized by slow waves predominantly in the posterior regions of the brain.

o These delta waves may be seen in children and young adults and are considered a normal variant of delta activity.

3.   Cone Waves:

oCone waves are another type of delta-wave pattern observed in wakefulness, characterized by a cone-shaped morphology with a broad base and tapering apex.

oThese waves are typically seen in children and may represent a normal variant of delta activity.

4.   Delta Brushes:

oDelta brushes are a distinctive EEG pattern characterized by rhythmic delta activity superimposed on faster frequencies, resembling the bristles of a brush.

oThis pattern is often seen in premature infants and may indicate immaturity of the central nervous system.

5.    Delta Waves in Slow-Wave Sleep (SWS):

oDelta waves are a prominent feature of slow-wave sleep (SWS), also known as NREM stage 3 sleep.

o During SWS, delta activity is synchronized and contributes to the restorative functions of deep sleep, including memory consolidation and physical recovery.

6.   Delta Slowing:

oDelta slowing refers to an increase in the proportion or amplitude of delta waves in the EEG, which may indicate brain dysfunction or pathological conditions.

oExcessive delta slowing can be observed in various neurological disorders, such as traumatic brain injury, encephalopathy, and certain types of epilepsy.

Understanding the different types of delta activities and their characteristics is essential for interpreting EEG recordings, assessing brain function, and identifying potential neurological abnormalities or sleep patterns. Each type of delta activity may have specific clinical implications and can provide valuable insights into the underlying brain activity and health status of the individual.

 

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