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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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Cone Waves Compared to Positive Occipital Sharp Transients of Sleep

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Dr. Rishabh Pathak

Cone waves and Positive Occipital Sharp Transients of Sleep (POSTS) are distinct EEG patterns that share some similarities but also have key differences. Here is a comparison between cone waves and POSTS:


1.     Morphology:

o  Both cone waves and POSTS exhibit a triangular morphology, with a sharp, distinctive shape resembling a cone.

o Cone waves and POSTS may appear similar in their waveform characteristics, including the presence of a sharp onset and offset.

2.   Occipital Distribution:

oBoth cone waves and POSTS are typically localized over the occipital regions of the brain.

o The occipital distribution of these waveforms distinguishes them from patterns that are more widespread or localized to other brain regions.

3.   Duration:

o Cone waves have a duration typically more than 250 milliseconds, while POSTS have a shorter duration, typically less than 200 milliseconds.

o The difference in duration can aid in distinguishing between cone waves and POSTS on EEG recordings.

4.   Age Dependency:

o Cone waves are more likely to occur in younger children, typically between the ages of 6 months and 3 years.

o POSTS are rare before 3 years of age and most common after childhood, indicating an age-dependent occurrence.

5.    Phase Reversal:

o POSTS are characterized by a phase reversal, with positivity at the center of the field, which is evident in the waveform.

o Cone waves do not exhibit a phase reversal in the same manner as POSTS, providing a distinguishing feature between the two patterns.

6.   Clinical Significance:

o Cone waves are considered a normal variant with no clinical significance in their presence or absence.

o POSTS, while also a normal variant, may have implications for EEG interpretation and clinical assessment due to their association with specific age groups and sleep states.

7.    Co-occurring Waves:

o Cone waves occur during non-rapid eye movement (NREM) sleep and are accompanied by other EEG features of this state, such as diffuse theta or delta background activity.

o POSTS are also observed during NREM sleep and may co-occur with other sleep-related EEG patterns, such as sleep spindles and K complexes.

Understanding the similarities and differences between cone waves and POSTS is essential for accurate EEG interpretation and recognition of normal variants versus abnormal patterns. By considering the unique characteristics of each waveform, clinicians can effectively differentiate between cone waves and POSTS in EEG recordings and assess their clinical significance in the context of patient evaluation.

 

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