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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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Co-occurring Patterns of Mittens

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Dr. Rishabh Pathak

Mittens in EEG recordings are often associated with several co-occurring patterns, particularly during non-rapid eye movement (NREM) sleep. These patterns include:

1. Sleep Spindles

    • Sleep spindles are bursts of oscillatory brain activity that typically occur in NREM sleep. They are characterized by a frequency of 12-16 Hz and can be seen alongside mittens, contributing to the overall electrographic features of sleep.

2. K Complexes

    • K complexes are large, biphasic waves that occur in NREM sleep and are often considered a marker of sleep stability. They can appear in conjunction with mittens, although they differ in waveform characteristics.

3. Positive Occipital Sharp Transients of Sleep (POSTS)

    • POSTS are transient waveforms that occur in the occipital region during sleep. They are typically positive and can co-occur with mittens, adding to the complexity of the EEG during deep sleep.

4. Generalized Delta Frequency Range Activity

    • Mittens are often accompanied by prominent delta activity, particularly in the deeper stages of NREM sleep. This delta activity is characterized by slower frequency waves and is a common background feature during sleep.

5. Anterior Rhythmic Activity

    • EEGs that include mittens may also show bursts of anterior rhythmic activity, which can be indicative of the brain's transition between different sleep stages or arousal states.

Summary

The co-occurring patterns of mittens highlight their presence within the broader context of NREM sleep, where they interact with various other sleep-related EEG features. Recognizing these associated patterns is important for accurate EEG interpretation and understanding the normal variations in sleep architecture.

 

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