Skip to main content

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...
Post a Comment

The Universe

Image
Dr. Rishabh Pathak

In the context of research methodology, the term "universe" refers to the total group of items or units that are of interest to the researcher and about which information is sought. Understanding the concept of the universe is fundamental in defining the scope of a research study and determining the population from which a sample will be drawn. Here is an explanation of the concept of the universe in research:


1.    Definition:

o    The universe, also known as the population, represents the entire group of elements or units that possess the characteristics under study. It includes all the individuals, objects, or events that meet the criteria for inclusion in the research. The universe can be finite or infinite, hypothetical or existent, depending on the nature of the study.

2.    Finite Universe:

o    A finite universe is one in which the total number of items or units is definite and known. For example, the population of a city, the number of employees in a company, or the students in a school are examples of finite universes. In a finite universe, researchers can theoretically enumerate all the elements, although it may not always be practical to do so.

3.    Infinite Universe:

o    An infinite universe is one in which the total number of items or units is uncertain and potentially limitless. Examples of infinite universes include the number of stars in the sky, the listeners of a radio program, or the possible outcomes of a random event. In an infinite universe, it is impossible to list or count all the elements, making sampling necessary for research purposes.

4.    Hypothetical vs. Existent Universe:

o    A hypothetical universe consists of items or units that are conceptual or imaginary in nature. For instance, tossing a coin or rolling a dice represent hypothetical universes where the outcomes are known but not physically present. In contrast, an existent universe comprises concrete objects or entities that actually exist in reality, such as the population of a country or the customers of a business.

5.    Role in Sampling:

o    The universe serves as the foundation for sampling in research. Researchers define the universe to establish the boundaries of the study and determine the target population from which a sample will be selected. The characteristics and diversity of the universe influence the sampling method, sample size, and generalizability of the study findings.

6.    Sampling Theory:

o    Sampling theory explores the relationship between the universe and the sample drawn from it. It provides a framework for selecting samples that are representative of the universe and for making statistical inferences about the population based on the sample data. Sampling theory is essential for ensuring the validity and reliability of research findings.

In summary, the universe in research methodology represents the total group of items or units that are the focus of a study. Understanding the nature of the universe, whether finite or infinite, hypothetical or existent, is crucial for designing sampling strategies, conducting data collection, and drawing meaningful conclusions in research.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Cancellous Bone

Dr. Rishabh Pathak
Cancellous bone, also known as trabecular or spongy bone, is the other main type of bone tissue found in the human skeleton alongside cortical bone. Cancellous bone has a porous and lattice-like structure, providing flexibility, shock absorption, and a site for hematopoiesis (blood cell formation). Here are key features and characteristics of cancellous bone: 1.     Structure : o     Trabeculae : Cancellous bone is composed of a network of thin, bony trabeculae that form an interconnected lattice structure. o     Bone Marrow : The spaces between trabeculae contain red bone marrow, which is involved in the production of blood cells (hematopoiesis). o     Less Compact : Cancellous bone is less dense and compact than cortical bone, with a higher surface area-to-volume ratio. 2.     Composition : o     Trabecular Bone : The trabeculae are made up of lamellae, osteocytes, and canaliculi similar to corti...
Post a Comment
Read more

Review Settings of EEG

Dr. Rishabh Pathak
The review settings of an EEG recording refer to the parameters that can be adjusted to optimize the visualization and interpretation of electrical brain activity. Here is an overview of the key review settings in EEG analysis: 1.       Amplification (Gain/Sensitivity) : o Definition : Amplification, also known as gain or sensitivity, determines how much the electrical signals from the brain are amplified before being displayed on the EEG recording. o Measurement : Typically measured in microvolts per millimeter (μV/mm). o Impact : Adjusting the amplification setting can affect the visibility of high-amplitude and low-amplitude activity. High-amplitude activity may require vertical compression to fit within the display range, while low-amplitude activity may require lower sensitivity settings for better visualization. 2.      Frequency Filtering : o Bandpass : The frequency range within which EEG signals are analyzed. Common settings include ...
Post a Comment
Read more

Anatomical Classification of Bones

Dr. Rishabh Pathak
Bones in the human body can be classified into five main anatomical categories based on their shape and structure. These classifications provide insights into the functions and characteristics of different bone types. Here are the five anatomical classifications of bones: 1.     Long Bones : o     Description : Long bones are characterized by their elongated shape, with a shaft (diaphysis) and two expanded ends (epiphyses). o     Examples : Femur, humerus, radius, ulna, tibia, fibula. o     Function : Long bones provide support, leverage, and mobility. They are essential for body movement and weight-bearing activities. 2.     Short Bones : o     Description : Short bones are roughly cube-shaped or have a similar length and width, providing stability and support. o     Examples : Carpals (wrist bones), tarsals (ankle bones). o     Function : Short bones contribute to we...
Post a Comment
Read more

Composition of Bone Tissue

Dr. Rishabh Pathak
Bone tissue is a complex and dynamic connective tissue composed of various components that contribute to its structure, strength, and functionality. The composition of bone tissue includes: 1.     Cells : o     Osteoblasts : Bone-forming cells responsible for synthesizing and depositing the organic matrix of bone. o     Osteocytes : Mature bone cells embedded in the bone matrix, involved in maintaining bone tissue and responding to mechanical stimuli. o     Osteoclasts : Bone-resorbing cells responsible for breaking down and remodeling bone tissue. 2.     Organic Matrix : o     Collagen Fibers : Type I collagen is the predominant protein in the organic matrix of bone, providing flexibility, tensile strength, and resilience to bone tissue. o     Non-Collagenous Proteins : Include osteocalcin, osteopontin, and osteonectin, which play roles in mineralization, cell adhesion, and matrix o...
Post a Comment
Read more

Frontal–central - Beta Activity

Dr. Rishabh Pathak
Frontal-central beta activity in EEG recordings refers to a specific pattern of beta waves that are predominantly observed in the frontal and central regions of the brain. Description : o   Frontal-central beta activity is characterized by increased beta waves present diffusely, with a buildup of greater beta activity specifically in the frontal-central regions. o   This pattern may be accompanied by generalized theta activity, which can be more visible when the beta activity declines. 2.      Frequency Range : o   Frontal-central beta activity typically falls within the beta frequency range, which is defined as 13 Hz or greater in EEG recordings. o   The frequency of frontal-central beta activity tends to be within the narrower range of 20 to 30 Hz, with variations in frequency observed based on age and state of consciousness. 3.      State Dependency : o    Frontal-central beta activity is considered state-dependent...
Post a Comment
Read more