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

Sampling Procedures

Image
Dr. Rishabh Pathak

Sampling procedures are essential components of research methodology that involve selecting a subset of individuals or items from a larger population to represent the whole. Sampling procedures play a crucial role in ensuring the validity and reliability of research findings. Here is an overview of sampling procedures in research:


1.    Types of Sampling Procedures:

o    Probability Sampling:

§  Simple Random Sampling: Involves selecting individuals from the population at random, where each member has an equal chance of being chosen.

§  Stratified Sampling: Divides the population into subgroups (strata) based on certain characteristics and then samples from each stratum.

§  Systematic Sampling: Selects every nth individual from a list of the population after a random start.

§  Cluster Sampling: Divides the population into clusters and then randomly selects clusters to sample.

o    Non-Probability Sampling:

§  Convenience Sampling: Involves selecting individuals who are readily available and accessible.

§  Purposive Sampling: Involves selecting individuals based on specific criteria or characteristics relevant to the research study.

§  Snowball Sampling: Involves initial participants recruiting additional participants, often used in studies where the population is hard to reach.

2.    Sampling Design Considerations:

o  Population: Understanding the characteristics and size of the population under study is crucial for selecting an appropriate sampling procedure.

o    Research Objectives: The research questions and objectives guide the selection of the sampling procedure to ensure that the sample represents the population of interest.

o  Resource Constraints: Budgetary limitations, time constraints, and availability of resources influence the choice of sampling procedure.

o    Sampling Error: Researchers aim to minimize sampling error by selecting a sampling procedure that provides a representative sample of the population.

3.    Sampling Procedure Selection:

o  Researchers must carefully consider the characteristics of the population, the research objectives, and the constraints of the study when selecting a sampling procedure.

o   The chosen sampling procedure should align with the research design, data collection methods, and analytical techniques to ensure the validity and reliability of the study findings.

4.    Sampling Error:

o  Sampling error refers to the discrepancy between the characteristics of the sample and the population. Minimizing sampling error is crucial for ensuring the generalizability of research findings.

o    Proper sampling procedures, such as random sampling techniques, can help reduce sampling error and improve the accuracy of research results.

5.    Sample Size Determination:

o  Sampling procedures also involve determining the appropriate sample size to achieve the desired level of precision and confidence in research findings.

o    Sample size calculations consider factors such as the variability of the population, the level of confidence required, and the margin of error acceptable in the study.

In conclusion, sampling procedures are fundamental in research methodology for selecting representative samples from populations of interest. Researchers must carefully choose appropriate sampling procedures based on the research objectives, population characteristics, resource constraints, and desired level of sampling error to ensure the validity and reliability of their research findings. Proper sampling procedures contribute to the credibility and generalizability of research results.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Cell Maturation (Dendrite and Axon Growth)

Dr. Rishabh Pathak
Cell maturation, encompassing dendrite and axon growth, is a crucial stage of brain development where neurons undergo structural changes to establish connections and form functional neural circuits. Here is an overview of cell maturation in the context of dendrite and axon growth: 1.      Dendrite Growth : o     Definition : Dendrites are branched extensions of a neuron that receive signals from other neurons and transmit these signals to the cell body. o     Dendritic Arborization : During maturation, neurons extend and elaborate their dendritic arbors, increasing the surface area available for synaptic connections. o     Synaptic Integration : Dendritic growth is essential for forming synapses with other neurons, allowing for the integration of incoming signals and information processing. o     Activity-Dependent Plasticity : Dendritic growth can be influenced by neural activity and sensory experiences, sh...
Post a Comment
Read more

Ocular Artifacts

Dr. Rishabh Pathak
Ocular artifacts in EEG recordings are commonly caused by movements of the eyes, such as blinking, eye flutter, and eye movements associated with eye opening and closure. These artifacts can mimic epileptiform discharges and other EEG patterns, making them important to recognize and differentiate.  Nature of Ocular Artifacts : o    Ocular artifacts are primarily due to the movement of the electrical dipoles created by the eyes, particularly during activities like eye opening, closure, and directed gaze. o    The movement of these dipoles generates changing electrical fields that appear as EEG activity, with characteristics such as slow waves and spikes. o    Ocular artifacts are typically limited to the frontal region and do not extend into the central region of the brain. 2.      Differentiation from Epileptiform Discharges : o   Ocular artifacts can sometimes appear as bifrontal spike and slow wave complexes, resembling inter...
Post a Comment
Read more

Amphiarthrodial or Cartilaginous Joints

Dr. Rishabh Pathak
Amphiarthrodial joints, also known as cartilaginous joints, are joints where the adjacent bones are connected by cartilage. These joints allow for limited movement and provide both stability and flexibility to the skeletal system. Here is an overview of amphiarthrodial or cartilaginous joints: Amphiarthrodial or Cartilaginous Joints: 1.     Structure : o     Cartilage : §   Amphiarthrodial joints are characterized by the presence of cartilage between the articulating surfaces of the bones. §   The cartilage can be hyaline cartilage or fibrocartilage, depending on the specific joint and its function. o     Lack of Joint Cavity : §   Similar to fibrous joints, cartilaginous joints do not have a synovial cavity, and the bones are held together by the cartilaginous tissue. 2.     Types : o     Synchondroses : §   Synchondroses are cartilaginous joints where the connecting material is hyaline carti...
Post a Comment
Read more

Cell Migration

Dr. Rishabh Pathak
Cell migration is a crucial stage of brain development where newly generated neurons move to their appropriate locations within the developing brain. Here is an overview of cell migration in the context of brain development: 1.      Definition : §   Cell migration refers to the process by which neurons and glial cells move from their site of origin to their final destination in the developing brain. §   Proper cell migration is essential for establishing the correct architecture and connectivity of the brain. 2.      Types of Cell Migration : §   Radial Migration : Radial migration involves neurons moving along radial glial fibers that span the developing brain. This type of migration is common in the cerebral cortex and helps neurons reach their appropriate cortical layers. §   Tangential Migration : Tangential migration occurs when neurons migrate horizontally across the developing brain. Interneurons, for example...
Post a Comment
Read more

Unrestricted Sampling

Dr. Rishabh Pathak
Unrestricted sampling, also known as simple random sampling, is a fundamental sampling technique where each element in the population has an equal and independent chance of being selected for the sample. In unrestricted sampling: 1.     Equal Probability of Selection : §   In simple random sampling, every element in the population has an equal probability of being chosen for the sample. This ensures that each unit is selected independently of other units, without any bias towards specific elements. 2.     Random Selection : §   The selection of sample elements is done randomly, without any systematic pattern or predetermined order. This randomness is essential to ensure that the sample is representative of the population and to minimize selection bias. 3.     Independence of Selection : §   Each selection is made independently of previous selections, meaning that the inclusion or exclusion of one element does not influence the ...
Post a Comment
Read more