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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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Quota Sampling

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Dr. Rishabh Pathak

Quota sampling is a non-probability sampling technique that involves dividing the population into subgroups or strata based on certain characteristics and then selecting samples from each subgroup in proportion to their presence in the population. Quota sampling is a method of convenience sampling where researchers establish quotas for different subgroups and then non-randomly select participants to fill those quotas. Here are some key points about quota sampling:


1.    Definition:

o Quota sampling is a non-probability sampling method where researchers divide the population into subgroups or strata based on specific characteristics (such as age, gender, income level) and then set quotas for each subgroup.

o    Participants are selected non-randomly to fill the quotas, typically based on convenience or availability, rather than through random selection.

2.    Process:

o    Researchers first identify key characteristics or variables of interest and create quotas to ensure that the sample reflects the diversity of the population.

o    Participants are then selected based on convenience or judgment to meet the predetermined quotas for each subgroup.

3.    Characteristics:

o  Quota sampling allows researchers to ensure that the sample includes representation from different subgroups in the population, making it useful for capturing diversity.

o    This method is often used in situations where random sampling is impractical or costly, but researchers still want to achieve some level of stratification in the sample.

4.    Advantages:

o    Quota sampling provides a structured approach to ensure diversity in the sample by setting quotas for different subgroups.

o    This method can be more efficient and cost-effective than random sampling, especially when specific subgroups need to be represented in the sample.

5.    Limitations:

o    Quota sampling may introduce bias if the selection of participants within each quota is not random or if certain characteristics are overrepresented or underrepresented.

o    Results obtained from quota samples may not be generalizable to the entire population due to the non-random selection process.

6.    Applications:

o   Quota sampling is commonly used in market research, opinion polls, and surveys where researchers want to ensure representation from different demographic groups.

o    This method is suitable for studies that require stratification by specific characteristics but do not require strict randomization.

7.    Considerations:

o    Researchers should carefully define the quotas based on relevant population characteristics and ensure that the selection process within each quota is consistent and transparent.

o    While quota sampling can provide valuable insights into specific subgroups, researchers should be cautious in generalizing findings beyond the sampled population.

Quota sampling offers a practical and structured approach to sampling that allows researchers to ensure diversity and representation from different subgroups in the population. While this method provides advantages in terms of stratification and efficiency, researchers should be aware of its limitations in terms of bias and generalizability. Careful planning and implementation are essential when using quota sampling to ensure the validity and reliability of research findings.

 

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