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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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Inappropriate Sampling Frame

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Dr. Rishabh Pathak

An inappropriate sampling frame can significantly impact the validity and reliability of research findings. A sampling frame is a list or source from which a sample is drawn, representing the target population. Here are some examples of situations where an inappropriate sampling frame may lead to biased or inaccurate results:


1.    Exclusion of Relevant Population Segments:

o    If the sampling frame does not include all relevant segments of the population under study, the sample may not be representative. For example, excluding certain demographic groups or geographic areas can lead to biased results.

2.    Outdated or Incomplete Information:

o  Using a sampling frame that contains outdated or incomplete information can result in sampling errors. For instance, if the frame does not reflect the current population characteristics, the sample may not be representative.

3.    Non-Response Bias:

o    An inappropriate sampling frame may lead to non-response bias if certain segments of the population are systematically excluded or underrepresented. This can skew the results and affect the generalizability of findings.

4.    Sampling from Non-Accessible Population:

o    If the sampling frame includes individuals or units that are not accessible or cannot be reached for data collection, the sample may not be feasible. This can result in practical challenges and compromise the validity of the study.

5.    Inadequate Coverage:

o  A sampling frame that lacks adequate coverage of the target population may introduce selection bias. For example, if the frame only includes certain regions or institutions, the sample may not be representative of the entire population.

6.    Inconsistencies in Sampling Units:

o    Using a sampling frame with inconsistencies in defining sampling units can lead to confusion and errors in sample selection. Inconsistent criteria for inclusion/exclusion can compromise the integrity of the sampling process.

7.    Sampling Frame Mismatch:

o When the sampling frame does not align with the research objectives or study design, it can result in misrepresentation of the population. A mismatch between the frame and the study parameters can lead to invalid conclusions.

8.    Biased Inclusion Criteria:

o    If the sampling frame is based on biased inclusion criteria that do not reflect the diversity of the population, the sample may not be representative. Biased inclusion criteria can distort the findings and limit the generalizability of results.

Addressing these issues and ensuring the appropriateness of the sampling frame is crucial for conducting valid and reliable research. Researchers should carefully evaluate the sampling frame to minimize biases, enhance the representativeness of the sample, and improve the quality of research outcomes.

 

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