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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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Quasi-Experimental Research Design

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Dr. Rishabh Pathak

Quasi-experimental research design is a type of research methodology that shares similarities with experimental research but lacks the key element of random assignment of participants to experimental and control groups. In quasi-experimental studies, researchers do not have full control over assigning participants to groups, which limits the ability to establish a causal relationship between the independent and dependent variables. Here are key characteristics and components of quasi-experimental research design:


1.    Non-Randomized Assignment:

o    Unlike true experimental designs where participants are randomly assigned to experimental and control groups, quasi-experimental designs involve non-randomized assignment based on existing characteristics, pre-existing groups, or natural conditions.

2.    Pre-Existing Groups:

o  Quasi-experimental research often utilizes pre-existing groups, such as different schools, communities, or clinics, as the basis for comparison. Researchers do not manipulate the assignment of participants but rather observe and compare naturally occurring groups.

3.    Control Over Variables:

o Quasi-experimental designs allow researchers to control and manipulate the independent variable but lack control over participant assignment to groups. This limits the ability to eliminate potential confounding variables that may influence the results.

4.    Multiple Groups:

o    Quasi-experimental studies may involve multiple groups, such as experimental groups, control groups, and comparison groups, to compare the effects of interventions or treatments across different conditions.

5.    Data Collection Methods:

o    Researchers use a variety of data collection methods, including surveys, observations, interviews, and tests, to gather data on the variables of interest. Data collection methods depend on the research questions and the nature of the study.

6.    Analysis of Results:

o  Quasi-experimental research involves analyzing the results to determine the effects of the independent variable on the dependent variable. Statistical techniques, such as t-tests, ANOVA, regression analysis, and propensity score matching, are commonly used to analyze quasi-experimental data.

7.    Internal Validity:

o    Quasi-experimental designs have lower internal validity compared to true experimental designs due to the lack of random assignment. Researchers must consider potential confounding variables and threats to internal validity when interpreting the results.

8.    External Validity:

o    Quasi-experimental studies may have limitations in generalizing the results to a broader population due to the non-randomized nature of participant assignment. Researchers should consider the external validity of the findings in relation to the specific context of the study.

9.    Applications:

o Quasi-experimental research design is commonly used in educational research, healthcare studies, social sciences, and program evaluations where random assignment is not feasible or ethical. It allows researchers to study real-world interventions, policies, or programs in natural settings.

10. Limitations:

o Causality: Quasi-experimental designs have limitations in establishing causal relationships between variables due to the lack of random assignment.

o    Confounding Variables: The presence of confounding variables can affect the internal validity of quasi-experimental studies, leading to potential biases in the results.

o Selection Bias: Non-randomized assignment may introduce selection bias, where certain characteristics of participants influence group assignment and outcomes.

Quasi-experimental research design offers a practical and ethical approach to studying interventions, treatments, or programs in real-world settings where random assignment is not feasible. While it has limitations in establishing causality and controlling for potential biases, quasi-experimental studies provide valuable insights into the effects of interventions and treatments under natural conditions.

 

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