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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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Non-respondents in Sample Design

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Dr. Rishabh Pathak

Non-respondents in sample design can introduce bias and affect the generalizability of research findings. Here are some ways in which non-respondents can impact the validity and reliability of a study:

1.    Non-Response Bias:

o    Non-respondents in a sample can introduce non-response bias, where the characteristics of those who do not participate differ systematically from those who do. This bias can distort the representativeness of the sample and lead to inaccurate conclusions.

2.    Underrepresentation of Certain Groups:

o    Non-respondents may belong to specific demographic or social groups that are less likely to participate in the study. This underrepresentation can skew the results and limit the ability to generalize findings to the entire population.

3.    Loss of Information:

o    Non-respondents result in missing data, leading to a loss of valuable information that could have contributed to the research outcomes. Incomplete data due to non-response can reduce the statistical power of the study and affect the reliability of results.

4.    Selection Bias:

o    Non-respondents may exhibit different characteristics or behaviors compared to respondents, leading to selection bias. This bias can distort the relationships between variables and compromise the internal validity of the study.

5.    Impact on Statistical Analysis:

o    Non-response can affect the statistical analysis of data, especially if the missing data are not handled appropriately. Ignoring non-response or using inadequate methods to address missing data can lead to biased estimates and erroneous conclusions.

6.    Difficulty in Generalizing Results:

o    High rates of non-response can make it challenging to generalize the findings of the study to the target population. The presence of non-respondents can raise concerns about the external validity of the research outcomes.

7.    Efficiency and Cost Considerations:

o    Dealing with non-respondents can increase the cost and time required for data collection and analysis. Researchers may need to implement strategies to improve response rates, such as follow-up procedures or incentives, to mitigate the impact of non-response.

8.    Ethical Considerations:

o    Ensuring that non-respondents are treated ethically and their privacy is respected is essential in research. Researchers should consider the reasons for non-response and take steps to minimize any negative consequences for non-respondents.

Addressing non-response in sample design requires proactive measures to minimize its impact on research outcomes. Strategies such as follow-up surveys, incentives for participation, and sensitivity analyses can help researchers mitigate the effects of non-response bias and enhance the validity and reliability of their findings.


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