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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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Experience Survey

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Dr. Rishabh Pathak

Experience survey is a research method that involves gathering insights and information from individuals who have practical experience with the problem or phenomenon being studied. This approach aims to tap into the knowledge, perspectives, and expertise of individuals who have firsthand experience in a particular area to gain valuable insights and generate new ideas related to the research problem.

Key features of an experience survey include:

1.    Selection of Respondents:

o    Researchers carefully select individuals who have relevant practical experience with the research problem. These respondents are chosen based on their expertise, knowledge, and ability to provide valuable insights into the issue under investigation.

2.    Interview Process:

o    Researchers conduct structured interviews with the selected respondents to gather information and insights. An interview schedule is prepared to guide the questioning process, ensuring that key topics and issues are covered systematically.

3.    Insight Generation:

o    The primary goal of an experience survey is to generate insights into the relationships between variables, uncover new ideas, and gain a deeper understanding of the research problem. By tapping into the practical knowledge of experienced individuals, researchers can identify patterns, trends, and potential solutions.

4.    Flexibility and Adaptability:

o    Experience surveys allow for flexibility in the interview process, enabling respondents to raise issues, questions, or insights that may not have been previously considered by the researcher. This adaptability helps in exploring new avenues of inquiry and gaining a comprehensive understanding of the problem.

5.    Representativeness:

o    Researchers aim to select a diverse group of respondents with varied experiences and perspectives to ensure a comprehensive representation of different types of practical knowledge. This diversity helps in capturing a range of insights and ideas related to the research problem.

6.    Data Collection:

o    Information gathered through experience surveys is typically qualitative in nature, focusing on narratives, anecdotes, and personal experiences shared by the respondents. Researchers analyze these qualitative data to identify themes, patterns, and insights relevant to the research problem.

7.    Application in Hypothesis Formulation:

o    Insights obtained from an experience survey can be valuable in formulating hypotheses, developing theoretical frameworks, or refining research questions. The practical knowledge shared by experienced individuals can inform the theoretical underpinnings of the study.

Overall, experience surveys provide researchers with a valuable method for tapping into the practical wisdom and expertise of individuals who have firsthand experience with the research problem. By engaging with experienced respondents, researchers can gain unique insights, explore new perspectives, and enrich their understanding of the phenomenon under investigation.

 

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