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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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Natural Bias in the reporting of data

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Dr. Rishabh Pathak

Natural bias in the reporting of data refers to the tendency of individuals to provide inaccurate or misleading information due to various factors such as social desirability, cognitive biases, or situational influences. Here are some key points related to natural bias in the reporting of data:


1.    Social Desirability Bias:

o    Social desirability bias occurs when individuals respond in a way that is socially acceptable or favorable, rather than providing honest or accurate information. This bias can lead to over-reporting of positive behaviors or under-reporting of negative behaviors, impacting the validity of research findings.

2.    Cognitive Biases:

o    Cognitive biases, such as memory errors or selective perception, can influence how individuals recall and report information. These biases can lead to inaccuracies in data reporting, as individuals may unintentionally distort or misremember details based on their cognitive processes.

3.    Response Bias:

o    Response bias occurs when individuals provide responses that are influenced by factors unrelated to the research question, such as the wording of the question, the context of the survey, or the characteristics of the interviewer. Response bias can introduce errors in data collection and analysis.

4.    Situational Influences:

o    Situational factors, such as the presence of others, time constraints, or the perceived importance of the information being reported, can impact how individuals report data. These situational influences can lead to variations in reporting behavior and affect the reliability of research outcomes.

5.    Measurement Error:

o    Natural bias in the reporting of data can contribute to measurement error, where the data collected deviates from the true values due to reporting inaccuracies. Researchers need to be aware of potential biases in data reporting and implement strategies to minimize measurement error in their studies.

6.    Research Design Considerations:

o    Researchers should consider the potential for natural bias in data reporting when designing studies and selecting data collection methods. By using validated instruments, ensuring participant confidentiality, and minimizing response biases, researchers can enhance the accuracy and reliability of data collected.

7.    Data Validation Techniques:

o    Implementing data validation techniques, such as cross-checking responses, conducting follow-up interviews, or using multiple sources of data, can help researchers identify and correct natural biases in data reporting. By verifying the consistency and accuracy of reported data, researchers can improve the quality of their findings.

Addressing natural bias in the reporting of data is crucial for ensuring the integrity and validity of research outcomes. By recognizing the potential sources of bias, implementing appropriate data collection and validation methods, and interpreting findings with caution, researchers can mitigate the impact of natural biases on their research results.

 

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