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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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Census

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Dr. Rishabh Pathak

A census is a research method that involves collecting data from every member of a population or universe of interest. Here are some key points related to census methodology:


1.    Definition:

o    A census is a complete enumeration of all individuals, households, or units in a given population or universe. It aims to gather information from every member of the population without sampling or estimation.

2.    Scope:

o Census data collection covers the entire population without excluding any individual or unit. This comprehensive approach provides a detailed and accurate snapshot of the characteristics, demographics, and other relevant information about the entire population.

3.    Accuracy:

o    Since a census attempts to collect data from every member of the population, it is considered to provide the most accurate and precise information about the population characteristics. By including all individuals, a census minimizes sampling errors and ensures a complete representation of the population.

4.    Time and Resources:

o    Conducting a census can be resource-intensive in terms of time, money, and manpower. Due to the comprehensive nature of a census, it requires significant planning, coordination, and logistical support to collect data from every individual or unit in the population.

5.    Frequency:

o    Census surveys are typically conducted at regular intervals, such as every ten years in the case of national population censuses. The periodic nature of census data collection allows for tracking changes in population characteristics over time and informing policy decisions.

6.    Government Role:

o    Census surveys are often conducted by government agencies at the national, state, or local levels. Governments use census data to allocate resources, plan public services, determine representation in legislative bodies, and make informed policy decisions based on accurate population information.

7.    Uses of Census Data:

o    Census data are used for various purposes, including:

§  Determining population size and demographics.

§  Allocating government funding and resources.

§  Planning infrastructure and public services.

§  Analyzing trends in population growth and distribution.

§  Ensuring fair representation in political processes.

8.    Challenges:

o    Despite its advantages, conducting a census can pose challenges such as ensuring complete coverage of hard-to-reach populations, maintaining data accuracy, protecting respondent confidentiality, and managing the logistical complexities of a large-scale data collection effort.

In conclusion, a census is a comprehensive data collection method that aims to gather information from every member of a population. While resource-intensive, census surveys provide accurate and detailed insights into population characteristics, which are essential for informed decision-making and policy planning.

 

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