Skip to main content

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...
Post a Comment

Ex Post Facto Research Design

Image
Dr. Rishabh Pathak

Ex post facto research design, also known as causal-comparative research, is a type of non-experimental research design that examines the relationship between independent and dependent variables after they have occurred naturally. In ex post facto studies, the researcher does not manipulate the independent variable but rather observes and analyzes the existing differences or relationships between variables. Here are key characteristics and components of ex post facto research design:


1. No Manipulation of Variables: In ex post facto research, the researcher does not have control over the independent variable. The independent variable has already occurred or been naturally assigned, and the researcher observes the effects or relationships with the dependent variable after the fact.


2.    Retrospective Analysis: Ex post facto research involves a retrospective analysis of existing data or conditions. Researchers analyze data that have already been collected or events that have already taken place to investigate possible causal relationships between variables.


3.    Causal-Comparative Analysis: Ex post facto research aims to compare groups or conditions that differ on the independent variable to determine the effects on the dependent variable. The researcher seeks to establish causal relationships or associations based on observed differences or correlations.


4.    Identifying Causal Relationships: While ex post facto research cannot establish causation definitively due to the lack of experimental control, it can provide valuable insights into potential causal relationships between variables. Researchers may use statistical analyses to explore the relationships and draw inferences based on the observed patterns.


5.    Control of Extraneous Variables: Researchers in ex post facto studies must consider and control for extraneous variables that could influence the relationship between the independent and dependent variables. Statistical techniques such as regression analysis or analysis of covariance may be used to account for these variables.


6.    Cross-Sectional or Longitudinal Design: Ex post facto research can utilize cross-sectional or longitudinal designs to examine relationships between variables at a specific point in time or over a period. Longitudinal studies allow researchers to track changes and trends in variables over time.


7.    Applications: Ex post facto research is commonly used in educational research, social sciences, and healthcare to investigate the effects of variables that cannot be manipulated for ethical or practical reasons. For example, studying the impact of gender on academic achievement or the relationship between socioeconomic status and health outcomes.


8.    Limitations: One of the main limitations of ex post facto research is the inability to establish causation definitively due to the lack of experimental control. Researchers must be cautious in interpreting the results and consider alternative explanations for the observed relationships.


Ex post facto research design provides a valuable approach for exploring causal relationships between variables in situations where experimental manipulation is not feasible or ethical. By analyzing existing data and conditions, researchers can gain insights into potential causal links and contribute to the understanding of complex phenomena in various fields of study.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Unrestricted Sampling

Dr. Rishabh Pathak
Unrestricted sampling, also known as simple random sampling, is a fundamental sampling technique where each element in the population has an equal and independent chance of being selected for the sample. In unrestricted sampling: 1.     Equal Probability of Selection : §   In simple random sampling, every element in the population has an equal probability of being chosen for the sample. This ensures that each unit is selected independently of other units, without any bias towards specific elements. 2.     Random Selection : §   The selection of sample elements is done randomly, without any systematic pattern or predetermined order. This randomness is essential to ensure that the sample is representative of the population and to minimize selection bias. 3.     Independence of Selection : §   Each selection is made independently of previous selections, meaning that the inclusion or exclusion of one element does not influence the ...
Post a Comment
Read more

Ocular Artifacts

Dr. Rishabh Pathak
Ocular artifacts in EEG recordings are commonly caused by movements of the eyes, such as blinking, eye flutter, and eye movements associated with eye opening and closure. These artifacts can mimic epileptiform discharges and other EEG patterns, making them important to recognize and differentiate.  Nature of Ocular Artifacts : o    Ocular artifacts are primarily due to the movement of the electrical dipoles created by the eyes, particularly during activities like eye opening, closure, and directed gaze. o    The movement of these dipoles generates changing electrical fields that appear as EEG activity, with characteristics such as slow waves and spikes. o    Ocular artifacts are typically limited to the frontal region and do not extend into the central region of the brain. 2.      Differentiation from Epileptiform Discharges : o   Ocular artifacts can sometimes appear as bifrontal spike and slow wave complexes, resembling inter...
Post a Comment
Read more

Cell Maturation (Dendrite and Axon Growth)

Dr. Rishabh Pathak
Cell maturation, encompassing dendrite and axon growth, is a crucial stage of brain development where neurons undergo structural changes to establish connections and form functional neural circuits. Here is an overview of cell maturation in the context of dendrite and axon growth: 1.      Dendrite Growth : o     Definition : Dendrites are branched extensions of a neuron that receive signals from other neurons and transmit these signals to the cell body. o     Dendritic Arborization : During maturation, neurons extend and elaborate their dendritic arbors, increasing the surface area available for synaptic connections. o     Synaptic Integration : Dendritic growth is essential for forming synapses with other neurons, allowing for the integration of incoming signals and information processing. o     Activity-Dependent Plasticity : Dendritic growth can be influenced by neural activity and sensory experiences, sh...
Post a Comment
Read more

Amphiarthrodial or Cartilaginous Joints

Dr. Rishabh Pathak
Amphiarthrodial joints, also known as cartilaginous joints, are joints where the adjacent bones are connected by cartilage. These joints allow for limited movement and provide both stability and flexibility to the skeletal system. Here is an overview of amphiarthrodial or cartilaginous joints: Amphiarthrodial or Cartilaginous Joints: 1.     Structure : o     Cartilage : §   Amphiarthrodial joints are characterized by the presence of cartilage between the articulating surfaces of the bones. §   The cartilage can be hyaline cartilage or fibrocartilage, depending on the specific joint and its function. o     Lack of Joint Cavity : §   Similar to fibrous joints, cartilaginous joints do not have a synovial cavity, and the bones are held together by the cartilaginous tissue. 2.     Types : o     Synchondroses : §   Synchondroses are cartilaginous joints where the connecting material is hyaline carti...
Post a Comment
Read more

Distinguishing Features Ictal Epileptiform Patterns

Dr. Rishabh Pathak
The distinguishing features of ictal epileptiform patterns are critical for differentiating them from other EEG activities and for accurate seizure diagnosis. Here are the key distinguishing features outlined in the document: 1.      Stereotyped Nature : Ictal patterns are often stereotyped across seizures for the individual patient. This means that the same pattern tends to recur in different seizures, which aids in identification. 2.    Evolution of Activity : A hallmark of ictal patterns is their evolution, which can manifest as changes in frequency, amplitude, distribution, and waveform. This evolution is a key feature that helps differentiate ictal patterns from other types of EEG activity, such as normal rhythms or artifacts. 3.   Behavioral Changes : Ictal patterns are typically associated with stereotyped behavioral changes. While some seizures may not exhibit obvious movements, the presence of behavioral changes is a significant indicator of s...
Post a Comment
Read more