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

Basics Principles of Local Control

Image
Dr. Rishabh Pathak

The principle of local control, also known as blocking, is a fundamental concept in experimental design that involves controlling for known sources of variability by grouping experimental units into homogeneous blocks. Here are the basic principles of local control:


1.    Definition:

o    Principle: Local control, or blocking, is the process of grouping experimental units into blocks based on a known source of variability that may affect the outcomes of the study. By controlling for this source of variation within each block, researchers can reduce the impact of extraneous factors on the results.

2.    Homogeneous Blocks:

o    Principle: Blocks are created to be as similar as possible in terms of the known source of variability being controlled. By grouping experimental units into homogeneous blocks, researchers ensure that any differences in the outcomes can be attributed to the treatments or interventions rather than the blocking factor.

3.    Reducing Variability:

o    Principle: The primary goal of local control is to reduce the overall variability in the study by holding constant the known source of variation within each block. By minimizing the impact of extraneous factors through blocking, researchers can increase the precision and accuracy of their results.

4.    Two-Way Analysis of Variance:

o    Principle: Local control facilitates the use of two-way analysis of variance (ANOVA) by partitioning the total variability in the data into components attributed to treatments and the blocking factor. By incorporating blocking into the analysis, researchers can assess the main effects and interactions more effectively.

5.    Eliminating Extraneous Factors:

o   Principle: Through local control, researchers can eliminate the variability introduced by known extraneous factors from the experimental error. By holding these factors constant within blocks, researchers can isolate the effects of the treatments and improve the internal validity of the study.

6.    Enhancing Precision:

o   Principle: Local control increases the precision of estimates by reducing the impact of extraneous variability on the results. By minimizing the influence of known sources of variation through blocking, researchers can obtain more accurate and reliable estimates of treatment effects.

7.    Blocking Procedures:

o Principle: Researchers should carefully plan and implement blocking procedures to ensure that the blocks are truly homogeneous with respect to the blocking factor. Transparent reporting of the blocking strategy is essential for replicability and understanding the design of the study.

By applying the principles of local control and incorporating blocking into experimental designs, researchers can enhance the internal validity, precision, and reliability of their studies. Local control is a valuable technique for controlling known sources of variability and improving the accuracy of research findings in experimental settings.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

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

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

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

Cell Migration

Dr. Rishabh Pathak
Cell migration is a crucial stage of brain development where newly generated neurons move to their appropriate locations within the developing brain. Here is an overview of cell migration in the context of brain development: 1.      Definition : §   Cell migration refers to the process by which neurons and glial cells move from their site of origin to their final destination in the developing brain. §   Proper cell migration is essential for establishing the correct architecture and connectivity of the brain. 2.      Types of Cell Migration : §   Radial Migration : Radial migration involves neurons moving along radial glial fibers that span the developing brain. This type of migration is common in the cerebral cortex and helps neurons reach their appropriate cortical layers. §   Tangential Migration : Tangential migration occurs when neurons migrate horizontally across the developing brain. Interneurons, for example...
Post a Comment
Read more

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