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

Judgement Sampling

Image
Dr. Rishabh Pathak

Judgment sampling, also known as purposive or selective sampling, is a non-probability sampling technique where researchers use their judgment and expertise to select sample units based on specific criteria or characteristics relevant to the research objectives. In judgment sampling, researchers intentionally choose sample units that they believe are representative or typical of the population of interest. Here are some key points about judgment sampling:


1.    Definition:

§  Judgment sampling is a non-probability sampling method where researchers select sample units based on their judgment, expertise, or knowledge of the population.

§  Sample units are chosen deliberately to represent certain traits, characteristics, or experiences that are deemed relevant to the research objectives.

2.    Characteristics:

§  Judgment sampling relies on the researcher's subjective judgment and understanding of the population to select sample units that are considered typical, informative, or representative.

§  Researchers may use their expertise to identify key characteristics or criteria for selecting sample units that align with the research focus.

3.    Types of Judgment Sampling:

§  Convenience Sampling: Selecting sample units based on their accessibility, availability, or convenience to the researcher.

§  Expert Sampling: Choosing sample units based on the expertise, knowledge, or qualifications of the individuals selected.

§  Typical Case Sampling: Selecting sample units that are considered typical or illustrative of the population's characteristics or behaviors.

4.    Advantages:

§  Judgment sampling allows researchers to focus on specific characteristics or traits of interest, making it suitable for targeted research objectives or exploratory studies.

§  This method is valuable for qualitative research, case studies, and situations where in-depth insights or unique perspectives are sought.

5.    Limitations:

§  Results obtained from judgment samples may be subject to bias, as the selection of sample units is based on the researcher's subjective judgment rather than randomization.

§  The generalizability of findings from judgment sampling may be limited, as the sample may not be representative of the entire population.

6.    Applications:

§  Judgment sampling is commonly used in qualitative research, ethnographic studies, and exploratory research where researchers seek to understand specific phenomena or behaviors.

§  This method is particularly useful when studying unique populations, rare events, or complex phenomena that require expert judgment in sample selection.

7.    Considerations:

§  Researchers should clearly define the criteria for selecting sample units in judgment sampling and justify their choices based on the research objectives.

§  While judgment sampling offers flexibility and targeted sampling, researchers should acknowledge its limitations in terms of generalizability and potential bias.

Judgment sampling is a valuable sampling technique that allows researchers to strategically select sample units based on specific criteria or characteristics relevant to their research goals. While this method offers advantages in terms of targeted sampling and in-depth exploration, researchers should be mindful of its limitations in terms of representativeness and potential bias. Careful consideration of the research objectives and criteria for sample selection is essential when employing judgment sampling in a study.

 

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

Distinguishing Features of Electrode Artifacts

Dr. Rishabh Pathak
Electrode artifacts in EEG recordings can present with distinct features that differentiate them from genuine brain activity.  1.      Types of Electrode Artifacts : o Variety : Electrode artifacts encompass several types, including electrode pop, electrode contact, electrode/lead movement, perspiration artifacts, salt bridge artifacts, and movement artifacts. o Characteristics : Each type of electrode artifact exhibits specific waveform patterns and spatial distributions that aid in their identification and differentiation from true EEG signals. 2.    Electrode Pop : o Description : Electrode pop artifacts are characterized by paroxysmal, sharply contoured transients that interrupt the background EEG activity. o Localization : These artifacts typically involve only one electrode and lack a field indicating a gradual decrease in potential amplitude across the scalp. o Waveform : Electrode pop waveforms have a rapid rise and a slower fall compared to in...
Post a Comment
Read more

Beta Activity compared to Muscles Artifacts

Dr. Rishabh Pathak
Beta activity in EEG recordings can sometimes be confused with muscle artifacts due to their overlapping frequency components. Frequency Components : o   Muscle artifacts often have frequency components of 25 Hz and greater, which can overlap with the frequency range of beta activity. o   Beta activity in EEG recordings typically falls within the beta frequency range of 13-30 Hz, with variations based on specific brain states and cognitive processes. 2.      Waveform Characteristics : o   Electromyographic (EMG) artifacts, which represent muscle activity, have distinct waveform characteristics that can help differentiate them from beta activity. o   EMG artifacts may exhibit a sharper contour with less rhythmicity, especially when the high-frequency filter is set at 70 Hz or higher, compared to the smoother contour and rhythmicity of beta activity. 3.      High-Frequency Filter Settings : o   Adjusting the high-frequency f...
Post a Comment
Read more

Elements Selection Techniques

Dr. Rishabh Pathak
Element selection techniques play a crucial role in determining how individual elements or units are chosen from the population to form a sample. Here are some common element selection techniques used in sampling: 1.     Unrestricted Sampling : §   In unrestricted sampling, each element in the population has an equal chance of being selected for the sample. This approach is commonly used in simple random sampling, where every element is selected independently of other elements. 2.     Restricted Sampling : §   Restricted sampling involves imposing certain restrictions or conditions on the selection of sample elements. This can include stratification, clustering, or other criteria that guide the selection process. Restricted sampling techniques include: §   Stratified Sampling: The population is divided into homogeneous subgroups (strata), and samples are selected from each stratum to ensure representation of different characteristics. § ...
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