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

Neuro-Computational Model of Subcortical Growth

Image
Dr. Rishabh Pathak

A neuro-computational model of subcortical growth integrates principles from neuroscience and computational modeling to study the development of brain regions beneath the cerebral cortex, known as the subcortex. Here are the key aspects of a neuro-computational model of subcortical growth:


1. Biologically Realistic Representation: The model incorporates biologically relevant features of subcortical development, such as the growth and elongation of axons, the formation of neural circuits, and the influence of growth factors on subcortical structures. By simulating these processes computationally, researchers can study how subcortical regions develop and interact with the cortex.


2.     Axonal Growth and Connectivity: The model accounts for the growth of axons and the establishment of connections between subcortical regions and cortical areas. By simulating axonal elongation and branching, researchers can study how subcortical structures contribute to the overall connectivity and function of the brain.


3. Mechanical Interactions: The model considers the mechanical interactions between the subcortex and the overlying cortex, as well as the effects of growth-induced deformations on subcortical structures. By incorporating mechanical properties and growth-induced stresses, the model can investigate how mechanical forces influence subcortical growth patterns.


4.  Stretch-Induced Growth: The model includes mechanisms of stretch-induced growth, where chronic stretching of axons in the subcortex leads to gradual elongation and deformation. By simulating how axons respond to mechanical stimuli, researchers can study the effects of stretch-induced growth on subcortical morphology.


5. Computational Simulations: Neuro-computational models use computational simulations, such as finite element analysis or agent-based models, to study the dynamics of subcortical growth. These simulations allow researchers to investigate how interactions between neurons, glial cells, and mechanical forces shape the development of subcortical structures.


6.  Sensitivity Analysis: The model can perform sensitivity analyses to assess the impact of varying parameters, such as growth rates, mechanical properties, and external stimuli, on subcortical growth. By systematically varying these parameters in simulations, researchers can identify key factors influencing the morphogenesis of subcortical regions.


7.    Validation and Comparison: Neuro-computational models are validated against experimental data, such as neuroimaging studies or histological analyses, to ensure their biological accuracy. By comparing model predictions with empirical observations, researchers can evaluate the model's ability to capture the dynamics of subcortical growth.


8.  Insights into Brain Development: By studying subcortical growth processes computationally, researchers can gain insights into the mechanisms underlying the development of brain structures below the cortex. These models help elucidate how subcortical regions contribute to overall brain function and connectivity, providing a deeper understanding of brain development. 


In summary, a neuro-computational model of subcortical growth offers a valuable framework for investigating the complex processes involved in the development of brain regions beneath the cerebral cortex. By combining neuroscience principles with computational modeling techniques, researchers can explore the dynamics of subcortical growth, connectivity formation, and mechanical interactions within the developing brain.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Cancellous Bone

Dr. Rishabh Pathak
Cancellous bone, also known as trabecular or spongy bone, is the other main type of bone tissue found in the human skeleton alongside cortical bone. Cancellous bone has a porous and lattice-like structure, providing flexibility, shock absorption, and a site for hematopoiesis (blood cell formation). Here are key features and characteristics of cancellous bone: 1.     Structure : o     Trabeculae : Cancellous bone is composed of a network of thin, bony trabeculae that form an interconnected lattice structure. o     Bone Marrow : The spaces between trabeculae contain red bone marrow, which is involved in the production of blood cells (hematopoiesis). o     Less Compact : Cancellous bone is less dense and compact than cortical bone, with a higher surface area-to-volume ratio. 2.     Composition : o     Trabecular Bone : The trabeculae are made up of lamellae, osteocytes, and canaliculi similar to corti...
Post a Comment
Read more

Review Settings of EEG

Dr. Rishabh Pathak
The review settings of an EEG recording refer to the parameters that can be adjusted to optimize the visualization and interpretation of electrical brain activity. Here is an overview of the key review settings in EEG analysis: 1.       Amplification (Gain/Sensitivity) : o Definition : Amplification, also known as gain or sensitivity, determines how much the electrical signals from the brain are amplified before being displayed on the EEG recording. o Measurement : Typically measured in microvolts per millimeter (μV/mm). o Impact : Adjusting the amplification setting can affect the visibility of high-amplitude and low-amplitude activity. High-amplitude activity may require vertical compression to fit within the display range, while low-amplitude activity may require lower sensitivity settings for better visualization. 2.      Frequency Filtering : o Bandpass : The frequency range within which EEG signals are analyzed. Common settings include ...
Post a Comment
Read more

Anatomical Classification of Bones

Dr. Rishabh Pathak
Bones in the human body can be classified into five main anatomical categories based on their shape and structure. These classifications provide insights into the functions and characteristics of different bone types. Here are the five anatomical classifications of bones: 1.     Long Bones : o     Description : Long bones are characterized by their elongated shape, with a shaft (diaphysis) and two expanded ends (epiphyses). o     Examples : Femur, humerus, radius, ulna, tibia, fibula. o     Function : Long bones provide support, leverage, and mobility. They are essential for body movement and weight-bearing activities. 2.     Short Bones : o     Description : Short bones are roughly cube-shaped or have a similar length and width, providing stability and support. o     Examples : Carpals (wrist bones), tarsals (ankle bones). o     Function : Short bones contribute to we...
Post a Comment
Read more

Composition of Bone Tissue

Dr. Rishabh Pathak
Bone tissue is a complex and dynamic connective tissue composed of various components that contribute to its structure, strength, and functionality. The composition of bone tissue includes: 1.     Cells : o     Osteoblasts : Bone-forming cells responsible for synthesizing and depositing the organic matrix of bone. o     Osteocytes : Mature bone cells embedded in the bone matrix, involved in maintaining bone tissue and responding to mechanical stimuli. o     Osteoclasts : Bone-resorbing cells responsible for breaking down and remodeling bone tissue. 2.     Organic Matrix : o     Collagen Fibers : Type I collagen is the predominant protein in the organic matrix of bone, providing flexibility, tensile strength, and resilience to bone tissue. o     Non-Collagenous Proteins : Include osteocalcin, osteopontin, and osteonectin, which play roles in mineralization, cell adhesion, and matrix o...
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