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

Gray Matter (GM)

Image
Dr. Rishabh Pathak

Gray matter (GM) refers to a major component of the central nervous system that contains neuronal cell bodies, dendrites, and synapses. Here is an overview of gray matter and its significance in the brain:


1.      Composition:

o  Neuronal Cell Bodies: Gray matter primarily consists of neuronal cell bodies, which play a crucial role in information processing and signal transmission within the brain.

o Dendrites and Synapses: Dendrites, the branching extensions of neurons, receive signals from other neurons, and synapses, the junctions between neurons, facilitate communication through neurotransmitter release.

2.     Distribution:

o  In the brain, gray matter is found in regions responsible for sensory perception, motor function, memory, emotions, and other cognitive processes.

o  Gray matter is abundant in areas such as the cerebral cortex, basal ganglia, thalamus, and brainstem, where complex neural computations and integration of information occur.

3.     Functions:

oInformation Processing: Neuronal cell bodies in gray matter regions process incoming signals, integrate information from various sources, and generate appropriate responses.

o Cognitive Functions: Gray matter areas are involved in higher-order cognitive functions such as decision-making, problem-solving, language processing, and emotional regulation.

o Motor Control: Gray matter regions in the motor cortex and basal ganglia play a key role in coordinating voluntary movements and motor skills.

o Sensory Processing: Gray matter structures in the sensory cortex process sensory inputs from the environment, including touch, vision, hearing, taste, and smell.

4.    Gray Matter Volume:

oChanges in gray matter volume can reflect alterations in brain structure and function associated with development, aging, learning, and neurological disorders.

oNeuroimaging techniques like magnetic resonance imaging (MRI) are used to measure gray matter volume and assess differences between individuals or groups.

5.     Clinical Implications:

oNeurological Disorders: Alterations in gray matter volume have been observed in conditions such as Alzheimer's disease, Parkinson's disease, schizophrenia, and mood disorders, providing insights into disease mechanisms and progression.

oNeuroplasticity: Changes in gray matter structure can occur in response to learning, experience, and environmental factors, highlighting the brain's ability to adapt and reorganize neural circuits.

6.    Research and Advances:

oOngoing research aims to elucidate the role of gray matter in brain function, cognition, and behavior, as well as to develop interventions targeting gray matter changes in neurological and psychiatric disorders.

oAdvances in neuroimaging technology and computational methods allow for detailed analysis of gray matter properties, connectivity, and functional contributions to brain networks.

In summary, gray matter is a fundamental component of the brain involved in information processing, cognitive functions, motor control, and sensory processing. Understanding the structure and function of gray matter is essential for unraveling the complexities of brain organization, behavior, and neurological health.

 

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

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 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

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