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 Cortical Growth

Image
Dr. Rishabh Pathak

A neuro-computational model of cortical growth integrates principles from neuroscience and computational modeling to study the development of the cerebral cortex, the outer layer of the brain responsible for higher cognitive functions. Here are the key aspects of a neuro-computational model of cortical growth:


1. Biologically Realistic Representation: The model incorporates biologically realistic features of cortical development, such as neuronal migration, synaptogenesis, and dendritic arborization. By simulating these processes computationally, researchers can study how neural activity and connectivity influence cortical growth.


2. Neuroanatomical Constraints: The model considers neuroanatomical constraints, such as the presence of radial glial cells and the formation of cortical layers, to accurately represent the structural organization of the developing cortex. By incorporating these constraints, the model can capture the spatiotemporal dynamics of cortical growth.


3. Neuronal Connectivity: The model accounts for the establishment of neuronal connections within the cortex, including the formation of local circuits and long-range connections. By simulating the growth of axonal and dendritic arbors, researchers can study how connectivity patterns emerge during cortical development.


4. Activity-Dependent Plasticity: The model incorporates activity-dependent mechanisms of synaptic plasticity, such as Hebbian learning rules, to simulate how neural activity influences the refinement of cortical circuits. By considering the role of activity in shaping connectivity patterns, the model can elucidate the impact of sensory experience on cortical growth.


5. Computational Simulations: Neuro-computational models use computational simulations, such as neural network models or biologically detailed simulations, to study the dynamics of cortical growth. These simulations allow researchers to investigate how interactions between neurons, glial cells, and growth factors contribute to the development of the cortex.


6.  Plasticity and Learning: The model explores how plasticity mechanisms and learning algorithms influence the organization and function of the developing cortex. By simulating learning tasks or sensory experiences, researchers can study how cortical circuits adapt and reorganize in response to environmental stimuli.


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


8.  Insights into Neurodevelopmental Disorders: By simulating aberrant growth patterns or disruptions in cortical development, neuro-computational models can provide insights into the mechanisms underlying neurodevelopmental disorders, such as autism spectrum disorders or intellectual disabilities. These models help researchers understand how alterations in cortical growth processes may contribute to neurological conditions.


In summary, a neuro-computational model of cortical growth offers a powerful framework for studying the intricate processes involved in the development of the cerebral cortex. By combining neuroscience principles with computational modeling techniques, researchers can gain valuable insights into the mechanisms driving cortical growth, connectivity formation, and the emergence of functional circuits in the developing brain.

 

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

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

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

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

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