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...
Connectomics is a field of neuroscience that focuses on the comprehensive mapping and study of neural connections in the brain at various scales, ranging from the microscale of individual neurons and synapses to the macroscale of functional and structural connectivity between different brain regions. Here are some key points about connectomics:
- Connectomics is the production and
analysis of connectomes, which are detailed maps of neural connections within
the nervous system of an organism, including the brain.
- Connectomics aims to understand the
structural and functional wiring of the brain, elucidating how neural circuits
are organized, how information flows between brain regions, and how
connectivity patterns relate to brain function and behavior.
- Connectomics can be studied at multiple
scales, encompassing the microscale of individual neurons and synapses, the
mesoscale of neural circuits and brain regions, and the macroscale of
large-scale brain networks and functional connectivity.
- Techniques such as electron microscopy,
diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI),
and electroencephalography (EEG) are used to investigate connectivity patterns
at different scales.
- Structural connectomics focuses on mapping
the anatomical connections between brain regions, revealing the physical
pathways of neural communication and information transfer in the brain.
- Techniques like diffusion MRI and
tractography are used to trace white matter pathways and reconstruct the
structural connectivity matrix of the brain, providing insights into the
organization of neural circuits.
- Functional connectomics examines the
dynamic patterns of neural activity and functional connectivity between brain
regions during different cognitive tasks, resting states, or behavioral states.
- Functional imaging techniques like fMRI
and EEG are employed to study how brain regions interact and communicate
functionally, revealing the coordinated activity within functional brain
networks.
- Connectomics research has implications for
understanding brain development, neural plasticity, learning and memory,
sensory processing, motor control, and cognitive functions.
- Connectomics approaches are also used to
investigate neurological and psychiatric disorders, identify biomarkers of
disease, and develop targeted interventions for brain-related conditions.
In
summary, connectomics is a multidisciplinary field that integrates
neuroscience, imaging technologies, and computational methods to map, analyze,
and interpret the complex network of neural connections in the brain. By
unraveling the structural and functional connectivity of the brain,
connectomics provides valuable insights into brain organization, information
processing, and the mechanisms underlying brain function and dysfunction.
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