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...
Greek contributions to neuroscience have been
significant throughout history, with notable figures making pioneering
advancements in understanding the brain and nervous system. Here are some key
Greek contributors to neuroscience from ancient times to the modern era:
1. Alcmaeon of Croton (5th century BC): Alcmaeon is considered one of the earliest Greek
philosophers and physicians who made important contributions to the field of
neuroscience. He is credited with being one of the first to recognize the brain
as the seat of intelligence and to study the optic nerve.
2. Hippocrates (460-370 BC): Known as the "Father of Medicine,"
Hippocrates was an ancient Greek physician whose work laid the foundation for
modern medicine. He emphasized the importance of observing and recording
symptoms of diseases, including those affecting the nervous system.
3. Galen (129-200 AD): Galen, a prominent Greek physician in the Roman
Empire, made significant contributions to anatomy and physiology. He conducted
extensive dissections of animals and described the structure and functions of
the brain and spinal cord.
4. Constantine Economos (20th century): Constantine Economos was a Greek neuroscientist
known for his research on the neurophysiology of vision. He made important
contributions to understanding the visual system and how the brain processes
visual information.
These Greek figures, among others, have played a
crucial role in shaping our understanding of neuroscience over the centuries.
Their work has laid the groundwork for modern neuroscience research and
continues to inspire advancements in the field today.
It is important to
recognize and appreciate the contributions of these Greek scholars to the field
of neuroscience, as their insights and discoveries have had a lasting impact on
our understanding of the brain and nervous system.
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