인문학
사회과학
자연과학
공학
의약학
농수해양학
예술체육학
복합학
DBpia AI
AI 에이전트
AI 아이디어
AI 리더
AI 뷰어
Citeasy
크롬 서지관리 다운로드
지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록·키워드
Gradient descent and its variants are foundational in solving optimization problems across many disciplines. In deep learning, these optimizers demonstrate a remarkable ability to dynamically navigate complex loss landscapes, ultimately converging to solutions that generalize well. To elucidate the mechanism underlying this ability, we introduce a theoretical framework that models the complexities of loss landscapes as multifractal. Our model unifies and explains a broad range of realistic geometrical signatures of loss landscapes, including clustered degenerate minima, multiscale structure, and rich optimization dynamics in deep neural networks, such as the edge of stability, non-stationary anomalous diffusion, and the extended edge of chaos without requiring fine-tuning parameters. We further develop a fractional diffusion theory to illustrate how these optimization dynamics, coupled with multifractal structure, effectively guide optimizers toward smooth solution spaces housing flatter minima, thus enhancing generalization. Our findings suggest that the complexities of loss landscapes do not hinder optimization; rather, they facilitate the process. This perspective not only has important implications for understanding deep learning but also extends potential applicability to other disciplines where optimization unfolds on complex landscapes.
#Maxima and minima
#Computer science
#Range (aeronautics)
#Deep learning
#Generalization
#Multifractal system
#Perspective (graphical)
#Gradient descent
#Optimization problem
#Statistical physics
#Stability (learning theory)
#Degenerate energy levels
#Artificial intelligence
#Process (computing)
#Mathematical optimization
#Artificial neural network
#Mathematics
#Machine learning
#Fractal
#Algorithm
#Physics
#Materials science
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