Основні поняття
HDFE enables decodable and sample invariant encoding of continuous objects for neural networks.
Анотація
Abstract:
Proposes Hyper-Dimensional Function Encoding (HDFE) for continuous object representation.
Enables neural networks to process continuous objects without training.
Introduction:
Describes challenges of continuous object learning and desired framework properties.
Data Extraction:
"HDFE serves as an interface for processing continuous objects."
"HDFE does not require any training and maps objects into an organized embedding space."
Explicit Function Encoding:
HDFE encodes explicit functions by mapping samples to a high-dimensional space.
Implicit Function Encoding:
Generalizes HDFE to implicit functions for encoding.
Vector-Valued Function Encoding:
Establishes a theoretical framework for encoding continuous functions practically.
Properties of HDFE:
HDFE is sample invariant, decodable, and isometric.
Experiment:
Applies HDFE to PDE solving and surface normal estimation tasks, outperforming baselines.
Related Work:
Compares HDFE with mesh-grid-based and sparse frameworks.
Conclusion:
HDFE shows strong applicability in low-dimensional inputs and complements PointNet-based architectures.
Статистика
"HDFE는 연속 객체를 처리하기 위한 인터페이스 역할을 합니다."
"HDFE는 어떤 훈련도 필요로 하지 않고 객체를 조직화된 임베딩 공간으로 매핑합니다."
Цитати
"HDFE serves as an interface for processing continuous objects."
"HDFE does not require any training and maps objects into an organized embedding space."