Neural Networks, Hypersurfaces, and Radon Transforms
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as operators on probability distributions for observed data, we show that the distribution of outputs for any node in a neural network can be interpreted as a nonlinear projection along hypersurfaces defined by level surfaces over the input data space. We utilize these descriptions to provide new interpretation for phenomena such as nonlinearity, pooling, activation functions, and adversarial examples in neural network-based learning problems.
Code (1)
Similar Papers 제목 키워드 기반
Radon-Gabor Barcodes for Medical Image Retrieval
In recent years, with the explosion of digital images on the Web, content-based retrieval has emerged as a significant research area. Shapes, textures, edges and segments may play a key role in describing the content of …
Image RetrievalMedical Image RetrievalRetrievalThe Radon cumulative distribution transform and its application to image classification
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current …
General Classificationimage-classificationImage ClassificationLearning end-to-end inversion of circular Radon transforms in the partial radial setup
We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value…
Radon-Nikodym approximation in application to image analysis
For an image pixel information can be converted to the moments of some basis $Q_k$, e.g. Fourier-Mellin, Zernike, monomials, etc. Given sufficient number of moments pixel information can be completely recovered, for insu…
Image ReconstructionFace Recognition Algorithms based on Transformed Shape Features
Human face recognition is, indeed, a challenging task, especially under the illumination and pose variations. We examine in the present paper effectiveness of two simple algorithms using coiflet packet and Radon transfor…
Face Recognition