1,322 research outputs found
Learning Distributions of Functions on a Continuous Time Domain
This work presents several contributions on the topic of learning representations of function spaces, as well as on learning the dynamics of glioma growth as a particular instance thereof. We begin with two preparatory efforts, showing how expert knowledge can be leveraged efficiently in an interactive segmentation context, and presenting a proof of concept for inferring non-deterministic glioma growth patterns purely from data. The remainder of our work builds upon the framework of Neural Processes. We show how these models represent function spaces and discover that they can implicitly decompose the space into different frequency components, not unlike a Fourier transform. In this context we derive an upper bound on the maximum signal frequency Neural Processes can represent and show how to
control the learned representations to only contain certain frequencies. We continue with an improvement of a more recent addition to the Neural Process family called ConvCNP, which we combine with a Gaussian Process to make it non-deterministic and to improve generalization. Finally, we show how to perform segmentation in the Neural Process framework by extending a typical segmentation
architecture with spatio-temporal attention. The resulting model can interpolate complex spatial variations of segmentations over time and, applied to glioma growth, it is able to represent multiple temporally consistent growth trajectories, exhibiting realistic and diverse spatial
growth patterns
Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks
This paper proposes a novel approach to integrating partial differential
equation (PDE)-based evolution models into neural networks through a new type
of regularization. Specifically, we propose inverse evolution layers (IELs)
based on evolution equations. These layers can achieve specific regularization
objectives and endow neural networks' outputs with corresponding properties of
the evolution models. Moreover, IELs are straightforward to construct and
implement, and can be easily designed for various physical evolutions and
neural networks. Additionally, the design process for these layers can provide
neural networks with intuitive and mathematical interpretability, thus
enhancing the transparency and explainability of the approach. To demonstrate
the effectiveness, efficiency, and simplicity of our approach, we present an
example of endowing semantic segmentation models with the smoothness property
based on the heat diffusion model. To achieve this goal, we design
heat-diffusion IELs and apply them to address the challenge of semantic
segmentation with noisy labels. The experimental results demonstrate that the
heat-diffusion IELs can effectively mitigate the overfitting problem caused by
noisy labels
Recommended from our members
The role of HG in the analysis of temporal iteration and interaural correlation
- …