This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms.

The network is a differentiable deep architecture consisting of feature extraction and diffusion distance modules for computing diffusion distance on image by end-to-end training. We design low resolution kernel matching loss and high resolution segment matching loss to enforce the network's output to beconsistent withhuman-labeled image segments.

Neural Information Processing Systems http://nips.cc/

GPUs remains a significant challenge.

However,the existing literature onparallel inference almost exclusively focuses on Euclidean data and parameters.

Neural Information Processing Systems http://nips.cc/

EPFO is the average of 9 query types with(,) operators, Negation is the average of 5 query types with the negation operator(). On average, a single ULTRAQUERY model outperforms the best baselines trained specifically on each dataset.

We adjust this regularization term so that it concentrates on increasing the entropy of the particular pairs of binary vectors that are not correlated in high-dimensional space.