In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Input: Consider Input: One of the main challenges in applying graph convolutional neural networks on gene-interaction data is the lack of understanding of the vector space to which they belong and also the inherent difficulties involved in representing those interactions on a significantly lower dimension, viz Euclidean spaces. The challenge becomes more prevalent when dealing with various types of heterogeneous data. We introduce a systematic, generalized method, called iSOM-GSN, used to transform ''multi-omic'' data with higher dimensions onto a two-dimensional grid. Afterwards, we apply a convolutional neural network to predict disease states of various types. Based on the idea of Kohonen's self-organizing map, we generate a two-dimensional grid for each sample for a given set of genes that represent a gene similarity network. We have tested the model to predict breast and prostate cancer using gene expression, DNA methylation and copy number alteration, yielding prediction accuracies in the 94-98% range for tumor stages of breast cancer and calculated Gleason scores of prostate cancer with just 11 input genes for both cases. The scheme not only outputs nearly perfect classification accuracy, but also provides an enhanced scheme for representation learning, visualization, dimensionality reduction, and interpretation of the results.

Output: This paper presents a deep learning model that combines self-organizing maps and convolutional neural networks for representation learning of multi-omics data

Input: Consider Input: Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased towards low frequency functions, meaning that they cannot have local fluctuations without affecting their global behavior. Intuitively, this property is in line with the observation that over-parameterized networks find simple patterns that generalize across data samples. We also investigate how the shape of the data manifold affects expressivity by showing evidence that learning high frequencies gets easier with increasing manifold complexity, and present a theoretical understanding of this behavior. Finally, we study the robustness of the frequency components with respect to parameter perturbation, to develop the intuition that the parameters must be finely tuned to express high frequency functions.

Output: We investigate ReLU networks in the Fourier domain and demonstrate peculiar behaviour.

Input: Consider Input: Most classification and segmentation datasets assume a closed-world scenario in which predictions are expressed as distribution over a predetermined set of visual classes. However, such assumption implies unavoidable and often unnoticeable failures in presence of out-of-distribution (OOD) input. These failures are bound to happen in most real-life applications since current visual ontologies are far from being comprehensive. We propose to address this issue by discriminative detection
of OOD pixels in input data. Different from recent approaches, we avoid to bring any decisions by only observing the training dataset of the primary model trained to solve the desired computer vision task. Instead, we train a dedicated OOD model
which discriminates the primary training set from a much larger "background" dataset which approximates the variety of the visual world. We perform our experiments on high resolution natural images in a dense prediction setup. We use several road driving datasets as our training distribution, while we approximate the background distribution with the ILSVRC dataset. We evaluate our approach on WildDash test, which is currently the only public test dataset with out-of-distribution images.
The obtained results show that the proposed approach succeeds to identify out-of-distribution pixels while outperforming previous work by a wide margin.
Output: We present a novel approach for detecting out-of-distribution pixels in semantic segmentation.