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.

Ex Input:
Supervised learning depends on annotated examples, which are taken to be the ground truth. But these labels often come from noisy crowdsourcing platforms, like Amazon Mechanical Turk. Practitioners typically collect multiple labels per example and aggregate the results to mitigate noise (the classic crowdsourcing problem). Given a fixed annotation budget and unlimited unlabeled data, redundant annotation comes at the expense of fewer labeled examples. This raises two fundamental questions: (1) How can we best learn from noisy workers? (2) How should we allocate our labeling budget to maximize the performance of a classifier? We propose a new algorithm for jointly modeling labels and worker quality from noisy crowd-sourced data. The alternating minimization proceeds in rounds, estimating worker quality from disagreement with the current model and then updating the model by optimizing a loss function that accounts for the current estimate of worker quality. Unlike previous approaches, even with only one annotation per example, our algorithm can estimate worker quality. We establish a generalization error bound for models learned with our algorithm and establish theoretically that it's better to label many examples once (vs less multiply) when worker quality exceeds a threshold. Experiments conducted on both ImageNet (with simulated noisy workers) and MS-COCO (using the real crowdsourced labels) confirm our algorithm's benefits.

Ex Output:
A new approach for learning a model from noisy crowdsourced annotations.

Ex Input:
It is easy for people to imagine what a man with pink hair looks like, even if they have never seen such a person before. We call the ability to create images of novel semantic concepts visually grounded imagination. In this paper, we show how we can modify variational auto-encoders to perform this task. Our method uses a novel training objective, and a novel product-of-experts inference network, which can handle partially specified (abstract) concepts in a principled and efficient way. We also propose a set of easy-to-compute evaluation metrics that capture our intuitive notions of what it means to have good visual imagination, namely correctness, coverage, and compositionality (the 3 C's). Finally, we perform a detailed comparison of our method with two existing joint image-attribute VAE methods (the JMVAE method of Suzuki et al., 2017 and the BiVCCA method of Wang et al., 2016) by applying them to two datasets: the MNIST-with-attributes dataset (which we introduce here), and the CelebA dataset (Liu et al., 2015).

Ex Output:
A VAE-variant which can create diverse images corresponding to novel concrete or abstract "concepts" described using attribute vectors.

Ex Input:
We study how the topology of a data set comprising two components representing two classes of objects in a binary classification problem changes as it passes through the layers of a well-trained neural network, i.e., one with perfect accuracy on training set and a generalization error of less than 1%. The goal is to shed light on two well-known mysteries in deep neural networks: (i) a nonsmooth activation function like ReLU outperforms a smooth one like hyperbolic tangent; (ii) successful neural network architectures rely on having many layers, despite the fact that a shallow network is able to approximate any function arbitrary well. We performed extensive experiments on persistent homology of a range of point cloud data sets. The results consistently demonstrate the following: (1) Neural networks operate by changing topology, transforming a topologically complicated data set into a topologically simple one as it passes through the layers. No matter how complicated the topology of the data set we begin with, when passed through a well-trained neural network, the Betti numbers of both components invariably reduce to their lowest possible values: zeroth Betti number is one and all higher Betti numbers are zero. Furthermore, (2) the reduction in Betti numbers is significantly faster for ReLU activation compared to hyperbolic tangent activation --- consistent with the fact that the former define nonhomeomorphic maps (that change topology) whereas the latter define homeomorphic maps (that preserve topology). Lastly, (3) shallow and deep networks process the same data set differently --- a shallow network operates mainly through changing geometry and changes topology only in its final layers, a deep network spreads topological changes more evenly across all its layers.

Ex Output:
We show that neural networks operate by changing topologly of a data set and explore how architectural choices effect this change.