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.

Q: The training of deep neural networks with Stochastic Gradient Descent (SGD) with a large learning rate or a small batch-size typically ends in flat regions of the weight space, as indicated by small eigenvalues of the Hessian of the training loss. This was found to correlate with a good final generalization performance.   In this paper we extend previous work by investigating the curvature of the loss surface along the whole training trajectory, rather than only at the endpoint. We find that initially SGD visits increasingly sharp regions, reaching a maximum sharpness determined by both the learning rate and the batch-size of SGD. At this peak value SGD starts to fail to minimize the loss along directions in the loss surface corresponding to the largest curvature (sharpest directions). To further investigate the effect of these dynamics in the training process, we study a variant of SGD using a reduced learning rate along the sharpest directions which we show can improve training speed while finding both sharper and better generalizing solution, compared to vanilla SGD. Overall, our results show that the SGD dynamics in the subspace of the sharpest directions influence the regions that SGD steers to (where larger learning rate or smaller batch size result in wider regions visited), the overall training speed, and the generalization ability of the final model.

A: SGD is steered early on in training towards a region in which its step is too large compared to curvature, which impacts the rest of training. 
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Q: Human reasoning involves recognising common underlying principles across many examples by utilising variables. The by-products of such reasoning are invariants that capture patterns across examples such as "if someone went somewhere then they are there" without mentioning specific people or places. Humans learn what variables are and how to use them at a young age, and the question this paper addresses is whether machines can also learn and use variables solely from examples without requiring human pre-engineering. We propose Unification Networks that incorporate soft unification into neural networks to learn variables and by doing so lift examples into invariants that can then be used to solve a given task. We evaluate our approach on four datasets to demonstrate that learning invariants captures patterns in the data and can improve performance over baselines.

A: End-to-end learning of invariant representations with variables across examples such as if someone went somewhere then they are there.
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Q: In one-class-learning tasks, only the normal case can be modeled with data, whereas the variation of all possible anomalies is too large to be described sufficiently by samples. Thus, due to the lack of representative data, the wide-spread discriminative approaches cannot cover such learning tasks, and rather generative models, which attempt to learn the input density of the normal cases, are used. However, generative models suffer from a large input dimensionality (as in images) and are typically inefficient learners. We propose to learn the data distribution more efficiently with a multi-hypotheses autoencoder. Moreover, the model is criticized by a discriminator, which prevents artificial data modes not supported by data, and which enforces diversity across hypotheses. This consistency-based anomaly detection (ConAD) framework allows the reliable identification of outof- distribution samples. For anomaly detection on CIFAR-10, it yields up to 3.9% points improvement over previously reported results. On a real anomaly detection task, the approach reduces the error of the baseline models from 6.8% to 1.5%.

A:
We propose an anomaly-detection approach that combines modeling the foreground class via multiple local densities with adversarial training.
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