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.

Understanding the behavior of stochastic gradient descent (SGD) in the context of deep neural networks has raised lots of concerns recently. Along this line, we theoretically study a general form of gradient based optimization dynamics with unbiased noise, which unifies SGD and standard Langevin dynamics. Through investigating this general optimization dynamics, we analyze the behavior of SGD on escaping from minima and its regularization effects. A novel indicator is derived to characterize the efficiency of escaping from minima through measuring the alignment of noise covariance and the curvature of loss function. Based on this indicator, two conditions are established to show which type of noise structure is superior to isotropic noise in term of escaping efficiency. We further show that the anisotropic noise in SGD satisfies the two conditions, and thus helps to escape from sharp and poor minima effectively, towards more stable and flat minima that typically generalize well. We verify our understanding through comparing
this anisotropic diffusion with full gradient descent plus isotropic diffusion (i.e. Langevin dynamics) and other types of position-dependent noise.
We provide theoretical and empirical analysis on the role of anisotropic noise introduced by stochastic gradient on escaping from minima.

This work addresses the long-standing problem of robust event localization in the presence of temporally of misaligned labels in the training data. We propose a novel versatile loss function that generalizes a number of training regimes from standard fully-supervised cross-entropy to count-based weakly-supervised learning. Unlike classical models which are constrained to strictly fit the annotations during training, our soft localization learning approach relaxes the reliance on the exact position of labels instead. Training with this new loss function exhibits strong robustness to temporal misalignment of labels, thus alleviating the burden of precise annotation of temporal sequences. We demonstrate state-of-the-art performance against standard benchmarks in a number of challenging experiments and further show that robustness to label noise is not achieved at the expense of raw performance.
This work introduces a novel loss function for the robust training of temporal localization DNN in the presence of misaligned labels.

We introduce dynamic instance hardness (DIH) to facilitate the training of machine learning models. DIH is a property of each training sample and is computed as the running mean of the sample's instantaneous hardness as measured over the training history. We use DIH to evaluate how well a model retains knowledge about each training sample over time. We find that for deep neural nets (DNNs), the DIH of a sample in relatively early training stages reflects its DIH in later stages and as a result, DIH can be effectively used to reduce the set of training samples in future epochs. Specifically, during each epoch, only samples with high DIH are trained (since they are historically hard) while samples with low DIH can be safely ignored. DIH is updated each epoch only for the selected samples, so it does not require additional computation. Hence, using DIH during training leads to an appreciable speedup. Also, since the model is focused on the historically more challenging samples, resultant models are more accurate. The above, when formulated as an algorithm, can be seen as a form of curriculum learning, so we call our framework DIH curriculum learning (or DIHCL). The advantages of DIHCL, compared to other curriculum learning approaches, are: (1) DIHCL does not require additional inference steps over the data not selected by DIHCL in each epoch, (2) the dynamic instance hardness, compared to static instance hardness (e.g., instantaneous loss), is more stable as it integrates information over the entire training history up to the present time. Making certain mathematical assumptions, we formulate the problem of DIHCL as finding a curriculum that maximizes a multi-set function $f(\cdot)$, and derive an approximation bound for a DIH-produced curriculum relative to the optimal curriculum. Empirically, DIHCL-trained DNNs significantly outperform random mini-batch SGD and other recently developed curriculum learning methods in terms of efficiency, early-stage convergence, and final performance, and this is shown in training several state-of-the-art DNNs on 11 modern datasets.
New understanding of training dynamics and metrics of memorization hardness lead to efficient and provable curriculum learning.