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.
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Question: Deep ensembles have been empirically shown to be a promising approach for improving accuracy, uncertainty and out-of-distribution robustness of deep learning models. While deep ensembles were theoretically motivated by the bootstrap, non-bootstrap ensembles trained with just random initialization also perform well in practice, which suggests that there could be other explanations for why deep ensembles work well. Bayesian neural networks, which learn distributions over the parameters of the network, are theoretically well-motivated by Bayesian principles, but do not perform as well as deep ensembles in practice, particularly under dataset shift. One possible explanation for this gap between theory and practice is that popular scalable approximate Bayesian methods tend to focus on a single mode, whereas deep ensembles tend to explore diverse modes in function space. We investigate this hypothesis by building on recent work on understanding the loss landscape of neural networks and adding our own exploration to measure the similarity of functions in the space of predictions. Our results show that random initializations explore entirely different modes, while functions along an optimization trajectory or sampled from the subspace thereof cluster within a single mode predictions-wise, while often deviating significantly in the weight space. We demonstrate that while low-loss connectors between modes exist, they are not connected in the space of predictions. Developing the concept of the diversity--accuracy plane, we show that the decorrelation power of random initializations is unmatched by popular subspace sampling methods.

Answer: We study deep ensembles through the lens of loss landscape and the space of predictions, demonstrating that the decorrelation power of random initializations is unmatched by subspace sampling that only explores a single mode.

Question: Spiking neural networks are being investigated both as biologically plausible models of neural computation and also as a potentially more efficient type of neural network. While convolutional spiking neural networks have been demonstrated to achieve near state-of-the-art performance, only one solution has been proposed to convert gated recurrent neural networks, so far.
Recurrent neural networks in the form of networks of gating memory cells have been central in state-of-the-art solutions in problem domains that involve sequence recognition or generation. Here, we design an analog gated LSTM cell where its neurons can be substituted for efficient stochastic spiking neurons. These adaptive spiking neurons implement an adaptive form of sigma-delta coding to convert internally computed analog activation values to spike-trains. For such neurons, we approximate the effective activation function, which resembles a sigmoid. We show how analog neurons with such activation functions can be used to create an analog LSTM cell; networks of these cells can then be trained with standard backpropagation. We train these LSTM networks on a noisy and noiseless version of the original sequence prediction task from Hochreiter & Schmidhuber (1997), and also on a noisy and noiseless version of a classical working memory reinforcement learning task, the T-Maze. Substituting the analog neurons for corresponding adaptive spiking neurons, we then show that almost all resulting spiking neural network equivalents correctly compute the original tasks.

Answer: We demonstrate a gated recurrent asynchronous spiking neural network that corresponds to an LSTM unit.

Question: We analyze speed of convergence to global optimum for gradient descent training a deep linear neural network by minimizing the L2 loss over whitened data. Convergence at a linear rate is guaranteed when the following hold: (i) dimensions of hidden layers are at least the minimum of the input and output dimensions; (ii) weight matrices at initialization are approximately balanced; and (iii) the initial loss is smaller than the loss of any rank-deficient solution. The assumptions on initialization (conditions (ii) and (iii)) are necessary, in the sense that violating any one of them may lead to convergence failure. Moreover, in the important case of output dimension 1, i.e. scalar regression, they are met, and thus convergence to global optimum holds, with constant probability under a random initialization scheme. Our results significantly extend previous analyses, e.g., of deep linear residual networks (Bartlett et al., 2018).

Answer:
We analyze gradient descent for deep linear neural networks, providing a guarantee of convergence to global optimum at a linear rate.