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: Neural network training depends on the structure of the underlying loss landscape, i.e. local minima, saddle points, flat plateaus, and loss barriers. In relation to the structure of the landscape, we study the permutation symmetry of neurons in each layer of a deep neural network, which gives rise not only to multiple equivalent global minima of the loss function but also to critical points in between partner minima. In a network of $d-1$ hidden layers with $n_k$ neurons in layers $k = 1, \ldots, d$, we construct continuous paths between equivalent global minima that lead through a `permutation point' where the input and output weight vectors of two neurons in the same hidden layer $k$ collide and interchange. We show that such permutation points are critical points which lie inside high-dimensional subspaces of equal loss, contributing to the global flatness of the landscape. We also find that a permutation point for the exchange of neurons $i$ and $j$ transits into a flat high-dimensional plateau that enables all $n_k!$ permutations of neurons in a given layer $k$ at the same loss value. Moreover , we introduce higher-order permutation points by exploiting the hierarchical structure in the loss landscapes of neural networks, and find that the number of $K$-th order permutation points is much larger than the (already huge) number of equivalent global minima -- at least by a polynomial factor of order $K$. In two tasks, we demonstrate numerically with our path finding method that continuous paths between partner minima exist: first, in a toy network with a single hidden layer on a function approximation task and, second, in a multilayer network on the MNIST task. Our geometric approach yields a lower bound on the number of critical points generated by weight-space symmetries and provides a simple intuitive link between previous theoretical results and numerical observations.

Output: Weight-space symmetry in neural network landscapes gives rise to numerous number of saddles and flat high-dimensional subspaces.


Input: Consider Input: A framework for efficient Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. Its strength lies in both ease of implementation and automatically tuning sampler parameters to speed up mixing time. Several strategies to approximate the evidence lower bound (ELBO) computation are introduced, including a rewriting of the ELBO objective. Experimental evidence is shown by performing experiments on an unconditional VAE on density estimation tasks; solving an influence diagram in a high-dimensional space with a conditional variational autoencoder (cVAE) as a deep Bayes classifier; and state-space models for time-series data.

Output: We embed SG-MCMC samplers inside a variational approximation


Input: Consider Input: Real-world Question Answering (QA) tasks consist of thousands of words that often represent many facts and entities. Existing models based on LSTMs require a large number of parameters to support external memory and do not generalize well for long sequence inputs. Memory networks attempt to address these limitations by storing information to an external memory module but must examine all inputs in the memory. Hence, for longer sequence inputs the intermediate memory components proportionally scale in size resulting in poor inference times and high computation costs.

 In this paper, we present Adaptive Memory Networks (AMN) that process input question pairs to dynamically construct a network architecture optimized for lower inference times. During inference, AMN parses input text into entities within different memory slots. However, distinct from previous approaches, AMN is a dynamic network architecture that creates variable numbers of memory banks weighted by question relevance. Thus, the decoder can select a variable number of memory banks to construct an answer using fewer banks, creating a runtime trade-off between accuracy and speed. 

 AMN is enabled by first, a novel bank controller that makes discrete decisions with high accuracy and second, the capabilities of a dynamic framework (such as PyTorch) that allow for dynamic network sizing and efficient variable mini-batching. In our results, we demonstrate that our model learns to construct a varying number of memory banks based on task complexity and achieves faster inference times for standard bAbI tasks, and modified bAbI tasks. We achieve state of the art accuracy over these tasks with an average 48% lower entities are examined during inference.


Output: Memory networks with faster inference