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.
--------
Question: This paper presents a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size. MINE is  back-propable and we prove that it is strongly consistent. We illustrate a handful of applications in which MINE is succesfully applied  to enhance the property of generative models in both unsupervised and supervised settings. We apply our framework to estimate the information bottleneck, and apply it in tasks related to supervised classification problems. Our results  demonstrate substantial added flexibility and improvement in these settings.


Answer: A scalable in sample size and dimensions mutual information estimator.


Question: Modern neural network architectures use structured linear transformations, such as low-rank matrices, sparse matrices, permutations, and the Fourier transform, to improve inference speed and reduce memory usage compared to general linear maps. However, choosing which of the myriad structured transformations to use (and its associated parameterization) is a laborious task that requires trading off speed, space, and accuracy. We consider a different approach: we introduce a family of matrices called kaleidoscope matrices (K-matrices) that provably capture any structured matrix with near-optimal space (parameter) and time (arithmetic operation) complexity. We empirically validate that K-matrices can be automatically learned within end-to-end pipelines to replace hand-crafted procedures, in order to improve model quality. For example, replacing channel shuffles in ShuffleNet improves classification accuracy on ImageNet by up to 5%. Learnable K-matrices can also simplify hand-engineered pipelines---we replace filter bank feature computation in speech data preprocessing with a kaleidoscope layer, resulting in only 0.4% loss in accuracy on the TIMIT speech recognition task. K-matrices can also capture latent structure in models: for a challenging permuted image classification task, adding a K-matrix to a standard convolutional architecture can enable learning the latent permutation and improve accuracy by over 8 points. We provide a practically efficient implementation of our approach, and use K-matrices in a Transformer network to attain 36% faster end-to-end inference speed on a language translation task.

Answer: We propose a differentiable family of "kaleidoscope matrices," prove that all structured matrices can be represented in this form, and use them to replace hand-crafted linear maps in deep learning models.


Question: Decades of research on the neural code underlying spatial navigation have revealed a diverse set of neural response properties. The Entorhinal Cortex (EC) of the mammalian brain contains a rich set of spatial correlates, including grid cells which encode space using tessellating patterns. However, the mechanisms and functional significance of these spatial representations remain largely mysterious. As a new way to understand these neural representations, we trained recurrent neural networks (RNNs) to perform navigation tasks in 2D arenas based on velocity inputs. Surprisingly, we find that grid-like spatial response patterns emerge in trained networks, along with units that exhibit other spatial correlates, including border cells and band-like cells. All these different functional types of neurons have been observed experimentally. The order of the emergence of grid-like and border cells is also consistent with observations from developmental studies. Together, our results suggest that grid cells, border cells and others as observed in EC may be a natural solution for representing space efficiently given the predominant recurrent connections in the neural circuits.


Answer:
To our knowledge, this is the first study to show how neural representations of space, including grid-like cells and border cells as observed in the brain, could emerge from training a recurrent neural network to perform navigation tasks.