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Nonconvex Low-Rank Tensor Completion from Noisy Data

Neural Information Processing Systems

Focusing on "incoherent" and well-conditioned tensors of a constant CP rank, we propose a two-stage nonconvex algorithm -- (vanilla) gradient descent following a rough initialization -- that achieves the best of both worlds.



Error Correction Code Transformer

Neural Information Processing Systems

BCH(7,4) code with N = 6, d = 32, similarly to the results presented in Section 6.1. Interestingly, in the early stage of the decoding, ECCT seems to focus its processing of the syndrome. Once the network corrects the bit (last layers(s)), the values return to normal. Using multiple heads is clearly beneficial for the model's performance. The proposed shallow ECCTs are able to compete and even surpass the SCL for some of the codes and SNRs.




Re-Analyze Gauss: Bounds for Private Matrix Approximation via Dyson Brownian Motion Oren Mangoubi Worcester Polytechnic Institute Nisheeth K. Vishnoi Yale University

Neural Information Processing Systems

Given a symmetric matrix M and a vector, we present new bounds on the Frobenius-distance utility of the Gaussian mechanism for approximating M by a matrix whose spectrum is,u n d e r ( ร, ") -di erential privacy. Our bounds depend on both and the gaps in the eigenvalues of M, and hold whenever the top k +1 eigenvalues of M have su ciently large gaps. When applied to the problems of private rank-k covariance matrix approximation and subspace recovery, our bounds yield improvements over previous bounds. Our bounds are obtained by viewing the addition of Gaussian noise as a continuous-time matrix Brownian motion. This viewpoint allows us to track the evolution of eigenvalues and eigenvectors of the matrix, which are governed by stochastic di erential equations discovered by Dyson. These equations allow us to bound the utility as the square-root of a sum-of-squares of perturbations to the eigenvectors, as opposed to a sum of perturbation bounds obtained via Davis-Kahan-type theorems.




ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction Supplementary Material Juan Nathaniel

Neural Information Processing Systems

ChaosBench is published under the open source GNU General Public License. Furthermore, we are committed to maintaining and preserving the ChaosBench benchmark. User feedback will be closely monitored via the GitHub issue tracker. Dataset: All our dataset, present and future (e.g., with more years, multi-resolution support, etc) are Here, we provide a detailed description on how to prepare the necessary data, perform training, and benchmark your own model. B.1 Data Preparation First, navigate to the repository directory and install the necessary dependencies.