As recommended by the NeurIPS dataset and benchmark track, we documented QM1B and intended uses through the Datasheets for Datasets framework [1]. The goal of dataset datasheets as outlined by [1] is to provide a standardized process for documentating datasets. The authors of [1] present a list of carefully selected questions which dataset authors should answer. We hope our answers to these questions will facilitate better communication between us (the dataset creators) and future users of QM1B. For what purpose was the dataset created? Prior gaussian-based Density Functional Theory (DFT) datasets contained fewer than 20 million training examples.

Neural Information Processing Systems http://nips.cc/

In Section B, we provide some preliminaries. In Section C, we provide sparsity analysis. We show convergence analysis in Section D. In Section E, we show how to combine the sparsity, convergence, running time all together. In Section F, we show correlation between sparsity and spectral gap of Hessian in neural tangent kernel. In Section G, we discuss how to generalize our result to quantum setting.

We study the parameterized complexity of training two-layer neural networks with respect to the dimension of the input data and the number of hidden neurons, considering ReLU and linear threshold activation functions. Albeit the computational complexity of these problems has been studied numerous times in recent years, several questions are still open. We answer questions by Arora et al. (ICLR 2018) and Khalife and Basu (IPCO 2022) showing that both problems are NP-hard for two dimensions, which excludes any polynomial-time algorithm for constant dimension. We also answer a question by Froese et al. (JAIR 2022) proving W[1]-hardness for four ReLUs (or two linear threshold neurons) with zero training error. Finally, in the ReLU case, we show fixed-parameter tractability for the combined parameter number of dimensions and number of ReLUs if the network is assumed to compute a convex map. Our results settle the complexity status regarding these parameters almost completely.

Online Normalization is a new technique for normalizing the hidden activations of a neural network.

Stochastic gradient descent with a large initial learning rate is widely used for training modern neural net architectures. Although a small initial learning rate allows for faster training and better test performance initially, the large learning rate achieves better generalization soon after the learning rate is annealed. Towards explaining this phenomenon, we devise a setting in which we can prove that a two layer network trained with large initial learning rate and annealing provably generalizes better than the same network trained with a small learning rate from the start. The key insight in our analysis is that the order of learning different types of patterns is crucial: because the small learning rate model first memorizes low-noise, hard-to-fit patterns, it generalizes worse on hard-to-generalize, easier-to-fit patterns than its large learning rate counterpart. This concept translates to a larger-scale setting: we demonstrate that one can add a small patch to CIFAR-10 images that is immediately memorizable by a model with small initial learning rate, but ignored by the model with large learning rate until after annealing. Our experiments show that this causes the small learning rate model's accuracy on unmodified images to suffer, as it relies too much on the patch early on.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the $k$ parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

Given a neural network, training data, and a threshold, finding weights for the neural network such that the total error is below the threshold is known to be NP-hard. We determine the algorithmic complexity of this fundamental problem precisely, by showing that it is $\exists\mathbb R$-complete. This means that the problem is equivalent, up to polynomial time reductions, to deciding whether a system of polynomial equations and inequalities with integer coefficients and real unknowns has a solution. If, as widely expected, $\exists\mathbb R$ is strictly larger than NP, our work implies that the problem of training neural networks is not even in NP.Neural networks are usually trained using some variation of backpropagation. The result of this paper gives an explanation why techniques commonly used to solve big instances of NP-complete problems (such as SAT solvers, IP solvers, local search, dynamic programming, etc.) seem to be of no use to this task.

Data augmentation is essential to achieve state-of-the-art performance in many deep learning applications. However, the most effective augmentation techniques become computationally prohibitive for even medium-sized datasets. To address this, we propose a rigorous technique to select subsets of data points that when augmented, closely capture the training dynamics of full data augmentation. We first show that data augmentation, modeled as additive perturbations, improves learning and generalization by relatively enlarging and perturbing the smaller singular values of the network Jacobian, while preserving its prominent directions. This prevents overfitting and enhances learning the harder to learn information.