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Uniform-precision neural network quantization has gained popularity since it simplifies densely packed arithmetic unit for high computing capability. However, it ignores heterogeneous sensitivity to the impact of quantization errors across…

Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…

The transferable neural network (TransNet) is a two-layer shallow neural network with pre-determined and uniformly distributed neurons in the hidden layer, and the least-squares solvers can be particularly used to compute the parameters of…

Deep learning algorithms achieve high classification accuracy at the expense of significant computation cost. To address this cost, a number of quantization schemes have been proposed - but most of these techniques focused on quantizing…

In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First, we introduce a validated Matrix Multiplication Transform…

We study the problem of constructing an estimator of the average treatment effect (ATE) with observational data. The celebrated doubly-robust, augmented-IPW (AIPW) estimator generally requires consistent estimation of both nuisance…

The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…

We present a novel methodology based on a Taylor expansion of the network output for obtaining analytical expressions for the expected value of the network weights and output under stochastic training. Using these analytical expressions the…

An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…

To backpropagate the gradients through stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator that is unbiased, exhibits low variance, and has low computational complexity. Exploiting variable augmentation,…

Many critical applications, from autonomous scientific discovery to personalized medicine, demand systems that can both strategically acquire the most informative data and instantaneously perform inference based upon it. While amortized…

In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adaptive method generating a two-layer spline NN and a numerical…

We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the…

Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures offer a more flexible…

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…

Deep neural networks (DNNs) are known to perform well when deployed to test distributions that shares high similarity with the training distribution. Feeding DNNs with new data sequentially that were unseen in the training distribution has…

Functional magnetic resonance imaging (fMRI) has been increasingly employed to investigate functional brain activity. Many fMRI-related software/toolboxes have been developed, providing specialized algorithms for fMRI analysis. However,…

Active learning can reduce the number of samples needed to perform a hypothesis test and to estimate the parameters of a model. In this paper, we revisit the work of Chernoff that described an asymptotically optimal algorithm for performing…

As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this paper, there is room for…

Incorporating the Forward Forward algorithm into neural network training represents a transformative shift from traditional methods, introducing a dual forward mechanism that streamlines the learning process by bypassing the complexities of…