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While existing predictive frameworks are able to handle Euclidean structured data (i.e, brain images), they might fail to generalize to geometric non-Euclidean data such as brain networks. Besides, these are rooted the sample selection step…
Advances in optical and electrophysiological recording technologies have made it possible to record the dynamics of thousands of neurons, opening up new possibilities for interpreting and controlling large neural populations in behaving…
A coreset for a set of points is a small subset of weighted points that approximately preserves important properties of the original set. Specifically, if $P$ is a set of points, $Q$ is a set of queries, and $f:P\times Q\to\mathbb{R}$ is a…
Wavelet neural network (WNN), which learns an unknown nonlinear mapping from the data, has been widely used in signal processing, and time-series analysis. However, challenges in constructing accurate wavelet bases and high computational…
Deep neural networks (DNNs) have been found to be vulnerable to backdoor attacks, raising security concerns about their deployment in mission-critical applications. While existing defense methods have demonstrated promising results, it is…
The remarkable performance of overparameterized deep neural networks (DNNs) must arise from an interplay between network architecture, training algorithms, and structure in the data. To disentangle these three components, we apply a…
Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges: (i) each target function often requires training a new…
A three-hidden-layer neural network with super approximation power is introduced. This network is built with the floor function ($\lfloor x\rfloor$), the exponential function ($2^x$), the step function ($1_{x\geq 0}$), or their compositions…
Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…
Deep Neural Networks (DNNs) have recently shown state of the art performance on semantic segmentation tasks, however, they still suffer from problems of poor boundary localization and spatial fragmented predictions. The difficulties lie in…
Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…
To improve the efficiency and sustainability of learning deep models, we propose CREST, the first scalable framework with rigorous theoretical guarantees to identify the most valuable examples for training non-convex models, particularly…
Prior-Fitted Networks (PFNs) have recently been proposed to efficiently perform tabular classification tasks. Although they achieve good performance on small datasets, they encounter limitations with larger datasets. These limitations…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning…
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…
Randomized neural networks (NNs) are an interesting alternative to conventional NNs that are more used for data modeling. The random vector functional-link (RVFL) network is an established and theoretically well-grounded randomized learning…
This paper develops a randomized approach for incrementally building deep neural networks, where a supervisory mechanism is proposed to constrain the random assignment of the weights and biases, and all the hidden layers have direct links…
Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…