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In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…
Neural architecture search (NAS) automates the design process of high-performing architectures, but remains bottlenecked by expensive performance evaluation. Most existing studies that achieve faster evaluation are mostly tied to cell-based…
Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a…
We study the approximation properties and optimization dynamics of recurrent neural networks (RNNs) when applied to learn input-output relationships in temporal data. We consider the simple but representative setting of using…
Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…
The complex and unique neural network topology of the human brain formed through natural evolution enables it to perform multiple cognitive functions simultaneously. Automated evolutionary mechanisms of biological network structure inspire…
Large training datasets almost always contain examples with inaccurate or incorrect labels. Deep Neural Networks (DNNs) tend to overfit training label noise, resulting in poorer model performance in practice. To address this problem, we…
Designing neural networks typically relies on manual trial and error or a neural architecture search (NAS) followed by weight training. The former is time-consuming and labor-intensive, while the latter often discretizes architecture search…
Deep neural networks (DNN) such as Multi-Layer Perception (MLP) and Convolutional Neural Networks (CNN) represent one of the most established deep learning algorithms. Given the tremendous effects of the number of hidden layers on network…
Sample-level rankings are increasingly used in data-centric NLP for analysis, filtering, debugging, and curation, yet existing pipelines typically score training examples pointwise and rank them as if they were independent. This assumption…
The firing dynamics of biological neurons in mathematical models is often determined by the model's parameters, representing the neurons' underlying properties. The parameter estimation problem seeks to recover those parameters of a single…
We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting models are typically equivalent to networks whose nonzero weights are also $\pm 1$. The method…
Optical computing has gained significant attention as a potential solution to the growing computational demands of machine learning, particularly for tasks requiring large-scale data processing and high energy efficiency. Optical systems…
Neural networks are powerful and flexible models that work well for many difficult learning tasks in image, speech and natural language understanding. Despite their success, neural networks are still hard to design. In this paper, we use a…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…
We study the supervised learning problem under either of the following two models: (1) Feature vectors ${\boldsymbol x}_i$ are $d$-dimensional Gaussians and responses are $y_i = f_*({\boldsymbol x}_i)$ for $f_*$ an unknown quadratic…
Errors in measurements are key to weighting the value of data, but are often neglected in Machine Learning (ML). We show how Convolutional Neural Networks (CNNs) are able to learn about the context and patterns of signal and noise, leading…
Self-delimiting (SLIM) programs are a central concept of theoretical computer science, particularly algorithmic information & probability theory, and asymptotically optimal program search (AOPS). To apply AOPS to (possibly recurrent) neural…