Related papers: A Statistical-Modelling Approach to Feedforward Ne…

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input…

We propose a scalable photonic architecture for implementation of feedforward and recurrent neural networks to perform the classification of handwritten digits from the MNIST database. Our experiment exploits off-the-shelf optical and…

According to conventional neural network theories, the feature of single-hidden-layer feedforward neural networks(SLFNs) resorts to parameters of the weighted connections and hidden nodes. SLFNs are universal approximators when at least the…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…

Bayesian neural networks (BNNs) offer a natural probabilistic formulation for inference in deep learning models. Despite their popularity, their optimality has received limited attention through the lens of statistical decision theory. In…

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…

For many scientific questions, understanding the underlying mechanism is the goal. To help investigators better understand the underlying mechanism, variable selection is a crucial step that permits the identification of the most associated…

Recent successes in image analysis with deep neural networks are achieved almost exclusively with Convolutional Neural Networks (CNNs), typically trained using the backpropagation (BP) algorithm. In a 2022 preprint, Geoffrey Hinton proposed…

Networks are characterized by structural features, such as degree distribution, triangular closures, and assortativity. This paper addresses the problem of reconstructing instances of continuously (and non-negatively) weighted networks from…

Recent years have witnessed a growing call for renewed emphasis on neuroscience-inspired approaches in artificial intelligence research, under the banner of NeuroAI. A prime example of this is predictive coding networks (PCNs), based on the…

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…

Many studies that gather social network data use survey methods that lead to censored, missing or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and…

Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied…

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

Despite the phenomenal success of deep neural networks in a broad range of learning tasks, there is a lack of theory to understand the way they work. In particular, Convolutional Neural Networks (CNNs) are known to perform much better than…

Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…

Techniques for feedforward networks (FFNs) and convolutional networks (CNNs) are frequently reused across families, but the relationship between the underlying model classes is rarely made explicit. We introduce a unified node-level…

The need for function estimation in label-limited settings is common in the natural sciences. At the same time, prior knowledge of function values is often available in these domains. For example, data-free biophysics-based models can be…

The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…