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Deep learning has shown substantial progress in image analysis. However, the computational demands of large, fully trained models remain a consideration. Transfer learning offers a strategy for adapting pre-trained models to new tasks.…

Even though deep neural networks have shown tremendous success in countless applications, explaining model behaviour or predictions is an open research problem. In this paper, we address this issue by employing a simple yet effective method…

In real-world applications, it is often expensive and time-consuming to obtain labeled examples. In such cases, knowledge transfer from related domains, where labels are abundant, could greatly reduce the need for extensive labeling…

Classical representation systems such as Fourier series, wavelets, and fixed dictionaries provide analytically tractable basis expansions, but they are not intrinsically adapted to the empirical structure of modern high-dimensional data.…

In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper…

The cluster Gutzwiller method is widely used to study the strongly correlated bosonic systems, owing to its ability to provide a more precise description of quantum fluctuations. However, its utility is limited by the exponential increase…

Exploiting data invariances is crucial for efficient learning in both artificial and biological neural circuits. Understanding how neural networks can discover appropriate representations capable of harnessing the underlying symmetries of…

In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motivated by the fact that differential deep learning can…

Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution…

This paper introduces and evaluates a novel training method for neural networks: Dual Variable Learning Rates (DVLR). Building on insights from behavioral psychology, the dual learning rates are used to emphasize correct and incorrect…

We introduce a simple permutation equivariant layer for deep learning with set structure.This type of layer, obtained by parameter-sharing, has a simple implementation and linear-time complexity in the size of each set. We use deep…

Nonlinear non-Abelian Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations and their links via Baecklund transformations are considered. The focus is on the construction of soliton solutions admitted by matrix modified…

Combining the merits of both denoising diffusion probabilistic models and gradient boosting, the diffusion boosting paradigm is introduced for tackling supervised learning problems. We develop Diffusion Boosted Trees (DBT), which can be…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…

In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…

Despite the prevalence and significance of tabular data across numerous industries and fields, it has been relatively underexplored in the realm of deep learning. Even today, neural networks are often overshadowed by techniques such as…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

Supervised deep convolutional neural networks (DCNNs) are currently one of the best computational models that can explain how the primate ventral visual stream solves object recognition. However, embodied cognition has not been considered…

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…

In this paper we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study the vibrations of molecular systems. The generated neural networks are trained with…