相关论文: The Linear Centroids Hypothesis: Features as Direc…

Recently, convolutional neural network (CNN) has demonstrated significant success for image restoration (IR) tasks (e.g., image super-resolution, image deblurring, rain streak removal, and dehazing). However, existing CNN based models are…

A central challenge in neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic…

We propose the Tikhonov layer, a graph neural network layer that is interpretable by design: once trained, its learned parameters directly reveal which node features and which aspects of the graph topology were leveraged for prediction. In…

Interest point descriptors have fueled progress on almost every problem in computer vision. Recent advances in deep neural networks have enabled task-specific learned descriptors that outperform hand-crafted descriptors on many problems. We…

We introduce a novel Deep Network architecture that implements the full feature point handling pipeline, that is, detection, orientation estimation, and feature description. While previous works have successfully tackled each one of these…

Normalization layers are essential in a Deep Convolutional Neural Network (DCNN). Various normalization methods have been proposed. The statistics used to normalize the feature maps can be computed at batch, channel, or instance level.…

Deep neural networks are inherently opaque and challenging to interpret. Unlike hand-crafted feature-based models, we struggle to comprehend the concepts learned and how they interact within these models. This understanding is crucial not…

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem…

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…

This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of…

Advancements in deep learning and machine learning have improved the ability to model complex, nonlinear relationships, such as those encountered in complex material inverse problems. However, the effectiveness of these methods often…

The interpretation of reasoning by Deep Neural Networks (DNN) is still challenging due to their perceived black-box nature. Therefore, deploying DNNs in several real-world tasks is restricted by the lack of transparency of these models. We…

We study feature learning in two-layer neural networks within the linear-width regime, where the number of hidden neurons, sample size, and input dimension scale proportionally. While recent work has analyzed feature learning via a single…

Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for…

This paper presents a new state-of-the-art for document image classification and retrieval, using features learned by deep convolutional neural networks (CNNs). In object and scene analysis, deep neural nets are capable of learning a…

This paper presents an unsupervised method to learn a neural network, namely an explainer, to interpret a pre-trained convolutional neural network (CNN), i.e., explaining knowledge representations hidden in middle conv-layers of the CNN.…

In this note, we elaborate on and explain in detail the proof given by Ziyin et al. (2025) of the ``perfect" Platonic Representation Hypothesis (PRH) for the embedded deep linear network model (EDLN). We show that if trained with the…

Deep neural networks have attained remarkable success across diverse classification tasks. Recent empirical studies have shown that deep networks learn features that are linearly separable across classes. However, these findings often lack…

We develop a rigorous algebraic framework for deep convolutional architectures, CNNs, ResNets, and encoder--decoder networks such as UNet, grounded in lattice theory and mathematical morphology. The central tool is the…

Recognition tasks, such as object recognition and keypoint estimation, have seen widespread adoption in recent years. Most state-of-the-art methods for these tasks use deep networks that are computationally expensive and have huge memory…