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Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long term prediction of the dynamics of the unknown system. In many real-world applications,…
Deep Neural Networks (DNNs) have shown unparalleled achievements in numerous applications, reflecting their proficiency in managing vast data sets. Yet, their static structure limits their adaptability in ever-changing environments. This…
Deep neural networks (DNNs) are powerful tools for compressing and distilling information. Their scale and complexity, often involving billions of inter-dependent parameters, render direct microscopic analysis difficult. Under such…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
In this paper, we interpret Deep Neural Networks with Complex Network Theory. Complex Network Theory (CNT) represents Deep Neural Networks (DNNs) as directed weighted graphs to study them as dynamical systems. We efficiently adapt CNT…
Even though convolutional neural networks (CNN) has achieved near-human performance in various computer vision tasks, its ability to tolerate scale variations is limited. The popular practise is making the model bigger first, and then train…
We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks…
Deep Neural Networks (DNNs) demonstrate remarkable capabilities in learning complex hierarchical data representations, but the nature of these representations remains largely unknown. Existing global explainability methods, such as Network…
Alignment between non-rigid stretchable structures is one of the most challenging tasks in computer vision, as the invariant properties are hard to define, and there is no labeled data for real datasets. We present unsupervised neural…
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
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 hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…
This paper conceptualizes the Deep Weight Spaces (DWS) of neural architectures as hierarchical, fractal-like, coarse geometric structures observable at discrete integer scales through recursive dilation. We introduce a coarse group action…
Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation…
An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…