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Neural nets are known to be universal approximators. In particular, formal neurons implementing wavelets have been shown to build nets able to approximate any multidimensional task. Such very specialized formal neurons may be, however,…

The brain is likely the most complex organ, given the variety of functions it controls, the number of cells it comprises, and their corresponding diversity. Studying and identifying neurons, the brain's primary building blocks, is a crucial…

Convoulutional Neural Networks (CNNs) exhibit extraordinary performance on a variety of machine learning tasks. However, their mathematical properties and behavior are quite poorly understood. There is some work, in the form of a framework,…

Two of the most useful tools in topological combinatorics are the nerve lemma and discrete Morse theory. In this note we introduce a theorem that interpolates between them and allows decompositions of complexes into non-contractible pieces…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…

Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…

Hardware-based neuromorphic computing remains an elusive goal with the potential to profoundly impact future technologies and deepen our understanding of emergent intelligence. The learning-from-mistakes algorithm is one of the few training…

Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets.…

Convolutional networks are ubiquitous in deep learning. They are particularly useful for images, as they reduce the number of parameters, reduce training time, and increase accuracy. However, as a model of the brain they are seriously…

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional…

Brain decoding is a hot spot in cognitive science, which focuses on reconstructing perceptual images from brain activities. Analyzing the correlations of collected data from human brain activities and representing activity patterns are two…

Convolutional neural networks demonstrated outstanding empirical results in computer vision and speech recognition tasks where labeled training data is abundant. In medical imaging, there is a huge variety of possible imaging modalities and…

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…

The human brain is a complex system, and understanding its mechanisms has been a long-standing challenge in neuroscience. The study of the functional connectome, which maps the functional connections between different brain regions, has…

The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can…

In this paper the Mechanical Neural Network(MNN) is introduced, a physical implementation of a multilayer perceptron(MLP) with ReLU activation functions, two input neurons, four hidden neurons and two output neurons. This physical model of…

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…

Understanding how brain structure and function interact is key to explaining intelligence yet modeling them jointly is challenging as the structural and functional connectome capture complementary aspects of organization. We introduced…