相关论文: High--Dimensional Brain in a High-Dimensional Worl…

The current acceleration of the universe leads us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We argue that the…

With fast developments in computational power and algorithms, deep learning has made breakthroughs and been applied in many fields. However, generalization remains to be a critical challenge, and the limited generalization capability…

Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic…

Deep neural networks trained with different architectures, objectives, and datasets have been reported to converge on similar visual representations. However, what remains unknown is which visual properties models actually converge on and…

Quantum systems of high dimensions are attracting a lot of attention because they feature interesting properties when it comes to observing entanglement or other forms of correlations. In particular, their improved resistance to noise is…

Effective data visualization is a key part of the discovery process in the era of big data. It is the bridge between the quantitative content of the data and human intuition, and thus an essential component of the scientific path from data…

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding…

Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a…

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…

Deep neural networks are highly expressive models that have recently achieved state of the art performance on speech and visual recognition tasks. While their expressiveness is the reason they succeed, it also causes them to learn…

The failure of the Euclidean norm to reliably distinguish between nearby and distant points in high dimensional space is well-known. This phenomenon of distance concentration manifests in a variety of data distributions, with iid or…

The multiple realizability thesis holds that psychological states may be implemented in a diversity of physical systems. The deep learning revolution seems to be bringing this possibility to life, offering the most plausible examples of…

The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…

In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…

Deep learning has triggered the current rise of artificial intelligence and is the workhorse of today's machine intelligence. Numerous success stories have rapidly spread all over science, industry and society, but its limitations have only…

The curse of dimensionality is a phenomenon frequently observed in machine learning (ML) and knowledge discovery (KD). There is a large body of literature investigating its origin and impact, using methods from mathematics as well as from…

A good theory of mathematical beauty is more practical than any current observation, as new predictions of physical reality can be verified self-consistently. This belief applies to the current status of understanding deep neural networks…

How do different brains create unique visual experiences from identical sensory input? While neural representations vary across individuals, the fundamental architecture underlying these differences remains poorly understood. Here, we…

Traditionally, higher-dimensional cosmological models have sought to provide a description of the fundamental forces in terms of a unifying geometrical construction. In this essay we discuss how, in their present incarnation,…