Related papers: Statistical mechanics of complex neural systems an…
The traditional approach of statistical physics to supervised learning routinely assumes unrealistic generative models for the data: usually inputs are independent random variables, uncorrelated with their labels. Only recently, statistical…
Recent years have seen rapid progress at the intersection between causality and machine learning. Motivated by scientific applications involving high-dimensional data, in particular in biomedicine, we propose a deep neural architecture for…
The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…
For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the…
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…
The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
Sensory perception (e.g. vision) relies on a hierarchy of cortical areas, in which neural activity propagates in both directions, to convey information not only about sensory inputs but also about cognitive states, expectations and…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
Despite the widely-spread consensus on the brain complexity, sprouts of the single neuron revolution emerged in neuroscience in the 1970s. They brought many unexpected discoveries, including grandmother or concept cells and sparse coding of…
The spatial distribution of neuronal cells is an important requirement for achieving proper neuronal function in several parts of the nervous system of most animals. For instance, specific distribution of photoreceptors and related neuronal…
The cognitive framework of conceptual spaces bridges the gap between symbolic and subsymbolic AI by proposing an intermediate conceptual layer where knowledge is represented geometrically. There are two main approaches for obtaining the…
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…
These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory,…
Modern neuroscience has evolved into a frontier field that draws on numerous disciplines, resulting in the flourishing of novel conceptual frames primarily inspired by physics and complex systems science. Contributing in this direction, we…
The massive data sets from today's particle physics experiments present a variety of challenges amenable to the tools developed by the statistics community. From the real-time decision of what subset of data to record on permanent storage,…
Economies are complex man-made systems where organisms and markets interact according to motivations and principles not entirely understood yet. The increasing dissatisfaction with the postulates of traditional economics i.e. perfectly…
Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…