Related papers: Geometric framework to predict structure from func…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behavior. The classical approach is to investigate how individual neurons encode the stimuli and how their tuning…
To understand the behavior of a neural circuit it is a presupposition that we have a model of the dynamical system describing this circuit. This model is determined by several parameters, including not only the synaptic weights, but also…
Metabolism is a fascinating cell machinery underlying life and disease and genome-scale reconstructions provide us with a captivating view of its complexity. However, deciphering the relationship between metabolic structure and function…
Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…
We study the expressivity of sparse maxout networks, where each neuron takes a fixed number of inputs from the previous layer and employs a, possibly multi-argument, maxout activation. This setting captures key characteristics of…
To understand the structure and organization of a large-scale social, biological or technological network, it can be helpful to describe and extract local communities or modules of the network. In this article, we develop a neurodynamic…
The characterization of dynamical processes in living systems provides important clues for their mechanistic interpretation and link to biological functions. Thanks to recent advances in microscopy techniques, it is now possible to…
This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the…
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal…
Neuroscientists are actively pursuing high-precision maps, or graphs, consisting of networks of neurons and connecting synapses in mammalian and non-mammalian brains. Such graphs, when coupled with physiological and behavioral data, are…
Transformers have emerged as the state of the art neural network architecture for natural language processing and computer vision. In the foundation model paradigm, large transformer models (BERT, GPT3/4, Bloom, ViT) are pre-trained on…
This article discusses how the individual morphological properties of basic objects (e.g. neurons, molecules and aggregates), jointly with their particular spatial distribution, can determine the connectivity and dynamics of systems…
We introduce Resonant Sparse Geometry Networks (RSGN), a brain-inspired architecture with self-organizing sparse hierarchical input-dependent connectivity. Unlike Transformer architectures that employ dense attention mechanisms with O(n^2)…
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…
Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of…
Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…
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…
We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. It is useful for dealing with networks in which the topology evolves according to some specified microscopic rules and,…
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…