Related papers: The Ising Model for Neural Data: Model Quality and…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
Computational modeling is becoming a widely used methodology in modern neuroscience. However, as the complexity of the phenomena under study increases, the analysis of the results emerging from the simulations concomitantly becomes more…
General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…
Multi-electrode arrays covering several square millimeters of neural tissue provide simultaneous access to population signals such as extracellular potentials and spiking activity of one hundred or more individual neurons. The…
We revisit and extend model stitching (Lenc & Vedaldi 2015) as a methodology to study the internal representations of neural networks. Given two trained and frozen models $A$ and $B$, we consider a "stitched model'' formed by connecting the…
We investigate analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alingment of spins in…
It was recently proposed that neural networks could be used to approximate many-dimensional probability distributions that appear e.g. in lattice field theories or statistical mechanics. Subsequently they can be used as variational…
The firing dynamics of biological neurons in mathematical models is often determined by the model's parameters, representing the neurons' underlying properties. The parameter estimation problem seeks to recover those parameters of a single…
In this note, we study the equivalence between planar Ising networks and cells in the positive orthogonal Grassmannian. We present a microscopic construction based on amalgamation, which establishes the correspondence for any planar Ising…
Maximum Entropy models can be inferred from large data-sets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multielectrode arrays in the human and monkey…
In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in…
In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results…
Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal…
Long-time series of neuronal recordings are resulting from the activity of connected neuronal networks. Yet how neuronal properties can be extracted remains empirical. We review here the data analysis based on network models to recover…
The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the…
In order to investigate the effects of connectivity and proximity in the specific heat, a special class of exactly solvable planar layered Ising models has been studied in the thermodynamic limit. The Ising models consist of repeated…
Decades of exponential scaling in high performance computing (HPC) efficiency is coming to an end. Transistor based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further…
To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging…
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…
The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks…