1,933 research outputs found
The Hopfield model and its role in the development of synthetic biology
Neural network models make extensive use of
concepts coming from physics and engineering. How do scientists
justify the use of these concepts in the representation of
biological systems? How is evidence for or against the use of
these concepts produced in the application and manipulation
of the models? It will be shown in this article that neural
network models are evaluated differently depending on the
scientific context and its modeling practice. In the case of
the Hopfield model, the different modeling practices related to
theoretical physics and neurobiology played a central role for
how the model was received and used in the different scientific
communities. In theoretical physics, where the Hopfield model
has its roots, mathematical modeling is much more common and
established than in neurobiology which is strongly experiment
driven. These differences in modeling practice contributed to
the development of the new field of synthetic biology which
introduced a third type of model which combines mathematical
modeling and experimenting on biological systems and by doing
so mediates between the different modeling practices
Modeling Quantum Mechanical Observers via Neural-Glial Networks
We investigate the theory of observers in the quantum mechanical world by
using a novel model of the human brain which incorporates the glial network
into the Hopfield model of the neural network. Our model is based on a
microscopic construction of a quantum Hamiltonian of the synaptic junctions.
Using the Eguchi-Kawai large N reduction, we show that, when the number of
neurons and astrocytes is exponentially large, the degrees of freedom of the
dynamics of the neural and glial networks can be completely removed and,
consequently, that the retention time of the superposition of the wave
functions in the brain is as long as that of the microscopic quantum system of
pre-synaptics sites. Based on this model, the classical information entropy of
the neural-glial network is introduced. Using this quantity, we propose a
criterion for the brain to be a quantum mechanical observer.Comment: 24 pages, published versio
Statistical Physics and Representations in Real and Artificial Neural Networks
This document presents the material of two lectures on statistical physics
and neural representations, delivered by one of us (R.M.) at the Fundamental
Problems in Statistical Physics XIV summer school in July 2017. In a first
part, we consider the neural representations of space (maps) in the
hippocampus. We introduce an extension of the Hopfield model, able to store
multiple spatial maps as continuous, finite-dimensional attractors. The phase
diagram and dynamical properties of the model are analyzed. We then show how
spatial representations can be dynamically decoded using an effective Ising
model capturing the correlation structure in the neural data, and compare
applications to data obtained from hippocampal multi-electrode recordings and
by (sub)sampling our attractor model. In a second part, we focus on the problem
of learning data representations in machine learning, in particular with
artificial neural networks. We start by introducing data representations
through some illustrations. We then analyze two important algorithms, Principal
Component Analysis and Restricted Boltzmann Machines, with tools from
statistical physics
Synthesis of neural networks for spatio-temporal spike pattern recognition and processing
The advent of large scale neural computational platforms has highlighted the
lack of algorithms for synthesis of neural structures to perform predefined
cognitive tasks. The Neural Engineering Framework offers one such synthesis,
but it is most effective for a spike rate representation of neural information,
and it requires a large number of neurons to implement simple functions. We
describe a neural network synthesis method that generates synaptic connectivity
for neurons which process time-encoded neural signals, and which makes very
sparse use of neurons. The method allows the user to specify, arbitrarily,
neuronal characteristics such as axonal and dendritic delays, and synaptic
transfer functions, and then solves for the optimal input-output relationship
using computed dendritic weights. The method may be used for batch or online
learning and has an extremely fast optimization process. We demonstrate its use
in generating a network to recognize speech which is sparsely encoded as spike
times.Comment: In submission to Frontiers in Neuromorphic Engineerin
Free energies of Boltzmann Machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit
Restricted Boltzmann machines (RBMs) constitute one of the main models for
machine statistical inference and they are widely employed in Artificial
Intelligence as powerful tools for (deep) learning. However, in contrast with
countless remarkable practical successes, their mathematical formalization has
been largely elusive: from a statistical-mechanics perspective these systems
display the same (random) Gibbs measure of bi-partite spin-glasses, whose
rigorous treatment is notoriously difficult. In this work, beyond providing a
brief review on RBMs from both the learning and the retrieval perspectives, we
aim to contribute to their analytical investigation, by considering two
distinct realizations of their weights (i.e., Boolean and Gaussian) and
studying the properties of their related free energies. More precisely,
focusing on a RBM characterized by digital couplings, we first extend the
Pastur-Shcherbina-Tirozzi method (originally developed for the Hopfield model)
to prove the self-averaging property for the free energy, over its quenched
expectation, in the infinite volume limit, then we explicitly calculate its
simplest approximation, namely its annealed bound. Next, focusing on a RBM
characterized by analogical weights, we extend Guerra's interpolating scheme to
obtain a control of the quenched free-energy under the assumption of replica
symmetry: we get self-consistencies for the order parameters (in full agreement
with the existing Literature) as well as the critical line for ergodicity
breaking that turns out to be the same obtained in AGS theory. As we discuss,
this analogy stems from the slow-noise universality. Finally, glancing beyond
replica symmetry, we analyze the fluctuations of the overlaps for an estimate
of the (slow) noise affecting the retrieval of the signal, and by a stability
analysis we recover the Aizenman-Contucci identities typical of glassy systems.Comment: 21 pages, 1 figur
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