3,639 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
High capacity associative memory with bipolar and binary, biased patterns
The high capacity associative memory model is interesting due to its significantly higher capacity when compared with the standard Hopfield model. These networks can use either bipolar or binary patterns, which may also be biased. This paper investigates the performance of a high capacity associative memory model trained with biased patterns, using either bipolar or binary representations. Our results indicate that the binary network performs less well under low bias, but better in other situations, compared with the bipolar network.Peer reviewe
Adiabatic Quantum Optimization for Associative Memory Recall
Hopfield networks are a variant of associative memory that recall information
stored in the couplings of an Ising model. Stored memories are fixed points for
the network dynamics that correspond to energetic minima of the spin state. We
formulate the recall of memories stored in a Hopfield network using energy
minimization by adiabatic quantum optimization (AQO). Numerical simulations of
the quantum dynamics allow us to quantify the AQO recall accuracy with respect
to the number of stored memories and the noise in the input key. We also
investigate AQO performance with respect to how memories are stored in the
Ising model using different learning rules. Our results indicate that AQO
performance varies strongly with learning rule due to the changes in the energy
landscape. Consequently, learning rules offer indirect methods for
investigating change to the computational complexity of the recall task and the
computational efficiency of AQO.Comment: 22 pages, 11 figures. Updated for clarity and figures, to appear in
Frontiers of Physic
Statistical physics of neural systems with non-additive dendritic coupling
How neurons process their inputs crucially determines the dynamics of
biological and artificial neural networks. In such neural and neural-like
systems, synaptic input is typically considered to be merely transmitted
linearly or sublinearly by the dendritic compartments. Yet, single-neuron
experiments report pronounced supralinear dendritic summation of sufficiently
synchronous and spatially close-by inputs. Here, we provide a statistical
physics approach to study the impact of such non-additive dendritic processing
on single neuron responses and the performance of associative memory tasks in
artificial neural networks. First, we compute the effect of random input to a
neuron incorporating nonlinear dendrites. This approach is independent of the
details of the neuronal dynamics. Second, we use those results to study the
impact of dendritic nonlinearities on the network dynamics in a paradigmatic
model for associative memory, both numerically and analytically. We find that
dendritic nonlinearities maintain network convergence and increase the
robustness of memory performance against noise. Interestingly, an intermediate
number of dendritic branches is optimal for memory functionality
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