34,318 research outputs found
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
Storage Capacity Diverges with Synaptic Efficiency in an Associative Memory Model with Synaptic Delay and Pruning
It is known that storage capacity per synapse increases by synaptic pruning
in the case of a correlation-type associative memory model. However, the
storage capacity of the entire network then decreases. To overcome this
difficulty, we propose decreasing the connecting rate while keeping the total
number of synapses constant by introducing delayed synapses. In this paper, a
discrete synchronous-type model with both delayed synapses and their prunings
is discussed as a concrete example of the proposal. First, we explain the
Yanai-Kim theory by employing the statistical neurodynamics. This theory
involves macrodynamical equations for the dynamics of a network with serial
delay elements. Next, considering the translational symmetry of the explained
equations, we re-derive macroscopic steady state equations of the model by
using the discrete Fourier transformation. The storage capacities are analyzed
quantitatively. Furthermore, two types of synaptic prunings are treated
analytically: random pruning and systematic pruning. As a result, it becomes
clear that in both prunings, the storage capacity increases as the length of
delay increases and the connecting rate of the synapses decreases when the
total number of synapses is constant. Moreover, an interesting fact becomes
clear: the storage capacity asymptotically approaches due to random
pruning. In contrast, the storage capacity diverges in proportion to the
logarithm of the length of delay by systematic pruning and the proportion
constant is . These results theoretically support the significance of
pruning following an overgrowth of synapses in the brain and strongly suggest
that the brain prefers to store dynamic attractors such as sequences and limit
cycles rather than equilibrium states.Comment: 27 pages, 14 figure
Adaptive optical networks using photorefractive crystals
The capabilities of photorefractive crystals as media for holographic interconnections in neural networks are examined. Limitations on the density of interconnections and the number of holographic associations which can be stored in photorefractive crystals are derived. Optical architectures for implementing various neural schemes are described. Experimental results are presented for one of these architectures
Synapse efficiency diverges due to synaptic pruning following over-growth
In the development of the brain, it is known that synapses are pruned
following over-growth. This pruning following over-growth seems to be a
universal phenomenon that occurs in almost all areas -- visual cortex, motor
area, association area, and so on. It has been shown numerically that the
synapse efficiency is increased by systematic deletion. We discuss the synapse
efficiency to evaluate the effect of pruning following over-growth, and
analytically show that the synapse efficiency diverges as O(log c) at the limit
where connecting rate c is extremely small. Under a fixed synapse number
criterion, the optimal connecting rate, which maximize memory performance,
exists.Comment: 15 pages, 16 figure
- …