2martens/uni
1
0
Fork 0
mirror of https://github.com/2martens/uni.git synced 2026-05-06 19:36:26 +02:00
Code Releases Activity

[NN] Added formulas to ease understanding

Browse Source 
Signed-off-by: Jim Martens <github@2martens.de>
This commit is contained in:
Jim Martens
2018-05-24 11:04:09 +02:00
parent f42ffae7f5
commit 1578ef4577
1 changed files with 30 additions and 15 deletions
Download Patch File Download Diff File Expand all files Collapse all files

45
neural-networks/seminarpaper.tex
View File

@ -370,23 +370,34 @@ the respective synapse.
\label{tab:mrs-synapse} \label{tab:mrs-synapse}
\end{table} \end{table}
Modulated random search means essentially random weight changes. Each synapse Modulated random search means essentially random weight changes. Each synapse \(i\)
has some parameters that are used (see table \ref{tab:mrs-synapse}). The weight has some parameters that are used (see table \ref{tab:mrs-synapse}). The weight
change probability is the product of the intrinsic weight change probability change probability \(p_i^w\) at time \(t\) is the product of the intrinsic weight
and the concentration of the neuromodulator the synapse is sensitive to change probability \(W_i\) and the concentration of the neuromodulator the synapse
at its location. Additionally the maximum neuromodulator sensitivity is is sensitive to \(c(t, x_i, y_i)\) at its location \((x_i, y_i)\). Additionally
the ceiling for the second part of that product. This means there is a maximum the maximum neuromodulator sensitivity \(M_i\) is the ceiling for the second part
weight change probability for each synapse. Should a weight change occur a new of that product. This means there is a maximum weight change probability for each
weight is chosen randomly from the range of values described by the minimum and synapse. Weight changes can happen at any time step. Therefore the intrinsic weight
maximum weight of the synapse. change probability has to be very small. Should a weight change occur a new weight
\(w_i\) is chosen randomly from the interval \([W_i^{min}, W_i^{max}]\).
\[
p_i^w = min(M_i, c(t, x_i, y_i)) \cdot W_i,\; 0 < W_i \lll 1
\]
Moreover a synapse can disable or enable itself. The actual disable/enable Moreover a synapse can disable or enable itself. The actual disable/enable
probability is the product of the intrinsic value saved as parameter and probability \(p_i^d\) is the product of the intrinsic value \(D_i\) saved as
the neuromodulator concentration. The concentration is again ceiled by the parameter and the neuromodulator concentration \(c(t, x_i, y_i)\). The concentration
maximum sensitivity limit given as parameter. This means there is a maximum is again ceiled by the maximum sensitivity limit \(M_i\) given as parameter.
disable/enable probability as well. A disabled synapse is treated as having This means there is a maximum disable/enable probability as well. The intrinsic
weight 0 but the actual value is stored so that it can be restored when the enable/disable probability must be smaller than the intrinsic weight change probability.
synapse is enabled again. A disabled synapse is treated as having weight 0 but the actual value is stored
so that it can be restored when the synapse is enabled again.
\[
p_i^d = min(M_i, c(t, x_i, y_i) \cdot D_i,\; 0 \leq D_i < W_i
\]
Given a so called neural network structure or substrate this makes it easier Given a so called neural network structure or substrate this makes it easier
to find different network topologies (structure and weights combined). to find different network topologies (structure and weights combined).
@ -401,7 +412,11 @@ but rather the difference to be added to the current weight is sampled from a
normal distribution with a mean of zero and \(\sigma^2\)-variance. The sampled normal distribution with a mean of zero and \(\sigma^2\)-variance. The sampled
value could be infinitely large and hence the new weight outside of the given value could be infinitely large and hence the new weight outside of the given
bounds for it. Therefore the value is sampled until the sum of the bounds for it. Therefore the value is sampled until the sum of the
current weight and the sampled value are within the range. current weight and the sampled value are within the interval \([W_i^{min}, W_i^{max}]\).
\[
w_i (t + 1) = w_i (t) + \Delta w_i \;\text{where}\; \Delta w_i \sim \mathcal{N}(0, \sigma^2)
\]
Toutunji and Pasemann implemented a mechanism for disabling synapses Toutunji and Pasemann implemented a mechanism for disabling synapses
in the modulated gaussian walk as well but did not make use of it later and in the modulated gaussian walk as well but did not make use of it later and