reservoir acts as a transformational operator to minimize dissimilarities. In both
cases, the target waveform is aesthetically similar to a sinusoidal wave and maintains
the overall shape of the input signal. Despite steeper edges in the triangle task, the
algorithm is able to correct any differences by selectively combining different
representations produced by the ASN.
The ASN generated sawtooth (Fig. 15c) waveforms with similar accuracy to
previously reported simulations of memristive networks at roughly 90% accuracy
[71]. Despite the requirement to produce an instantaneous drop, the ASN delivered
the sawtooth waveform with astounding accuracy. Figure 15c illustrates significant
mismatch between the target and generated waveform at the turning point leading to
a minor drop in accuracy. Basic visual inspection shows the sawtooth task retains the
overall shape of the sinusoidal input while the square wave task requires complete
transformation of the input signal into a two-valued function.
Figure 15d, on the other hand, shows significant mismatch throughout the series.
The square wave generation was carried out with roughly a 78% accuracy, which
was much lower than the accuracy of the other tasks. To recreate a straight horizontal
line, an infinite series of higher harmonics is necessary in order to satisfy the spectral
theorem in the algorithm [49]. Fourier analysis showed that the square wave task was
relatively selective in utilizing higher harmonics to construct the waveform. While
the sawtooth and square wave both require an infinite series of sinusoidal harmonics,
the square wave requires continuous constructive interference patterns to produce a
horizontal line, which limits it to odd or even harmonics and drastically diminishes
the regression algorithm. In this case, the ASN was only capable of producing a finite
number of higher harmonics. However, further post-processing such as setting a
threshold on the voltage to binarize the data can be performed to expand the device’s
response to a square wave input, a necessity for reliable Boolean logic
computing [72].
It was found that the ASN was capable of replicating computing performances
typical of reservoirs with 10
3 output signals [73]. Theoretical studies predicts the
performance to scale with an increasing number of output signals due to the
dependence on the regression algorithm [74]. However, how can a reservoir with
much fewer output signals outperform reservoirs with output signals orders of
magnitude higher than the ASN? Further inspection of the mathematical formalism
[74] show that performance is additionally characterized by the uniqueness of each
output signal. Obtaining a set of unique signals allows us to linearly combine the
output signals into a number of unique solutions, where the number of unique
solutions scales with the number of unique output signals. The larger set of solutions
increases the size of the “net” we cast which increases the probability and approximation of producing the correct solution (Fig. 16).
6.2.2 Logic
Expanded efforts to assess their performance in Boolean logic operations using
non-temporal inputs based on randomized Boolean input streams. Zero and one
236
R. Aguilera et al.
cases, the target waveform is aesthetically similar to a sinusoidal wave and maintains
the overall shape of the input signal. Despite steeper edges in the triangle task, the
algorithm is able to correct any differences by selectively combining different
representations produced by the ASN.
The ASN generated sawtooth (Fig. 15c) waveforms with similar accuracy to
previously reported simulations of memristive networks at roughly 90% accuracy
[71]. Despite the requirement to produce an instantaneous drop, the ASN delivered
the sawtooth waveform with astounding accuracy. Figure 15c illustrates significant
mismatch between the target and generated waveform at the turning point leading to
a minor drop in accuracy. Basic visual inspection shows the sawtooth task retains the
overall shape of the sinusoidal input while the square wave task requires complete
transformation of the input signal into a two-valued function.
Figure 15d, on the other hand, shows significant mismatch throughout the series.
The square wave generation was carried out with roughly a 78% accuracy, which
was much lower than the accuracy of the other tasks. To recreate a straight horizontal
line, an infinite series of higher harmonics is necessary in order to satisfy the spectral
theorem in the algorithm [49]. Fourier analysis showed that the square wave task was
relatively selective in utilizing higher harmonics to construct the waveform. While
the sawtooth and square wave both require an infinite series of sinusoidal harmonics,
the square wave requires continuous constructive interference patterns to produce a
horizontal line, which limits it to odd or even harmonics and drastically diminishes
the regression algorithm. In this case, the ASN was only capable of producing a finite
number of higher harmonics. However, further post-processing such as setting a
threshold on the voltage to binarize the data can be performed to expand the device’s
response to a square wave input, a necessity for reliable Boolean logic
computing [72].
It was found that the ASN was capable of replicating computing performances
typical of reservoirs with 10
3 output signals [73]. Theoretical studies predicts the
performance to scale with an increasing number of output signals due to the
dependence on the regression algorithm [74]. However, how can a reservoir with
much fewer output signals outperform reservoirs with output signals orders of
magnitude higher than the ASN? Further inspection of the mathematical formalism
[74] show that performance is additionally characterized by the uniqueness of each
output signal. Obtaining a set of unique signals allows us to linearly combine the
output signals into a number of unique solutions, where the number of unique
solutions scales with the number of unique output signals. The larger set of solutions
increases the size of the “net” we cast which increases the probability and approximation of producing the correct solution (Fig. 16).
6.2.2 Logic
Expanded efforts to assess their performance in Boolean logic operations using
non-temporal inputs based on randomized Boolean input streams. Zero and one
236
R. Aguilera et al.