integrating desired representations. Within this representation space, reservoir computing is able to identify useful elements of the output function to attempt to solve a
specific task. Depending on the degree of non-linearity, which in turn determines the
size and resolution of the reservoir, a task may be optimally solved in this higher
dimensional representation space. In the ASN device, variations in connectivity,
atomic switch density, and junctions contribute to the degree of non-linearity by
creating a larger range of functional elements that have different activation and
operational voltages.
6.2 Implementations
6.2.1 Waveform Regression
Simulations of ASNs have indicated that the system has the fundamental capacity to
perform waveform regression [66]. From simulation results, performance depended
on the level of higher harmonics produced and the harmonic distortion (Fig. 16)
required for the specific task. For example, the cosine task only requires a shift in its
periodicity and, therefore, does not require extensive higher harmonic generation.
Conversely, the square wave task requires infinitely distributed harmonics to produce a straight line through wave interference. Further, voltage dependent simulations showed that increasing device activation controlled these harmonic
generations. Here, the device was expected to perform in a similar way with task
difficulty increasing from cosine, triangle, sawtooth, and square due to increasing
harmonic requirements. Device initialization and activation to achieve the best
performance is described in the previous section.
Experimental performance of various waveform regression tasks using ASN
devices are presented in Fig. 15. To implement waveform regression the ASN was
stimulated with a bipolar sinusoidal voltage, inducing switching activity and placing
the network in an active state. The output potentials measured at each electrode were
then combined using the Moore-Penrose linear regression and optimized during a
training period [67–69]. Two-second epochs of data were used to evaluate the
ASN’s computational capability, where 1 s of data was allocated for both training
and testing. Performance was measured during a 1 s period after training where the
ASN accomplished various tasks (Fig. 15). The performance of the ASN was
quantified by calculating the normalized mean squared error between the target
and generated waveforms [70]. Here, the difference between error and unity was
used to calculate accuracy.
The ASN was capable in achieving up to ~90% accuracy using 62 of the
64 measurement electrodes for each task. Task complexity increased from cosine
to square wave due to the increasing mismatch between the sinusoidal input and the
target waveform. In the case of cosine generation, the overall waveform of the input
is preserved save for a shift in its periodicity. The cosine generation was the simplest
task where the ASN performed with the highest accuracy, ~90%. Note that the
234
R. Aguilera et al.
specific task. Depending on the degree of non-linearity, which in turn determines the
size and resolution of the reservoir, a task may be optimally solved in this higher
dimensional representation space. In the ASN device, variations in connectivity,
atomic switch density, and junctions contribute to the degree of non-linearity by
creating a larger range of functional elements that have different activation and
operational voltages.
6.2 Implementations
6.2.1 Waveform Regression
Simulations of ASNs have indicated that the system has the fundamental capacity to
perform waveform regression [66]. From simulation results, performance depended
on the level of higher harmonics produced and the harmonic distortion (Fig. 16)
required for the specific task. For example, the cosine task only requires a shift in its
periodicity and, therefore, does not require extensive higher harmonic generation.
Conversely, the square wave task requires infinitely distributed harmonics to produce a straight line through wave interference. Further, voltage dependent simulations showed that increasing device activation controlled these harmonic
generations. Here, the device was expected to perform in a similar way with task
difficulty increasing from cosine, triangle, sawtooth, and square due to increasing
harmonic requirements. Device initialization and activation to achieve the best
performance is described in the previous section.
Experimental performance of various waveform regression tasks using ASN
devices are presented in Fig. 15. To implement waveform regression the ASN was
stimulated with a bipolar sinusoidal voltage, inducing switching activity and placing
the network in an active state. The output potentials measured at each electrode were
then combined using the Moore-Penrose linear regression and optimized during a
training period [67–69]. Two-second epochs of data were used to evaluate the
ASN’s computational capability, where 1 s of data was allocated for both training
and testing. Performance was measured during a 1 s period after training where the
ASN accomplished various tasks (Fig. 15). The performance of the ASN was
quantified by calculating the normalized mean squared error between the target
and generated waveforms [70]. Here, the difference between error and unity was
used to calculate accuracy.
The ASN was capable in achieving up to ~90% accuracy using 62 of the
64 measurement electrodes for each task. Task complexity increased from cosine
to square wave due to the increasing mismatch between the sinusoidal input and the
target waveform. In the case of cosine generation, the overall waveform of the input
is preserved save for a shift in its periodicity. The cosine generation was the simplest
task where the ASN performed with the highest accuracy, ~90%. Note that the
234
R. Aguilera et al.