4 research outputs found
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
In this paper, we address the stability of a broad class of discrete-time
hypercomplex-valued Hopfield-type neural networks. To ensure the neural
networks belonging to this class always settle down at a stationary state, we
introduce novel hypercomplex number systems referred to as real-part
associative hypercomplex number systems. Real-part associative hypercomplex
number systems generalize the well-known Cayley-Dickson algebras and real
Clifford algebras and include the systems of real numbers, complex numbers,
dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as
particular instances. Apart from the novel hypercomplex number systems, we
introduce a family of hypercomplex-valued activation functions called
-projection functions. Broadly speaking, a
-projection function projects the activation potential onto the
set of all possible states of a hypercomplex-valued neuron. Using the theory
presented in this paper, we confirm the stability analysis of several
discrete-time hypercomplex-valued Hopfield-type neural networks from the
literature. Moreover, we introduce and provide the stability analysis of a
general class of Hopfield-type neural networks on Cayley-Dickson algebras
Learning Schemes for Recurrent Neural Networks
兵庫県立大学大学院202
Complex Neural Networks for Audio
Audio is represented in two mathematically equivalent ways: the real-valued time domain (i.e., waveform) and the complex-valued frequency domain (i.e., spectrum). There are advantages to the frequency-domain representation, e.g., the human auditory system is known to process sound in the frequency-domain. Furthermore, linear time-invariant systems are convolved with sources in the time-domain, whereas they may be factorized in the frequency-domain. Neural networks have become rather useful when applied to audio tasks such as machine listening and audio synthesis, which are related by their dependencies on high quality acoustic models. They ideally encapsulate fine-scale temporal structure, such as that encoded in the phase of frequency-domain audio, yet there are no authoritative deep learning methods for complex audio. This manuscript is dedicated to addressing the shortcoming. Chapter 2 motivates complex networks by their affinity with complex-domain audio, while Chapter 3 contributes methods for building and optimizing complex networks. We show that the naive implementation of Adam optimization is incorrect for complex random variables and show that selection of input and output representation has a significant impact on the performance of a complex network. Experimental results with novel complex neural architectures are provided in the second half of this manuscript. Chapter 4 introduces a complex model for binaural audio source localization. We show that, like humans, the complex model can generalize to different anatomical filters, which is important in the context of machine listening. The complex model\u27s performance is better than that of the real-valued models, as well as real- and complex-valued baselines. Chapter 5 proposes a two-stage method for speech enhancement. In the first stage, a complex-valued stochastic autoencoder projects complex vectors to a discrete space. In the second stage, long-term temporal dependencies are modeled in the discrete space. The autoencoder raises the performance ceiling for state of the art speech enhancement, but the dynamic enhancement model does not outperform other baselines. We discuss areas for improvement and note that the complex Adam optimizer improves training convergence over the naive implementation
Threshold Switching and Self-Oscillation in Niobium Oxide
Volatile threshold switching, or current controlled negative
differential resistance (CC-NDR), has been observed in a range of
transition metal oxides. Threshold switching devices exhibit a
large non-linear change in electrical conductivity, switching
from an insulating to a metallic state under external stimuli.
Compact, scalable and low power threshold switching devices are
of significant interest for use in existing and emerging
technologies, including as a selector element in high-density
memory arrays and as solid-state oscillators for hardware-based
neuromorphic computing.
This thesis explores the threshold switching in amorphous NbOx
and the properties of individual and coupled oscillators based on
this response. The study begins with an investigation of
threshold switching in Pt/NbOx/TiN devices as a function device
area, NbOx film thickness and temperature, which provides
important insight into the structure of the self-assembled
switching region. The devices exhibit combined threshold-memory
behaviour after an initial voltage-controlled forming
process, but exhibit symmetric threshold switching when the RESET
and SET currents are kept below a critical value. In this mode,
the threshold and hold voltages are shown to be independent of
the device area and film thickness, and the threshold power,
while independent of device area, is shown to decrease with
increasing film thickness. These results are shown to be
consistent with a structure in which the threshold switching
volume is confined, both laterally and vertically, to the region
between the residual memory filament and the electrode, and where
the memory filament has a core-shell structure comprising a
metallic core and a semiconducting shell. The veracity of this
structure is demonstrated by comparing experimental results with
the predictions of a resistor network model, and detailed finite
element simulations.
The next study focuses on electrical self-oscillation of an NbOx
threshold switching device incorporated into a Pearson-Anson
circuit configuration. Measurements confirm stable operation of
the oscillator at source voltages as low as 1.06 V, and
demonstrate frequency control in the range from 2.5 to 20.5 MHz
with maximum frequency tuning range of 18 MHz/V. The oscillator
exhibit three distinct oscillation regimes: sporadic spiking,
stable oscillation and damped oscillation. The oscillation
frequency, peak-to-peak amplitude and frequency are shown to be
temperature and voltage dependent with stable oscillation
achieved for temperatures up to ∼380 K. A physics-based
threshold switching model with inclusion of device and circuit
parameters is shown to explain the oscillation waveform and
characteristic.
The final study explores the oscillation dynamics of capacitively
coupled Nb/Nb2O5 relaxation oscillators. The coupled system
exhibits rich collective behaviour, from weak coupling to
synchronisation, depending on the negative differential
resistance response of the individual devices, the operating
voltage and the coupling capacitance. These coupled oscillators
are shown to exhibit stable frequency and phase locking states at
source voltages as low as 2.2 V with MHz frequency tunable range.
The numerical simulation of the coupled system highlights the
role of source voltage, and circuit and device capacitance in
controlling the coupling modes and dynamics