Memristive tonotopic mapping with volatile resistive switching memory devices

The human brain's energy efficiency and computational power are unmatched by current computing systems. Neuromorphic computing aims to emulate biological neural networks to achieve similar performance. Resistive switching memory (RRAM) devices are strong candidates for building large-scale, energy-efficient neuromorphic systems due to their scalability. However, effectively using RRAM devices to process both spatial and temporal information remains a challenge. This research focuses on the auditory system, a biological system renowned for its efficient processing of temporal signals (sound). Unlike retinotopic or somatosensory maps that rely on spatial arrangement of neurons, the auditory system processes sounds internally via a tonotopic map in the cochlea. This map organizes sounds by frequency along the cochlea, transforming temporal sound signals into a spatial representation. Mimicking this spatiotemporal processing using simple and scalable hardware is a key goal of neuromorphic computing. While RRAM devices have been used in artificial neural networks primarily for spatial coding (using spatial arrangement of memristors), integrating temporal processing necessitates complex CMOS circuitry, losing RRAM's benefits in energy efficiency and biological plausibility. This study investigates the use of volatile memristors, leveraging their dynamic and stochastic response to directly capture the temporal component of signals at the device level. The volatility allows for spontaneous relaxation to a resting state, making the system ready for new computation without the need for resetting.

Existing neuromorphic computing systems often rely on spatial coding using RRAM devices as static memristors, requiring auxiliary CMOS circuitry for temporal information processing. This approach compromises energy efficiency, area occupation, and biological plausibility. Previous research has explored using memristors to emulate specific neural functions like spike-timing-dependent plasticity (STDP) and Hebbian learning, but fully exploiting the potential of device-level computation within the memristor remains largely unexplored. The human cochlea, with its tonotopic mapping of frequencies, provides a compelling biological model for spatiotemporal processing. Studies on cochlear mechanics and signal processing (e.g., Zwislocki's model) highlight the logarithmic spacing of frequency representation within the cochlea, which is essential for covering the wide range of audible frequencies. The goal of this research is to build upon these prior studies to create a hardware implementation that mirrors the cochlea's efficient frequency processing.

The researchers used volatile RRAM devices with a one-transistor/one-resistor (1T1R) structure. The RRAM devices utilize a hafnium oxide (HfOx) switching layer between silver (Ag) and carbon (C) electrodes. The devices exhibit volatile resistive switching, transitioning to a low resistive state (LRS) when a sufficient positive voltage is applied, forming a conductive filament (CF) of migrated Ag atoms. When the voltage is removed, the CF spontaneously dissolves, returning the device to a high resistive state (HRS). This volatility eliminates the need for a reset phase, allowing operation with unipolar voltages. The switching behavior is inherently stochastic, with the threshold voltage (Vset) varying from cycle to cycle. This stochasticity was characterized experimentally by applying trains of voltage pulses with varying amplitudes and frequencies. The switching probability (Pswitch) was measured as the fraction of pulse trains that caused the device to switch to the LRS. A probabilistic model was developed to describe the switching probability as a function of voltage amplitude and frequency. This model was then used to simulate larger networks. For frequency sensing, a circuit was designed with multiple parallel RRAM devices, each with a separate top electrode (TE) and a common bottom electrode (BE). The TE voltages were scaled, with higher voltages corresponding to higher frequency sensitivity. By applying spike trains of varying frequencies, the number of devices switching to the LRS was measured, demonstrating a logarithmic dependence on frequency, mirroring the cochlea's tonotopic map. A memristive tonotopic map (MTM) circuit was developed by adding an XOR gate to compare the outputs of pairs of RRAM devices, helping to identify the boundary between activated and inactive devices. Simulations using the probabilistic model were conducted to verify the MTM's performance. The MTM was further tested with speech recognition, using spectrograms of spoken words as input. An analog-to-spike (A2S) conversion algorithm was used to process the audio signals, and the MTM outputs were fed to a feedforward neural network for classification.

The study successfully demonstrated volatile RRAM's capability to implement core auditory processing functions. The stochastic switching characteristics of the RRAM devices were thoroughly characterized, revealing a logarithmic relationship between switching probability and the frequency of input spike trains. The researchers designed and tested circuits that mimicked the cochlea's tonotopic mapping. A parallel circuit of RRAM devices showed that the number of devices switching ON increased linearly with the logarithm of the input frequency, effectively replicating the cochlear logarithmic frequency response. The memristive tonotopic map (MTM) circuit, incorporating XOR gates, was able to successfully distinguish between different frequencies in input audio signals. Simulations showed that the response of each XOR gate peaks at a specific frequency, providing a frequency representation similar to the biological cochlea. The MTM successfully recognized spoken words with a high accuracy (96.5%) by leveraging the distinct spectral characteristics of the words' phonemes. The system's ability to perform tonotopic mapping is based on the logarithmic dependence of the switching probability of the RRAM on the frequency of the applied stimuli, allowing it to span several orders of magnitude in frequency. The stochastic nature of the switching is well-modeled, allowing for scaling to larger numbers of devices. The system is inherently energy efficient due to the low power consumption of the RRAM devices and the lack of need for a reset phase. The energy consumption of a single spike was estimated to be 40 pJ, with potential for further reduction.

This work demonstrates a novel approach to neuromorphic computing using volatile RRAM devices. The device-level computation, leveraging the inherent stochasticity of volatile RRAM, achieves both logarithmic integration and tonotopic mapping, key features of the biological cochlea. The successful speech recognition task highlights the potential of this approach for complex signal processing applications. The methodology provides a more biologically plausible and energy-efficient alternative to traditional CMOS-based neuromorphic systems. The use of volatile memristors simplifies the circuitry and reduces energy consumption by eliminating the need for a reset phase. The logarithmic nature of the frequency mapping provided by the RRAM network is crucial for efficiently representing a wide range of frequencies, mimicking the biological auditory system. The results demonstrate the feasibility of building explainable and biologically inspired systems using memristive devices for temporal signal processing. The approach transcends audio signals, with potential applications in other sensory modalities such as touch and vision.

This research successfully demonstrated the feasibility of creating neuromorphic circuits for spatiotemporal signal processing using volatile RRAM. Key auditory processing primitives, including logarithmic integration and tonotopic mapping, were successfully implemented at the device level, leading to an energy-efficient and biologically plausible system. The application of the memristive tonotopic map (MTM) to speech recognition showed its potential for complex tasks. This work opens avenues for future research in building larger-scale systems and exploring applications beyond audio processing, potentially transforming the field of neuromorphic computing.

The current study primarily focuses on proof-of-concept demonstrations. While a probabilistic model was developed and validated, further work is needed to thoroughly explore the scalability and robustness of the system with a much larger number of devices and more complex auditory signals. The speech recognition task used a limited vocabulary, and expanding the vocabulary and introducing variations in speakers and noise conditions will be important future steps. The A2S conversion method could also be refined for better signal representation and to account for diverse amplitude variations. Finally, the energy consumption estimates were made based on specific experimental conditions and might vary depending on device parameters and operating conditions.