Energy-Information Trade-Off in Self-Directed Channel Memristors

TL;DR

The paper tackles the problem of quantifying the energy-information trade-off in Self-Directed Channel memristors under delay-induced resistive drift. It introduces an energy-cost function to map programming energy to target states and uses a delay-conditioned generative model (cGAN) to capture resistive drift over time, enabling Blahut-Arimoto-based capacity estimation under energy constraints. Key findings show an equilibrium resistance around $7.2\times10^6\,\Omega$, a logarithmic form for the energy-cost relation, and a delay-dependent capacity where shorter delays permit higher capacity at lower energy. The work demonstrates how these insights can guide energy-efficient memristive storage and neuromorphic system design, with potential for multi-stream storage strategies to achieve graceful data retention over varying delays.

Abstract

Understanding the nature of information storage on memristors is vital to enable their use in novel data storage and neuromorphic applications. One key consideration in information storage is the energy cost of storage and what impact the available energy has on the information capacity of the devices. In this paper, we propose and study an energy-information trade-off for a particular kind of memristive device - Self-Directed Channel (SDC) memristors. We perform experiments to model the energy required to set the devices into various states, as well as assessing the stability of these states over time. Based on these results, we employ a generative modelling approach, using a conditional Generative Adversarial Network (cGAN) to characterise the storage conditional distribution, allowing us to estimate energy-information curves for a range of storage delays, showing the graceful trade-off between energy consumed and the effective capacity of the devices.

Figures (7)

• Figure 1: READ (a), SET (b), and RESET (c) waveforms, and composite RESET-READ-SET-READ cycle (d). $T_{x}$ and $A_{x}$ denote waveform periods/amplitudes, respectively.
• Figure 2: To reverse unknown systematic offsets, we minimise $|v \cdot i|$ in quadrants that should be empty for passive devices.
• Figure 3: The estimated empirical energies of the SET pulses for experiments with set pulse magnitudes in the range $[500mV, 1600mV]$, plotted alongside the energy estimated for bringing the device into the given state from the equilibrium (high resistance) state according to the proposed energy cost function. Programming noise results in a distribution of samples around the predicted cost function zhengErrorResilientAnalogImage2018.
• Figure 4: State characterisation of the memristive state for retention experiments with different (arbitrary) initial states. Dotted lines are moving averages, while solid lines are the estimated states. The estimated equilibrium state (B) is $7.1853 \times 10^6 \Omega$, with states expected to tend toward this value over time. For the red series with the highest starting state, the state trends down as the device starts above equilibrium.
• Figure 5: The training scheme for the cGAN including the delay discriminator. Generated sequences are produced recursively.