Delay Conditioned Generative Modelling of Resistive Drift in Memristors

TL;DR

The work addresses resistive drift in memristors by learning a delay- and initial-resistance conditioned distribution $p(r(d)|r(0), d)$ via a delay-conditioned cGAN. A novel delay discrimination mechanism enforces cross-timescale consistency, enabling single-shot, differentiable generation for end-to-end learning and fast Monte Carlo evaluation. Key contributions include data normalisation with a residual-difference transform and a fully differentiable framework demonstrated on end-to-end quantisation optimisation using a stochastic memristor drift simulator. Results show accurate conditional distribution modelling, improved delay-consistency, and practical benefits for gradient-based design-space exploration in memristor-based storage and neuromorphic systems. This framework offers efficient, differentiable memristor drift simulation suitable for end-to-end training and optimization tasks in in-memory computing contexts.

Abstract

The modelling of memristive devices is an essential part of the development of novel in-memory computing systems. Models are needed to enable the accurate and efficient simulation of memristor device characteristics, for purposes of testing the performance of the devices or the feasibility of their use in future neuromorphic and in-memory computing architectures. The consideration of memristor non-idealities is an essential part of any modelling approach. The nature of the deviation of memristive devices from their initial state, particularly at ambient temperature and in the absence of a stimulating voltage, is of key interest, as it dictates their reliability as information storage media - a property that is of importance for both traditional storage and neuromorphic applications. In this paper, we investigate the use of a generative modelling approach for the simulation of the delay and initial resistance-conditioned resistive drift distribution of memristive devices. We introduce a data normalisation scheme and a novel training technique to enable the generative model to be conditioned on the continuous inputs. The proposed generative modelling approach is suited for use in end-to-end training and device modelling scenarios, including learned data storage applications, due to its simulation efficiency and differentiability.

Figures (12)

• Figure 1: Left: An illustrative subset of the time series dataset used for training the cGAN, generated using the event-based model of el-geresyEventBasedSimulationStochastic2024. It clearly illustrates the stochasticity of the resistance values, and their convergence to the equilibrium point of 500$k\Omega$. The variance of the state transitions increases with increasing initial resistance. Right: The proposed modelling approach evaluated on the same initial resistances for a timestep of 10 and a series length of 100 (a total delay of 1000). It is clear that the model is able to approximate the conditional drift distribution.
• Figure 2: Histogram of final resistance values in the drift dataset at different delays. We see that as the delay increases to 1000s, the distribution becomes centred around the equilibrium resistance value - i.e. any information present in the encoding of the initial value is lost. The legend shows the mean value for each delay conditioned distribution, $\mu$, and the standard deviation, $\sigma$.
• Figure 3: Histograms of the values in the dataset, $D$ following the initial pointwise application of the resistance normalisation transform (Figure \ref{['fig:chapsorage_normalisation_transforms_series']}) and subsequent application of the difference normalisation transform for pairs of values from the dataset separated by a given delay (Figure \ref{['fig:chapsorage_normalisation_transforms_differences']}).
• Figure 4: Structure of the cGAN used for training. The delay processor and resistance processor map the delay $d$ and the normalised resistance at time $t$, denoted by $\bar{r}_{\text{init}}$, to independent embeddings. The combined processor network then processes these embeddings along with the diagonal Gaussian noise vector of dimension $z$, which is the latent prior for the generative model. The output of the combined processor is a normalised difference, to which the inverse difference normalisation transform is applied, followed by addition to $\bar{r}_{\text{init}}$ to produce the predicted resistance after delay $d$, $\bar{r}_{\text{final}}$.
• Figure 5: The discriminator architecture and the multiple sample discrimination approach. The condition processor processes the first element of the sequence, i.e., the initial condition, in addition to the delay. The remaining elements of the sequence vector: $r_2 \ldots r_s$, are passed to the sequence processor, along with the output of the difference normalisation transform applied to each sequence. The output embeddings of both processors are concatenated and passed to the combined processor. When using the technique of multiple sample discrimination, we pass $n$ sequences (and $n$ delays) to the network simultaneously, with the condition processor and sequence processor input dimensions being scaled up by $n$ and the effective batch size for the discriminator scaled down by $n$. The same architecture is used for the main and auxiliary delay discriminators described in Section \ref{['sec:delay_discriminator']}.