Synaptogen: A cross-domain generative device model for large-scale neuromorphic circuit design

TL;DR

A fast generative modeling approach for resistive memories that reproduces the complex statistical properties of real-world devices and achieves read/write speeds several orders of magnitude higher than a variability-aware physics-based compact model and faster than even a simplified and deterministic compact model.

Abstract

We present a fast generative modeling approach for resistive memories that reproduces the complex statistical properties of real-world devices. To enable efficient modeling of analog circuits, the model is implemented in Verilog-A. By training on extensive measurement data of integrated 1T1R arrays (6,000 cycles of 512 devices), an autoregressive stochastic process accurately accounts for the cross-correlations between the switching parameters, while non-linear transformations ensure agreement with both cycle-to-cycle (C2C) and device-to-device (D2D) variability. Benchmarks show that this statistically comprehensive model achieves read/write throughputs exceeding those of even highly simplified and deterministic compact models.

Figures (12)

• Figure 1: The ReRAM chip layout in the MAD200 process design kit (left) and an optical image of the fabricated 1T1R ReRAM array (right).
• Figure 2: Simplified circuit diagram showing a connected vector of 512 1T1R ReRAM devices which were individually selected for measurement of model training data. Transistor bodies ("Gnd" terminal) were biased to -1.8 V as bipolar voltage sweeps were applied to the WL and current was measured at the respective BL (at 0 V).
• Figure 3: Graphical depiction of the VAR($p$) base process used to reproduce memory cycling statistics. Past features within cycle range $p$ have a linear deterministic impact on future values, and a 4-dimensional white noise process $\epsilon_n$ contributes stochasticity to each feature.
• Figure 4: An overview of the generative modeling approach. Training direction: (A) collect $I, V$ data ($N$ cycles $\times$$M$ devices), (B) extract feature vectors, (C) learn a distribution of normalizing transformations, (D) fit a stochastic process (VAR) to the normalized data. Generative direction: (E) realize an independent VAR process for each simulated cell, (F) apply device-specific random de-normalizing transformations to the VAR outputs, (G) as voltages are applied, reconstruct $I, V$ dependence of each cell.
• Figure 5: A standardizing affine transformation applied to a representative sample of 20 different devices. The forward transformation $\bm{\Psi}_m$ is applied in the training direction as a first step to normalize the feature distributions. Here, $\bm{\mu}_m$ and $\bm{\sigma}_m$ are the sample means and standard deviations of the feature vectors for device $m$ across all cycles. The inverse transformation is used in the generative direction, where $\bm{\mu}_m^*$ and $\bm{\sigma}_m^*$ are sampled from a distribution estimated from the entire training set.