We demonstrate the simulation of noise- dependent point cloud processing using a compact model of non-volatile memories (NVMs). We investigate how classification accuracy is affected by programming variations in NVMs, representing circuit noise, and distortions in point clouds, representing sensor noise. We employ a PointNet-based framework and explore how the inherent weight-sharing properties of PointNet can leverage NVM crossbars for energy-efficient processing. By benchmarking the performance of both NVM-based PointNet across various noise levels, we demonstrate the impact of different noise types on classification accuracy. Our findings show that while certain circuit and sensor noise degrade classification performance, our NVM-based PointNet achieves competitive results with reduced trainable parameters, providing a path toward neuromorphic 3D vision and computing with co-optimization of software and hardware. Our work highlights the potential for using NVM crossbars to efficiently handle noise-dependent processing in edge inference units.

Energy-based learning algorithms have recently gained a surge of interest due to their compatibility with analog (post-digital) hardware. Existing algorithms include contrastive learning (CL), equilibrium propagation (EP) and coupled learning (CpL), all consisting in contrasting two states, and differing in the type of perturbation used to obtain the second state from the first one. However, these algorithms have never been explicitly compared on equal footing with same models and datasets, making it difficult to assess their scalability and decide which one to select in practice. In this work, we carry out a comparison of seven learning algorithms, namely CL and different variants of EP and CpL depending on the signs of the perturbations. Specifically, using these learning algorithms, we train deep convolutional Hopfield networks (DCHNs) on five vision tasks (MNIST, F-MNIST, SVHN, CIFAR-10 and CIFAR-100). We find that, while all algorithms yield comparable performance on MNIST, important differences in performance arise as the difficulty of the task increases. Our key findings reveal that negative perturbations are better than positive ones, and highlight the centered variant of EP (which uses two perturbations of opposite sign) as the best-performing algorithm. We also endorse these findings with theoretical arguments. Additionally, we establish new SOTA results with DCHNs on all five datasets, both in performance and speed. In particular, our DCHN simulations are 13.5 times faster with respect to Laborieux et al. (2021), which we achieve thanks to the use of a novel energy minimisation algorithm based on asynchronous updates, combined with reduced precision (16 bits).

We demonstrate via simulations that transient perturbations introduced by non-zero diagonal elements in a Hopfield network can improve NP-hard graph optimization efficiency by more than a factor of two. Such perturbations enhance the known effects of circuit noise typical of memristor-based networks in escaping local minima (incorrect solutions) and finding the global minimum (correct solution) of the Hopfield energy. We provide systematic simulations of NP-hard graph problems with controlled nonidealities in memristor arrays modeled as noise amplitude and diagonal perturbations. Furthermore, our approach improves Hopfield network optimization efficiencies to solve NP-hard problems regardless of the graph size (30 × 30, 60 × 60, and 80 × 80) and connectivity (30%, 50%, and 70%).

We illustrate novel optimization techniques via simulations for Hopfield networks constructed from manufacturable three-terminal Silicon-Oxide-Nitride-Oxide-Silicon (SONOS) synaptic circuit elements. We first present a computationally-light, memristor-based, highly accurate static compact model for the SONOS synapses used in our simulations. We then show how to exploit analog errors in programming resistances and current leakage, and the continuous tunability of the SONOS synapses to enable transient chaotic group dynamics, to accelerate the convergence of a Hopfield network. We project improvements in energy consumption and time to solution relative to existing CPUs and GPUs by at least 4 orders of magnitude, and also exceed the projected performance of two-terminal memristor-based crossbars in addition to a 100-fold increase in error-resilient array size (i.e. problem size).

In this paper, we propose a new model for practical, nano-scale, NbO2-based Mott memristors, which is based on a thorough analysis performed on a recently presented physics-based model for these devices. Our investigations revealed that the 3D Poole-Frenkel conduction mechanism adopted in the aforementioned model, can be well-approximated by a transport equation in which: a) memristor current is expressed as a linear function of memristor voltage and b) the device memductance is solely dependent on the device temperature which represents the memristor state. The resulting simplified mathematical form of the original differential algebraic equation set is not only more suitable for simulating large-scale, nano-scale NbO2-based memristor circuits, but is also ideal for circuit-theoretic investigations which may allow an in depth understanding of the peculiar nonlinear behaviors of these devices.