badcrossbar: A Python tool for computing and plotting currents and voltages in passive crossbar arrays

Crossbar arrays are a popular solution when implementing systems that have array-like architecture. With the recent developments in the field of neuromorphic engineering, crossbars are now routinely used to implement artificial neural networks or, more generally, to perform vector–matrix multiplication in hardware. However, the interconnect resistance present in all crossbars can lead to significant deviations from the intended behaviour of these structures. In this work, we present badcrossbar—an open-source tool for computing currents and voltages in such non-ideal passive crossbar arrays. Additionally, the package allows to easily visualise currents and voltages (or other numerical variables) in the branches and on the nodes of these structures

Nonideality-aware training for accurate and robust low-power memristive neural networks

Recent years have seen a rapid rise of artificial neural networks being employed in a number of cognitive tasks. The ever-increasing computing requirements of these structures have contributed to a desire for novel technologies and paradigms, including memristor-based hardware accelerators. Solutions based on memristive crossbars and analog data processing promise to improve the overall energy efficiency. However, memristor nonidealities can lead to the degradation of neural network accuracy, while the attempts to mitigate these negative effects often introduce design trade-offs, such as those between power and reliability. In this work, we design nonideality-aware training of memristor-based neural networks capable of dealing with the most common device nonidealities. We demonstrate the feasibility of using high-resistance devices that exhibit high $I$-$V$ nonlinearity -- by analyzing experimental data and employing nonideality-aware training, we estimate that the energy efficiency of memristive vector-matrix multipliers is improved by three orders of magnitude ($0.715\ \mathrm{TOPs}^{-1}\mathrm{W}^{-1}$ to $381\ \mathrm{TOPs}^{-1}\mathrm{W}^{-1}$) while maintaining similar accuracy. We show that associating the parameters of neural networks with individual memristors allows to bias these devices towards less conductive states through regularization of the corresponding optimization problem, while modifying the validation procedure leads to more reliable estimates of performance. We demonstrate the universality and robustness of our approach when dealing with a wide range of nonidealities

Committee Machines—A Universal Method to Deal with Non-Idealities in RRAM-Based Neural Networks

Artificial neural networks (ANNs) are notoriously power- and time-consuming when implemented on conventional von Neumann computing systems. Recent years have seen an emergence of research in hardware that strives to break the bottleneck of von Neumann architecture and optimise the data flow; namely to bring memory and computing closer together. One of the most often suggested solutions is the physical implementation of ANNs in which their synaptic weights are realised with analogue resistive devices, such as resistive random-access memory (RRAM). However, various device- and system-level non-idealities usually prevent these physical implementations from achieving high inference accuracy. We suggest applying a well-known concept in computer science -- committee machine (CM) -- in the context of RRAM-based neural networks. Using simulations and experimental data from three different types of RRAM devices, we show that CMs employing ensemble averaging can successfully increase inference accuracy in physically implemented neural networks that suffer from faulty devices, programming non-linearities, random telegraph noise, cycle-to-cycle variability and line resistance. Importantly, we show that the accuracy can be improved even without increasing the number of devices

Simulation of Inference Accuracy Using Realistic RRAM Devices

Resistive Random Access Memory (RRAM) is a promising technology for power efficient hardware in applications of artificial intelligence (AI) and machine learning (ML) implemented in non-von Neumann architectures. However, there is an unanswered question if the device non-idealities preclude the use of RRAM devices in this potentially disruptive technology. Here we investigate the question for the case of inference. Using experimental results from silicon oxide (SiOx) RRAM devices, that we use as proxies for physical weights, we demonstrate that acceptable accuracies in classification of handwritten digits (MNIST data set) can be achieved using non-ideal devices. We find that, for this test, the ratio of the high- and low-resistance device states is a crucial determinant of classification accuracy, with ~96.8% accuracy achievable for ratios >3, compared to ~97.3% accuracy achieved with ideal weights. Further, we investigate the effects of a finite number of discrete resistance states, sub-100% device yield, devices stuck at one of the resistance states, current/voltage non-linearities, programming non-linearities and device-to-device variability. Detailed analysis of the effects of the non-idealities will better inform the need for the optimization of particular device properties

Committee machines -- a universal method to deal with non-idealities in memristor-based neural networks

Artificial neural networks are notoriously power- and time-consuming when implemented on conventional von Neumann computing systems. Consequently, recent years have seen an emergence of research in machine learning hardware that strives to bring memory and computing closer together. A popular approach is to realise artificial neural networks in hardware by implementing their synaptic weights using memristive devices. However, various device- and system-level non-idealities usually prevent these physical implementations from achieving high inference accuracy. We suggest applying a well-known concept in computer science -- committee machines -- in the context of memristor-based neural networks. Using simulations and experimental data from three different types of memristive devices, we show that committee machines employing ensemble averaging can successfully increase inference accuracy in physically implemented neural networks that suffer from faulty devices, device-to-device variability, random telegraph noise and line resistance. Importantly, we demonstrate that the accuracy can be improved even without increasing the total number of memristors.Comment: 22 pages, 18 figures, 4 table

The interplay between structure and function in redox-based resistance switching

We report a study of the relationship between oxide microstructure at the scale of tens of nanometres and resistance switching behaviour in silicon oxide. In the case of sputtered amorphous oxides, the presence of columnar structure enables efficient resistance switching by providing an intial structured distribution of defects that can act as precursors for the formation of chains of conductive oxygen vacancies under the application of appropriate electrical bias. Increasing electrode interface roughness decreases electroforming voltages and reduces the distribution of switching voltages. Any contribution to these effects from field enhancement at rough interfaces is secondary to changes in oxide microstructure templated by interface structure

Committee Machines—A Universal Method to Deal with Non-Idealities in Memristor-Based Neural Networks

Arti ficial neural networks are notoriously power- and time-consuming when implemented on conventional von Neumann computing systems. Consequently, recent years have seen an emergence of research in machine learning hardware that strives to bring memory and computing closer together. A popular approach is to realise artifi cial neural networks in hardware by implementing their synaptic weights using memristive devices. However, various device- and system-level non-idealities usually prevent these physical implementations from achieving high inference accuracy. We suggest applying a well-known concept in computer science|committee machines|in the context of memristor-based neural networks. Using simulations and experimental data from three different types of memristive devices, we show that committee machines employing ensemble averaging can successfully increase inference accuracy in physically implemented neural networks that suffer from faulty devices, device-to-device variability, random telegraph noise and line resistance. Importantly, we demonstrate that the accuracy can be improved even without increasing the total number of memristors

Dual antiplatelet therapy duration after coronary stenting in clinical practice: results of an EAPCI survey

Aims: Our aim was to report on a survey initiated by the EuropeanAssociation of Percutaneous Cardiovascular Interventions (EAPCI) concerning opinion on the evidence relating to dual antiplatelet therapy (DAPT) duration after coronary stenting.Methods and results: Results from three randomised clinical trials were scheduled to be presented at the American Heart Association Scientific Sessions 2014 (ARIA 2014). A web-based survey was distributed to all individuals registered in the EuroIntervention mailing list (n=15,200) both before and after ARIA 2014. A total of 1,134 physicians responded to the first (i.e., before AHA 2014) and 542 to the second (i.e., after ARIA 2014) survey. The majority of respondents interpreted trial results consistent with a substantial equipoise regarding the benefits and risks of an extended versus a standard DAPT strategy. Two respondents out of ten believed extended DAFT should be implemented in selected patients. After ARIA 2014, 46.1% of participants expressed uncertainty about the available evidence on DAFT duration, and 40.0% the need for clinical guidance.Conclusions: This EAPCI survey highlights considerable uncertainty within the medical community with regard to the optimal duration of DAFT after coronary stenting in the light of recent reported trial results. Updated recommendations for practising physicians to guide treatment decisions in routine clinical practice should be provided by international societies