Joseph S. Friedman

Neuromorphic Computing with Magnetic Domain Walls

Magnetic domain wall neurons and synapses emulate the behavior of neurobiological elements through manipulation of magnetic domain walls. The proposed artificial neurons are the first that intrinsically provide the leaking, integrating, firing, and lateral inhibition capabilities without any additional devices or circuitry. This structure is used to perform handwritten digit recognition with 94% accuracy.

Leaky Integrate-and-Fire Neuron

Artificial neurons and synapses are integrated into neural networks to emulate the behavior of neurobiological systems. While artificial synapses need only maintain a resistance state, artificial neurons must provide more complex behavior as exemplified by the leaky integrate-and-fire neuron model. Though neuron behavior can be implemented in software or with inefficient CMOS/electronic hardware, the ideal artificial neuron would provide the leaking, integrating, and firing capabilities within a single device.

The three-terminal magnetic domain wall neuron is the first artificial neuron that provides these three capabilities without requiring any additional devices or circuitry. As illustrated in the micromagnetic simulation video, these three functionalities are achieved through manipulation of the position of the domain wall along the ferromagnetic nanowire track.
  • Leaking: in the absence of any external excitation, the magnetic field from the fixed ferromagnet pushes the domain wall to the left.
  • Integrating: the application of current through the ferromagnetic track pushes the domain wall to the right through spin-transfer torque.
  • Firing: when the domain wall crosses beneath the tunnel barrier, the resistance across the tunnel barrier switches.

Intrinsic Lateral Inhibition

Neurobiological neurons have been shown to exhibit lateral inhibition in addition to leaking, integrating, and firing, whereby integration and firing in one neuron impedes integration and firing in a neighboring neuron. This magnetic domain wall neuron intrinscially provides this lateral inhibition behavior, as the magnetic field created by one neuron can inhibit integration by a neighboring neuron. This is the first artificial neuron proposal that provides lateral inhibition without any additional devices or circuitry.

Handwritten Digit Recognition

These laterally-inhibited domain wall neurons can be integrated into a neural network to perform neuromorphic tasks such as handwritten digit recognition. The presentation of each handwritten digit causes current to flow through synapses to the ten-neuron output layer, where each domain wall neuron represents the recognition of a particular digit. As shown in the video, the neurons integrate the current by moving the domain walls to the right, eventually firing and resetting the neuron output layer. This neuron output layer achieved a 94% recognition rate of the handwritten digits.

Alternative Leaking Phenomena

While leaking functionaly can be achieved with an additional magnetic layer, two alternative phenomena can also achieve leaking. First, the use of an anisotropy gradient can cause domain wall drift. Second, as shown in the video below, a trapezoidal structure achieves the required leaking through shape-based domain wall drift.

Three Terminal-Magnetic Tunnel Junction Logic

These three-terminal magnetic tunnel junction devices were originally proposed for use in non-volatile Boolean logic. Recently, a SPICE-only model has been developed that enables efficient simulation of these logic circuits. This model has been leveraged for large-scale circuit simulation to demonstrate the potential of this logic paradigm to be more energy-efficient than conventional CMOS.

Related Publications

  1. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, C. Cui, A. Velasquez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Leaky Integrate-and-Fire Activation Functions in Domain Wall Magnetic Tunnel Junction Devices, International Conference on Neuromorphic Systems, Aug. 2023.
  2. X. Hu, C. Cui, S. Liu, F. Garcia-Sanchez, W. H. Brigner, B. W. Walker, A. J. Edwards, T. P. Xiao, C. Bennett, N. Hassan, M. P. Frank, J. A. C. Incorvia, J. S. Friedman, Magnetic Skyrmions and Domain Walls for Logical and Neuromorphic Computing, Neuromorphic Computing and Engineering (accepted).
  3. N. Hassan, F. Garcia-Sanchez, D. Querlioz, J. S. Friedman, Modeling Magnetic Domain Wall Motion with Neural Ordinary Differential Equations, Neuro-Inspired Computational Elements, Apr. 2023.
  4. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, C. Cui, A. Velasquez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Configurable Activation Functions based on DW-MTJ LIF Neurons, Neuro-Inspired Computational Elements, Apr. 2023.
  5. P. O. Mathews*, C. B. Duffee*, A. Thayil*, T. E. Stovall, C. H. Bennett, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, N. Hassan, X. Hu, J. S. Friedman, High-Speed CMOS-Free Purely Spintronic Asynchronous Recurrent Neural Network, APL Machine Learning 1, 016107 (2023).
  6. T. Leonard, S. Liu, M. Alamdar, H. Jin, C. Cui, O. G. Akinola, L. Xue, T. P. Xiao, J. S. Friedman, M. J. Marinella, C. H. Bennett, J. A. C. Incorvia, Shape-Dependent Multi-Weight Magnetic Artificial Synapses for Neuromorphic Computing, Advanced Electronic Materials 8:12, 2200563 (2022).
    7.   • Featured as Frontispiece for Issue
  7. N. Hassan, F. Garcia-Sanchez, D. Querlioz, J. S. Friedman, Modeling Magnetic Domain Wall Motion with Neural Ordinary Differential Equations, Conference on Magnetism and Magnetic Materials, Oct.-Nov. 2022.
  8. J. S. Friedman, P. Zhou, X. Hu, A. J. Edwards, N. Hassan, W. H. Brigner, F. Garcia-Sanchez, C. H. Bennett, A. Velasquez, J. A. C. Incorvia, F. B. Mancoff, S. Aggarwal, Unsupervised Learning and Recognition with Single-Domain and Domain-Wall MTJs, Tohoku University Center for Science and Innovation in Spintronics Symposium, Oct. 2022 (invited).
  9. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, C. Cui, A. Velasquez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Shape-Based Activation Functions in Magnetic Domain Wall Leaky Integrate-and-Fire Neurons for Artificial Intelligence Applications, IEEE International Conference on Nanotechnology, July 2022.
  10. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, C. Cui, A. Velasquez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Domain Wall Leaky Integrate-and-Fire Neurons with Shape-Based Configurable Activation Functions, IEEE Transactions on Electron Devices 69:5, 2353-2359 (2022).
  11. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Purely Spintronic Leaky Integrate-and-Fire Neurons, IEEE International Symposium on Circuits & Systems, May 2022.
  12. C. Cui, O. G. Akinola, N. Hassan, C. H. Bennett, M. J. Marinella, J. S. Friedman, J. A. C. Incorvia, Intrinsic Lateral Inhibition Facilitates Winner-Take-All in Domain Wall Racetrack Arrays for Neuromorphic Computing, IEEE International Symposium on Circuits & Systems, May 2022.
  13. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, CMOS-Free Multilayer Perceptron Enabled by Four-Terminal MTJ Device, ACM Neuro-Inspired Computational Elements Workshop, Mar.-Apr. 2022.
  14. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, C. Cui, A. Velasquez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Shape-Based Activation Functions in Magnetic Domain Wall Leaky Integrate-and-Fire Neurons for Artificial Intelligence Applications, APS March Meeting, Mar. 2022.
  15. S. Liu, T. Leonard, M. Alamdar, C. Cui, O. G. Akinola, L. Xue, P. Xiao, J. S. Friedman, M. J. Marinella, C. H. Bennett, J. A. C. Incorvia, Multifunctional Design of Quantized Domain Wall-Magnetic Tunnel Junction Artificial Synapses for Flexible Training of Neural Networks, IEEE International Electron Devices Meeting - MRAM Poster Session, Dec. 2021.
  16. K. Doleh, C. M. Linseisen, L. M. Humphrey, F. Garcia-Sanchez, X. Hu, W. H. Brigner, C. Cui, J. M. Martin, J. A. C. Incorvia, N. Hassan, A. J. Edwards, J. S. Friedman, Kinematic Domain Wall Model for Large-Scale Neuromorphic Network Simulation, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2022.
  17. C. B. Duffee, P. O. Mathews, A. Thayil, T. E. Stovall, C. H. Bennett, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, N. Hassan, X. Hu, J. S. Friedman, High-Speed CMOS-Free Purely Spintronic Asynchronous Recurrent Neural Network, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2022.
  18. M. Alamdar, T. Leonard, S. Liu, O. G. Akinola, L. Xue, J. S. Friedman, M. J. Marinella, T. P. Xiao, C. H. Bennett, J. A. C. Incorvia, Multi-Weight Artificial Synapses with Straight Notched Geometry for Neuromorphic Computing, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2022.
  19. T. Leonard, M. Alamdar, S. Liu, C. Cui, O. G. Akinola, L. Xue, T. P. Xiao, J. S. Friedman, M. J. Marinella, C. H. Bennett, J. A. C. Incorvia, Multi-Weight Directional Artificial Synapses with Trapezoidal Geometry for Neuromorphic Computing, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2022.
  20. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, A. Velasquez, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, CMOS-Free Multilayer Perceptron Enabled by Four-Terminal MTJ Device, IEEE International Conference on Rebooting Computing, Nov. - Dec. 2021.
  21. N. Hassan, W. H. Brigner, C. H. Bennett, A. Velasquez, X. Hu, S. Liu, C. Cui, M. J. Marinella, F. Garcia-Sanchez, J. A. C. Incorvia, J. S. Friedman, Unsupervised Learning in a Purely Spintronic Multilayer Perceptron Enabled by Four-Terminal Domain Wall Magnetic Tunnel Junction Neuron, SPIE Spintronics, Aug. 2021 (invited).
  22. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Purely Spintronic Leaky Integrate-and-Fire Neurons, International Conference on Neuromorphic Systems, July 2021.
  23. S. Liu, C. H. Bennett, J. S. Friedman, M. J. Marinella, D. Paydarfar, J. A. C. Incorvia, Controllable Reset Behavior in Domain Wall-Magnetic Tunnel Junction Artificial Neurons for Task-Adaptable Computation, IEEE Magnetics Letters 12, 4500805 (2021).
  24. M. Alamdar, T. Leonard, C. Cui, B. P. Rimal, L. Xue, O. G. Akinola, T. P. Xiao, J. S. Friedman, C. H. Bennett, M. J. Marinella, J. A. C. Incorvia, Domain Wall-Magnetic Tunnel Junction Spin Orbit Torque Devices and Circuits for In-Memory Computing, Applied Physics Letters 118, 112401 (2021).
  25. W. H. Brigner, N. Hassan, C. H. Bennett, X. Hu, A. Velasquez, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, CMOS-Free Spintronic Neural Network with Unsupervised Learning, Government Microcircuit Applications & Critical Technology Conference, Mar. 2021.
  26. N. Hassan, W. H. Brigner, C. H. Bennett, A. Velasquez, X. Hu, O. G. Akinola, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Purely Spintronic Perceptron with Unsupervised Learning Enabled by Four-Terminal Domain Wall-Magnetic Tunnel Junction Neuron, APS March Meeting, Mar. 2021.
  27. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Magnetic Domain Wall Leaky Integrate-and-Fire Neurons with Shape-Based Configurable Activation Functions, APS March Meeting, Mar. 2021.
  28. M. Alamdar, T. Leonard, C. Cui, B. P. Rimal, L. Xue, O. G. Akinola, T. P. Xiao, J. S. Friedman, C. H. Bennett, M. J. Marinella, J. A. C. Incorvia, Spin Orbit Torque Domain Wall-Magnetic Tunnel Junction Devices and Circuits for In-Memory and Neuromorphic Computing, APS March Meeting, Mar. 2021.
  29. C. Cui, O. G. Akinola, N. Hassan, C. H. Bennett, M. J. Marinella, J. S. Friedman, J. A. C. Incorvia, Emulating Winner-Take-All in Magnetic Domain Wall Racetrack Arrays for Neuromorphic Computing, IEEE International Conference on Rebooting Computing, Dec. 2020.
  30. N. Hassan, W. H. Brigner, C. H. Bennett, A. Velasquez, X. Hu, O. G. Akinola, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Purely Spintronic Multilayer Perceptron Enabled by Four-Terminal Domain Wall-Magnetic Tunnel Junction Neuron, Conference on Magnetism and Magnetic Materials, Nov. 2020.
  31. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Linear Intrinsic Leaking in a Domain-Wall Magnetic Tunnel Junction Neuron, Conference on Magnetism and Magnetic Materials, Nov. 2020.
  32. J. A. C. Incorvia, J. S. Friedman, M. J. Marinella, O. G. Akinola, C. Cui, N. Hassan, C. H. Bennett, X. Hu, L. Jiang-Wei, W. H. Brigner, F. Garcia-Sanchez, M. Pasquale, Modeling Biological Behavior in Domain Wall-Magnetic Tunnel Junction Artificial Neurons and Synapses for Energy-Efficient Neuromorphic Computing, Conference on Magnetism and Magnetic Materials, Nov. 2020 (invited).
  33. O. G. Akinola, B. Mendawar, C. H. Bennett, X. Hu, J. S. Friedman, M. J. Marinella, J. A. C. Incorvia, Online Training of Spiking Neural Networks Using Domain Wall Magnetic Tunnel Junction Synapses, Conference on Magnetism and Magnetic Materials, Nov. 2020.
  34. C. Cui, O. G. Akinola, N. Hassan, C. H. Bennett, M. J. Marinella, J. S. Friedman, J. A. C. Incorvia, Lateral Inhibition in Magnetic Domain Wall Racetrack Arrays for Neuromorphic Computing, Conference on Magnetism and Magnetic Materials, Nov. 2020.
  35. J. A. C. Incorvia, J. S. Friedman, M. J. Marinella, O. G. Akinola, C. Cui, N. Hassan, C. H. Bennett, X. Hu, L. Jiang-Wei, W. H. Brigner, F. Garcia-Sanchez, M. Pasquale, Capturing Biological Behavior in Nanomagnetic Artificial Neurons and Synapses for Energy-Efficient Neuromorphic Computing, Pacific Rim Meeting on Electrochemical & Solid-State Science, Oct. 2020 (invited).
  36. W. H. Brigner, N. Hassan, C. H. Bennett, X. Hu, A. Velasquez, F. Garcia-Sanchez, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, CMOS-Free Spintronic Neural Network with Unsupervised Learning, IBM/IEEE AI Compute Symposium, Oct. 2020.
  37. C. Cui, O. G. Akinola, N. Hassan, C. H. Bennett, M. J. Marinella, J. S. Friedman, J. A. C. Incorvia, Maximized Lateral Inhibition in Paired Magnetic Domain Wall Racetracks for Neuromorphic Computing, Nanotechnology 31:29, 294001 (2020).
  38. C. Cui, O. G. Akinola, N. Hassan, C. H. Bennett, M. J. Marinella, J. S. Friedman, J. A. C. Incorvia, Lateral Inhibition in Magnetic Domain Wall Racetrack Arrays for Neuromorphic Computing, SPIE Spintronics, Aug. 2020 (invited).
  39. T. P. Xiao, C. H. Bennett, X. Hu, B. Feinberg, R. Jacobs-Gedrim, S. Agarwal, J. S. Brunhaver, J. S. Friedman, J. A. C. Incorvia, M. J. Marinella, Energy-Efficient Stateful Logic with Magnetic Domain Walls, SPIE Spintronics, Aug. 2020 (invited).
  40. W. H. Brigner, X. Hu, N. Hassan, L. Jiang-Wei, C. H. Bennett, F. Garcia-Sanchez, O. Akinola, M. Pasquale, M. J. Marinella, J. A. C. Incorvia, J. S. Friedman, Three Artificial Spintronic Leaky Integrate-and-Fire Neurons, SPIN 10:2, 2040003 (2020).
    41.   • Featured as Cover Image for Issue
  41. N. Hassan, W. H. Brigner, X. Hu, O. G. Akinola, C. H. Bennett, M. J. Marinella, F. Garcia-Sanchez, J. A. C. Incorvia, J. S. Friedman, CMOS-Free Magnetic Domain Wall Leaky Integrate-and-Fire Neurons with Intrinsic Lateral Inhibition, IEEE International Symposium on Circuits & Systems, Oct. 2020 (invited).
  42. X. Hu, A. J. Edwards, T. P. Xiao, C. H. Bennett, J. A. C. Incorvia, M. J. Marinella, J. S. Friedman, Process Variation Model and Analysis for Domain Wall-Magnetic Tunnel Junction Logic, IEEE International Symposium on Circuits & Systems, Oct. 2020.
  43. C. H. Bennett, T. P. Xiao, C. Cui, N. Hassan, O. Akinola, J. A. C. Incorvia, A. Velasquez, J. S. Friedman, M. J. Marinella, Plasticity-Enhanced Domain-Wall MTJ Neural Networks for Energy-Efficient Online Learning, IEEE International Symposium on Circuits & Systems, Oct. 2020 (invited).
  44. W. H. Brigner, N. Hassan, X. Hu, C. H. Bennett, M. J. Marinella, F. Garcia-Sanchez, J. A. C. Incorvia, J. S. Friedman, CMOS-Free Multilayer Perceptron Enabled by Four-Terminal MTJ Device, Government Microcircuit Applications & Critical Technology Conference, Mar. 2020.
  45. A. Velasquez, C. H. Bennett, N. Hassan, W. H. Brigner, O. G. Akinola, J. A. C. Incorvia, M. J. Marinella, J. S. Friedman, Unsupervised Competitive Hardware Learning Rule for Spintronic Clustering Architecture, Government Microcircuit Applications & Critical Technology Conference, Mar. 2020.
  46. T. P. Xiao, C. H. Bennett, X. Hu, B. Feinberg, R. Jacobs-Gedrim, S. Agarwal, J. Brunhaver, J. S. Friedman, J. A. C. Incorvia, M. J. Marinella, Energy and Performance Benchmarking of a Domain Wall-Magnetic Tunnel Junction Multibit Adder, IEEE Journal on Exploratory Solid-State Computational Devices and Circuits 5:2, 188-196 (2019).
  47. W. H. Brigner, N. Hassan, L. Jiang-Wei, X. Hu, D. Saha, C. H. Bennett, M. J. Marinella, J. A. C. Incorvia, F. Garcia-Sanchez, J. S. Friedman, Shape-Based Magnetic Domain Wall Drift for an Artificial Spintronic Leaky Integrate-and-Fire Neuron, IEEE Transactions on Electron Devices 66:11, 4970-4975 (2019).
  48. O. Akinola, X. Hu, C. H. Bennett, M. J. Marinella, J. S. Friedman, J. A. C. Incorvia, Three-Terminal Magnetic Tunnel Junction Synapse Circuits Showing Spike-Timing-Dependent Plasticity, Journal of Physics D: Applied Physics 52:49, 49LT01 (2019).
  49. W. H. Brigner, N. Hassan, X. Hu, L. Jiang-Wei, D. Saha, C. H. Bennett, M. J. Marinella, F. Garcia-Sanchez, J. A. C. Incorvia, J. S. Friedman, Magnetic Domain Wall Neurons with Intrinsic Leaking, Conference on Magnetism and Magnetic Materials, Nov. 2019.
  50. C. Cui, N. Hassan, C. H. Bennett, M. J. Marinella, J. S. Friedman, J. A. C. Incorvia, Optimized Lateral Inhibition in Magnetic Domain Wall Tracks for Neuromorphic Computing, Conference on Magnetism and Magnetic Materials, Nov. 2019.
  51. N. Hassan, X. Hu, L. Jiang-Wei, W. H. Brigner, O. G. Akinola, F. Garcia-Sanchez, M. Pasquale, C. H. Bennett, J. A. C. Incorvia, J. S. Friedman, Magnetic Domain Wall Neuron with Intrinsic Leaking and Lateral Inhibition Capability, SPIE Spintronics, Aug. 2019 (invited).
  52. O. G. Akinola, M. Alamdar, N. Hassan, X. Hu, T. Leonard, J. S. Friedman, J. A. C. Incorvia, Three-Terminal Magnetic Tunnel Junctions for In-Memory and Neuromorphic Computing, SPIE Spintronics, Aug. 2019 (invited).
  53. C. H. Bennett, J. A. C. Incorvia, X. Hu, N. Hassan, J. S. Friedman, M. J. Marinella, Semi-Supervised Learning and Inference in Domain-Wall Magnetic Tunnel Junction (DW-MTJ) Neural Networks, SPIE Spintronics, Aug. 2019 (invited).
  54. W. H. Brigner, X. Hu, N. Hassan, C. H. Bennett, J. A. C. Incorvia, F. Garcia-Sanchez, J. S. Friedman, Graded-Anisotropy-Induced Magnetic Domain Wall Drift for an Artificial Spintronic Leaky Integrate-and-Fire Neuron, IEEE Journal on Exploratory Solid-State Computational Devices and Circuits 5:1, 19-24 (2019).
  55. X. Hu, A. Timm, W. H. Brigner, J. A. C. Incorvia, J. S. Friedman, SPICE-Only Model for Spin-Transfer Torque Domain Wall MTJ Logic, IEEE Transactions on Electron Devices 66:6, 2817-2821 (2019).
    56.   • Corrections
      • Device Model
  56. N. Hassan, X. Hu, L. Jiang-Wei, W. H. Brigner, O. G. Akinola, F. Garcia-Sanchez, M. Pasquale, C. H. Bennett, J. A. C. Incorvia, J. S. Friedman, Neuromorphic Computing with Domain Wall-Based Three-Terminal Magnetic Tunnel Junctions: Neurons, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2019.
  57. O. Akinola, E. J. Kim, N. Hassan, J. S. Friedman, J. A. C. Incorvia, Neuromorphic Computing with Domain Wall-Based Three-Terminal Magnetic Tunnel Junctions: Synapse, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2019.
  58. N. Hassan*, X. Hu*, L. Jiang-Wei, W. H. Brigner, O. G. Akinola, F. Garcia-Sanchez, M. Pasquale, C. H. Bennett, J. A. C. Incorvia, J. S. Friedman, Magnetic Domain Wall Neuron with Lateral Inhibition, Journal of Applied Physics 124:15, 152127 (2018).

This research is sponsored in part by the National Science Foundation under CCF awards #1910800 and #2146439.