Mapping and Validating a Point Neuron Model on Intel's Neuromorphic Hardware Loihi

Abstract

Neuromorphic hardware is based on emulating the natural biological structure of the brain. Since its computational model is similar to standard neural models, it could serve as a computational accelerator for research projects in the field of neuroscience and artificial intelligence, including biomedical applications. However, in order to exploit this new generation of computer chips, we ought to perform rigorous simulation and consequent validation of neuromorphic models against their conventional implementations. In this work, we lay out the numeric groundwork to enable a comparison between neuromorphic and conventional platforms. "Loihi"-Intel's fifth generation neuromorphic chip, which is based on the idea of Spiking Neural Networks (SNNs) emulating the activity of neurons in the brain, serves as our neuromorphic platform. The work here focuses on Leaky Integrate and Fire (LIF) models based on neurons in the mouse primary visual cortex and matched to a rich data set of anatomical, physiological and behavioral constraints. Simulations on classical hardware serve as the validation platform for the neuromorphic implementation. We find that Loihi replicates classical simulations very efficiently with high precision. As a by-product, we also investigate Loihi's potential in terms of scalability and performance and find that it scales notably well in terms of run-time performance as the simulated networks become larger.

Keywords: LIF models; neural simulations; neuromorphic computing; performance analysis; validation.

Figure 1

As the network size increases, Loihi outperforms consistently in terms of time. The figure shows runtime comparison of 500 ms of dynamics for up to 20,000 neurons for Loihi and BMTK, with the values scaled by the respective smallest runtime. Loihi has a maximum runtime of up to 12 ms, whereas BMTK runtime goes up to 273 s (See Table 3 for the explicit runtime values and Section 4.4 for further details about the network.).

Figure 2

Loihi internal neuron model—Time multiplexed pipeline architecture of a neural unit (Figure 4 in Davies et al., 2018). Reproduced from WikiCommons (2018).

Figure 3

Membrane potential response for single-neuron network based on two different neuron parameters. (A) Simulation is driven by bias current. (B) Simulation is driven by external spikes.

Figure 4

Validation plots for simulations based on two different stimuli—(A) Validation plots for bias current stimulus (B) Validation plots for external spike stimulus, based on the Distribution Function, Raster Plot, and Scatter Plot, respectively.

Figure 5

Single neuron model in BMTK—(A) Membrane potential response. (B) Current response.

Figure 6

Comparison of membrane potential and current plots with different temporal precisions in Loihi. Membrane potential plots are on the left with (A) dt = 0.1 (B) dt = 1.0 (C) dt = 10.0. Current plots are on the right with (D) dt = 0.1 (E) dt = 1.0 (F) dt = 10.0. For dt = 10.0, number of time-steps are 50 and for dt = 0.1, number of time-steps are 5,000.

Figure 7

Error comparison for different temporal precisions—(A) Membrane potential error. (B) Current error. In both panels, the RMSE for the corresponding state is plotted against the log of the temporal precision dt.

Figure 8

Comparison of membrane potential and current plots with different voltage precisions. Membrane potential plots are on the left with (A) $V_s=1.0\times 10^{-3}$ (B) $V_s=1.0\times 10^{-4}$ (C) $V_s=1.0\times 10^{-5}.$ Current plots are on the right with (D) $V_s=1.0\times 10^{-3}$ (E) $V_s=1.0\times 10^{-4}$ (F) $V_s=1.0\times 10^{-5}$.

Figure 9

Error comparison for different membrane potential precisions—(A) Membrane potential error. (B) Current error. In both panels, the RMSE for the corresponding state is plotted against the –log of the voltage scale V_s.

Figure 10

Loihi replicates various neuron class responses of BMTK. (A) BMTK simulation of 20 neuron classes. (B) Loihi simulation of 20 neuron classes.

Figure 11

Scatter plots showing the range of parameters for the 20 neurons classes comprising of both excitatory and inhibitory neurons grouped by RMSE of the simulations. (A) Scatter plot for membrane capacitance (C_m) vs. membrane time constant (τ_v). (B) Scatter plot for bias current (I_bias) vs. membrane time constant (τ_v). The marker size is determined by the corresponding RMSE.

Figure 12

Performance comparison between BMTK and Loihi for network sizes ranging from 1 to 20,000 for the simulation of 500 ms of dynamics. The values for each curve are scaled by the respective smallest runtime. The Loihi runtime units are in “milliseconds” and BMTK runtime is in “seconds”.

Figure 13

Loihi runtime for a network of upto 250K neurons for the simulation of 500 ms of dynamics.