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Deep learning incorporating biologically inspired neural dynamics and in-memory computing


Spiking neural networks (SNNs) incorporating biologically plausible neurons hold great promise because of their unique temporal dynamics and energy efficiency. However, SNNs have developed separately from artificial neural networks (ANNs), limiting the impact of deep learning advances for SNNs. Here, we present an alternative perspective of the spiking neuron that incorporates its neural dynamics into a recurrent ANN unit called a spiking neural unit (SNU). SNUs may operate as SNNs, using a step function activation, or as ANNs, using continuous activations. We demonstrate the advantages of SNU dynamics through simulations on multiple tasks and obtain accuracies comparable to, or better than, those of ANNs. The SNU concept enables an efficient implementation with in-memory acceleration for both training and inference. We experimentally demonstrate its efficacy for a music-prediction task in an in-memory-based SNN accelerator prototype using 52,800 phase-change memory devices. Our results open up an avenue for broad adoption of biologically inspired neural dynamics in challenging applications and acceleration with neuromorphic hardware.

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Fig. 1: Spiking neural dynamics.
Fig. 2: Comparison with the state-of-the-art ANNs.
Fig. 3: Full-precision simulation results.
Fig. 4: Performance under limited weight precision.
Fig. 5: Neuromorphic architecture with in-memory acceleration.
Fig. 6: Music-prediction hardware experiment.

Data availability

Publicly available datasets were used and referenced with their descriptions in the paper.

Code availability

Open source frameworks were used for the implementation. Sample source code in TensorFlow is provided in the Supplementary Information.


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We thank U. Egger for assistance with the setup, R. Khaddam-Aljameh for assistance in the analysis of the energy consumption and the computation time of a PCM crossbar array in 14-nm CMOS technology, M. Dazzi and M. Stanisavljevic for assistance in the system-level analysis of the energy consumption and the computation time, M. Stanisavljevic for assistance in the design of digital circuitry implementing both artificial and spiking neurons, N. Gustafsson for editing the manuscript, O. Simeone, B. Rajendran and N. S. Rajalekshmi for comments on the initial draft, W. Maass, E. Neftci and colleagues from IBM’s Neuromorphic and In-Memory Computing team for discussions.

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Authors and Affiliations



S.W. and A.P. conceived the idea of SNU. E.E. and A.P. proposed the idea of in-memory acceleration based on SNUs. S.W., A.P. and E.E. designed the benchmarks. S.W. implemented and performed the software benchmarks. T.B. implemented the hardware in-the-loop functionality and performed the experiments. All authors developed the biologically inspired functional extensions. T.B. and E.E. analysed the stability of the gradient-based training. All authors analysed the results. S.W., A.P. and E.E. co-wrote the manuscript. All authors compiled the Supplementary Notes. E.E. supervised the work.

Corresponding author

Correspondence to Evangelos Eleftheriou.

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Extended Data

Extended Data Fig. 1 Correspondence between an SNU and an LIF neuron.

a, The respective LIF parameters directly correspond to the SNU parameters, such that the same set of parameter values can be used in an SNU-based network, implemented by utilizing standard ANN frameworks, as well as in a native LIF-based implementation, utilizing standard SNN frameworks. b, To demonstrate this, we used TensorFlow78 to produce sample plots of the spiking dynamics for a single SNU. The state variable of the SNU increases each time an input spike arrives at the neuron, and decreases following the exponential decay dynamics. When the spiking threshold is reached, an output spike is emitted (vertical dashed line) and the membrane potential is reset. These dynamics are aligned with the reference LIF dynamics, which we obtained for the corresponding parameters by running a simulation in the well-known Brian286 SNN framework.

Extended Data Fig. 2 Training an SNU with backpropagation through time.

The temporal dynamics of an SNU are unfolded over time during the forward pass, and error gradients are propagated backwards through the computational graph to determine the parameters’ adjustments during the backward pass.

Extended Data Fig. 3 Image classification details.

a, Complete spiking CNN architecture. b, CNN learning curve for rate-coded inputs without preprocessing. The accuracy was calculated by averaging over ten different initializations (vertical brackets) or over the last 50 epochs (horizontal brackets). c, Analogous CNN learning curve for rate-coded inputs obtained from MNIST images preprocessed with elastic distortions. d, Table comparing the state-of-the-art fully-connected (FC) and convolutional (CNN) SNN architectures27,46,49,53,57,87,88 in terms of parameters and obtained MNIST accuracy.

Extended Data Fig. 4 Sequence prediction details.

The values in all the panes of this figure were obtained by averaging over ten different initializations. Standard deviation is reported along the results and marked with error bars in the plots. a, Language modelling training perplexity evolution for SNU- and sSNU-based architectures. b, Comparison of test perplexity with other results70,81,89. ANN results using standard architectures with similar training techniques were considered, that is no pre- or post-processing, single network, truncated BPTT, no dropout. WT denotes weight tying of the output layer with the embedding layer. c, Music prediction loss evolution for sSNU-based network. d, Comparison with other results71,72.

Extended Data Fig. 5 Impact of limited precision for the handwritten digit recognition dataset.

Final test performance of a neural network using a, sSNUs and b, LSTMs. The numbers below the test performance indicate the standard deviation over five different runs.

Extended Data Fig. 6 Schematic diagram of the experimental setup.

a, The network architecture is designed using SNUs and standard tools from the TensorFlow framework. The training is performed in the same way as in other networks: a loss function is defined, and an optimizer is configured to minimize it using gradient descent. b, A wrapper provides functions to read and write the weights similarly to any regular TensorFlow variable. These functions manage the communication with the hardware through a Python-MATLAB interface that translates the read or write requests into FPGA commands, and converts conductance values obtained from the FPGA board back to TensorFlow. The writing can be performed without rereading the updated values from the hardware: steps 3 and 4 are optional. c, The FPGA board interacts with the prototype chip holding the PCM devices (not at scale): indirectly, through the Analog Front-End Board, to provide the power supply, and to clock and generate the current pulses; and directly, to control the chip operation and read conductance values from the on-chip analog-to-digital converter. d, An inference example: information about a chord propagates through the network with spikes to the sigmoidal output layer that generates next notes’ probabilities. e, At each layer, the weights of activated 2-PCM synapses are constructed from f, and conductance values are returned by the on-chip analog-to-digital converter.

Extended Data Fig. 7 Hardware experiment details.

a, A 2-PCM synapse is implemented with two PCM devices operating in a differential configuration, that is a weight w is proportional to the difference between the conductances of the G + and the G- device. Weight increase is performed through crystallization of the positive device with programming pulses and weight decrease is performed through crystallization of the negative device with programming pulses. The plot on the left contains an example of an evolution of the 2-PCM synapse over the course of training. Aside from programming pulses, the fluctuations in the conductance values arise owing to PCM-specific physical phenomena, such as read noise or conductance drift. b, Snapshots of the weight distributions over the course of training, depicted for the two trainable layers.

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Woźniak, S., Pantazi, A., Bohnstingl, T. et al. Deep learning incorporating biologically inspired neural dynamics and in-memory computing. Nat Mach Intell 2, 325–336 (2020).

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