Event-Driven Random Backpropagation: Enabling Neuromorphic Deep . - SRC
Event-Driven Random Backpropagation: EnablingNeuromorphic Deep Learning MachinesEmre NeftciDepartment of Cognitive Sciences, UC Irvine,Department of Computer Science, UC Irvine,March 7, 2017
Scalable Event-Driven Learning MachinesCauwenberghs, Proceedings of the National Academy of Sciences, 2013Karakiewicz, Genov, and Cauwenberghs, IEEE Sensors Journal, 2012Neftci, Augustine, Paul, and Detorakis, arXiv preprint arXiv:1612.05596, 20161000x power improvements compared to future GPU technologythrough two factors: Architecture and device level optimization in event-based computing Algorithmic optimization in neurally inspired learning and inference
Neuromorphic Computing Can Enable Low-power, Massively Parallel Computing Only spikes are communicated & routed between neurons (weights,internal states are local) To use this architecture for practical workloads, we need algorithms thatoperate on local information
Why Do Embedded Learning?For many industrial applications involving controlled environments, whereexisting data is readily available, off-chip/off-line learning is often sufficient.So why do embedded learning?Two main use cases: Mobile, low-power platform in uncontrolled environments, whereadaptive behavior is required. Working around device mismatch/non-idealities.Potentially rules out: Self-driving cars Data mining Fraud Detection
Neuromorphic Learning MachinesNeuromorphic Learning Machines: Online learning for data-driven autonomyand algorithmic efficiency Hardware & Architecture: Scalable Neuromorphic Learning HardwareDesign Programmability: Neuromorphic supervised, unsupervised andreinforcement learning framework
Foundations for Neuromorphic Machine Learning Software Framework & Libraryneon mlp extract.py# setup model layerslayers [Affine(nout 100, init init norm, activation Rectlin()),Affine(nout 10, init init norm, activation Logistic(shortcut True))]# setup cost function as CrossEntropycost GeneralizedCost(costfunc CrossEntropyBinary())# setup optimizeroptimizer GradientDescentMomentum(0.1, momentum coef 0.9, stochastic round args.rounding)
Can we design a digital neuromorphic learning machinethat is flexible and efficient?
Examples of linear I&F neuron models Leaky Stochastic I&F Neuron (LIF)V[t 1] αV[t] nXξj wj (t)sj (t)(1a)j 1V[t 1] T : V[t 1] Vreset(1b)
Examples of linear I&F neuron modelsContinued LIF with first order kinetic synapseV[t 1] αV[t] IsynIsyn [t 1] a1 Isyn [t] nX(2a)wj (t)sj (t)(2b)j 1V[t 1] T : V[t 1] Vreset(2c)
Examples of linear I&F neuron modelsContinued LIF with second order kinetic synapseV[t 1] αV[t] Isyn Isyn ,Isyn [t 1] a1 Isyn [t] c1 Is [t] η[t] bIs [t 1] a2 Is [t] nXwj sj [t](3a)(3b)(3c)j 1V[t 1] T : V[t 1] Vreset(3d)
Examples of linear I&F neuron modelsContinued Dual-Compartment LIF with synapsesV1 [t 1] αV1 [t] α21 V2 [t](4a)V2 [t 1] αV2 [t] α12 V1 [t] Isyn(4b)Isyn [t 1] a1 Isyn [t] nXw1j (t)sj (t) η[t] b(4c)j 1V1 [t 1] T : V1 [t 1] Vreset(4d)
Mihalas-Niebur NeuronContinued Mihalas Niebur Neuron (MNN)V[t 1] αV[t] Ie G · EL nXIi [t](5a)i 1Θ[t 1] (1 b)Θ[t] aV[t] aEL b(5b)I1 [t 1] α1 I1 [t](5c)I2 [t 1] α2 I2 [t](5d)V[t 1] Θ[t 1] : Reset(V[t 1], I1 , I2 , Θ)(5e)MNN can produce a wide variety of spiking behaviorsMihalas and Niebur, Neural Computation, 2009
Digital Neural and Synaptic Array Transceiver Multicompartment generalized integrate-and-fire neurons Multiplierless design Weight sharing (convnets) at the level of the coreEquivalent software simulations for analyzing fault tolerance, precision,performance, and efficiency trade-offs (available publicly soon!)
Amplitude (mV)Amplitude (mV)Amplitude (mV)NSAT Neural Dynamics FlexibilityTonic spikingMixed modeClass IClass IIPhasic spikingTonic bursting-30-50-70-30-50-70-30-50-700100 200 300 400 500Time (ticks)0100 200 300 400 500Time (ticks)Detorakis, Augustine, Paul, Pedroni, Sheik, Cauwenberghs, and Neftci (in preparation)
Flexible Learning Dynamicswk [t 1] wk [t] sk [t 1]ekek xm (K[t tk ] K[tk tlast ]){z} STDPXxm γi xi(Weight update)(Eligibilty)(Modulation)iDetorakis, Augustine, Paul, Pedroni, Sheik, Cauwenberghs, and Neftci (in preparation)
Flexible Learning Dynamicswk [t 1] wk [t] sk [t 1]ekek xm (K[t tk ] K[tk tlast ]){z} STDPXxm γi xi(Weight update)(Eligibilty)(Modulation)iDetorakis, Augustine, Paul, Pedroni, Sheik, Cauwenberghs, and Neftci (in preparation)Based on two insights:Causal and acausal STDP weight updates on pre-synaptic spikesonly, using only forward lookup access of the synaptic connectivitytablePedroni et al.,, 2016“Plasticity involves as a third factor a local dendritic potential,besides pre- and postsynaptic firing times”Urbanczik and Senn, Neuron, 2014Clopath, Büsing, Vasilaki, and Gerstner, Nature Neuroscience, 2010
Applications for Three-factor Plasticity RulesExample learning rules Reinforcement Learning wij ηrSTDPijFlorian, Neural Computation, 2007 Unsupervised Representation Learning wij ηg(t)STDPijNeftci, Das, Pedroni, Kreutz-Delgado, and Cauwenberghs, Frontiers in Neuroscience, 2014 Unsupervised Sequence Learning wij η (Θ(V) α(νi C)) νjSheik et al. 2016 Supervised Deep Learning wij η(νtgt νi )φ0 (V)νjNeftci, Augustine, Paul, and Detorakis, arXiv preprint arXiv:1612.05596, 2016
Applications for Three-factor Plasticity RulesExample learning rules Reinforcement Learning wij ηrSTDPijFlorian, Neural Computation, 2007 Unsupervised Representation Learning wij ηg(t)STDPijNeftci, Das, Pedroni, Kreutz-Delgado, and Cauwenberghs, Frontiers in Neuroscience, 2014 Unsupervised Sequence Learning wij η (Θ(V) α(νi C)) νjSheik et al. 2016 Supervised Deep Learning wij η(νtgt νi )φ0 (V)νjNeftci, Augustine, Paul, and Detorakis, arXiv preprint arXiv:1612.05596, 2016
Gradient Backpropagation (BP) is non-local on Neural SubstratesPotential incompatibilities of BP on a neural (neuromorphic) substrate:1Symmetric Weights2Computing Multiplications and Derivatives3Propagating error signals with high precision4Precise alternation between forward and backward passes5Synaptic weights can change sign6Availability of targets
Feedback AlignmentReplace weight matrices in backprop phase with (fixed) random weightsLillicrap, Cownden, Tweed, and Akerman, arXiv preprint arXiv:1411.0247, 2014Baldi, Sadowski, and Lu, arXiv preprint arXiv:1612.02734, 2016
Event-Driven Random Backpropagation (eRBP) for Deep Supervised Learning Event-driven Random Backpropagation Learning Rule:Error-modulated, membrane voltage-gated, event-driven,supervised.X wik φ0 (Isyn,i [t]) Sk [t]Gij (Lj [t] Pj [t])(eRBP) {z } {z}jDerivativeError
Event-Driven Random Backpropagation (eRBP) for Deep Supervised Learning Event-driven Random Backpropagation Learning Rule:Error-modulated, membrane voltage-gated, event-driven,supervised.X(eRBP) wik φ0 (Isyn,i [t]) Sk [t]Gij (Lj [t] Pj [t]) {z } {z}jDerivativeError {z}TiApproximate derivative with a boxcar function:Neftci, Augustine, Paul, and Detorakis, arXiv preprint arXiv:1612.05596, 2016One addition and two comparison per synaptic event
eRBP PI MNIST BenchmarksNetworkDatasetPI MNIST 784-100-10PI MNIST 784-200-10PI MNIST 784-500-10PI MNIST 784-200-200-10PI MNIST on ErrorpeRBPRBP 2.20%peRBP eRBP with stochastic synapsesBP (GPU)2.19%1.81%1.8%1.91%1.90%
peRBP MNIST Benchmarks (Convolutional Neural Net)NetworkDatasetMNISTClassification ErrorpeRBPRBP (GPU)3.8 (5 epochs)% 1.95%BP (GPU)1.23%
Energetic EfficiencyEnergy Efficieny During Inference: Inference: 100k Synops until first spike: 5% error, 100, 000 SynOpsper yTechnologyeRBP(20 pJ/Synop)95%2 µJDropConnect (GPU)CPU/GPU99.79%1265 µJ28 nmSpinnakerASIC95%6000 µJUnknownTrue NorthASIC95%4µJ28 nm
Energetic EfficiencyEnergy Efficieny During Training: Training: SynOp-MAC parityEmbedded local plasticity dynamics for continuous (life-long) learning
Learning using Fixed Point Variables 16 bits neural states 8 bits synaptic weights 1Mbit Synaptic Weight MemoryAll-digital implementation for exploring scalable event-based learningUCI (Neftci, Krichmar, Dutt), UCSD (Cauwenberghs)
Summary & AcknowledgementsSummary:1NSAT: Flexible and efficient neural learning machines2Supervised deep learning with event-driven random back-propagationcan achieve good learning results at 100x energy improvementsChallenges:1Catastrophic Forgetting: Need for Hippocampus, Intrinsic Replay andNeurogenesis2Build a neuromorphic library of “deep learning tricks” (Batchnormalization, Adam, . . . )
AcknowledgementsCollaborators:Georgios Detorakis(UCI)Support:Somnath Paul (Intel)Charles Augustine(Intel)
P. Baldi, P. Sadowski, and Zhiqin Lu. “Learning in the Machine:Random Backpropagation and the Learning Channel”. In: arXivpreprint arXiv:1612.02734 (2016).Gert Cauwenberghs. “Reverse engineering the cognitive brain”. In:Proceedings of the National Academy of Sciences 110.39 (2013),pp. 15512–15513.C. Clopath, L. Büsing, E. Vasilaki, and W. Gerstner. “Connectivityreflects coding: a model of voltage-based STDP with homeostasis”. In:Nature Neuroscience 13.3 (2010), pp. 344–352.R.V. Florian. “Reinforcement learning through modulation ofspike-timing-dependent synaptic plasticity”. In: Neural Computation19.6 (2007), pp. 1468–1502.R. Karakiewicz, R. Genov, and G. Cauwenberghs. “1.1 TMACS/mWFine-Grained Stochastic Resonant Charge-Recycling ArrayProcessor”. In: IEEE Sensors Journal 12.4 (Apr. 2012), pp. 785–792.Timothy P Lillicrap, Daniel Cownden, Douglas B Tweed, andColin J Akerman. “Random feedback weights support learning in deepneural networks”. In: arXiv preprint arXiv:1411.0247 (2014).
S. Mihalas and E. Niebur. “A generalized linear integrate-and-fireneural model produces diverse spiking behavior”. In: NeuralComputation 21 (2009), pp. 704–718.E. Neftci, S. Das, B. Pedroni, K. Kreutz-Delgado, andG. Cauwenberghs. “Event-Driven Contrastive Divergence for SpikingNeuromorphic Systems”. In: Frontiers in Neuroscience 7.272 (Jan.2014). ISSN: 1662-453X. DOI: 10.3389/fnins.2013.00272. URL:http://www.frontiersin.org/neuromorphic engineering/10.3389/fnins.2013.00272/abstract.Emre Neftci, Charles Augustine, Somnath Paul, andGeorgios Detorakis. “Event-driven Random Back-Propagation:Enabling Neuromorphic Deep Learning Machines”. In: arXiv preprintarXiv:1612.05596 (2016).Bruno U Pedroni, Sadique Sheik, Siddharth Joshi, Georgios Detorakis,Somnath Paul, Charles Augustine, Emre Neftci, andGert Cauwenberghs. “Forward Table-Based PresynapticEvent-Triggered Spike-Timing-Dependent Plasticity”. In: Oct. 2016.URL : 7.03070%7D.
Robert Urbanczik and Walter Senn. “Learning by the dendriticprediction of somatic spiking”. In: Neuron 81.3 (2014), pp. 521–528.
Neuromorphic Computing Can Enable Low-power, Massively Parallel Computing . Based on two insights: Causal and acausal STDP weight updates on pre-synaptic spikes . Challenges: 1 Catastrophic Forgetting: Need for Hippocampus, Intrinsic Replay and Neurogenesis
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