Bayesian continual learning via spiking neural networks

Abstract

Among the main features of biological intelligence are energy efficiency, capacity for continual adaptation, and risk management via uncertainty quantification. Neuromorphic engineering has been thus far mostly driven by the goal of implementing energy-efficient machines that take inspiration from the time-based computing paradigm of biological brains. In this paper, we take steps toward the design of neuromorphic systems that are capable of adaptation to changing learning tasks, while producing well-calibrated uncertainty quantification estimates. To this end, we derive online learning rules for spiking neural networks (SNNs) within a Bayesian continual learning framework. In it, each synaptic weight is represented by parameters that quantify the current epistemic uncertainty resulting from prior knowledge and observed data. The proposed online rules update the distribution parameters in a streaming fashion as data are observed. We instantiate the proposed approach for both real-valued and binary synaptic weights. Experimental results using Intel's Lava platform show the merits of Bayesian over frequentist learning in terms of capacity for adaptation and uncertainty quantification.

Agreeing to Stop: Reliable Latency-Adaptive Decision Making via Ensembles of Spiking Neural Networks

“…For DE, we follow the standard random initialization made available by PyTorch, while for VI, we set the prior distribution variance to 0.03. The parameter r in (15) for CM is set to 1, yielding standard model averaging [15]; while r in (19) for PM is set to r = 45, with a r = K 1/r following ( [33], Table 1) based on the numerical minimization of latency on a held-out dataset. The results are averaged over 50 different realizations of calibration and test datasets, and the number of ensemble K is set to 6.…”

“…Conventional SNN models consist of a single SNN making decisions on the basis of the confidence levels (2), or (3), at a fixed time t = T. Neuroscience has long explored the connection between networks of spiking neurons and Bayesian reasoning [23], and the recent work [15] has explored the advantages of Bayesian learning and model ensembling in terms of uncertainty quantification for SNN classifiers. In this work, we leverage the enhanced uncertainty quantification capabilities of ensemble models to improve the reliability of adaptive-latency decision making via SNN models.…”

“…Gaussian prior distribution N (0, σ 2 ) for the model parameter vector θ, one optimizes over a variational posterior distribution N (µ, ζ 2 ) parameterized by mean vector µ and diagonal covariance matrix with diagonal elements given by vector ζ 2 . The optimization is done by using gradient descent via the reparameterization trick [15]. At inference time, the K models are generated by sampling the weight vectors θ k from the optimized distribution N (µ, ζ 2 ).…”

“…By relying on conventional SNN models, SpikeCP does not attempt to quantify epistemic uncertainty and instead focuses only on aleatoric uncertainty quantification. The application of Bayesian learning and model ensembling as means to quantify epistemic uncertainty in SNNs was investigated in [15][16][17] and showed improvements in standard calibration metrics.…”

“…As shown in Table 1, we compare two ensembling strategies-deep ensembles (DE) [18,19] and Bayesian learning via variational inference (VI) [14,15]-and introduce two methods to efficiently combine the decisions from multiple models: namely, confidence merging (CM) and p-variable merging (PM). In both cases, the resulting set predictors satisfy theoretical reliability guarantees.…”