Neuromorphic Split Computing with Wake-Up Radios: Architecture and Design via Digital Twinning

TL;DR

This work proposes a novel architecture that integrates a wake-up radio mechanism within a split computing system consisting of remote, wirelessly connected, NPUs and proposes a novel methodology that leverages the use of a digital twin, i.e., a simulator, of the physical system coupled with a sequential statistical testing approach known as Learn Then Test (LTT) to provide theoretical reliability guarantees.

Abstract

Neuromorphic computing leverages the sparsity of temporal data to reduce processing energy by activating a small subset of neurons and synapses at each time step. When deployed for split computing in edge-based systems, remote neuromorphic processing units (NPUs) can reduce the communication power budget by communicating asynchronously using sparse impulse radio (IR) waveforms. This way, the input signal sparsity translates directly into energy savings both in terms of computation and communication. However, with IR transmission, the main contributor to the overall energy consumption remains the power required to maintain the main radio on. This work proposes a novel architecture that integrates a wake-up radio mechanism within a split computing system consisting of remote, wirelessly connected, NPUs. A key challenge in the design of a wake-up radio-based neuromorphic split computing system is the selection of thresholds for sensing, wake-up signal detection, and decision making. To address this problem, as a second contribution, this work proposes a novel methodology that leverages the use of a digital twin (DT), i.e., a simulator, of the physical system, coupled with a sequential statistical testing approach known as Learn Then Test (LTT) to provide theoretical reliability guarantees. The proposed DT-LTT methodology is broadly applicable to other design problems, and is showcased here for neuromorphic communications. Experimental results validate the design and the analysis, confirming the theoretical reliability guarantees and illustrating trade-offs among reliability, energy consumption, and informativeness of the decisions.

Figures (7)

• Figure 1: In this work, we propose a low-power wake-up radio aided wireless split computing system, which operates through the following steps. (i) Signal detection at the Tx: The sensor captures a time-series data $\hbox{\boldmath{$u$}}$ for $L^{\rm max}$ time steps, containing meaningful information from an unknown time $l^{\rm start}$ for a duration of $L^{\rm sig}$. A change detector is applied simultaneously to determine whether the sensed sequence contains a signal of interest. (ii) Wake-up signal transmission: If a signal of interest is detected at some specific time, the wake-up Tx and encoding SNN are turned on, and a WUS is transmitted by the wake-up Tx. (iii) Data transmission: After a fixed delay following the transmission of the WUS, the input signal $\{\hbox{\boldmath{$u$}}_l\}_{l=l^{\rm start}}^{L^{\rm max}}$ is processed by the encoding NPU, and the output spikes are modulated using impulse radio (IR) and transmitted over the wireless channel to the main Rx. (iv) Wake-up signal reception and activation of the main radio: The WUS is detected by the wake-up Rx, leading to the activation of the main Rx. (v) Decision Making: Upon waking up of the main Rx, the NPU at the receiver side processes the signal received by the main Rx to make an inference decision. Our goal is to optimize the threshold applied by signal detection, WUS detection, and decision making in order to provably control the average loss of the decision to a predetermined level, while minimizing the overall energy consumption.
• Figure 2: Hyperparameters optimization is carried out by leveraging a dataset $\mathcal{D}$ of data examples, as well as access to a simulator of the channel implemented in a digital twin. The simulator produces channel variables $\Tilde{\mathbf{h}}$ with a distribution $\Tilde{p}(\mathbf{h})$ that is generally mismatched with respect to the true distribution $p(\mathbf{h})$. In a first phase, the digital twin uses the simulator to pre-select a subset $\Lambda$ of candidate hyperparameters $\hbox{\boldmath{$\lambda$}}$. In a second phase, on-air calibration leverages transmission on the actual system (physical twin) to identify a solution $\hbox{\boldmath{$\lambda$}}^*$ that is guaranteed to satisfy the constraint in \ref{['eq:goal']}.
• Figure 3: Illustration of the working flow of the Tx and Rx. (a) WUS and data transmission: The WUS is sent by the wake-up Tx once the signal of interest is detected at time $\hat{l}^{\rm start}$, followed by the transmission of the pilot and the data after $L^{\rm d}$ delay. (b) Correct wake-up: The wake-up receiver detects the WUS at time $\hat{l}^{\rm det}$ and activates the main receiver. The main receiver takes $\delta^{\rm wake}$ time to be fully activated. Importantly, the wake-up time of the main receiver precedes the commencement of data transmission. (c) Delayed wake-up: In this scenario, the main receiver wakes up after the data transmission has initiated, leading to data loss.
• Figure 4: Illustration of the proposed DT-LTT design strategy: During the first phase of pre-selection, the digital twin determines a subset of candidate hyperparameters that yield estimated $\hat{E}^{\rm DT}(\hbox{\boldmath{$\lambda$}})+\gamma \hat{I}^{\rm DT}(\hbox{\boldmath{$\lambda$}})$ and loss $\hat{L}^{\rm DT}(\hbox{\boldmath{$\lambda$}})$ on the Pareto frontier. Then, during on-air calibration, the physical twin transmits on the actual channel to test the candidates in set $\Lambda$ sequentially, stopping when the estimated loss crosses a threshold $\psi(\alpha, \delta)$. The solution $\hbox{\boldmath{$\lambda$}}^*$ is then obtained by choosing the value of $\hbox{\boldmath{$\lambda$}}$ that yields the minimum estimated objective $\hat{E}^{\rm PT}(\hbox{\boldmath{$\lambda$}})+\gamma \hat{I}^{\rm PT}(\hbox{\boldmath{$\lambda$}})$, while guaranteeing the inequality $\hat{L}^{\rm PT}(\hbox{\boldmath{$\lambda$}})< \psi(\alpha, \delta)$.
• Figure 5: Illustration of the operation of DT-LTT: (a) Digital twin-based pre-selection: Expected loss $\hat{L}^{\rm DT}(\hbox{\boldmath{$\lambda$}})$ versus weighted sum $\hat{E}^{\rm DT}(\hbox{\boldmath{$\lambda$}})+\gamma \hat{I}^{\rm DT}(\hbox{\boldmath{$\lambda$}})$ estimated at the digital twin using dataset $\mathcal{D}^{\rm DT}$ and channel simulators via \ref{['erisk']}, \ref{['epower']} and \ref{['esize']}, with each point corresponding to the evaluation of a hyperparameter $\hbox{\boldmath{$\lambda$}}$ in a grid of options. The red points represent the selected candidates, which lie on the Pareto frontier $\Lambda$. (b) On-air calibration: Expected loss $\hat{L}^{\rm PT}(\hbox{\boldmath{$\lambda$}})$ versus weighted sum $\hat{E}^{\rm PT}(\hbox{\boldmath{$\lambda$}})+\gamma \hat{I}^{\rm PT}(\hbox{\boldmath{$\lambda$}})$ estimated using actual wireless transmissions with each point representing the evaluation for one of the hyperparameters $\hbox{\boldmath{$\lambda$}}$ in the set $\Lambda$. The star is the hyperparameter selected by on-air calibration with $\alpha=0.2$, $\delta=0.05$, $\gamma=10$ and $L^{\rm max}=60$.

Theorems & Definitions (2)

• Theorem 1: Reliability of DT-LTT
• proof