# Train Me If You Can: Decentralized Learning on the Deep Edge
###### Abstract  
The end of Moore's Law aligned with data privacy concerns is forcing machine learning (ML) to shift from the cloud to the deep edge. In the next-generation ML systems, the inference and part of the training process will perform at the edge, while the cloud stays responsible for major updates. This new computing paradigm, called federated learning (FL), alleviates the cloud and network infrastructure while increasing data privacy. Recent advances empowered the inference pass of quantized artificial neural networks (ANNs) on Arm Cortex-M and RISC-V microcontroller units (MCUs). Nevertheless, the training remains confined to the cloud, imposing the transaction of high volumes of private data over a network and leading to unpredictable delays when ML applications attempt to adapt to adversarial environments. To fill this gap, we make the first attempt to evaluate the feasibility of ANN training in Arm Cortex-M MCUs. From the available optimization algorithms, stochastic gradient descent (SGD) has the best trade-off between accuracy, memory footprint, and latency. However, its original form and the variants available in the literature still do not fit the stringent requirements of Arm Cortex-M MCUs. We propose L-SGD, a lightweight implementation of SGD optimized for maximum speed and minimal memory footprint in this class of MCUs. We developed a floating-point version and another that operates over quantized weights. For a fully-connected ANN trained on the MNIST dataset, L-SGD (float-32) is 4.20\(\times\) faster than the SGD while requiring only 2.80% of the memory with negligible accuracy loss. Results also show that quantized training is still unfeasible to train an ANN from the scratch but is a lightweight solution to perform minor model fixes and counteract the fairness problem in typical FL systems. federated learning; machine learning; artificial neural networks; artificial intelligence; machine learning algorithms; intelligent systems; internet of things; arm cortex-M  
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a lack of trust from end-users as well as to difficulty in complying with the general data protection regulation (GDPR) [18]. Cloud dependability also makes it challenging to deploy smart IoT applications in areas with unreliable network connectivity [17]. Given this background, academia and industry have been developing software and hardware solutions to shift intelligence to the deep edge [27; 28; 29; 30], providing it with the ability to autonomously infer and adapt to the surrounding environment, while leveraging the cloud to major model updates [31; 32]. This new paradigm, referred to as federated learning (FL), considers that the inference and part of the training mechanisms are performed at the edge, leaving the server with the responsibility of merging the minor model updates performed at the edge [33; 34; 35; 36; 37; 38; 39; 40; 41]. FL not only addresses the stringent requirements for real-time decisions, alleviating network congestion and cloud workload but also enables the deployment of smart IoT applications in regions with unreliable network connectivity. FL also comes with additional security guarantees as user data are kept on the data source [18; 42]. Recent advances already enable the inference pass of ML services on low-power microcontroller units (MCU) [27; 43], opening a new aisle of smart applications, such as low-power image processing and segmentation, keyword spotting, and predictive maintenance [44]. The most recent Arm Cortex-M and RISC-V (RV32 IMCXpulp) MCUs feature instruction set architectures (ISA) that support single instruction multiple data (SIMD) were tuned to speed up the inference pass of quantized artificial neural networks (ANNs) with minimal accuracy loss [45; 46]. Supported by open-source libraries such as CMSIS-NN [17] and PULP-NN [47], porting a trained ANN to these families of MCUs is a feasible process.