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PrototypeNAS: Rapid Design of Deep Neural Networks for Microcontroller Units
Mark Deutel, Simon Geis, Axel Plinge
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Summary
PrototypeNAS is a zero-shot neural architecture search (NAS) framework designed to automate the selection, compression, and specialization of deep neural networks (DNNs) for resource-constrained microcontroller units (MCUs). It utilizes a three-step process: a constrained multi-objective optimization using an ensemble of zero-shot proxies, Hypervolume subset selection to identify Pareto-optimal models, and a dataset evaluator for training, pruning, and quantization. The method effectively decouples architecture design from training, enabling rapid deployment of efficient DNNs on edge hardware.
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PrototypeNAS → targets → Microcontroller Units
confidence 100% · we propose PrototypeNAS, a zero-shot NAS method to accelerate and automate the selection, compression, and specialization of DNNs to different target microcontroller units (MCUs).
PrototypeNAS → uses → Hypervolume subset selection
confidence 100% · we propose the use of Hypervolume subset selection to distill DNN architectures from the Pareto front
PrototypeNAS → comparedto → TinyNAS
confidence 95% · We also compare PrototypeNAS to two other hardware-aware NAS methods, TinyNAS (MCUNet)
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Abstract
Abstract:Enabling efficient deep neural network (DNN) inference on edge devices with different hardware constraints is a challenging task that typically requires DNN architectures to be specialized for each device separately. To avoid the huge manual effort, one can use neural architecture search (NAS). However, many existing NAS methods are resource-intensive and time-consuming because they require the training of many different DNNs from scratch. Furthermore, they do not take the resource constraints of the target system into account. To address these shortcomings, we propose PrototypeNAS, a zero-shot NAS method to accelerate and automate the selection, compression, and specialization of DNNs to different target microcontroller units (MCUs). We propose a novel three-step search method that decouples DNN design and specialization from DNN training for a given target platform. First, we present a novel search space that not only cuts out smaller DNNs from a single large architecture, but instead combines the structural optimization of multiple architecture types, as well as optimization of their pruning and quantization configurations. Second, we explore the use of an ensemble of zero-shot proxies during optimization instead of a single one. Third, we propose the use of Hypervolume subset selection to distill DNN architectures from the Pareto front of the multi-objective optimization that represent the most meaningful tradeoffs between accuracy and FLOPs. We evaluate the effectiveness of PrototypeNAS on 12 different datasets in three different tasks: image classification, time series classification, and object detection. Our results demonstrate that PrototypeNAS is able to identify DNN models within minutes that are small enough to be deployed on off-the-shelf MCUs and still achieve accuracies comparable to the performance of large DNN models.
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- Source: https://arxiv.org/abs/2603.15106v1
- Canonical: https://arxiv.org/abs/2603.15106v1
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PrototypeNAS: Rapid Design of Deep Neural Networks for Microcontroller Units Mark Deutel, Simon Geis, and Axel Plinge Fraunhofer Institute for Integrated Circuits, Fraunhofer IIS, Germany mark.deutel, simon.geis, axel.plinge@iis.fraunhofer.de Abstract. Enabling efficient deep neural network (DNN) inference on edge de- vices with different hardware constraints is a challenging task that typically re- quires DNN architectures to be specialized for each device separately. To avoid the huge manual effort, one can use neural architecture search (NAS). However, many existing NAS methods are resource-intensive and time-consuming because they require the training of many different DNNs from scratch. Furthermore, they do not take the resource constraints of the target system into account. To address these shortcomings, we propose PrototypeNAS, a zero-shot NAS method to ac- celerate and automate the selection, compression, and specialization of DNNs to different target microcontroller units (MCUs). We propose a novel three-step search method that decouples DNN design and specialization from DNN training for a given target platform. First, we present a novel search space that not only cuts out smaller DNNs from a single large architecture, but instead combines the structural optimization of multiple architecture types, as well as optimization of their pruning and quantization configurations. Second, we explore the use of an ensemble of zero-shot proxies during optimization instead of a single one. Third, we propose the use of Hypervolume subset selection to distill DNN architectures from the Pareto front of the multi-objective optimization (MOO) that represent the most meaningful tradeoffs between accuracy and floating-point operations (FLOPs). We evaluate the effectiveness of PrototypeNAS on 12 different datasets in three different tasks: image classification, time series classification, and object detection. Our results demonstrate that PrototypeNAS is able to identify DNNs within minutes that are small enough to be deployed on off-the-shelf MCUs and still achieve accuracies comparable to the performance of large DNN architec- tures. Keywords: Neural Architecture Search · Multi-Objective Optimization · Effi- cient AI · Microcontrollers. 1 Introduction We address the problem of quickly and efficiently designing and training deep neural networks (DNNs) for inference on resource-constrained microcontroller units (MCUs). DNNs have become the de facto standard for data analysis and machine learning tasks. However, with the growth of DNNs in both size and computational cost over the last years, running DNNs, especially on a diverse set of different resource constrained em- bedded systems and at low latency, has become a major challenge. arXiv:2603.15106v1 [cs.AI] 16 Mar 2026 2M. Deutel et al. To address this problem, we propose PrototypeNAS, a zero-shot neural architecture search (NAS) framework for rapidly designing DNNs for MCUs with different hard- ware and resource constraints. Compared to other hardware-aware NAS frameworks, PrototypeNAS is novel in three aspects. First, it uses an ensemble of zero-shot proxies that compete as objectives in a multi-objective optimization (MOO) rather than being weighted and linearized into a single ensemble proxy score. Second, it implements a novel search space that combines architecture selection, size and structure optimiza- tion, and optimization of pruning and quantization configuration, instead of optimizing them as unrelated problems. Third, it introduces Hypervolume subset selection to fur- ther refine the Pareto optimal models from optimization to a set of 3-5 models that cover the most meaningful tradeoffs between accuracy and resource consumption. Additionally, in our extensive evaluation, we demonstrate the effectiveness and ver- satility of PrototypeNAS by using it to find optimized DNNs deployable on an ARM Cortex-M MCU for 12 datasets from three tasks: image classification, time series clas- sification, and object detection. We also compare PrototypeNAS to two other hardware- aware NAS methods, TinyNAS (MCUNet) [22] and NATS-Bench [8]. On average, the DNN architectures found by PrototypeNAS outperformed the ones proposed by the other two frameworks by 5% in accuracy on the CIFAR10 datasets. As a result, PrototypeNAS is a resource- and time-efficient way to search for DNN architectures without having to train hundreds of DNN architectures to find a single good candidate. Instead, PrototypeNAS reduces the training to only 3-5 DNN candi- dates while still considering hundreds of architectures in its search. 2 Related Work NAS is a set of techniques used to automate the DNN architecture design process, gen- erally by solving an optimization problem. While the initial focus was on maximizing accuracy and using reinforcement learning to control the search process [37,4], more recently, hardware-aware NAS [31,35], i.e., considering memory and inference speed in addition to accuracy as a MOO, has become a major focus of research. A subset of this work focuses more specifically on NAS for resource-constrained devices such as MCUs [5,22,6]. In addition, zero-shot NAS [19,33,23,27,15,21] has received considerable attention to address the problem of having to train a large number of DNN candidates, for ex- ample, when using black-box optimization [6] or reinforcement learning [37,4]. All zero-shot NAS techniques rely on using a proxy metric for accuracy to avoid training. As a result, a large number of different zero-shot proxies have been proposed, focusing on different features that can be computed from an untrained DNN, such as the Pearson correlation matrix of the intermediate feature maps [15] or the number of linear regions in the input space [27]. In addition, zero-shot NAS techniques, especially when used for hardware-aware NAS, often propose the use of a very large pre-trained “super-net” architecture from which smaller networks more suited to the constraints of the target hardware are then derived and tuned [5]. While zero-shot NAS works to find a sufficiently good architecture in a relatively short time, there are still challenges to overcome. Zero-shot proxies are known to be PrototypeNAS: Rapid Design of DNNs for MCUs3 Hypervolume Subset Selection Top-k selection from the Pareto front of the multiobjective optimization using Hypervolume subset selection. Hypervolume subset selection implemented with evolutionary search. Architectural Prototype Exploration Multi-objective optimization with FLOPs and zero-shot proxies as objectives Combination of architecture, structural, and size (pruning configuration) optimization in a single combined search space Dataset Evaluator Top-k selection can be trained, pruned, and quantized for many datasets for the same MCU Different trainers can be used to cover a variety of tasks like classification or object detection. 123 Fig. 1: Schematic of the three step pipeline of PrototypeNAS. imprecise and bias certain DNN architectures [16,3], often leading to poor correlation with actual training accuracy. Furthermore, the reliance on a single large supernet means that the resulting search space is limited to exploitation around a pre-existing optimum and never explores the full architectural landscape of DNNs. In parallel to NAS, other techniques for DNN compression have been explored. A significant number of efficient human-engineered DNN architectures have been pro- posed over the years. Starting with SqueezeNet [13], MobileNet [30], and Efficient- Net [32], to more recent designs such as MCUNet [22], which specifically targets microcontrollers, and ConvNeXt [25], which combines a traditional CNN with trans- former elements. In addition, pruning and quantization [9,7] have become common techniques for designing efficient DNN architectures for resource-constrained MCUs. 3 Method PrototypeNAS is a zero-shot NAS method that enables rapid exploration of optimized DNNs for MCU deployment by decoupling design space exploration, i.e., the search for prototypical network architectures and their compression configuration, from training on the target datasets. We give a schematic overview of PrototypeNAS, which is a three-step method, in Fig. 1. 1 First, a constrained multi-objective optimization is performed with the en- semble of zero-shot proxies and the number of floating-point operations (FLOPs) as a proxy for the computational cost of DNN inference as objectives. The optimization is constrained by the memory limits of the target MCU to ensure that the exploration focuses only on DNN architectures that can actually be deployed on the target. The search space of the optimization combines both architectural selection from a pool of predefined baseline architectures and their structural and size optimization, i.e., pruning parameter configuration, into a single search space. 2Second, a top-k selection is per- 4M. Deutel et al. Table 1: Search space X of the MOO,∀i∈0, 1, 2, 3 resulting in 14 tunable hyperpa- rameters in total. OptimizationHyperparameterTypeRange/Values Architecturebaseline architecturecategoricalTask dependent Structural group depth icategorical[0, 1, 2, 3] kernel & stride icategorical [[3, 2],[3, 1],[5, 2],[5, 1],[7, 2],[7, 1]] Size width multipliercontinuous[0.1, 1.0] pruning sparsity icontinuous[0.1, 0.9] formed from the resulting Pareto set using Hypervolume subset selection.3Finally, the resulting selection of optimized DNN architectures is trained, pruned, and quantized on the target datasets. In the following sections, we describe each of the three steps of PrototypeNAS in more detail. 3.1 Architectural Prototype Exploration We formulate the architectural prototype exploration as a constrained MOO in Eq. (1). The objectives are to minimize the number of FLOPs of a model flops(x) while maxi- mizing an ensemble of four proxy metrics prox i (x) with i∈0,..., 3. The four proxies used in this work are MeCo [15], ZiCo [21], NASWOT [27], and SNIP [19], which we selected due to the different DNN features they use for evaluation, compare [12]. The constraints of the optimization ram max , rom max , and flops max are derived from the hard- ware limits of the targeted MCU. We designed the search space from which PrototypeNAS samples DNNs, focusing on emulating the process that a specialist makes when designing an efficient DNN ar- chitecture for an MCU. Based on this premise, we make the following assumptions: First, there is a set of baseline architectures from which DNN candidates can be de- rived. Second, each of the baseline architectures can be abstracted as follows: An initial layer pattern, followed by a set of repeatable layer patterns (superblocks), followed by a classifier. Third, a pruning and quantization scheme is defined that is executed during training to dynamically compress and scale down the model during training. Based on these three assumptions, we define the search space X in Table 1. min x∈X flops(x),−prox 1 (x),...,−prox 3 (x) s.t. ram(x)≤ ram max rom(x)≤ rom max flops(x)≤ flops max (1) In the following, we describe how X is structured and how DNN prototypes can be created from it, see Fig. 2 for a schematic overview. The architecture hyperparameter allows the optimizer to choose a baseline DNN architecture from a pool of predefined PrototypeNAS: Rapid Design of DNNs for MCUs5 Group 3 Baseline Architecture Group Depth, i.e., number of Superblocks Pruning Sparsity of Superblocks Layer Output Width Multiplier Kernel & Stride of first layer in Superblock Group Depth, i.e., number of Superblocks Pruning Sparsity of Superblocks Kernel & Stride of first layer in Superblock Group 0 ... Architecture Optimization Structural Optimization Size Optimization Fig. 2: The proposed search space and how a DNN prototype can be created from it. Each baseline architecture consists of repeatable superblocks, i.e., a predefined pattern of layers, organized in the search space into four groups to be optimized separately. architectures. In the scope of this work, six DNN architectures are supported for im- age classification, two architectures for time series classification, and one for object detection (see Section 4 for details). The backbone of the selected baseline DNN is then split into repeatable superblocks as described above, for example depthwise separable convolutions in MobileNetV2. How each architecture is split into superblocks is defined prior. The superblocks are then organized into four groups. Each group contains at least one super block and up to four additional blocks, which is controlled for each group via the group depth hyper- parameter. In addition, each group has an optimizable kernel & stride hyperparameter which is used to configure the first convolution of each superblock of the group. To- gether, these hyperparameters allow structural optimization of the baseline DNNs. The part of the search space allowing for size optimization of the baseline DNNs consists of the width multiplier and pruning sparsity hyperparameters. The width mul- tiplier parameter controlls the initial size of the baseline DNN architecture at the begin- ning of training by scaling the output channels in all convolutional layers uniformly. In addition, an iterative pruning schedule is defined that will be executed during training. For each of the four groups of superblocks, a separate pruning sparsity hyperparameter controls the target percentage of channels to be removed by pruning. The objective function evaluation for a set of hyperparameters proposed by the op- timizer consists of three steps: First, the selected baseline architecture is initialized and configured according to the structural optimization. Second, pruning and quantization are applied (without any training) to query parameter and size reduction. Third, the resulting model is translated to C code to get the actual ROM and RAM usage when deployed on te targeted MCU. To calculate the number of FLOPs of a DNN, Pytorch’s built-in profiler is used. Since the objective function evaluation does not require any training due to the use of zero-shot proxies, sampling is both resource and time effi- cient, allowing for rapid exploration of the search space. 3.2 Hypervolume Subset Selection We obtain a set of Pareto-optimal architecture and compression configurations from the prototype exploration described in the previous section. The size of this set can be be- 6M. Deutel et al. tween one and as many solutions as there were DNNs explored during the optimization. However, in practice, a set of 3-5 architectural tradeoffs is usually sufficient for a deci- sion maker to select a DNN for a given use case. A smallest model, a model with the highest accuracy, and 2-3 tradeoffs in between. To avoid situations where large Pareto sets proposed by the optimization have to be trained, compressed, evaluated, and finally presented to the decision maker, we implemented a Hypervolume subset selection algo- rithm based on evolutionary programming and inspired by algorithms like [1] that use Hypervolume as a selection criterion. Let H(S) be the Hypervolume indicator of a solution set S as described in [36]. We formulate an optimization problem in Eq. (2) which maximizes H(S) of a subset A⊂ P with k∈0, 1,...,|P| where P is the Pareto set resulting from the prototype exploration. H(A) = max B⊂P |B|=k H(B)(2) We solve this optimization problem using a greedy selection strategy that retains solutions with higher Hypervolume contributions. First, we encode P as a binary gene g, where each bit in g corresponds to a solution in P, which is either set to 1 if the sample should be part of B, or 0 if not. Consequently, for each gene, only k bits can be set to 1, while all other bits are set to 0. We then evolve an initial population G∈g 0 ,g 1 ,...,g n−1 of size n, using mutation and crossover operators, and the Hy- pervolume indicator to evaluate the fitness of each g∈ G. Naturally, crossover, mutation, and the initial generation of G can lead to the cre- ation of “invalid” genes, i.e. genes with more than k bits set to 1. Our algorithm greedily repairs such genes. If there are less than k bits set to 1, it iteratively sets bits to 1 until exactly k bits are set to 1. This has no negative effect on the fitness of the gene, since the Hypervolume can only increase or stay the same with additional solutions added, but never decrease. If there are more than k bits set to 1, the algorithm instead tries to set additional bits to zero while keeping the Hypervolume as high as possible. To do this, it sets every bit that is 1 to 0 one by one and recalculates the Hypervolume. Then the algorithm sorts all bits by their calculated Hypervolumes in ascending order. Finally, it selects the top k bits whose removal has the largest negative impact on the fitness of the gene, while setting all other bits to 0. In all our experiments, we configured the Hypervolume subset sampling algorithm with an initial population size of 2000, a mutation rate of 0.3, and ran it for 10 000 generations. 3.3 Dataset Evaluator To train, prune, and quantize the subsets of DNNs designed by PrototypeNAS, we im- plement two dataset evaluators. One evaluator is for training image and time series classification tasks using Pytorch Lightning, while the other one is for training the ob- ject detection task with the YOLOv5 framework. As baseline architectures for Proto- typeNAS we used implementations provided by torchvision and torchaudio with slight PrototypeNAS: Rapid Design of DNNs for MCUs7 modifications so that they can be generated from a set of hyperparameters from the search space introduced in Section 3.1. We also implemented iterative structure pruning and quantization for both trainers. We used post-training static quantization (PTQ) for the image classification and ob- ject detection tasks, and quantization-aware training (QAT) with 15 additional training epochs for the time series classification task. Since PTQ is applied to DNNs after train- ing, it is generally faster to use and less computationally intensive, while QAT is more resource intensive since it is applied during training, but also more accurate. While we found during our experiments that PTQ worked reliably well for the two image-based tasks, we experienced significant drops in accuracy for the time series datasets when using PTQ. As a result, we used QAT for the time series datasets, as it yielded signif- icantly better accuracies. This is most likely due to QAT’s ability to better account for the varying activation ranges resulting from the time series input. 4 Evaluation We evaluate PrototypeNAS on three different tasks and 12 datasets in total: image clas- sification for the CIFAR10 [18], CIFAR100 [18], GTSRB [11], Flowers [28], Birds [34], Cars [17], Pets [29], and ArxPhotos314 1 datasets, time series classification for the Daliac [20], MAFULDA 2 , and BitBrain Sleep [26] datasets, and person detection using a subset of COCO [24]. For the three tasks, we first performed the prototype exploration as described in Sec- tion 3.1 for 500 trials, then performed the Hypervolume subset selection as described in Section 3.2, and finally evaluated the top-5 selection of each of the tasks on the respec- tive datasets. For training, we used the same configuration for all datasets: A batch size of 48, stochastic gradient descent with a learning rate of 0.001 and a momentum of 0.9, and 100 training epochs. We provide detailed insight and discussion of our results in Section 4.1 and 4.3. Furthermore, in Section 4.2 we discuss the precision of the proxy ensemble used in PrototypeNAS during exploration. Finally, in Section 4.4 we give a comparison of PrototypeNAS to two other hardware aware NAS frameworks, TinyNAS (MCUNet) [22] and NATS-Bench [8]. 4.1 Results for Image and Time Series Classification Fig. 3 shows the results of the prototype exploration for image and time series classi- fication and the four proxy scores MeCo, NASWOT, SNIP, and ZiCo 3 . We performed separate optimizations for the image and time series datasets because we used differ- ent sets of baseline architectures for the two tasks, four DNN architectures for image classification and two for time-series classification, which we denote in the plots with different colors and markers. For image classification, our baseline set includes Mo- bileNetV2 [30], ResNet18 [10], Squeezenet [13], and MbedNet (our own DNN archi- tecture derived from MobileNet), see Fig. 3a. For time series classification we used 1 https://web.arx.net 2 https://w02.smt.ufrj.br/~offshore/mfs/page_01.html 3 DNNs and pre-trained weights: https://doi.org/10.5281/zenodo.18878249 8M. Deutel et al. 0246 Compute [FLOPs] 1e8 −20 −15 −10 −5 0 MeCo MobileNetV2 MbedNet ResNet SqueezeNet Selected 0246 Compute [FLOPs] 1e8 13 14 15 NASWOT 0246 Compute [FLOPs] 1e8 0 1 2 3 4 SNIP 1e4 0246 Compute [FLOPs] 1e8 2 3 4 5 ZiCo 1e2 (a) Image classification 024 Compute [FLOPs] 1e8 −40 −30 −20 −10 0 MeCo InceptionTime MbedNet Selected 024 Compute [FLOPs] 1e8 11 12 13 14 NASWOT 024 Compute [FLOPs] 1e8 0 2 4 6 SNIP 1e3 024 Compute [FLOPs] 1e8 0.2 0.4 0.6 0.8 1.0 ZiCo 1e3 (b) Time series classification Fig. 3: Optimization results. The top-5 DNNs selected from the Pareto front by Hyper- volume subset selection are marked with red circles. InceptionTime [14] and a version of MbedNet where we replaced all 2D convolutions with their 1D counterparts, see Fig. 3b. For image classification, we used a 128× 128 pixel input for all experiments, while for the time series classification experiments we split the input into windows of constant length and used them without any further pre- processing. After optimization, we identified five models from the final Pareto front using Hypervolume subset selection as described in Section 3.2 and mark the selected models in Fig. 3 with red circles. For both image and time series optimization, the results in Fig. 3 show that the four proxies rank the base architectures of their respective search spaces differently. For example, SNIP gave a significantly higher score to almost all architectural variants of SqueezeNet than any of the other three proxies in Fig. 3a. Another example of this apparent “disagreement” among the proxies can be seen in Fig. 3b, where NASWOT and MeCo rank MBedNet higher than InceptionTime, while the other two proxies do the opposite. Another observation that can be made is that all DNNs of a single architecture type cluster around their unmodified baseline architecture in the target space. This is not un- expected, since once a baseline architecture is selected, the other hyperparameters in PrototypeNAS’s search space focus on modifying the structure of the baseline architec- ture within the limits of its predefined superblocks, or scaling the architecture in width, but do not fundamentally change its design. This is intentional, as the goal of Proto- typeNAS is to quickly fine-tune a DNN to fit the constraints of a given MCU and not to come up with completely new DNN designs from scratch. Therefore, another way to interpret the results in Fig. 3 is that each baseline architecture represents a local opti- mum, with the search space being designed in a way to encourage an efficient search around it. PrototypeNAS: Rapid Design of DNNs for MCUs9 Table 2: Test accuracy of the trained, pruned, and quantized DNNs found by Proto- typeNAS for the image datasets. Latency and energy was measured on an iMXRT1062 Cortex-M7 MCU. Optim. Index210283190311237 ArchitectureMbedNetMbedNetSqueezeNetSqueezeNetMbedNet Quantized Test Accuracy [%] CIFAR1091.892.590.390.093.7 CIFAR10067.470.566.563.772.3 ArxPhotos31490.895.497.479.593.6 Flowers88.991.682.986.393.3 Birds62.865.759.555.669.9 Pets99.899.897.596.199.9 Cars64.864.159.855.276.4 GTSRB96.396.195.897.095.5 Compute [MFLOPs]50.170.0105.0147.5151.0 ROM [kB]605.4774.9758.4434.7356.5 RAM [kB]111.7118.3364.7281.6189.7 Latency [ms]224.1± 0.1312.9± 0.1367.1± 0.1447.2± 0.1753.2± 0.1 Energy [mJ]77.6± 8.6108.6± 10.0 126.0± 12.7 156.3± 16.8 254.5± 13.7 Regarding the difference in proxy scoring observed in our results, we point to the general consensus found in related work that zero-shot proxies are often imprecise and tend to favor certain architectures [16,3]. As a result, and similar to related work such as [12], this motivates us to consider the evaluation of multiple proxies to guide our optimization, rather than relying on a single proxy. In constrast, we do not attempt to weight and linearize the different proxies to form a new proxy score, but instead treat them as competing objectives in our MOO. As a result, the top k = 5 architectures selected by the Hypervolume subset selection at the end of the optimization do not directly follow the ranking of any of the individ- ual proxies and FLOPs, but are instead derived from the Pareto front between FLOPs and all four proxies. As a result, PrototypeNAS avoids being biased toward particular architectures in its search and achieves a balanced evaluation. We show the test accuracy on all evaluated datasets of the five trained, pruned, and quantized DNN prototypes selected by Hypervolume subset selection in Table 2 (image classification) and Table 3 (time series classification) sorted in ascending order by FLOPs. For each of the five DNNs shown in the two tables, we additionally report the base architecture from which the prototype was derived, the model’s RAM and ROM requirements in kilobytes, reflecting the actual memory requirements on the target MCU, as well as the average inference latency and energy consumption of the DNNs when executed on an iMXRT1062 Cortex-M7 MCU. For each dataset, we highlighted the model with the highest test accuracy. For time series classification, we trained with randomly initialized weights, while for image classification, we performed 50 epochs of ImageNet pre-training. 10M. Deutel et al. Table 3: Test accuracy of the trained, pruned, and quantized DNNs found by Prototype- NAS for the time series datasets. Latency and energy was measured on an iMXRT1062 Cortex-M7 MCU. Optim. Index22422673273347 ArchitectureMbedNetMbedNetInceptionTimeMbedNetInceptionTime Quantized Test Accuracy [%] BitBrain83.787.281.788.078.9 Mafaulda96.898.397.497.898.5 Daliac95.997.197.297.096.1 Compute [MFLOPs]36.343.2101.5123.5215.3 ROM [kB]149231571337978 RAM [kB]246244251252250 Latency [ms]162.3± 0.1183.6± 0.1447.2± 0.1467.9± 0.3635.0± 1.4 Energy [mJ]55.8± 5.763.7± 6.4156.0± 16.7 165.8± 15.9 227.6± 17.6 For both the image and time series classification tasks, the selection of DNNs found by PrototypeNAS achieved accuracies competitive with or better than related embedded DNN architectures, see also Section 4.4 for a direct comparison of our approach with other NAS methods. Furthermore, while a correlation between FLOPs and accuracy can be observed within an architecture type, e.g. both the MbedNet-based architec- tures 210, 283, and 237 and the SqueezeNet-based architectures 190 and 311 in Table 2 show a linear correlation between FLOPs and accuracy, this correlation cannot be ob- served when ranking across the two different architecture types. Since the Prototype- NAS search space optimizes multiple architecture types together, ranking by FLOPs is not sufficient, meaning that the structure and expressiveness of the architectures must also be considered, motivating our use of zero-shot proxies in this work. In addition, when considering resource consumption, we noticed that the RAM re- quirements are very similar across all five DNNs for both the image and time series classification tasks, even though they have very different compute and ROM require- ments. The reason is that the deployment framework we utilize for our experiments reuses memory for multiple intermediate feature maps during inference. This means that the larger initial feature maps typically dominate the overall RAM requirements, since they are often similar in size, as all models share the same input size. As a result, we are only modeling memory requirements as constraints rather than objectives during optimization. Finally, our results show that latency and energy per sample scale linearly with FLOPs, making it a good proxy for optimizing these two metrics without having hardware in the loop. 4.2 Proxy Ensemble Analysis We give a detailed analysis of the proxy “disagreement” we described in the previous section in Table 4. To quantify “disagreement”, we compute the Kendall rank corre- lation coefficient (Kendall’sτ score) to measure the ordinal association between each PrototypeNAS: Rapid Design of DNNs for MCUs11 Table 4: Kendall’sτ scores for the datasets and results shown in Tables 2 and 3 DatasetMeCoNASWOTSNIPZiCoFLOPs CIFAR100.00.0-0.20.60.0 CIFAR1000.00.0-0.20.60.0 ArxPhotos3140.00.00.2-0.20.0 Flowers0.20.2-0.40.40.2 Birds0.00.0-0.20.60.0 Pets0.1-0.40.20.8-0.3 Cars-0.2-0.20.00.8-0.2 GTSRB0.4-0.40.2-0.2-0.4 BitBrain1.00.8-0.6-0.4-0.2 Mafaulda-0.20.00.60.40.6 Daliac0.1-0.10.30.1-0.1 of the four proxy scores and the quantized post-training accuracy we presented in Ta- bles. 2 and 3. In addition, we provide theτ score between FLOPs and accuracy. Theτ ∈ [−1, 1] score quantifies the strength and direction of monotonic relation- ships between two variables based on order, where 1 describes a perfect agreement, i.e. the rankings are identical,−1 a perfect disagreement, i.e. the rankings are the opposite of each other, and 0 denotes no correlation between the rankings of the two variables. Ideally, for zero-shot NAS proxies, aτ score close to 1 is desirable, as this means that DNNs with higher proxy scores will also achieve higher accuracy, while especially a score below 0 is undesirable, as it misguides the NAS algorithm during optimization. In Table 4, it can be seen that none of the four proxies has a consistent and high positiveτ score for all to evaluate datasets. Even worse, the proxies sometimes have a negative relationship with accuracy for some datasets, while working well for others. This can be observed especially well with ZiCo and SNIP. On the other hand, it can be seen that for all datasets, at least one of the four proxies achieved a high positiveτ score and, more importantly, outperformed the score achieved by FLOPs. As a result, we concluded that for our search space (a) using a proxy ensemble is necessary to find a Pareto front of DNNs that, when trained, achieve consistently good ranking across many datasets and prevent biases and inaccuracies of individual proxies from misguiding the exploration and (b) using zero-shot NAS proxies is a better metric to rank models by approximated accuracy than using FLOPs. Finally, in Fig. 4, we show theτ scores calculated among the proxies themselves for the image and time series optimization as heatmaps. Note that the lower and upper triangular matrices describe the same relationship. In Fig. 4a and 4b we observe that for both optimizations the proxies generally did not have a strong relationship with each other, and in the few cases where they did, such as SNIP and ZiCo in Fig. 4b, it was positive, i.e. the proxies were in agreement. These results confirm that the use of this specific ensemble of proxies provides PrototypeNAS with diverse and balanced evalu- ations, thus mitigating the biases and inaccuracies of individual proxies. Furthermore, our results are in agreement with [12], who proposed the same ensemble of proxies. 12M. Deutel et al. 4.3 Object Detection To further demonstrate the flexibility of PrototypeNAS, we applied it to an object de- tection task, specifically person detection, trained on the COCO dataset. We used the YOLOv5 framework, replacing its regular backbone network with MbedNet, which we also used in the results presented in Section 4.1, but keeping the original YOLOv5 de- tector instead of a normal classification head. This allowed us to use the same search space for prototype exploration as for the image classification task, while using the YOLOv5 data augmentation, loss function, anchor boxes, and training hyperparame- ters for dataset evaluation after optimization. We ran two different experiments, one with an input image resolution of 128× 128 targeting the iMXRT1062, i.e. the same MCU we used for the image classification task, and the second with a larger input image resolution of 320× 320 and without any memory or FLOPs constraints targeting a larger Raspberry Pi 5 Cortex-A SoC. Identical to the image and time series classification tasks, we used PrototypeNAS to explore 500 DNNs, from which we selected a subset of k = 5 architectures for evaluation. We show the results between megaflops and mAP 50 , the mean average accuracy of the model at 50% intersection over union, a key performance indicator of object recognition models, for the five architectures selected after optimization and after 100 epochs of training for both the 128× 128 and 320× 320 pixel input resolutions (see Fig. 5). The results show that PrototypeNAS was also able to work for use cases outside of the classification tasks that are usually the sole focus of zero-shot NAS research, providing a good k = 5 selection, where each selected DNN model provides another meaningful tradeoff between the two evaluation metrics. 4.4 Comparison with MCUNet and NATS-Bench We compare PrototypeNAS to two related hardware aware NAS methods on the CI- FAR10 dataset, see Fig. 6. First, a comparison with MCUNet which is a selection of five DNNs searched with TinyNAS [22], and second a comparison with models from the two search spaces proposed in NATS-Bench [8]. MeCo NASWOT SNIP ZiCo MeCo NASWOT SNIP ZiCo 1.00-0.100.160.15 -0.101.00-0.180.31 0.16-0.181.00-0.08 0.150.31-0.081.00 (a) Image classification MeCo NASWOT SNIP ZiCo MeCo NASWOT SNIP ZiCo 1.000.08-0.03-0.37 0.081.00-0.12-0.04 -0.03-0.121.000.39 -0.37-0.040.391.00 (b) Time series classification Fig. 4: Kendall’sτ scores between the four zero-shot proxies for the image and time series classification tasks. PrototypeNAS: Rapid Design of DNNs for MCUs13 0246 Compute [FLOPs] 1e8 0.2 0.3 0.4 0.5 mAP 50 128x128 px 320x320 px Fig. 5: Tradeoff between mAP 50 and FLOPs of the MbedNet YOLO architectures de- signed by PrototypeNAS TinyNAS is a two-step optimization method based on the Mobile search space [31] that is specifically designed for finding DNNs for MCU deployment. TinyNAS first optimizes the Mobile search search space to fit the resource constraints of an MCU and then performs one-shot NAS [2] only on the optimized subset to find an efficient model. The optimized search spaces are found by changing the input resolution and the model width hyperparameters. The quality of the sampled search spaces are evaluated by randomly sampling a number of DNNs from them and evaluating the cumulative distribution function of the sampled DNNs’s FLOPs. In their paper, Lin et al. [22] de- scribe a set of five DNNs (MCUNet in0-in4) which were designed using TinyEngine and for which the authors provide pre-trained weights on ImageNet. We show a comparision between the DNNs designed by PrototypeNAS with MCU- Net for CIFAR10 in Fig. 6a. For PrototypeNAS, we used the same results shown in Table 2, while for MCUNet we fine-tuned the pre-trained ImageNet weights for 100 epochs on CIFAR10. The results show that the five DNN proposed by PrototypeNAS consistently outperform MCUNet in terms of accuracy, sometimes by as much as 5%, at roughly the same computational cost. This shows that compared to other zero-shot search spaces that limit their search to finding subnetworks within a single large super- network architecture, expanding the search space to include pruning and different archi- tecture classes, as is done in PrototypeNAS, allows finding models with higher knowl- edge density within the same resource footprint. NATS-Bench is a NAS benchmark for optimizing both DNN topology and size. NATS-Bench contains two search spaces, one with 15, 625 trained DNN candidates focusing on architecture topology (TSS) and one with 32, 768 DNN candidates focusing on architecture size (S). NATS-Bench uses a cell-based approach where the skeleton of each cell is constructed from remaining blocks with a fixed topology. In the size search space, the number of channels of each cell is optimized, effectively allowing the DNN candidates to scale in width. The topology search space, on the other hand, optimizes a predefined set of operations within each cell, i.e., the combination of layers. The comparison between PrototypeNAS and the two NATS-Bench search spaces is shown in Fig. 6b. For NATS-Bench, we plot all DNNs that have an accuracy higher 14M. Deutel et al. 0.500.751.001.251.50 Compute [FLOPs] 1e8 88 90 92 94 Accuracy [%] 190 210 237 383 311 in0 in1 in2 in3 in4 PrototypeNAS MCUNet (a) TinyNAS (MCUNet in0-in4) 01234 Compute [FLOPs] 1e8 40 50 60 70 80 90 Accuracy [%] PrototypeNAS Size search space (S) Topography search space (TSS) (b) NATS-Bench Fig. 6: Comparison of PrototypeNAS with TinyNAS (left) and NATS-Bench (right) for CIFAR10 than 70% on CIFAR10 after the maximum number of training epochs reported by the authors. For PrototypeNAS, we again use the results shown in Table 2 for CIFAR10, with the only difference that we re-trained the models for 100 epochs on a smaller input image resolution of 69× 69 pixels instead of 128× 128 to more closely match the 32× 32 pixel resolution used by NATS-Bench. We chose 69× 69 pixels because it was the smallest input size supported by all the DNNs. The results show that the DNNs architectures designed by PrototypeNAS are again competitive with the best architectures found by NATS-Bench in both of its search spaces. However, it should be noted that for the NATS-Bench results, each of the 48, 393 DNNs had to be trained separately for up to 200 epochs, while for PrototypeNAS only 5 DNNs had to be trained for 100 epochs to obtain models with similar results. 5 Conclusion We propose PrototypeNAS, a novel three-step zero-shot NAS method for rapidly de- signing DNNs for MCUs. 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