NExUME: Adaptive Training and Inference for DNNs under Intermittent Power Environments
Authors: Cyan Subhra Mishra
Deeksha Chaudhary
Jack Sampson
Mahmut Kandemir
Chita R. Das
Venue: ICLR 2025 Poster (2025)
Keywords: Intermittent Computing
Energy Harvesting
Intermittency Aware Training
Hardware-Software codesign
Primary area: infrastructure, software libraries, hardware, systems, etc.
TL;DR: We introduce NExUME, a framework for training DNNs in settings with intermittent power, like remote sensors. It dynamically adjusts training to fluctuating energy, making networks adaptable and reliable even in energy-constrained environments.

Abstract: The deployment of Deep Neural Networks (DNNs) in energy-constrained environments, such as Energy Harvesting Wireless Sensor Networks (EH-WSNs), introduces significant challenges due to the intermittent nature of power availability. This study introduces NExUME, a novel training methodology designed specifically for DNNs operating under such constraints. We propose a dynamic adjustment of training parameters—dropout rates and quantization levels—that adapt in real-time to the available energy, which varies in energy harvesting scenarios.

This approach utilizes a model that integrates the characteristics of the network architecture and the specific energy harvesting profile. It dynamically adjusts training strategies, such as the intensity and timing of dropout and quantization, based on predictions of energy availability. This method not only conserves energy but also enhances the network’s adaptability, ensuring robust learning and inference capabilities even under stringent power constraints. Our results show a 6% to 22% improvement in accuracy over current methods, with an increase of less than 5% in computational overhead. This paper details the development of the adaptive training framework, describes the integration of energy profiles with dropout and quantization adjustments, and presents a comprehensive evaluation using real-world data. Additionally, we introduce a novel dataset aimed at furthering the application of energy harvesting in computational settings.

Published as a conference paper at ICLR 2025
NEXUME: ADAPTIVE TRAINING AND INFERENCE FOR DNNS UNDER INTERMITTENT POWER ENVIRONMENTS
Cyan Subhra Mishra, Deeksha Chaudhary, Jack Sampson, Mahmut Taylan Knademir, Chita Das CSE Department, The Pennsylvania State University
cyan dmc6955
jms
mtk2 exd12 @psu.edu
ABSTRACT
The deployment of Deep Neural Networks (DNNs) in energy- constraind envi- ronments, such as Energy Harvesting Wireless Sensor Networks (EH-WSNG, introduces significant challenges due to the intermittent nature of power availability. This study introduces NEXUME, a novel training methodology designed specifically for DNNS operating under such constraints. We propose dynamic adjustment of training parameters-dropouu rates and quantization levels-that adapt in real-time the available energy, which varies in energy harvesting scenarios.
This approach utilizes a model that integrates the characteristics of the network architecture and the specific energy harvesting profile. It dynamically adjusts training strategies, such as the intensity and timing of dropout and quantization, based predictions of energy availability. This method not only conserves energy but also enhances the network's adaptability, ensuring robust learning and inference capabilities even under stringent power constraints. Our results show 6% to 22% improvement in accuracy over current methods, with an increase of less than 5% in computational overhead. This paper details the development of the adaptive training framework, describes the integration of energy profiles with dropout and quantization adjustments, and presents comprehensive evaluation using real- world data. Additionally, we introduce a novel dataset aimed at furthering the application of energy harvesting computational settings.
INTRODUCTION
The increasing demand for ubiquitous, sustainable, and energy-efficient computing, combined with advancements in energy harvesting systems, has spurred significant research into battery-less devices (Gobieski et al. 2019 Resch et al. 20200 Mishra al., 2021 Saffari al.) [022]] Afzal et al.) 2022). Such platforms represent the future of the Internet of Things (IoT) and energy harvesting wireless sensor networks (EH-WSNs)) Equipped with modern machine learning (ML) techniques, these devices can revolutionize computing. monitoring, and analytics in remote, risky, and critical environments such oil wells, mines, deep forests, oceans, remote industries, and smart cities. However, the intermittent and limited energy income of these deployments demands optimizations for ML applications the algorithm (Yang al. 2017 Shen et al., 2022 Mendis et al. 202I). orchestration (Maeng & Lucia 2018 Mishra et al. 2021). compilation (Gobieski et al. 2018). and hardware development (Qiu al.) 2020 Islam et al.) 2022, Mishra et al. 2024) layers. Despite these advancements, achieving consistent and accurate inference theeenyeethhrebyyeeee meeting service level objectives (SLOs)-ine in such intermittent environments remains a significant challenge, exacerbated by unpredictable resources, form-factor limitations, and variable computational availability, particularly when employing task-optimized deep neural networks (DNNs).
There are two major problems with performing DNN inference under intermittent power. (I) Energy Variability: Even though DNNs can be tailored to match the average energy income of the energy harvesting (EH) source through pruning, quantization, distillation, or network architecture search (NAS) Yang et al. 2018 2017 Mendis et al., 2021). there no guarantee that the energy income con- sistently meets exceeds this average. When the income falls below the threshold, the system halts the inference and checkpoints the intermediate states (via software or persistent hardware) (Maeng
& Lucia 2018 Quu al. 2020), resuming upon energy recovery. Depending the EH profile,

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this might lead to significant delays and SLO violations. (II) Computational Approximation: To address (I) and maintain continuous operation, EH- HSSS may skip some compute during energy shortfalls by dropping neurons (zero padding) or by approximating computations (quantization). Adding further approximation to save energy atop an already heavily reduced network can propagate emrors through the layers, leading to significant accuracy drops (Islam & Nirjon 2019 Kang et al.. 2022
Lv & Xu 2022. Kang et al. (020), further violating SLOs.
In certain energy-critical scenarios, even EH-WSNs applying state-of-the-art techniques fail to consistently meet SLOs, sometimes skipping entire inferences to deliver results on time. Funda- mentally, while current DNNs can be trained or fine-tuned to fit within given resource budget- be it compute, memory, or energy they are not trained to expect variable or intermittent resource income. Although intermittenc--wware NAS (Mendis et al. 2021). could alleviate certain problems, they often assume fixed resource constraints and do not account for real-time energy fluctuations. Moreover, existing works like Keep in Balance (Yen al. 2023), Stateful Neural Networks (Yen) et al. 2022). ePerceptive (Montanari et al. 2020), and Zygarde (Islam & Nirjon| 2019) address aspects of intermittent computing but do not integrate energy variability awareness directly into the training and inference processes to enable dynamic adaptation. This calls for revisiting the entire training process; we need to train the DNN in such a way that is aware of the intermittency and adapts to it.
Motivated by these challenges, we propose NEXUME (Neural Execution Under InterMittent Environments), novel framework designed specifically for environments with intermittent power and EH-WSNs, with potential applications in any ultra-low-pows inference system. NEXUME uniquely integrates energy variability awareness directly into both the training (DynFit) and inference (DynInfer) processes, enabling DNNs to dynamically adapt computations based on real-time energy availability. This involves an innovative strategy of learning instantaneous energy-aware dynamic dropout and quantization selection during training, and an intermitteneyaawant aware task scheduler during inference. The method includes targeted fine-tuning that not only regularizes the model but also pre- vents overfitting, enhancing robustness to fluctuations in resource availability. Our key contributions can be summarized as follows:
DynFit: novel training optimizer that embeds energy variability awareness directly into the DNN training process. This optimizer allows for dynamic adjustments of dropout rates and quantization levels based on real-time energy availability, thus maintaining learning stability and improving model accuracy under power constraints.
DynInfer: An intermittency- and platform-aware task scheduler that optimizes computational tasks for intermittent power supply, ensuring consistent and reliable DNN operation. DynInfer leverages cetttwar--oomiler--haae
co-design to manage and deploy tasks. With the help of DynFit, DynInfer provides 6%-22% accuracy improvements with S 5% additional compute over existing methods.
Dataset: A first-of-it-kind machine status monitoring dataset, involving multiple types of EH sensors mounted at various locations on a Bridgeport machine to monitor its activity status, facilitating research in predictive maintenance and Industry 4.0 applications.
2 BACKGROUND AND RELATED WORK
Energy Harvesting and Intermittent Computing: The exploding usage of IoTs, connected devices, and wearable electronies project the number of battery operated devices to be 24.1 Billion by 2030 (Insights 2023). This has a significant economic (users, products and data generating dollar value) as well as environmental (battery and e-waste) impact (Mishra et al. [224).. In fact, advances in EH has lead to staggering development in intermittently powered battery-free devices (Maeng Lucia 2018 Gobieski al., 2019: Qiu et al. 2020 Saffari et al., 2021 Atzal et al.) 2022). A typical EH setup consists of 5 components, namely, energy capture (solar panel, thermocouple, etc). power conditioning, voltage regulation (buck or boost converter), energy storage (super capacitor) and compute unit (refer SAppendix for details about each of them). To cater towards the sporadic power income and failures, an existing body of works explores algorithms, orchestration, compiler support, and hardware development (Yang al. 20177|201 Mendis al. [222 Maeng & Lucia 2018, Gobieski et al. 2018 Qiu et al.) 2020; Islam et al. 2022 Mishra et al. 2024; 2021] Ma
al. 2016 2017
Liu al. 2015). Most of these works rely on software checkpointing (static
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and dynamic (Maeng & Lucia, 2018). refer $Appendix C and restore, while some of the prior works developed nonvolatile hardware (Ma et al. 2016 2017) which inherently takes care of the checkpointing. Considering the scope of these initiatives, crucial to acknowledge that, despite the substantial support for energy harvesting and intermittency management, developing intermittency-awwann applications and hardware necessitates multi-dimensional efforts that span from theoretical foundations to circuit design.
Intermittent DNN Execution Traininn::rri As the applications deployed on such EH devices demand analytics, executing DNNs on EH devices and EH-WSNs have become prominent (Lv & Xu 2022
Gobieski et al. 2019 Quu al. 2020 Mishra et al. (02I). However, due to computational constraints, limited memory capacity and restricted operating frequencies, many of these applications fail to complete inference execution with satisfactory SI.Os, despite comprehensive software and hardware support (Mishra et al. (021). While the works relying on nooppeccopooittion or task partition (e.g..
see (Qiu et al. 2020 Gobieski et al.) 2019) and the references therein) ensure "forward progress". they do not guarantee inference completion while meeting SLOs. Optimizing DNNs for the energy constraints (Yang et al. 2018: 2017). or performing early exit and depth-first slicing (Lv & Xu 2022
Islam & Nirjon 2019) does ensure more forward progress, but such approaches compromise accuracy while often imposing scheduling overheads and higher memory footprint. One major issue is, most of the works leverage "pre-existing" DNNs, which are typically designed for running
stable resource
environment, while being deployed on an intermittent environment with pseudo notion of stability via check pponntin,, and therefore, one direction of works (Mendis et al., (02I)) looks for performing network architecture search for intermittent devices. However, this research direction only accounts for fixed lower and upper bounds of energy and compute capacities, overlooking the "sporadic" nature of energy availability and the elasticity of the compute hardware (i.e., the ability to dynamically scale frequency, compute, and memory). Moreover, while the DNN designed to operate within a specific power window, it is not trained to adapt to these fluctuations. Consequently, during extended periods of energy scarcity, the system lacks mechanisms for computational approximation, such as dynamic dropouts (neuron skipping) and dynamic quantization. Essentially. the DNN is trained to manage within a static resource budget, ignoring the "dynamism" " of the resources. In contrast, our work prioritizes the integration of this dynamism in both the network architecture search (NAS) and the training phases, adapting more effectively to fluctuating energy and compute conditions.
NEXUME FRAMEWORK
To address the issues with intermiitency-avare DNN training and inference, we propose NEXUME:
(Neural Execution Under InterMittent Environments). NExUME has three interrelated compo- nents: (1) DynNAS: Intermittency- and platform-aware neural architecture search; (2) DynFit: Intermittency- and platform- aaarf DNN training with dynamic dropouts and quantization; and (3) Intermittency- and platform-aware task scheduling for inference. While each component can individually optimize DNNs for intermittent environments, their combination yields the best results. Our innovation lies in the integration of energy variability awareness directly into both the training and inference processes, enabling dynamic adaptation to real-time energy conditions, which is not addressed by existing methods (Mendis et al., [2021] Yen et al. 2023 2022; Montanari et al.) 2020 Islam& & Nirjon 2019). To search for the best architecture for the given intermittent environ- ment, DynNAS utilizes the approach proposed by iNAS (Mendis al.. 2021). After the network architecture is determined, DynFit is used to train the network considering energy intermittency, and DynInfer is employed to perform inference under intermittent power conditions.
DynInfer:
In this section, we elaborate on the key components, focusing on DynFit and DynInfer, and explain how they uniquely adapt DNN training and inference to intermittent power conditions.
3.1 DYNFIT: INTERMITTENCY-AWARY LEARNING
DynFit is designed to optimize deep neural networks (DNNs) for execution in environments char- acterized by intermittent power supply due energy harvesting. The primary goal of DynFit is to adapt the DNN's s training process to operate efficiently under unpredictable energy budgets while maintaining acceptable accuracy and adhering to predefined service level objectives (SLOOs).
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DynFit introduces key mechanisms to dynamically adjust computational complexity based energy availability, thereby enabling energy-efficient exccution of DNN models in constrained environments. These mechanisms include: (i) Dynamic Dropout, which adjusts the dropout rates based on available energy to reduce computational load; (ii) Dynamic Quantization, which modifies quantization levels in response to energy constraints save energy; and (iii) Quanta design, which defines atomic computational units that can be executed without interruption given the energy budget.
Unlike standard implementations where dropout rates and quantization levels are fixed adjusted solely based on training dynamics, DynFit adjusts these parameters in real-time based on the energy profile of the device. Specifically, during training, we simulate energy variabilityy by incorporating energy traces into the training loop. At each training iteration, the available energy Eg is sampled from these traces. Based on Fbs, we adjust the dropout rate dj for each layer i according to:
dj = dmax (I- Emax
(1)
where dmaxx the maximum allowable dropout rate, and Emax is the maximum energy observed in the traces. Similarly, the quantization levels qj are adjusted:
Es
g qmin
(4max
qmin)
Emax
This ensures that when energy is low, higher dropout rates and lower quantization bit-widths are used reduce computational load, and vice versa.
Modeling Energy Consumption: The energy consumption of DNN operations is modeled based empirical profiling data from the hardware platform. Let Cop denote the energy consumed per computational operation, which varies with operation type and data precision. The total energy consumption of QuantaTask q is modeled as Eg Cop Ey. where l, is the number of operations in the task. By integrating the energy model into the training process, DynFit ensures the adjustments dropout and quantization directly correspond to actual energy savings on the target hardware.
A QuantaTask is defined as the smallest atomic unit of computation that can be executed entirely without interruption under the current energy and hardware constraints. Each QuantaTask ensures that execution proceeds without partial computation, which would otherwise lead to overhead from checkpointing and potential data corruption. The main properties QuantaTasks are atomicity and respect for energy constraints. Figure illustrates Quanta Task execution with simple example.
A3
63
E E
EB S
Es
E,
B
A1
Figure 1: An example of variable QuantaTask in matrix multiplication scenario. Depending on the available energy, the task (vector inner product) can be divided into multiple iterations such that each QuantaTask is guaranteed finish given the energy availability. E is available energy, and E,, is the energy required to finish one inner product.
The optimization problem is formulated with variables: the weights W, dropout rates d. quantization levels q, and QuantaTask sizes e. The objective is to minimize the total loss, including prediction loss and regularization terms penalizing energy consumption (subject to energy constraints):
Optimization Variables, Constraints, and Objective Function:
min w,d.g&
C(Y
A
(
Co
+
Ao
ca(d.).
Formulation of the Composite Optimization Problem: The problem is non-convex due to the discrete nature of quantization levels and dropout rates. We employ an alternating optimization strategy, iteratively optimizing subsets of variables while keeping others fixed. Our method differs from standard approaches by integrating energy constraints directly into the optimization, ensuring that the network learns to adapt its parameters based energy availability.
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3.1.1 ADAPTIVE REGULARIZATION STRATEGY
DynFit introduces an adaptive regularization strategy to address potential overfitting and under- training due to uneven weight updates caused by dynamic dropout and quantization. We monitor the update frequency Fp of each weight up over window of T iterations:
1, if up is updated at iteration P U U,,,, U₂(1)
0, otherwise
Weights with Fp < 8lo are considered under-trained, and those with Fp > Ohigh are considered overfitting. We adjust dropout rates and apply 1.2 regularization accordingly to balance the training process. This adaptive strategy ensures that all weights are adequately trained despite the dynamic adjustments. Dropout scheduling techniques are incorporated, where dropout rates are increased or decreased over time based on the training progress and energy availability, mitigating potential overfitting introduced by static dropout variations.
The time complexity of DynFit during training is O(N - T), where N is the number of weights and T is the number of training iterations. The overhead introduced by monitoring update frequencies and adjusting dropout rates is negligible compared to the overall training time, as these operations are simple arithmetic computations per iteration. The space complexity is O(N) for storing the update frequencies and additional parameters. Compared to classical training, DynFit adds minimal overhead, with a tradeoff of s 5% additional compute for significant gains in accuracy under intermittent power conditions.
Complexity Analysis of DynFit:
3.2 DYNINFER: INTERMITTENCY-ANE
INFERENCE SCHEDULING
DynInfer optimizes the inference phase of DNNs operating under intermittent power conditions. Unlike traditional systems with stable power, intermittent environments pose unique challenges for executing inference tasks efficiently and reliably.
The inference process is represented as set of tasks T , T2...., Tv}, where each task T; is characterized by its energy requirement Eg, execution time TG, priority ps, deadline D,, and criticality level ct. At any given time t, the available energy is denoted as (t).
Task Fusion and Scheduling: DynInfer introduces a novel task scheduling algorithm that dynam- ically adjusts real-time energy availability. When the energy required for executing multiple QuantaTasks exceeds the available energy budget, DynInfer employs task fusion to combine smaller tasks into larger atomic units that can be executed within the energy constraints.
Formal Definition of Task Fusion: Let Q = {q1, ............. } be a set of Quanta Tasks with in- dividual energy requirements F.g.- If Σ; F.g. < Fg. the available energy budget, then tasks can be executed sequentially without interruption. However, if Σ, F.g. > Ft. we aim to fuse tasks to minimize checkpointing overhead. Task fusion formalized as finding a partition of Q into subsets 21, Q2...., Qm such that, for each subset 2j. En,o, Eg. I Es, and m is minimized. This reduces the number of checkpoints and the overhead associated with task switching. For example, Consider two convolution operations C and C2 with energy requirements FE; and Fc,,, respectively. If individually Fec,, FEc, > Fs, but FEc, + FEc, I F... we fuse C1 and C2 into single task. The fused task executes both convolutions atomically within the energy budget, avoiding the overhead of checkpointing between them.
The scheduling problem is formulated with decision variables s; (task start times) and binary variables 2, E {0. (indicating whether task is scheduled). The energy availability constraint over time is expressed as (subject to energy and task constraints): Enagies E. S Et( The objective is to maximize the total weighted priority of scheduled tasks:
Scheduling Problem Formulation:
N
max (
Σ
(p. (p-
x..
(5)
Our scheduling heuristic, Energy-Aware Priority Scheduling, while sub-optimal in the theoretical sense, is designed to perform optimlly in practice for real- time systems. We ensure its performance by: 1. Empirical Validation: We compare the heuristic's
Scheduling Performance Assurance:
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performance with the optimal solution smaller problem instances using exhaustive search and find that the heuristic achieves within 95% of the optimal task completion rate. 2. Theoretical Analysis: The heuristic prioritizes tasks based on effective priority Pr E. x Oi where Φ; accounts for deadline urgency. This balances task importance against energy consumption, leading to efficient utilization of available energy. 3. Complexity Analysis: The heuristic has a time complexity of O log N) due to sorting tasks based on p: which is acceptable for real-time applications.
Complexity Analysis of DynInfer: The time complexity of the scheduling algorithm is O(N log N) due to sorting tasks, and the space complexity is O(N) for storing task parameters. Compared to classical inference, DynInfer introduces additional overhead for scheduling and task fusion, but this offset by the gains in reliability and efficiency under intermittent power.
In environments with extremely low or sporadic energy levels where consistent dropout and quantization adjustments may not be feasible, NEXUME handles this by: 1. Implementing a minimum viable model configuration that operates the lowest acceptable energy consumption, achieved by maximizing dropout rates and using the lowest quantization bit-widths. 2. Prioritizing essential tasks and deferring non non-critee connciiiical computations. Employing predictive energy harvesting models to anticipate energy availability and adjust computations proactively. In extreme cases, the system can enter into low-power standby mode and resume operation when sufficient energy is available. These strategies ensure that the system remains operational and provides degraded but acceptable performance under severe energy constraints.
Handling Extremely Low or Sporadic Energy Levels:
Novelty in Energy-Aware Scheduling: While energy-aware scheduling not novel in itself, our contribution lies in adapting scheduling algorithms specifically for intermittent power environments. Existing scheduling algorithms typically assume stable energy availability and do not account for the atomicity constraints imposed by intermittent power supply. Our scheduling approach uniquely integrates: 1. Real-time energy availability into scheduling decisions. 2. Task fusion to minimize checkpointing overhead, which is critical in intermittent environments. 3. Dynamic adjustment of computational tasks based on both energy and task criticality. These innovations enable efficient and reliable DNN inference under intermittent power conditions, differentiating our work from existing energy-ane -waree schedulers.
Rationale Behind Method Design: The overall method design of NExUME is motivated by the need to enable DNNs to function reliably in environments with intermittent and unpredictable energy supply. By integrating energy variability into both training and inference, we allow the DNN to adapt its computational load dynamically, ensuring that critical tasks are completed within energy constraints. This holistic approach addresses the limitations of existing methods that treat training and inference separately or do not account for real-time energy fluctuations.
Implementation Details: We propose a software-comppier--ardde
co-designed framework for
devices with non-volatility (c.g., 4SSP-EX4430FR5994
User Progran
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Figure 2: Software-Compiier- Driven DynInfer Flow.
mized in assembly. NV FeRAM is used for backup and restore during power emergencies.

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4 EXPERIMENTAL RESULTS
NEXUME can be seamlessly integrated as a "plug-in" for both training and inference frameworks in deep neural network (DNN) applications, specifically designed for intermittent and (ultra) low-power deployments. In this section, we discuss the effectiveness of NExUME across two distinct types of environments, highlighting
versatility and broad applicability. Firstly, we evaluate NEXUME using publicly available datasets ($4.2) commonly utilized in embedded applications across multiple modalities including image, time series sensor, and audio data. These datasets represent typical use cases in embedded systems where energy efficiency and minimal computational overhead are crucial. (COTS) hardware and state-of- -hrte-rrt ReRAM Xbar-based hardware for this evaluation. Secondly, introduce novel dataset aimed at advancing research in predictive maintenance and Industry 4.0 (Lasi et al. 2014), and test NEXUME on a real manufacturing testbed ($4.3) with COTS hardware. We have developed dataset, available at atsttps: : h/t////aakee /hacckaa..mmmm / e @Ga Tben/ rk 7 Y ( JmR which involves mounting multiple types of sensors various locations on a Bridgeport machine to monitor its activity status.
We use both commerciallofftthe--hhe
cost-of-its-king machine status monitoring
4.1 DEVELOPMENT AND PROFILING OF NEXUME
NEXUME uses a combination of programming languages and technologies to optimize its funetional- ity in intermittent and low-power computing environments. The software stack comprises Python3 (2.7k lines of code), CUDA 1k lines of code), and Embedded C (2. 1k lines of code, not including DSP libraries). Our training infrastructure utilizes NVIDIA A6000 GPUs with 48 GiB of memory, supported by a 24-core Intel Xeon Gold 6336 CPU. We employ Py Torch v2.3.0 coupled with CUDA version 11.8 as primary training framework. To assess the computational overhead introduced by DynFit, a component of NEXUME, we use NVIDIA Nsight Compute. During the training sessions enhanced by DynFit,
observed increase in the number of instructions ranging from minimum of 11.4% to a maximum of 34.2%. While the overhead in streaming multi multi-processor (SM) utilization was marginal (within 5%), there was a noticeable increase in memory bandwidth usage, ranging from 6% to 17% Moreover, we have implemented a modified version of the matrix multiplication operation that strategically skips the loading of rows and/or columns from the input matrices into the GPU's shared memory and register files. This adaptation is guided by the dropout mask vector and the specific type of sparse matrix operation being performed. This technique effectively reduces the number of load operations by an average of 12%, thereby enhancing the efficiency of computations under energy constraints and contributing to the overall performance improvements in NEXUME.
4.2 NEXUME ON PUBLICLY AVAILABLE DATASETS
For image data, we consider the Bushion-MNISTT (iaoo et al. 2017 and CIFARIO (Alxx 2009 datasets; for time series sensor data, focus popular human activity recognition (HAR) datasets, MHEALTH (Banos et al.] 2014) and PAMAP2 (Reiss & Stricker 2012); and for audio, we
Datasets:
use the AudiOMNIST (Becker al. 2023) dataset.
Inference Deployment Embedded Platforms: For commercially off-the-shelf micro-controllerss, we choose Texas Instruments MSP440FR5994 (Instruments) (024a), and Arduino Nano 33 BLE Sense (Arduino| (2024) as our deployment platforms with a Pixel-5 phone as the host device. The host device is used for data logging- running the "baseline" inferences without intermittency.
SLOs, violations, power failures, etc., along with
Baselines: We take the combination of best available approaches for DNN inference on intermittent environment as baselines. All these DNNs are executed with the state-of-the-an checkpointing and scheduling approach (Maeng & Lucia 2018). Baseline Full Power DNN designed by iNAS (Mendis et al. (021) for running while the system is
and has to hit a target SLO (latency < 500ms). Baseline AP is a DNN compressed to fit the average power of the energy harvesting (EH) environment using iNAS (Mendis et al. 1021) and energy- pruning (EAP) (Yang et al.
2017: 2018). Baseline PT takes the Full Power DNN and uses techniques proposed by (Yang et al.
2018) and (Yang et al., 2017) prune, quantize, and compress the model. Baseline iNAS+PT
designs the network from the ground up while combining the work of iNAS (Mendis et al. 2021 and
EAP (Yang et al., 2018 2017)
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We also compare approach with recent of-te-of-the-ar methods specifically designed for in- termittent systems, namely Stateful (Yen et al., 2022). ePerceptive (Montanari et al. 2020), and DynBal (Yen et al. 2023). These methods introduce various techniques such embedding state information into the DNN, multi-resolution inference, multi-exit architectures, and runtime reconfig- urability handle intermittency in energy-harvesting devices. We have faithfully re-implemented these methods as per the descriptions and adjusted them for fair comparison under our setup.
Table I shows the accuracy of our approach against the baselines and the recent state-of-the- art methods using the TI MSP board powered by piezoelectric energy harvesting. The inferences meeting the SLO requirements are the only ones considered for accuracy; i... correct classification violating the latency SLO is considered as "incorrect".
Results:
Datasets
Full Power
AP
PT
iNAS+PT
Stateful
ePerceptive
DynBal
NExUME
FMNIST
98.70
71.90
79.72
83.68
85.40
86.25
87.50
88.90
CIFARIO
89.81
55.05
62.00
66.98
68.50
70.20
71.75
76.29
MHEALTH
89.62
59.76
65.40
71.56
73.80
74.95
76.10
80.75
PAMAP
87.30
57.38
65.77
70.33
72.20
73.35
74.50
75.16
AudioMNIST
88.20
67.29
73.16
75.41
76.80
77.95
78.60
80.01
Table Accuracy comparison on TI MSP board using piezoelectric energy harvesting.
As observed in Table T NExUME consistently outperforms the state-of-the-art methods across all datasets. For instance, on CIFARIO, NExUME achieves an accuracy of 76.29%, which is approximately 4.54% higher than DynBal, the next best method. This improvement is significant in the context of energy-hand hhrggsiharvssiingg intermittent systems, where achieving high accuracy under strict energy constraints is challenging. The superior performance of NEXUME can be attributed to its unique integration of energy variability awareness directly into both the training (DynFit) and inference (DynInfer) processes. Unlike other methods that either focus on modifying the DNN architecture optimizing inference configurations, NEXUME adapts the DNN's computational complexity in real-time based on instantancous energy availability, leading to more efficient use of scarce energy resources and improved accuracy.
Dataset
Platform
Energy Source
Stateful
ePerceptive
DynBal
NExUME
FMNIST
MSP430FR5994
Piezoelectric
20.1
20.8
21.5
23.4
CIFARIO
Arduino Nano
Thermal
16.0
16.5
17.0
18.5
MHEALTH
ESP32 S3 Eye
Piezoelectric
18.5
19.0
19.6
21.0
PAMAP
STM32H7
Thermal
16.5
17.0
17.5
19.0
AudioMNIST
Raspberry Pi Pico
Piczoelectric
20.5
21.0
21.7
23.2
Table 2: Energy efficiency comparison on different hardware platforms.
Table presents the energy efficiency MOps/Joule for each dataset on different hardware platforms using piezoelectric and thermal energy harvesting. NEXUME achieves the highest energy efficiency across all platforms and datasets. This demonstrates that NExUME not only improves accuracy but also enhances energy utilization, making highly suitable for deployment in mnergy-constraine, intermittent environments. The improvements in energy efficiency are due to NExUME's ability to adjust computational workload dynamically, minimizing energy wastage and ensuring that computa- tions are matched to the available energy budget. NExUME, thanks to its inherent learnt adaptability, significantly reduces saves, restores, reconfigurations and READ/WRITE from/to nonvolatile memory or to the flash memory in the cases and devices where NVMs are not present which gives it edge over the baselines across multiple devices.
Discussion of Results: 1. Dynamic Adaptation: NExUME's DynFit and DynInfer components enable real-time adjustments of dropout rates and quantization levels during training and inference based instantaneous energy availability. This allows the DNN to maintain high accuracy even under severe energy constraints. 2. Energy Variability Awareness: By integrating energy profiles directly into the training process, NExUME ensures that the model learns to handle fluctuations in energy supply, leading to more robust performance compared to methods that do not consider energy variability during training. 3. Efficient Scheduling: DynInfer's 's energy- task scheduling and task
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fusion mechanisms reduce overhead from checkpointing and optimize the execution of tasks within the available energy budget. 4. Holistic Approach: Unlike other methods that focus on either training or inference optimizations, NExUME provides comprchensive solution that addresses both phases, leading to superior overall performance.
4.3 NEXUME ON MACHINE STATUS MONITORING (Our New Dataset]
Automation and monitoring and analyties the key ingredients in the upcoming Industry 4.0. To enable sustainable machine status monitoring with energy harvesting (from machine vibrations or Wifi signals) we evaluate our setup using Bridgeport machines for monitoring their status. Prior works (Center 2018) majorly focused on fault analysis but there are little to no datasets on predictive maintenance. Setup and Sensor Arrangement: Two different types of 3-axis accelerometers (with 100Hz and 200Hz sampling rate) were placed in three different locations of a Bridgeport machine to collect and analyze data under different operating status. There were 5 operating statuses: three different speeds of rotation of the spindle (R1: 100RPM, R2: 200RPM, R3: 300RMP with no job; RPM rotations per minute), spindle under job (SJ), and spindle idle (SI). We collected over 700,000 samples over period of 2 hours for each of the sensors. The sensor data were cleaned, normalized, and converted to the power spectrum density for further analysis. We use iNAS (Mendis al. (02T) to find the DNNs meeting the energy income and train them using proposed DynFit. Table shows the accuracy of classification tasks against the different baselines and state-of-the-an methods.
Class
Full Power
AP
iNAS+PT
Stateful
ePerceptive
DynBal
NEXUME
RI
84.93
74.46
77.02
79.62
80.85
81.50
82.15
83,60
R2
85,85
76.21
79.18
80.36
81.95
82,60
83.25
84.50
R3
81.09
72.43
75.38
78.18
79.05
79.70
80.35
80.85
SJ 90.95
82.33
85.00
87.58
88.60
89.15
89.80
90.50
SI 94.76
85.31
88.05
89.90
91.00
91.65
92.30
93.00
Table 3:
Accuracy of NExUME and other methods for industry status monitoring dataset using TI MSP board and piezoelectric energy source. Results collected over 200 experiment cycles.
NEXUME demonstrates superior performance across all operating classes, achieving the highest accuracy in each case. For example, for the spindle idle (SI) class, NEXUME attains accuracy of 93.00%, outperforming DynBal by 0.70%. While the margins may appear small, in industrial settings, even minor improvements in classification accuracy can have significant implications for predictive maintenance and operational efficiency. The improved performance of NExUME in this real-world application further validates its effectiveness and practical utility. By effectively managing energy constraints and adapting to intermittent power conditions, NEXUME enables more reliable and accurate monitoring industrial environments where energy harvesting is viable power solution.
4.4 SENSITIVITY AND ABLATION STUDIES OF NEXUME
To elucidate the influence of variable SLOs and hardware-speciin settings system performance, we conducted a comprehensive sensitivity study. This study involved adjusting the acceptable latency and the capacitance of the energy harvesting setup assess their impacts on accuracy. As shown in Figure 3al the accuracy improves with increased latency, but with diminishing returns. Similarly, Figure 3b demonstrates that, while increasing capacitance should theoretically stabilize the system, its charging characteristies can lead to extended charging times, thus exceeding the latency SL... Notably, some anomalies in the data were attributed to abrupt power failures, a common challenge in intermittent energy harvesting systems. An ablation study evaluates the contributions of individual components within NEXUME. The results, plotted in Figure Bc indicate that the greatest improvements are derived from the "synergistic operation" of all components, particularly DynFit and DynInfer. Although iNAS enhances network selection, its lack of intermittency awareness significantly impacts accuracy.
4.5 LIMITATIONS AND DISCUSSION
We recognize that modern architectures like Transformers have become prevalent in the ML commu- nity due to their superior performance large-scale datasets. However, deploying such architectures

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Accuracy ss. Latarny lor Oifernnt Classes
Ascurecy 15. Capec lance for diflarett Clesses
Mobbtee Stady
42
240
Recariing 152
266
282
250 300 400 500 Lanency (166)
600
2.5
3.5 4.
5.5
Choactance (F)
1900 ALSORAE Packia
R1
R2
R3
R1
82
R3
(c) Ablation Study Figure 3: Sensitivity and ablation study. DN is DynNAS, DF is DynFit, and DI is Dyninfer.
(a) Accuracy vs Latency
(b) Accuracy vs Capacitance
on ultra-low-pp power, energy-harvenee devices presents significant challenges due to their substantial computational and memory requirements. NExUME focuses on enabling efficient and reliable deployment DNNs in intermittent environments, which are often constrained in terms of com- putational resources and energy availability. In many real-world applications, especially in loT and edge computing, there is a critical need for smaller, energy- effficient models that can operate batteries. These tiny, reusable devices contribute to reducing
autonomously without reliance embodied carbon and represent a significant step toward sustainability. Moreover, we believe that advancing the capabilities of smaller models in intermittent environments is crucial for widespread adoption of sustainable, battery-free devices in various domains, including environmental monitoring, industrial IoT, and healthcare. By addressing the challenges of intermittent computing, our work contributes to the broader goal of enabling pervasive, sustainable intelligence at the edge.
NEXUME is especially advantageous in intermittent environments, and its utility extends ultra- low-power or energy scavenging systems. However, the efficacy of DynFit and iNAS is contingent upon the breadth and depth of the available dataset. Additionally, profiling devices ascertain their energy consumption, computational capabilities, and memory footprint necessitates detailed micro- profiling using embedded programming. This process, while informative, yields only approximate models that are inherently prone to errors. DynFit, with its stochastic dropout features, occasionally leads to overfitting, necessitating meticulous fine-tuning. While effective in smaller networks, our studies involving larger datasets (such as ImageNet) and more complex network architectures (like MobileNetV2 and ResNet) reveal challenges in achieving convergence without precise fine-tuning. DynFit tends to introduce multiple intermediate states during the training process, resulting in approximately 14% additional wall-time on average. The development of DynInfer requires an in-depth understanding of microcontroller programming and compiler directives. The absence of comprehensive library functions along with the need for computational efficiency frequently necessitates the development of in-line assembly code for certain computational kernels.
5 CONCLUSIONS
This study presents NEXUME, an advanced framework designed to optimize the training and inference phases of deep neural networks within the constraints of intermittently powered, meegy-harvesting devices. By integrating adaptive neural architecture and energy-aware training techniques, NExUME significantly enhances the viability of deploying machine learning models environments with limited and unreliable energy sources. The results from extensive evaluations demonstrate that NEXUME can substantially outperform traditional methods in mmergy-constrainet settings, with improvements in accuracy and efficiency that facilitate real-world applications in remote and wearable technology. Specifically, improvements ranging from 6. 6.10 to 17.13% over existing methods highlight NEXUME's capability adapt dynamically to fluctuating energy conditions, ensuring both operational longevity and computational integrity. The broader implication of this work extends beyond technological udvancements, suggesting a paradigm shift in how the machine learning community approaches the design and deployment of systems in energy-limited environments. By prioritizing energy efficiency and system adaptability, NExUME contributes to the sustainability and accessibility of machine learning solutions, enabling their deployment in regions where power infrastructure absent or unreliable. This is particularly crucial in developing regions where such technology can drive innovation in healthcare, agriculture, and education. Furthermore, the development of effigy-efficient, adaptive systems like UEX is aligned with the growing need for sustainable computing practices across all disciplines of technology. It challenges the machine learning community to consider not only the accuracy and efficiency of algorithms but also their environmental impact and accessibility, ensuring broader positive social impact.
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ACKNOWLEDGMENTS
We sincerely thank the anonymous reviewers for their insightful comments, which have significantly improved this paper. This work was supported in part by Semiconductor Research Corporation (SRC), the Center for Brain-inspired Computing (C-BRIC), NSF Grant #1 8222923, NSF Grant #2346953, and the Clean Energy Smart Manufacturing Innovation Institute award #136067. We also gratefully acknowledge the Factory for Advanced Manufacturing Education Lab at The Pennsylvania State University for their support in data collection on the Bridgeport machine. All product names are used solely for identification purposes and may be trademarks of their respective companies.
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APPENDIX
A
MORE RESULTS ON OTHER PLATFORMS AND EH SOURCES
Figure 4: Hardware setup of NEXUME using MSP-EXP43OFRS594 as the edge compute, Adafruit ItsyBitsy nRF52840 Express for communicating, Energy Harvester Breakout LTC3588 with super- capacitors as energy rectification and storage and a Pixel-5 phone as the host.
MSP on Piezo
Datasets
Full Power
AP
PT
iNAS+PT
NExUME
Better
FMNIST
98.70
71.90
79.72
83.68
88.90
6.24%
CIFAR10
89.81
55.05
62.00
66.98
76.29
13.90%
MHEALTH
89.62
59.76
65.40
71.56
80.75
12.84%
PAMAP 87.30
57.38
65.77
65.38
75.16
14.97%
AudioMNIST 88.20
67.29
73.16
75.41
80.01
6.10%
Table 4: Accuracy of NEXUME MSP board using vibration from Piezoelectric harvestor. Better refers to the improvement over iNAS+PT baseline.
MSP on Thermal
Datasets
Full Power
AP
PT
iNAS+PT
NExUME
Better
FMNIST
98.70
80.92
86.32
88.93
95.62
7.53%
CIFAR10
89.81
64.78
69.29
71.53
83.78
17.13%
MHEALTH
89.62
69.77
73.99
77.70
89.62
15.34%
РAMAP 87.30
66.33
71.84
74.47
85.24
14.46%
AUdiOMNIST
88.20
73.84
78.03
81.60
87.64
7.40%
Table Accuracy of NEXUME on MSP board using thermocouple based thermal harvester. Better refers to the improvement over iNAS+PT baseline.
Arduino on RF
Datasets
Full Power
AP
PT
iNAS+PT
NExUME
Better
FMNIST
98.70
74.44
79.63
83.61
90.44
8.17%
CIFAR10
89.81
58.11
63.91
65.01
79.60
22.44%
MHEALTH
89.62
63.52
67.40
74.30
83.86
12.87%
PAMAP 87.30
61.39
67.24
69.45
77.00
10.87%
AudiOMNIST 88.20
66.11
74.28
76.60
78.87
2.97%
Table 6: Accuracy of NExUME on Arduino nano board using WiFi based RF harvester. Better refers to the improvement over iNAS+PT baseline.
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Arduino on Thermal
Datasets
Full Power
AP
PT
iNAS+PT
NEXUME
Better
FMNIST
98.70
77.04
80.44
83.08
89.90
8.20%
CIFARIO
89.81
60.38
65.90
66.98
80.70
20.48%
MHEALTH 89,62
65.74
69.88
72.41
85.75
18.42%
PAMAP 87.30
62.76
65.93
71,46
81.27
13.73%
AudioMNIST 88.20
69.12
73.86
77.79
83.54
7.39%
Table 7: Accuracy of NExUME on Arduino nano board using thermocouple based thermal harvester. Better refers the improvement over iNAS+PT baseline.
B DETAILS ON ENERGY HARVESTING
A typical energy harvesting (EH) setup captures and converts environmental energy into usable electrical power, which can then support various electronic devices. Here's simplified breakdown of the process:
1. Energy Capture:
The setup begins with harvester, such solar panel, piezoelectric sensor, or thermocouple. These devices are designed to collect energy from their surround- lngh-light, mechanical vibrations, heat, respectively.
2. Power Conditioning:
Once energy harvested, often needs be converted and stabilized for use. This is done using a rectifier, which transforms alternating current (AC) into more usable direct current (DC).
3. Voltage Regulation:
After rectification, the power might not at the right voltage for the device it needs to support. A matching circuit, including components like buck or boost converters, adjusts the voltage to the appropriate level, ensuring the device receives the correct current and voltage.
4. Energy Storage:
Finally, ensure continuous power supply even when the immediate energy source is inconsistent (like when cloud passes over a solar panel), the system includes temporary storage unit, such super-capacitor. This component helps smooth out the supply, providing steady power to the compute circuit.
By integrating these components, EH system sustainably power devices without relying traditional power grids, making it ideal for remote or mobile applications.
C INTERMITTENT COMPUTING AND CHECK-POINTING
C.I IIERMIITENCY-AWARE GENERAL MATRIX MULTIPLICATION (GEMM)
Here we explain the operation of an energy-aware algorithm for performing General Matrix Multipli- cation (GeMM). The algorithm is designed operate in environments where energy availability is intermittent, such as in devices powered by energy harvesting. It includes mechanisms for loop tiling, checkpointing, and resumption to manage computation across power interruptions effectively.
C.1.1 ALGORITHM OVERVIEW
The GeMM operation, typically expressed as = A x B, where A, B, and C' are matrices, is imple- mented with considerations for energy limitations. The algorithm breaks the matrix multiplication into smaller chunks (tiles), periodically saves the state before potential power losses, and resumes computation from the last saved state upon power restoration.
1.1.2 FUNCTION DEFINITIONS
SAVE STATE: Saves the current indices and the partial result of the output matrix to non-volatile memory to allow recovery after power interruption.
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LOAD_SDTTT STATE: Retrieves the last saved indices and partial result from non- non-volatile memory to resume computation.
C.1.3 LOOP TILING
The algorithm uses loop tiling to divide the computation into smaller blocks that can be managed between power interruptions. This tiling not only makes the computation manageable but also optimizes memory usage and cache performance, which critical constrained environments.
C.1.4 CHECK-POINTING MECHANISM
Before each power interruption, detected through an energy monitoring system, the algorithm saves the current state using the LAVE_STATE function. This state includes the loop indices and the current value of the element being processed in C. This ensures that no computation is lost when the power goes out.
C.1.5 RESUMPTION MECHANISM
Upon resuming, the algorithm loads the saved state using the LOAD STATE function. This state is used to continue the computation exactly where it left off, minimizing redundant operations and ensuring efficiency.
D FORMULATION OF DYNAMIC DROPOUTS:
D.1 L2 DYNAMIC DROPOUT WITH QUANTATASK OPTIMIZATION
L2 Dynamic Dropout leverages the L2 norm of the weights to influence dropout rates, combined with the QuantaTask optimization to handle energy constraints in intermittent systems.
Mathematical Formulation: Let W be the weight matrix layer. The L2 norm of the weights is calculated as:
W
W3
Define the dropout probability p; for neuron i based the L2 norm of its corresponding weights. The idea is to use the inverse of the L2 norm to determine the probability:
Pr =
W W +
where a a scaling factor adjust the overall dropout rate, and is small constant to avoid division by zero. Define binary dropout mask [m,, m2,.... ................................ m..] where m, E {0, 1}. Each element of the mask is determined by sampling from Bernoulli distribution with probability 1-p;;
m; Bernoulli(1 pp:)
Apply the dropout mask during the forward pass. Let a, denote the activation of neuron i:
dropout
a;
Training with L, Dynamic Dropout and Quanta Task Task Optimization: Initialize the network parameters W, dropout mask m, and scaling factor a. Define the energy budget Es for single quanta and for the entire inference. Initialize the loop iteration parameters L. Compute the activations and apply the dropout mask:
dropout a; m2 a,
Compute the loss L(Y, Y) where the output of the network and Y the target output. Calculate the gradients of the loss with respect to the weights:
Oc
ow,
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For each layer L and loop within the layer, estimate the energy E, required for the current quanta size 4;:
E, DynagemtessimmachheryyLLLL,,
If B > Eb. fuse tasks to reduce the overhead:
(,, Bb)
Update E, after task fusion:
E K DynAggen.sstimateFFerryy i,44
Update the dropout mask based on the L2 norm of the weights:
Pi
W 12 +e
0 if Bernoulli(1 - pp) =0
m, =
otherwise
Perform the backward pass to update the network weights, considering the dropout mask:
OC
W
m
OW
where 7) the learning rate and @ denotes element-wise multiplication.
Check the available energy using DynAgent. If energy below threshold, increase the dropout rate ensure the inference be completed within the energy budget. Otherwise, maintain or reduce the dropout rate to improve accuracy. Perform the forward pass with the updated dropout mask to obtain the output Y. This approach ensures that the network is robust to varying energy conditions by incorporating dynamic dropout influenced by the L2 norm of the weights, along with the QuantaTask optimization to handle energy constraints.
Inference with 1.2 Dynamic Dropout and Quanta Optimization:
D.2 OPTIMAL BRAIN DAMAGE DROPOUT WITH QUANTATASK OPTIMIZATION
Optimal Brain Damage Dropout leverages a simplified version the Optimal Brain Damage pruning method to adjust dropout rates, combined with the QuantaTask optimization to handle energy constraints in intermittent systems.
Mathematical Formulation: Let W be the weight matrix of layer. The sensitivity of each weight Wi is calculated using the second-order Taylor expansion of the loss function
02 C
AC
OW2
8'c where aw? the second-order derivative (Hessian) of the loss with respect to the weights.
Define the dropout probability p, for neuron i based the sensitivity of its corresponding weights. The idea is to use the sensitivity to determine the probability:
BΣ, aw2
8cc (W,))²
P:
max
Σ
OW?
82C
(W.))²
+
where 3 is scaling factor adjust the overall dropout rate, and is small constant to avoid division by zero.
Define binary dropout mask m [m1, my.............................. m.] where m, {0, 1}. Each element of the mask determined by sampling from a Bernoulli distribution with probability - p::
m,
Bernoulie1 pt)
Apply the dropout mask during the forward pass. Let a; denote the activation of neuron i:
dropout a; m24
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Training with Optimal Brain Damage Dropout and Quanta Optimization: Initialize the network parameters W, dropout mask m, and scaling factor 3. Define the energy budget Eb for single quanta and for the entire inference. Initialize the loop iteration parameters L.
Compute the activations a and apply the dropout mask:
dropout
a. m
Compute the loss L(Y, Y) where is the output of the network and Y is the target output. Calculate the gradients and Hessians of the loss with respect to the weights:
Oc
0CC
aw 6
a
For each layer L and loop within the layer, estimate the energy E, required for the current quanta size 4;
If Eg > Es, fuse tasks to reduce the overhead:
Fuse FuseTaskssL,,,44 Es)
Update E; after task fusion:
E, + DynaAgen..ssimaattennegg
Update the dropout mask m based on the sensitivities:
8 B E, (W,j))
aw?
P:
max
E
(Wiz)² + aw?
82
{
0 if Bernouuli(1 - p:) = 0
otherwise
Perform the backward pass update the network weights, considering the dropout mask:
OC
W + W
oW
m
where 17 is the learning rate and @ denotes element-wiss multiplication.
Inference with Optimal Brain Damage Dropout and Quanta Optimization: Check the available energy using DynAgent. If energy is below threshold, increase the dropout rate to ensure the inference can completed within the energy budget. Otherwise, maintain reduce the dropout rate to improve accuracy. Perform the forward pass with the updated dropout mask to obtain the output Y. This approach ensures that the network is robust to varying energy conditions by incorporating dynamic dropout influenced by the sensitivity of the weights, along with the Quanta Task optimization handle energy constraints.
D.3 FEATURE MAP RECONSTRUCTION ERROR DROPOUT WITH QUANTATASK OPTIMIZATION
Feature Map Reconstruction Error Dropout leverages the reconstruction error of feature maps to adjust dropout rates, combined with the Quanta optimization to handle energy constraints in intermittent systems.
Mathematical Formulation: Let W be the weight matrix of a layer and F be the feature maps produced by the layer. The reconstruction error of feature map is calculated as:
RE,
F, Fzllz
where F; is the reconstructed feature map, and || denotes the 1.2 norm.
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Define the dropout probability p; for neuron based the reconstruction error of its corresponding feature map. The idca to use the reconstruction error to determine the probability:
Pi 7 RE,
max RE) +
where is scaling factor to adjust the overall dropout rate, and is small constant to avoid division by zero.
Define binary dropout mask m [m,,, , .......,........................ m.] where {0, 1). Each element of the mask determined by sampling from a Bernoulli distribution with probability - p::
Bernoulii11 - p.)
Apply the dropout mask during the forward pass. Let a, denote the activation of neuron i:
dropout
a
a. m
Training with Feature Map Reconstruction Error Dropout and QuantaTask Optimization: Initialize the network parameters W, dropout mask m, and scaling factor Define the energy budget Eg for single quanta and for the entire inference. Initialize the loop iteration parameters 1.
Compute the activations and apply the dropout mask:
dropout
a; 1m4
Compute the loss L(Y, Y) where is the output of the network and Ý is the target output. Calculate the gradients of the loss with respect the weights:
Oc
ow
For each layer L and loop within the layer, estimate the energy E, required for the current quanta size 4;
E, - DynAgent. LannAgeenestimmattEnnrgyLLL 4,
Eg > Eg, fuse tasks to reduce the overhead:
FuseTTasks(,, i Ex)
Update E, after task fusion:
E, Dynnggen.esstimaateennnryLLL i,
Update the dropout mask m based on the reconstruction error of the feature maps:
7 ,RE,
P: max RE) +
0 if Bernoulli - -p:) =0
otherwise
Perform the backward pass to update the network weights, considering the dropout mask:
OC
W <
W
DOW
where v) the learning rate and @ denotes element-wise multiplication.
Inference with Feature Map Reconstruction Error Dropout and QuantaTask Optimization: Check the available energy using DynAgent. If energy is below a threshold, increase the dropout rate to ensure the inference can be completed within the energy budget. Otherwise, maintain reduce the dropout rate to improve accuracy. Perform the forward pass with the updated dropout mask to obtain the output Y. This approach ensures that the network is robust varying energy conditions by incorporating dynamic dropout influenced by the reconstruction error of the feature maps, along with the Quanta Task optimization to handle energy constraints.
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D.4 LEARNING SPARSE MASKS DROPOUT WITH QUANTATASK OPTIMIZATION
Learning Sparse Masks Dropout adapts dropout masks as learnable parameters within the network, inspired by Wen al. (2016), combined with the QuantaTask optimization to handle energy constraints in intermittent systems.
Mathematical Formulation: Let W be the weight matrix of layer. Define binary dropout mask m [m, m...... Mu.] where m, E {0, 1]. In Learning Sparse Masks Dropout, the dropout masks treated learnable parameters. The mask values determined using a sigmoid function to ensure they lie between 0 and I:
m; ((2)
where are learnable parameters and (-) is the sigmoid function.
Apply the dropout mask during the forward pass. Let a, denote the activation of neuron i: dropout a;
a; mi
Compute the loss L(Y, Y) where Y is the output of the network and Y is the target output.
DynFit integrates closely with DynAgent, which serves as a repository of EH profiles and hardware characteristics. Let Q represent the set of execution quanta, where each quanta q Q is defined by tuple (1, e):
q q= e))
Here, / the number of loop iterations and e is the estimated energy required for these iterations. The goal is to optimize the loop iteration parameter 1 such that the energy consumption E.y for each quanta is within the energy budget Eg:
minimize
Σ Eg 9
subject to Ey S Es
Training with Learning Sparse Masks Dropout and QuantaTask Task Optimization: Initialize the network parameters W, dropout mask parameters and scaling factor Define the energy budget Eg for a single quanta and for the entire inference. Initialize the loop iteration parameters l.
Compute the activations and apply the dropout mask:
m; = a(2)) dmpouu a, -774
a
Compute the loss C(Y, Y). Calculate the gradients of the loss with respect to the weights and dropout mask parameters:
ac O
OW,j Oz,
For each layer L and loop within the layer, estimate the energy E, required for the current quanta size 4;
E, Dynnggen.estimateennryyLLLL 1,
Fg > Fb,, fuse tasks to reduce the overhead:
PuseTTaks((A) I, i, Eb)
Update E, after task fusion:
DynnAgentestimmaceEnnrry (L, i, 4,4)
Update the dropout mask parameters based on the gradients:
OC
2i < 21 0z:
Perform the backward pass update the network weights, considering the dropout mask:
ØL
W W 7 low
+ m
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where 7) is the learning rate and @ denotes element-win multiplication.
Inference with Learning Sparse Masks Dropout and QuantaTask Optimization: Check the available energy using DynAgent. If energy is below threshold, increase the dropout rate to ensure the inference can be completed within the energy budget. Otherwise, maintain or reduce the dropout rate to improve accuracy. Perform the forward pass with the updated dropout mask obtain the output Y. This approach ensures that the network is robust to varying energy conditions by incorporating dynamic dropout with learnable mask parameters, along with the QuantaTast optimization to handle energy constraints.
D.5 NEURON SHIPLEY VALUE DROPOUT WITH QUANTATASK OPTIMIZATION
Neuron Shapley Value Dropout applies the concept of Shapley values from game theory (Aas et al., 2021) to assess neuron importance for dropout, combined with the Quanta Task optimization to handle energy constraints in intermittent systems.
The Shapley value o, of neuron is measure of its contribution to the overall network performance. It is calculated by considering all possible subsets of neurons and computing the marginal contribution of neuron to the network's 's output:
Mathematical Formulation:
|S| 1)! ((SS(()) ((S))
Φ
Σ
WI
W
SCNVO
where A is the set of all neurons, S is subset of neurons not containing i, and L(-) denotes the loss function.
Define the dropout probability p; for neuron i based on its Shapley value. Neurons with lower Shapley values are more likely to be dropped:
8
Ø +
where is a scaling factor to adjust the overall dropout rate, and c is a small constant to avoid division by zero.
Define a binary dropout mask m = [m, m2,, , Mm. where m, E {0. 13. Each element of the mask determined by sampling from Bernoulli distribution with probability p::
m, Bernoulli1 ps)
Apply the dropout mask during the forward pass. Let a, denote the activation of neuron i:
dropout
a
a; m2g
Training with Neuron Shapley Value Dropout and QuantaTask Optimization: Initialize the network parameters W, dropout mask and scaling factor 5. Define the energy budget Eg for single quanta and for the entire inference. Initialize the loop iteration parameters l.
Compute the activations and apply the dropout mask:
dropout
a; 774
Compute the loss L(Y, Y) where is the output of the network and Y is the target output.
Calculate the Shapley values de for each neuron based on their contribution to the network's perfor- mance.
For each layer L and loop within the layer, estimate the energy E, required for the current quanta size 4:
E, DyauAgemesstimateenrryy.....
If E, > Es, fuse tasks to reduce the overhead:
FuseTTasks i,44, Fb)
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Update E, after task fusion:
E, SynnAgentestimateEneeee (L, i,4,
Update the dropout mask m based on the Shapley values:
8
0, +
{
if Bernouli(1 - p:) =
otherwise
Perform the backward pass to update the network weights, considering the dropout mask:
Oc
W W " aw
m
where 7) is the learning rate and @ denotes element-wise multiplication.
Inference with Neuron Shapley Value Dropout and QuantaTask Optimization: Check the available energy using DynAgent. energy is below a threshold, increase the dropout rate to be completed within the energy budget. Otherwise, maintain reduce
ensure the inference the dropout rate to improve accuracy. Perform the forward pass with the updated dropout mask to obtain the output Y. This approach ensures that the network is robust varying energy conditions by incorporating dynamic dropout influenced by the Shapley values of the neurons, along with the QuantaTask optimization to handle energy constraints.
D.6 TAYLOR EXPANSION DROPOUT WITH QUANTATASK OPTIMIZATION
Taylor Expansion Dropout uses Taylor expansion (Li et al., 2016) to evaluate the impact of neurons on loss for dropout adjustments, combined with the QuantaTask optimization handle energy constraints in intermittent systems.
Mathematical Formulation: Let W be the weight matrix of layer. The impact of neuron on the loss function C can be approximated using the first-order Taylor expansion:
OC
AC RM
0a. a
where a, the activation neuron i, and da the gradient loss with respect to the activation.
Define the dropout probability pt for neuron based on the Taylor expansion approximation of its impact on the loss:
X
P:
ac
0a.
a;
+
where À is a scaling factor adjust the overall dropout rate, and i small constant avoid division by zero.
Define binary dropout mask m [m, m2g...... .... m., where m, (0, 1}. Each element of the mask is determined by sampling from a Bernoulli distribution with probability - p::
my Bernoulli -1ppl) pp)
Apply the dropout mask during the forward pass. Let a; denote the activation of neuron i:
dropout
a
a, m7g
Training with Taylor Expansion Dropout and Quanta Task Optimization: Initialize the network parameters W. dropout mask m, and scaling factor X. Define the energy budget Fg for single quanta and for the entire inference. Initialize the loop iteration parameters l.
Compute the activations and apply the dropout mask:
dropout
a; 174
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Compute the loss L(Y, Y) where Y is the output of the network and Y is the target output.
Calculate the gradients of the loss with respect to the activations:
ac
Da
For each layer L and loop within the layer, estimate the energy E, required for the current quanta size 4;:
E, f
E, > En, fuse tasks to reduce the overhead:
Fuse Fuse'Tasks(44 4,4 Eb)
Update E, after task fusion:
E, -
DynuAgentessimmacEnnggyLyy
Update the dropout mask m based on the Taylor expansion approximation:
P:
Da:
a;
+
0
if Bernoulli(1 - pp;) =
my
otherwise
Perform the backward pass to update the network weights, considering the dropout mask:
OL
W - W
ao
where 1) the learning rate and @ denotes element-wise multiplication.
Inference with Taylor Expansion Dropout and QuantaTask Optimization: Check the available energy using DynAgent. If energy is below a threshold, increase the dropout rate to ensure the inference can be completed within the energy budget. Otherwise, maintain or reduce the dropout rate to improve accuracy. Perform the forward pass with the updated dropout mask to obtain the output Y. This approach ensures that the network is robust to varying energy conditions by incorporating dynamic dropout influenced by the Taylor expansion approximation of the neurons' impact on the loss, along with the QuantaTTask optimization to handle energy constraints.
E WORKINGS OF RE-RAM CROSSBAR
E. RE-RAM CROSS-BAR BAR FOR DNN INFERENCE:
ReRAM x-bars are an emerging class of computing devices that leverage resistive random-access memory (ReRAM) technology for efficient and low-power computing. These devices can perform multiplication and addition operations a single operation, making them ideal for many signal pro- cessing and machine learning applications. Moreover, these devices can also be used for performing convolution operations, which are widely used in image and signal processing applications.
E. SIMPLE SINGLE CELL EXAMPLE:
consider a simple example of a ReRAM crossbar array with two cells, where V1 and V2 are the input voltages, G1 and G2 are the conductance values of the ReRAM devices, and II and 12 are the resulting output currents. To perform cultiplication-addiionn and V2 to the rows of the crossbar array. The conductance values GI and G2 of the ReRAM devices are set to the corresponding weight values for the multiplication operation. The output currents I1 and 12 then computed follows:
we first apply the input voltages V1
I- /1+112 12
- V2
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V1
G14
=V
V2
1264 22
G2
M.61
12
SSH
SSH
S&H
ADC
(a) RAM Cell
(b) A Full Re-RAM tile
Figure 5: DNN computation using ReRAM xBAR.
Here, the output currents II and 12 the result of the multiplication of the input voltages V1 and V2 by their respective weight values, which are summed together using the crossbar wires. Please refer Figure for more details. As we can see, the input voltages V and V2 are applied the rows of the crossbar array, while the conductance values GI and G2 are applied to the columns. The output currents Il and 12 are the result of the cattiiliicationaddiiiii operation, and are obtained by summing the currents flowing through the ReRAM devices.
In practice, ReRAM crossbar arrays can have many more cells, and can be used to perform more complex multiplication-adee
and convolution operations. However, the basic principle remains the same, where the input signals are applied to the rows, the weights are applied to the columns, and the output signals are obtained by summing the currents flowing through the ReRAM devices.
E.1.2 EXTENDING TO COMPLEX COMPUTE:
In order to perform multiplication-addiaee -adiition in ReRAM x-bars, two arrays of weights and inputs are used. The inputs are fed to the x-bar, which is two-dimensional array of ReRAM crossbar arrays. The crossbar arrays are composed of a set of row and column wires that intersect set of ReRAM devices (refer Figure 5bp. The ReRAM devices are programmed have different resistance values, which are used to store the weights.
operation, the input signals are applied to the rows of the x-bar, and the weights are applied to the columns. The output of each ReRAM device is the product of the input and weight signals, which are added together using the crossbar wires. This results in single output signal that represents the sum of the weighted inputs.
During the multiplication-addiiii
To perform convolution, ReRAM x-bars The input signal applied to the x-bar in the same way, but the weights are now applied a more structured way. Specifically, the weights are arranged in way that mimics the convolution operation, such that each weight corresponds to a specific location in the input signal. To perform the convolution operation, the input signal is applied to the rows of the x-bar, and the weights are applied to the columns in a structured way. The output signal is obtained by summing the weighted input signals over sliding window, which moves across the input signal compute the convolution.
similar approach, but with
complex circuit.
At the circuit level, the ReRAM x- x-bar for caltiplicationn-addiiioo typically includes several com- ponents, such as digital-to-analog converters (DACs), analog-to-diging converters (ADCs), shift registers, and hold capacitors. The DACs and ADCs are used to convert the digital input and weight signals into analog signals that can be applied to the rows and columns of the x-bar. The shift registers are used to apply the weight signals in a structured way, and the hold capacitors are used to store the operation. Similarly, for performing convolution,
analog signals during the multiplication-addiiie the ReRAM x-bar typically includes additional components, such delay lines and adders. The delay lines are used to implement the sliding window for the convolution operation, while the adders used to sum the weighted input signals over the sliding window.
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F
PSEUDO CODES
F.1 DEPTH-WISE SEPARABLE CONVOLUTION 2D USING TI LEA
Dipt separable convolution is an efficient form of convolution that reduces the computational cost compared to standard convolution. Here we describe the implementation of depth- sep- arable convolution 2D using the Low Energy Accelerator (LEA) in Texas Instruments' MSP430 microcontrollers.
F.1.1 DEPTH-WISE SEPARABLE CONVOLUTION 2D USING CONVID
The pseudo code described in Algorithm implements depth separable convolution 2D (DWSConv2D) using a ID convolution primitive function (convlD). The DWSConv2D function takes four inputs: input matrix, depth-wise kernels (eWskeenels), point-wise kernels (PrWsKernel), and an output matrix. The depth-wise separable convolution is performed in two main steps: depth-wise convolution and point-wise convolution.
Algorithm Implementing Depth-wise Separable Convolution DWSSCow2DO using CONVID
1: Function DWWSeeCCn2DDiinntMaaall Malria,, DW & ernels, PIW sWWsKe Kernel, output Mulpul.Malriz)..
2: Initialize DW sOulput with zero values, same shape impul alrir
3: # Depth-wise Separable (DWs) convolution
4: for + 0 to channels ((mputt atrix) 1:
5: # Apply ID convolution along rows
6: for < 0 to (nuustttttt.Marriiaaaa
7:
conv D(input M :), DW s DW DOOutputtlli))
8:
# Apply ID convolution along columns
9:
for j +- to cols( DW sOulpullc)
10:
conv IDDW (o]uttt[[c[[]:]]] DW Kerseeesssc].: DW DW sOutput(c[(:..)
11:
# Point--ise (PtWs) convolution
12:
Initialize finalOutput with zero values, with cOuttpt) channels BreWsKerree sKernel)] for + 0 to rows (DWsssWWscc) sOutput) - 1:
shape
(tows(DssOuppul
13:
for j to cols(DW sOutput) 1:
15:
for k: 10++0 channels( PtW PPWWsKerii sKernel) - 1: Initialize PtW s.um < for 4 to channelsí DW WWwtOtppttt -
17:
PSmm <- PLW SSmn + DW sOutput (c][]) &Kernel
19:
fínalO [ +- PtWsSum
return /uitalOupput
F.1.2 PSEUDOCODE WITH MICRO-CONTROLLER PRIMITIVES
The following pseudocode describes the steps to implement depth-wise separable convolution using LEA primitives from TT's DSP Library.
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Algorithm 2 depth-wise Separable Convolution 2D Using TEA
DW Kernelss PIWs s K Krrnel, outpud M atrix) 2: Initialize lemp-aatrial and Ceriaaa with zero values, same shape as inpul M alrix
1: function DW
3: Depth-wise convolution
4: for < to chonnels (inpttt (
do
5: !I Apply ID convolution along rows do
6: for & < 0 to rows( (onpusiipttaaaiii (input.Matris(cc)
7:
MSP MSP_CONV CONV_ CCONV_IQ31 (input
DWsK &ernnll [c][0,
LempMatrizl[cIees :]. cols (ibssintttMatrra)) PILTERSSIZ))
8:
end for
9:
I/ Apply ID convolution along columns
for j to cels(teemp/aarraall)))
11:
MSP CONV IQ3 [tempMatrraal(]l:...
DW KKrnels|e][s:00
tempMatriar((]]::.)) rowss((empMarriiii FILTER_S12E)
12:
end for end for
13:
14:
// wosnt-wise convolution
15:
Initialize finalOutput with zero values, [owstemppaarrraa), botp:///iiit)doosttttmm/aaaatii channels(PtW s. erene]])]
16:
for i + to cowss(eepMaarring
- do
for j 0 to cols((empMMarria)) for l < to channels( PIW s sKernel) do Initialize PtW sSum t for с +- 0 to chamellsfeeppMatriin PtWsSum < PtW sSum + tempMattrin2(([ill] PiW (WWseerne[c[[[]] end for FinalOutpul [ + PtW sum end for end for
do
18:
20:
do
22:
23:
24:
25:
26:
end for
27:
return finalOutpur
28:
end function
F.1.3 IMPLEMENTATION CODE
C code that implements the pseudo-code using TI's LEA (Instruments 2024b) functions.
#include <msp430.
#include "DSPLib.h"
#define ROWS 64
#define COLS 64
#define CHANNELS 3
#define FILTER_SIZE 3
// Initialize your input, depth-wise kernels, point-wise kernels,
// and output matrices appropriately
_q31 inputMatrix [enbMMaatrix(HAANEEE..... [CHANNELS] [ROWS] [COLS);
_q31 DWsKernels [CHANNELS] [FILTER SSIEESIEE]] (IILTER_SIEE
_931 PtäsKernel (CHANNELS) [CHANNELS];
_911 tempMatrix1 [CHANNELS] [ROWS] [COLS]
_931 tempMatrix2 [CHANNELS] [ROWS] [COLS]
_31 finalOutput [ROWS] [COLS] [CHANNELS];
void DWSepConv2D () {
// Depth-wise convolution
for (int 0; a < CHANNELS; a++) {
// Apply 1D convolution along rows
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for (int i = C; 1 ROWS; i++) {
happ_cov__aae ic31 (einputMatrix(o) [1] [0], DisKernels [c] [0],
&tempMatrixl [c] [1]] COLS, FILTER SIZE);
// Apply 1D convolution along columns
for (int j - C; j < COLS; i++) {
msp_ lis__cov_iqiiee (6tempMatrixl [c] [i] DisKernels [c] [0],
stempMatrix2 [i], ROwS, [ELTE__SI2E]
// Point-wi se convolution.
for (int 0; i < ROWS; i++) {
for (int = 0;
COLS; j++)
for (int k = 0;
CHANNELS; k++)
_931 PtWsSum 0;
for (int с 0; с < CHANNELS; c++) {
PtWsSum tempMatrix2 [c] [i] [j] PtWskernel [c] [k];
FinalOutput [i] [i] [k] PtWsSum;
F.2 CONv2D
Here deseribe the implementation of task-based 'CONV2D' function using the Low Energy Accelerator (LEA) in Texas Instruments' MSP430 microcontrollers. The function is designed to handle energy constraints by decomposing the convolution loops into smaller quanta tasks. Foloowing are the outline of the requirements:
1. Define "QuantaTaskk as the minimum iterations that can run.
2. Decomposable loops: Each 'QuantaTask" runs certain part of the loop.
3. Check for sufficient energy before launching 'QuantaTask".
4. Fuse multiple 'QuantaTask's to minimize load/store operations.
5. Check for power loss after each 'Quanta'Takk or fused 'QuantaTask"" and checkpoint if necessary.
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Algorithm 3 Task-Based CONV2D Using TILEA
1: Define QuantaT Task ask as the minimum iterations we can run function MAsxBBssECCOVV2GGnppuu Matriz, kernel, output Matria))
2:
3: Initialize tempMatris with values, same shape imput aatria rows rows imputM atrix
5:
cols + cols of inputMatria
6: kernelSize size of kernel
7: i 0
8:
while < rows do
9:
j f-0
10:
while j < cols do
11:
remaiining <- CEAKKKENEEGGQQuanalll (ank))
12:
if remainning is sufficient then
13:
EXEEUUEEQUANTATASKII,, J, input kernel, tempMatria) UPDATEPROGRESS( J, QuantaTasst assk)
14:
15:
if POWERLLSSDEEEECED then
16:
CHECKPOINTÚ.jj j, tempMatria) Memp break end if else
17:
19:
20:
wait for energy to replenish
21:
end if
22:
end while
23: end while
24: FUSETASKS
25: return oulpulMatriz
26:
end function
27:
function EXECUTEEQUANTTTASKK,,, htrp://ww.....ttii.pp.ttttrrrrrr kernel, tempMatria)
28:
for ki + to kernelSize - do
29:
for kj t 0 to kernelSize - do
30:
ki]li + kj). kernelkki][k]], tempMatria(([jj. cots.
SizeelSize)
31:
end end for
32:
33:
end function
34: function FUSETASKS
35:
remmininggverrgy <- CHECKENERGY (AEECKEEENGGYYmullplll.. (mrlltipl QuentaTaskk
36:
while remaminggnergy is sufficient do
37:
EXECUTTEQUANTATTASKI inputMMaria kernel, temp UPDATEPROGRESSSi, multiple_Quantol] QuontaTTask) remainingEEnrrgy CHECKENERGY (mulleiylllllp QuantaTask) if PoTEELLSSDDEEEEEEEE then CHECKPOINT( tempMatriar break end
38:
39:
40:
41:
42:
43:
end while
44: end function
45: function CHuCKKENERGY(HuantaTT ask)
46: # Check if there is enough energy to run the quanta task
47: return Fnnnninnnnnnnneggg
48: end function
49: function PoweRLoSSDETECTED
50: # Check if power loss is detected
51: return Lose
52: end function
53: function CHECKPOINT(i,) j, tampMatriz)
54:
Save the current state to non-volatile memory
55: end function
56: function UPDATEPROGRESSSE j. Quanta Task)
57:
Update loop indices hased the quanta task executed
58:
x-) j Quantolaa Task
59:
if j Z cols then
60:
j 0
61:
1 QuantaTase aas
62:
end if
63:
end function
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F.2.1 IMPLEMENTATION CODE
#include <msp430.
#include "DSPLib.h"
#define ROWS 64
#define COLS 64
#define KERNEL SIZE 3
#define QuantaTask 8
Define the FeRAM addresses for storing the checkpoint data #define TERAM_ADD__] CxF000
#define FERAM ADDR_ CxF002
4define FERAM 1ERAM_ADDR_11 ADDR_TEMPMATRIIN 0XF004
-931 inputMatrix [ROWS] [COLS];
_931 kernel [KERNFI__TZZE] [KERNEL__TZZ]]
_q11 tempMatrix [COLS];
_q31 outputMatrix [COLS];
void TaskBasedcoNV2D () {
int rows ROWS;
int cols COLS;
int kernelSize KERNEL_STZE; int i 0;
while (i rows) (
int j 0;
while (j cols)
int remainingEnergy CheckEnergy (QuantaTask),
if (remainingEnerqy > 0) { Exeeute@unntaaaaxti,,, j, inputMatrix, kernel, tempMatrix) UpdateProgress &j, QuantaTask);
if (Poser
Checkpoint (i, 5, tempMatrix); break;
else
// Mait for energy to replenish
FuseTasks ();
void Execute@uantaTTskkinn (int i, int i, _q31 inputMatrix [] [COLS),
_q31 kernel [] [KERNEI_SIZE), _q31 tempMatrix [COLS])
for (int ki 0; ki < KERNEL_SIZE, ki++) {
for (int kj 0; xj KERNEL_ kj++) {
msp_ccov _irlliilll (EinputMatrix ki]li + kil,
&kernel [ki] [kj], [tempMatrixx [3], COLS, KERNEL_SIZE)) ;
void FuseTasks
int zemainingEnerqy CheckEnergy (TuantaTask); ; while (remainingEneergy 0)
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Published as a conference paper at ICLR 2025
ExecuteQuantaTask (i, ), inputMatrix, kernel, tempMatrix) UpdateProgress (&i, &j, ; remainingfherry CheckEnergy (QuantaTask), if ()owerlossDerectted)) Checkpoint (i, }, tempMatrix); break;
int CheckEnergy (int QuantaTask)
// Energy checking HW interrupt return 1;
int PowerLossDteccted) {
// ower loss detection HW interrupt logic return 0;
void Checkpoint (int i, int i, _q31 tempMatrix (COLS])
// Disable interrupts to prevent corruption during the write process disable_interrupt ();
// Save the indices i and to FeRAM
* ((volatile int*) [ERAM_ADDR_]]] = i; ((volatile FERA) JDDR_
// Save the current state of tempMatrix
FeRAM
// Assuming tempMatrix is a 2D array of dimensions [ROWS] [COLS]
for (int row 0; row ROWS; row++)
for (int col = 0; col < COLS; col++) {
( ((volatile _q31*) FERAM_ADDR_ ADDR_TEMPMATRIX) [row COLS + col] tempMatrix [row] [col];
// Re-enable interrupis emaale_interroug
void RestoreCheckpoint (int xi, int *j, _q31 tempMatrix [COLS] {
// Disable interrupts ()
// Restore the indices and j from FeRAM
*i = + ((volatile int*) ADDR_T);
*j = * ((volatile
// Restore the state of tempMatrix from FeRAM
for (int row 0; row ROWS; row++)
for (int col = 0; col COLS; col++)
tempMatrix [row] [col] (vvoatilee _g31*)
PERAM_AADR.L ADDR_TEEPMATRRXX [row COLS + coll;
/eeenabbe interrupts
enable interruttterruttttc ()
30

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Published as a conference paper at ICLR 2025
void UpdateProgress (int xi, int *j, int QuantaTask) { *j += QuantaTask;
if (*j > COLS) {
*j 0;
*i += QuantaTask;
31


Reviews:
[{"review_id": "9gOJluAI8W", "reviewer": "Reviewer_P7Bk", "summary": "The paper introduces NExUME, a framework addressing issues with DNN training for energy-constrained environments which can't guarantee a sufficient amount of power at all times, such as Energy Harvesting Wireless Sensor Networks. In order to optimise DNN-Training for these unstable conditions, NExUME relies on an estimation of the available resources. For this, a first-of-its-kind dataset containing energy harvesting traces and available computation libraries is introduced.\nThe training process reduces intermittency-related failures by treating the number of loop iterations as learnable parameters and task-fusions to meet energy budgets. Additionally, dynamic dropouts during execution ensure the completion of layers and dynamic quantization balances out the accuracy degradation. An adaptive regularization strategy prevents weights from being undertrained. Lastly, the authors introduce a task-scheduler that adjusts in real-time to the energy conditions estimated.", "questions": "* the BLE board does not have FeRAM and thereby not a classic board for intermittent computing. Why do the authors choose it? How does the intermittent part work here, especially QuantaTask?\n\n* what are the contributions over SOTA?\n\n* what is the performance compared SOTA baselines?\n\n* can you consider a different title?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Embedding energy variability into the training process is a novel idea.\n- Extends existing Neural Architecture Search for intermittent computing systems\n- Evaluation on SOTA datasets and DNNs (in the context of intermittent computing)", "weaknesses": "- Evaluation on SOTA datasets and DNNs (in the context of intermittent computing). While also a strength, it also raises a questions. The ML community has moved on to Attention and Transformers and large scale datasets. This paper does not discuss how such modern architectures can be deployed in the intermittent setting. \n\n- contribution over SOTA remains unclear. The paper cites numerous NAS frameworks for intermittent/MCU computing (and there are more like [1]) and a large body of work on intermittent execution of DNNs such as [2, 3] and numerous papers cited in the introduction. To me, the contribution over these remains unclear, as many aspects are also in these papers. \n\n- lack of SOTA baselines: The paper should compare to SOTA approaches. \n\n- statement such as \"Since we are the first work to propose a new training approach targeted for intermittent devices and inference optimizations\" should be toned down. Instead, please carefully explain your contributions over SOTA and compare them to SOTA baseline. \n\n- ablation study: accuracy and overhead if full power is available \n\n- Overall: this paper is better suited at a system conference, such as SenSys or MobiSys\n\n- the title is misleading, the paper is about more than DNN training. \n\n- BLE board does not have FeRAM and thereby not a classic board for intermittent computing. Why do the authors choose it? How does the intermittent part work here, especially QuantaTask?\n\n\n-  On several occurrences, the paper is written (too) vaguely. E.g. \n      - There is no hint as to how tasks are \"fused\" when executing multiple quanta would exceed the energy budget. To my understanding, the function in only explained in the appendix as part of the source code but not the text.\n      -  Dropout rates are adjusted on \"specific\" criteria. Even though the appendix provides details, this vague style of writing reads weirdly and is better served with examples\n\n- As mentioned on several occasions, a big part of the presented work is the availability of the database of DynAgent which also contains hardware-information, yet only 2 different microcontrollers are used for evaluating the framework. Testing a broader variety of systems seems sensible here\n\n- Drawbacks like up to 34% increased instruction count and up to 17% increased memory bandwidth usage are stated but hardly discussed or put into perspective. While this is not surprising for intermittent computing, the numbers should still be discussed and be compared to other approaches.\n\n- Typos: Figure 3: Sensitivity and ablation study. DN is DynNAS, DF is FynFit, and DI is DynInfer: FynFit -> DynFit\n\n- with a Pixel-5 phone as the host device: does this matter? Any device should do the job.\n\n- the paper has a section LIMITATIONS AND DISCUSSION which also discussed limitations, such as the runtime overhead. The last two sentences, however, read a bit bumpy and should be streamlined and also discussed (and not just stated). \n\n\n[1] Edgar Liberis, Łukasz Dudziak, and Nicholas D. Lane. 2021. ΜNAS: Constrained Neural Architecture Search for Microcontrollers. In Proceedings of the 1st Workshop on Machine Learning and Systems (EuroMLSys '21). Association for Computing Machinery, New York, NY, USA, 70–79. https://doi.org/10.1145/3437984.3458836\n\n[2] Chih-Hsuan Yen, Hashan Roshantha Mendis, Tei-Wei Kuo, and Pi-Cheng Hsiu. 2023. Keep in Balance: Runtime-reconfigurable Intermittent Deep Inference. ACM Trans. Embed. Comput. Syst. 22, 5s, Article 124 (October 2023), 25 pages. https://doi.org/10.1145/3607918\n\n[3] C. -H. Yen, H. R. Mendis, T. -W. Kuo and P. -C. Hsiu, \"Stateful Neural Networks for Intermittent Systems,\" in IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 41, no. 11, pp. 4229-4240, Nov. 2022, doi: 10.1109/TCAD.2022.3197513", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "5Wej5X5dcF", "reviewer": "Reviewer_qDus", "summary": "The paper introduces a framework designed to enable consistent and accurate deep neural network inference on energy-harvesting wireless sensor networks that operate under intermittent power conditions. This framework addresses the challenges of unreliable energy supply and computational limitations in such environments. The proposed framework uses energy variability aware network architecture search, dynamic training optimizations, and an intermittency-aware task scheduler to adapt DNN computations based on real-time energy availability, in order to meet service level objectives (SLOs) in resource-constrained settings.", "questions": "1. How much of the resource of the method is used or what is its time complexity?\n\n2. As a sub-optimal scheduling solution, how would its scheduling performance to be ensured?\n\n3. What is the rationale behind the overall method design?\n\n4. Whether the accuracy is more important than the other performance metrics in your design?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper studies an interesting and important problem of enabling reliable DNN inference in energy-harvesting wireless sensor networks. The writing is overall clear and well-organized. The motivations, methods, and experimental findings are easy to follow.", "weaknesses": "The proposed method relies on detailed profiling of the hardware to model energy consumption, computational capabilities, and memory footprint. This process can be time-consuming and complex, requiring extensive micro-profiling. \n\nIn DynInfer, an energy-aware priority scheduling heuristic is used. With no theoretical analysis of its performance compared to optimal scheduling solution, its scheduling optimality is hard to estimate.\n\nThe explanations of some techniques in the methods section, particularly within the DynFit and DynInfer components, remain at a high level, lacking depth in technical specifics. For example, while the dynamic dropout and quantization strategies in DynFit are introduced, there is limited detail on how dropout rates and quantization levels are adjusted based on energy profiles or how these adjustments differ from standard implementations. Additionally, the methods used in each component lack a sense of innovation, as they seem to be a simple use of existing techniques without substantial enhancements. \n\nThe impact of under-trained and overfitting weights requires further examination. More frequent updates of certain weights do not necessarily lead to \"overfitting,\" and, conversely, infrequent updates do not inherently imply \"underfitting.\" From a layer perspective, the effect of varying update frequencies on individual weights may be limited, suggesting that this issue may be less impactful than indicated. \n\nThe experiments mainly focus on accuracy improvement. Other performance metrics, such as energy consumption, latency, computational overhead, and the number of power failures or SLO violations, are not extensively analysed. \n\nThe experiments are conducted on relatively small datasets and models.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4ddLqWwXxZ", "reviewer": "Reviewer_GUp2", "summary": "The paper presents NExUME, a novel framework for training and deploying deep neural networks (DNNs) on energy-harvesting micro-computers with intermittent power. The authors introduce dynamic dropout rates and quantization levels that adapt based on real-time energy availability, improving the accuracy and robustness of DNNs in constrained power settings. The paper demonstrates NExUME's efficacy in optimizing both training and inference phases through extensive experiments, showcasing significant accuracy gains over traditional approaches in intermittently powered environments. Additionally, the introduction of a unique dataset to facilitate further research on energy-harvesting applications is a noteworthy contribution.", "questions": "1. Can the authors clarify the robustness of NExUME across various hardware platforms beyond those tested? Would modifications be required for different types of microcontrollers or energy-harvesting setups?\n2. How does NExUME handle environments with extremely low or sporadic energy levels, where consistent dropout and quantization adjustments may not be feasible?\n3. Can the authors provide more detail on the potential effects of overfitting introduced by DynFit’s dropout variations? Would techniques like dropout scheduling help mitigate this?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper addresses an important challenge in deploying DNNs on resource-constrained, intermittently powered devices, an area that is underexplored in current literature. By incorporating real-time energy-aware adaptations, this work proposes a unique and valuable solution.\n2. The work is thorough, presenting a well-structured methodology, clearly defined optimization functions, and a series of experiments across various datasets and hardware platforms. The choice of energy-aware dropout and quantization strategies tailored to intermittent environments is both innovative and well-validated.\n3. The paper is well-written, with each component of the proposed framework (DynFit, DynInfer) and the optimization strategies clearly explained. Figures and tables effectively support the results and comparisons.\n4. The proposed approach has broad implications for real-world applications in energy-limited environments, such as remote monitoring and IoT systems, where consistent power is unavailable. The improvements in accuracy (6-22%) and the novel dataset enhance the significance and impact of the research.", "weaknesses": "1. The experiments, while comprehensive, rely on specific hardware configurations that may not be accessible for replication. The reliance on components like MSP430FR5994 and certain energy-harvesting setups may limit reproducibility.\n2. While the paper compares NExUME to iNAS and other energy-aware methods, it lacks a detailed comparison with additional state-of-the-art adaptive or intermittent DNN training techniques. Including broader comparisons could enhance the validation of its claims.\n3. The paper mentions challenges with larger networks and datasets. However, there is limited discussion on potential approaches to address these limitations, which would be valuable for practitioners aiming to scale this approach.\n4. The profiling is based on conservative estimates, which, while practical, may not be universally applicable. Further analysis of the impact of profiling variations on model performance could strengthen the evaluation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FrTQYkrVub", "reviewer": "Reviewer_tANu", "summary": "This paper presents NExUME, a training methodology that is designed to cater to intermittent power energy harvesting systems.   The authors proposed two key contributions which are (1) a new method for training where one can dynamically adjust dropout rate and quantization levels to cater to varying energy availability in the EH system, and (2) a task scheduler that optimizes task completion in EH systems. The authors also contribute a machine status monitoring dataset. NExUME shows a 6 to 22 % accuracy improvement over existing baselines on simple ML tasks. However, at the same time, NExUME incurs a 5% overhead in computation, an increase in the number of instructions ranging between  11.4%-  34.2%, and an increase in memory bandwidth from 6 to 17%.", "questions": "Details on the machine status monitoring dataset are missing in Sec 4.3 How are R1, R2, and R3 different? What are the RPM speeds? What is S1 and S2?\n\nEnergy-aware scheduling is not novel. Can you clarify your novelty with respect to existing scheduling algorithms? \n\nThe authors claim that their machine status monitoring is the first of its kind. Can they clarify what datasets already exist and how the dataset introduced in the paper is different?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "+ This paper is the first to present novel training and inference methods that take dropouts and quantization into account in the context of energy harvesting systems. \n+ A new machine monitoring dataset \n+ The results shown are good when compared to the baselines presented in the paper.\n+ Writing and the presentation of the work are clear. \n+ Choice of datasets is appropriate given that the work is designed for resource-constrained embedded systems. \n+ Decent ablation studies \n+ Actual implementation of such a system is not trivial.", "weaknesses": "- The idea of dynamically adjusting dropout rates and quantization levels is not novel. It is novel in the context of EH systems. \n- Energy-aware scheduling is not novel. \n- The quantification of overheads is done. However, its implications are not discussed. The range in terms of % is indicated. However, how does it vary with the datasets? \n- Some of the existing work in intermittent systems are not compared such as ePerceptive: energy reactive embedded intelligence for batteryless sensors and Zygarde: Time-Sensitive On-Device Deep Inference and Adaptation on Intermittently-Powered Systems\n- Details on the machine status monitoring dataset are missing in Sec 4.3 How are R1, R2, and R3 different? What are their RPM speeds? What is S1 and S2? \n- Only accuracy results are shown.  It is also important to know the latency/inference. and memory requirements of the system. \n- DynFit comprises adjusting quantization levels and dropouts. In the ablation studies, it is unclear which of these is bringing more benefits to the system.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)