MoE-Gyro: Self-Supervised Over-Range Reconstruction and Denoising for MEMS Gyroscopes
Authors: Feiyang Pan
Shenghe Zheng
Chunyan Yin
Guangbin Dou
Venue: NeurIPS 2025 poster ()
Keywords: MEMS Gyroscopes; Signal reconstruction; Noise suppression
Primary area: machine_learning_for_sciences
TL;DR: Self‑supervised MoE‑Gyro restores clipped gyro peaks and denoises without labels, boosting range ±450 deg/s MEMS gyroscopes to ±1500 deg/s and cutting bias instability by 98 %.

Abstract: MEMS gyroscopes play a critical role in inertial navigation and motion control applications but typically suffer from a fundamental trade-off between measurement range and noise performance. Existing hardware-based solutions aimed at mitigating this issue introduce additional complexity, cost, and scalability challenges. Deep-learning methods primarily focus on noise reduction and typically require precisely aligned ground-truth signals, making them difficult to deploy in practical scenarios and leaving the fundamental trade-off unresolved.  To address these challenges, we introduce Mixture of Experts for MEMS Gyroscopes (MoE-Gyro), a novel self-supervised framework specifically designed for simultaneous over-range signal reconstruction and noise suppression. MoE-Gyro employs two experts: an Over‑Range Reconstruction Expert (ORE), featuring a Gaussian-Decay Attention mechanism for reconstructing saturated segments; and a Denoise Expert (DE), utilizing dual-branch complementary masking combined with FFT-guided augmentation for robust noise reduction. A lightweight gating module dynamically routes input segments to the appropriate expert. Furthermore, existing evaluation lack a comprehensive standard for assessing multi-dimensional signal enhancement. To bridge this gap, we introduce IMU Signal Enhancement Benchmark (ISEBench), an open-source benchmarking platform comprising the GyroPeak-100 dataset and a unified evaluation of IMU signal enhancement methods. We evaluate MoE-Gyro using our proposed ISEBench, demonstrating that our framework significantly extends the measurable range from ±450°/s to ±1500°/s, reduces Bias Instability by 98.4%, and achieves state-of-the-art performance, effectively addressing the long-standing trade-off in inertial sensing.Our code is available at:
https://github.com/2002-Pan/Moe-Gyro

MoE-Gyro: Self-Supervised Over-Range Reconstruction and Denoising for MEMS Gyroscopes
Feiyang Pan't, Shenghe t Chunyan Yin'*, Guangbin Dou
1 Southeast University 2 Harbin Institute of Technology
2302384370seu www.sseeeuuueeeeeeeeeoeoeeeee.ee cn
Abstract
MEMS gyroscopes play critical role in inertial navigation and motion control applications but typically suffer from a fundamental trade-off between measure- ment range and noise performance. Existing hardware-based solutions aimed mitigating this issue introduce additional complexity, cost, and scalability chal- lenges. Deep-learning methods primarily focus noise reduction and typically require precisely aligned ground-truth signals, making them difficult to deploy in practical scenarios and leaving the fundamental trade-off unresolved. To address these challenges, we introduce Mixture of Experts for MEMS Gyroscopes (MoE- Gyro). novel self- supervsde framework specifically designed for simultaneous over-range signal reconstruction and noise suppression. MoE-Gyro employs two experts: an Over-Range Reconstruction Expert (ORE), featuring a Gaussian-Deccs Attention mechanism for reconstructing saturated segments; and Denoise Expert (DE), utilizing dual-branch complementary masking combined with FFT-guided augmentation for robust noise reduction. A lightweight gating module dynamically routes input segments to the appropriate expert. Furthermore, existing evaluation lack comprehensive standard for assessing multi-dimensional signal enhance- ment. To bridge this gap, we introduce IMU Signal Enhancement Benchmark (ISEBench), open-souree benchmarking platform comprising the GyroPeak- 100 dataset and a unified evaluation of IMU signal enhancement methods. We evaluate MoE-Gyro using our proposed ISEBench, demonstrating that our framework significantly extends the measurable range from +450% to = +1500% reduces Bias Instability by 98.4%, and achieves state-of-the-ar performance, effectively addressing the long-standing trade-off in inertial sensing. Our code is available at: /ttpp:///itthut com www. Mooe-
Introduction
MEMS gyroscopes are essential inertial sensors extensively utilized in navigation and control systems such as autonomous vehicles, unmanned acrial vehicles (UAVs), robotics, and precssiongguidd munitions 32. In these high-dynamic applications, critical performance metrics of gyroscopes include measurement range (full-scald angular velocity) and noise characteristics, notably Angle Random Walk (ARW) and Bias Instability (BI). However, commercial MEMS gyroscopes typically encounter fundamental performance trade-off: enhancing the measurement range generally results in elevated ARW and BI, whereas sensors optimized for low noise inherently possess restricted angular velocity measurement capability [ (. This fundamental contradiction significantly limits their effectiveness in high-angular-rate scenarios requiring precise inertial measurements.
Addressing this critical limitation without incurring additional sensor complexity or manufacturing costs remains a significant and unresolved challenge in inertial sensor research. Traditional solutions
CCoresponding Author(yincy seu.edu.cn; gdou@ seu.edu.cn). Equal Contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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primarily involve structural and circuit-level strategies, such as resonant frequency tuning (mode- splitting) ( M. closed-loop force-fe control [9, and multi-range readout electronies [O] Although these methods deliver incremental gains, they require tighter fabrication tolerances and more complex control cireuitry, increasing both power draw and manufacturing cost 11] Thus, traditional strategies have yet to adequately resolve these critical trade-offs[[2], Recent advancements in deep learning have emerged as promising solutions for mitigating noise in gyroscopes and, by extension, in complete
(IMU) signals (e.g., CNN LSTM_ [14] (5) ). However, these approaches rely on fully supervised training and thus require
HEROS_ HIROO_GANNLS precisely time-synchree synchronized noisy/clean rotation pairs data that are expensive to collect. Meanwhile, current seff-sueeee methods (e.g., (M IMUDB lack a unified framework that handles both denoising and over-range reconstruction, leaving unresolved the core trade-off that low-noise sensors accept only a limited angular rate range. Moreover, previous work is limited to few single-signal test environments, lacking multidimensional benchmark that captures the full spectrum of enhancement performance; a public suite spanning diverse operational scenarios is essential for fair comparison and real progress.
To overcome the limitations above, we introduce MoE-Gyro, the first self-supervised unified archi- tecture that tackles both over-range reconstruction and denoising. A lightweight gate dynamically routes each input signal segment to two specialized experts, an Over-Range Reconstruction Expert (ORE) and a Denoise Expert (DE), thus cutting inference memory because, in practice, only single expert is active for most segments. Both experts are trained end-to-end on a shared Masked Autoencoder(MAA)
[8 backbone with purely self-supervised objectives, climinating the need for costly, time-synchronised ground-truth labels. We further introduce task-specific more optimisations. For the ORE, Gaussian-Decay Attention (GD-Attn) module in the decoder automatically focuses on the most relevant context for peak reconstruction, while a physics-ifformed energy regulariser (PINN) enforces consistency with the gyroscope's mechanical model, boosting generalisation across sensors. For the DE, we adopt a dual-branch complementary cross-mask that captures weak signal features while smoothing tigh-freeuency noise, and we employ FFT-guided noise injection during training to strengthen the learned denoising mapping. Together, these innovations deliver unified, fully self-supervised solution that simultaneously broadens range and suppresses noise commercial MEMS gyroscopes. In addition, we release ISEBench, the first open-source benchmark with unified suite of evaluation metrics, providing common benchmark for future research on IMU signal enhancement. Our key contributions can be summarized as follows:
Unified self-supervised MoE framework that simultaneously reconstructs over-range signals and reduces noise, breaking the long-standing range-noise trade-off without extra hardware.
We propose a Gaussian-Decas Attention (GD-Attn) and physics-informed neural network (PINN) loss, extending the measurable range of a typical +:400 / MEMS gyroscope to + 1500 %/s.
We design brauhbbranchhee complementary masking strategy combined with FFT-guided augmenta- tion, significantly reducing Bias Instability on the test set by 98.4%.
We release ISEBench, the first open source benchmark specifically tailored for comprehensive evaluation of IMU signal enhancement, along with dedicated dataset for over-range reconstruction, facilitating fair comparisons and fostering rapid progress within the community.
2 Related Works
2.1 IMU over-range signal reconstruction.
Reconstructing saturated signal segments in IMUs remains a critical but significantly under explored problem. Among the few representative studies, HEROS-GAN[IS] formulates the problem as fully supervised generative task, relying heavily on paired saturated and reference data for training. Alternatiely, Matlab 2023b release introduced polynomial based extrapolation function that estimates saturated peaks from their neighboring points; however, this model-driven approach is inherently sensitive to noise and struggles under highly dynamic conditions. However, existing studies have not explored self-super approaches or integrated IMU-specific physical constraints into the reconstruction task.

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Inference Pipeline
Training Pipeline
Kg
K
IKa
Kg
Over-range Reconstruction Expert
aconstruction
Q
0.K
Add PFN
Softmax
2
Denoöse
Encoder
A Allention
Decay
A1
Aug
MAE
Decoder
GD-Attention
Concat
Loss Calculator
Cadle
ORE
DE
Denoise Expert
Threshuld mask
Complementary mask
R Router
Enc.
Dec.
Latent tokens
MOE
Valid output
Noosse
Invalid output
Noise
Dec.
W Wigght share
Clip
Supervision
Pipeline of MoE-Gyro framework. During inference, a low-quality signal stream is segmented, routed by a gate to suitable expert, and the enhanced outputs are concatenated to form the final signal. During training, both experts are optimised in fully self-supervised manner on shared MAE backbone, each equipped with task-specific masking, attention, and loss mechanisms.
Figure
2.2 IMU signal denoise.
In contrast to the sparse literature on over-range reconstruction, signal enhancement research for IMUs has largely centred on noise suppression. Classical, model-driven filters such as EMD denoising 20) and Savitzky- Golay smoothing [1] can isolate and attenuate noise, yet they depend on accurate noise priors, which often fail transfer across sensors or operating conditions. More recent data-driven approaches, including CN) LSTM-GRU hybrids[[4), and the IMUDB [1], replace explicit priors with learned representations and have therefore attracted wider adoption.
3 Method
Although recent supervised and self-supervised models have markedly improved IMU denoising, simply grafting multiple task heads onto one backbone to unify denoising and over-range reconstruction proves unreliable. After normalization, clipped-peat errors dwarf background noise by several orders of magnitude, so reconstruction gradients dominate training, and the network largely ignores the denoising head. The resulting scale-imbalance leaves one task under-fitted and the other
Motivation.
only partially solved, curbing overall accuracy and generalization 22
23 24
This observation motivates decoupled, self-supervised Mixture-off Ex-eeers
Experts design in which each task handled by dedicated specialist while global features are shared only when beneficial. By adopting shared Masked Autoencoder (MAE) encoder combined with lightweight task-specific decoders, each expert is allowed to specialize independently. Moreover, we introduce dedicated task-oriented masking strategies, Gaussian- Attention mechanism, and physics-informed constraints to ensure stable and targeted optimization. This modular, decoupled design ultimately enables more effective training and significantly improved enhancement performance.
Overview. Figure Seguueeshore shows the MoE-Gyro architecture for self-supervised inertial signal enhance- ment. The raw signal is first segmented, and gate then applies simple heuristic to route each segment to the Over-Range Reconstruction Expert (ORE), the Denoise Expert (DE), both experts, or directly to the output. The ORE follows standard MAE backbone but adds task-specific threshold mask to focus on in-range features, and inserts a Gaussian Decaa Attention block in the decoder to selectively amplify peak region information during reconstruction. The DE adopts a dual-branch MAE design in which two parameter-shared encoders/decoders operate on complementary masks, allowing the network to capture intrinsic signal correlations while aggressively suppressing high-

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frequency noise. Finally, the gated outputs of the two experts are concatenated to yield the enhanced signal. The precise routing and concating logic is summarized Algorithm
3.1 Over-range Reconstruction Expert
Gaussian-Decar Attention. Windowed or local attention has proved effective in vision and language models because reduces dis- traction from distant, less relevant context
Algorithm 1: MoR route and concat
Input:
segment x11:L] Output: enhanced y(1:L]
y + x;
26]. Such locality is especially valuable for over-range reconstruction, because the infor- mation required to restore a clipped peak concentrated within short temporal window around the peak. However, a fixed window ignores sensor-speeific dynamics and, being a non-differentiable mask, cannot adapt it- self during learning. Inspired by these is- sues, we introduce Gaussian-Decay Atten- tion (GD-Attn). which replaces the binary window mask with learnable, continuous Gaussian bias. For query-key pair (i:j) sep- arated by dij- = j jl steps, GD-Attn adds a
2 peak < consecutive clipped?;
noise +- run of samples < 7?;
if peak then
s p + PeakExxprt(zz)
end
if noise then
â DenoiseExpert(2)
end 10 for + to L do if peak and xı clipped then < pi;
else noise and [ then
Mer+n-1 &- Pe 6- m
is
end
de, learnable Gaussian bias Bij 22-2 where the single trainable parameter a is initialised
end return y
nominal window size and clamped for stability, With queries Q, keys K, and values V, the resulting attention is
Output AV, A= softmax(QK" /V +
(I)
This Gaussian bias yields a soft, differentiable window whose effective width is learned end-to-end; - 3o the bias disappears and GD-Attn reduces standard global attention, whereas finite smoothly down-weights distant tokens and concentrates capacity on the peak region.
Correlation Loss. Pure L2 reconstruction matches amplitudes but overlooks local dynamics, often smoothing peaks. recover both trend and extrema we define a two-term correlation loss Leor:
Coor
Σ (Ar, A8,)2 + Asign Σ (x. 1 22)² [M
1
where Az, = xt -1 and Ad, are first-order differences of the ground-truth and reconstructed signals; M the set of masked time steps; & {( MM sign(Av.) A (ggn(rr++1)) 1)) marks sign-change (peak/valley) positions within the mask; and Asign weights the extremum term (Asign = 1 by default). The first term aligns local slopes, while the second preserves peak and valley amplitudes. jointly yielding sharper and more faithful reconstructions.
Physics-informed energy loss (PINN), To improve generalisation and ensure that the reconstructed waveform remains physically plausible, we add physics-informed regulariser derived from the displacement-pouke powwe relationship of an IMU's proof mass. Let si denote the reconstructed angular- rate (or acceleration) sequence inside the masked region M. We compute the first and second discrete
derivatives Ar, It Tt-1, 2 Fz+1 2x, + It-1, and define the instantaneous. specific
power = (A 1 + 2 Are- Averaging over the mask gives the normalised energy
E
1
Σ
ct
Fmurm = (F.)
M
BEM
where (()) is the sigmoid. Extremely low or high power violates the mass-spring dynamics implicit in most MEMS sensors, penalise both extremes with barrier term
Cpinn - Eoom) K log( 1 ExcU))
(4)

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where x balances the two sides (x=1 in all experiments). This loss drives the reconstructed segment toward a moderate energy level, complementing the L2 and correlation objectives.
3.2 Denoise expert
Dual-branch complementary masking. The Denoise Expert employs dual-branch MAE whose two branches share all encoder and decoder weights 28]. For each length-L L segment construct two fixed 50 % masks in a cross pattern so that every even patch index is visible to branch and masked for branch B, and vice-versa Formally, MA U MM {1, ..... L} and MA O MB Ø, guaranteeing complementarity. Each branch receives the same noisy input but reconstructs only its own masked positions, which prevents information leakage while ensuring that no salient sample is ever hidden from both branches. After patch embedding the two masked sequences are processed by the shared encoder, padded with mask tokens, and decoded. The partial reconstructions ya and UB are fused as !/inal = V/ MA + YB yB:MB MB, yielding a full-length denoised signal. Weight sharing regularises the model and promotes the extraction of universal features, enabling more effective suppression of nigh-frequency random noise.
FFT-guided training augmentation. Inspired by noise-injection strategies proven effective in speech enhancement 29 30), we introduce an FFT-guided noise-injection scheme that synthesises spectrally matched corruption to create realistic training pairs. We create realistic pairs on-the-fly by injecting weak but genuine motion snippets, guided by the noise power spectrum: (1) Noise-floo estimation: For each raw noise segment we compute its FFT and obtain the power-spectral density (PSD). The median PSD value serves as the local noise floor I moise. randomly sample short motion clip s() from separate repository of real IMU recordings (e.g.. walking. hand-held rotations). The clip is amplitude-scales to a s(t) with = 3 /P max, (s(t), where / is constant. The scaled clip then added the raw noise, yielding Tiixx (4) = Tnoise (1) s(t) (3) Additional corruption: After analysing the PSD,, we synthesise spectrally matched noise (targeting the frequency bands that dominate QN, ARW, and BI) and add the mixture, producing a heavier corruption that forces the model to learn a true denoising mapping rather than smoothing Tmix f Tmix + Tosss (f). (4) Training target: The mixture Tiix is fed to the dual-branch MAE, while the reference signal is defined as Telean = Tnoise (t) + s(t,, without the extra corruption. This forces the network to suppress the added noise yet retain the weak real motion. This FFT-guided augmentation supplies realistic, controllable SNR and teaches the model enhance subtle motion cues rather than over-smooth them.
(2) Weak-signal injection: We
The rationale for using synthesized noise stems from established knowledge of MEMS gyroscope error sources, which are well-chaaacterrizd by IEEE standards and Allan Variance analysis (1]. As any real sensor's noise profile is a composite of these known types, our FFT-guided approach is designed to physically realistic. We first analyze the PSD of real static sensor data to identify the bands corresponding to Quantization Noise (QN), Angle Random Walk (ARW), and Bias Instability (BI). Then, we synthesize noise with a matched PSD, ensuring the key characteristies are replicated. This data-driven weak prior provides significant advantage over injecting generic Gaussian noise or requiring expensive, crffectly--aignndd ground-truth data from gigh-precision sensors.
4 Datasets & Benchmark
This section first details the datasets used for training and evaluation, and then describes IMU Signal Enhancement Benchmark (ISEBench), the unified benchmark we release for fair and comprehensive assessment of IMU signal enhancement methods.
4.1
Datasets
We conduct all experiments on three publicly available dataset. GyroPeak-100 (released with this paper) is 100 Hz collection captured from the iPhone 14 on-board IMU with ground-truth peak annotations and serves as the sole source for training and evaluating the over-range reconstruction network. For the denoising task we adopt the Visual-Inertial dataset [17] and the Autonomous Platform Inertial dataset [32 both down-sampled to 100 Hz. for consistency. Together, these datasets cover a broad spectrum of motion dynamics, providing balanced and comprehensive testbed for the
5

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proposed signal- eehanementnnem pipeline. We follow an / split of each dataset for training and testing, respectively, and all experiments are executed on a single NVIDIA RTX-4060 GPU.
4.2 ISEBench: IMU Signal Enhancement Benchmark
To systematically and objectively evaluate the performance of the proposed inertial signal enhance- ment methods, we introduce and design a comprehensive testbench named IMU Signal Enhancement Benchmark (ISEBench). The ISEBench specifically tailored for inertial measurement unit (IMU) signal enhancement, providing unified evaluation framework that covers multiple practical scenarios. Different from prior works that typically rely isolated single evaluation metrics, ISEBench incorporates structured metric set categorized into three distinct aspects to thoroughly quantify enhancement performance.
Evaluation Metrics: 1. Over-range Reconstruction Metrics: Over-range reconstruction assesses the model's ability to recover over-range peaks that lost when the raw signal is clipped at dynamic-range threshold r before being fed to the network. During evaluation we supply the model with the clipped input zelip clip(z, = while using the unclipped signal ground truth, and we compute all metrics only on those samples for which |a|| т. Concretely, we report Peak Signal-to-Noise Ratio (PSNR), which measures the reconstruction quality of the clipped portions:
1 2 (1 - 22)²,
(Peakmax
[r])
MSE =
PSNR = 10 log
(5)
MSE
Correlation (Corr), the Pearson linear correlation 33 between the reconstructed and ground-truth waveforms over the same peak regions; and Peak Mean-Squared Error (PMSE), which provides a point-wise accuracy measure at the detected peak locations. Let P be the index set of local peaks;
PMSE
E (v 6t)
(6)
[P]
2. Weak Signal Enhancement Metrie: This metric assesses the capability of the proposed approach in extracting and enhancing low-amplitude signals: Signal-to-Noise Ratio (SNR) evaluates weak signal recovery effectiveness. Static Noise Performance Metries: To characterize sensor perfor- mance in static (non-moving. conditions, we adopt standard inertial measurement unit performance metrics defined by Allan variance[3I] [3]] including: Angle Random Walk (ARW), Quantization Noise (QN) and Bias Instability (Bi).These metrics are computed following standard Allan variance analysis methodology described comprehensively in prior studies. The formulas for the above seven metrics are given in the Appendix
Together, these metries constitute ISEBench, unified and transparent yardstick for research. In the following experiments we leverage ISEBench to benchmark our model against state-of-the-ee baselines, highlighting its effectiveness.
Experiments
5.1
Comparison with Previous Results
For the quantitative comparison, we pit MoE-Gyro against nine carefully reproduced baselines drawn from three methodological families: classic model-driven signal processors (EMD, Savitzky-oola filtering, and the Matlab over-range signal reconstruction function); fully supervised deep networks (CNN, KNN, LSTM-GRU and HEROS GAN); and the self-supervised model, IMUDB. To ensure fairness, all supervised baselines retrained on matched data: clipped and full pairs from our Peak database for over-range reconstruction and clean/noisy pairs from the Autonomous Platform Inertial dataset for denoising. Each method is executed exactly specified in its original paper, using the authors' code when available or validated re-implementation otherwise. The resulting performance in ISEBench is summarized in Table I MoE-Gyro attains the best average rank across all metries.
We analyze the performance of different methods separately for over-range reconstruction and denoising tasks. Regarding over-range reconstruction, Table I shows that classical model-driven methods indeed raise PSNR and Corr, but their P P_MSE remains large, revealing limited accuracy at the peak locations. Because these methods extrapolate by incrementally fitting the visible portion

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Table Performance comparison on ISEBench. The best result boldfaced and the second best is underlined. For clarity, each P MSE entry is written as P P_MSE/P MSERAW. and all Allan-variane variance metrics are reported as percentage reduction relative the raw signal (the omitted values are provided in Appendix Cp.
Peak Rec. (T 450' /s)
Weak Sig. SNR
Allan Variance
ModelMetric
PSNR
P P_MSE Corr f
QN L
ARW (//V)
BI
AVG.rank
dB
dB
(%/s
(1/h)
RAW
2.67
10.18
0
Matlab 2023 19
6.03
0.515
0.86
10.02
-25.8%
-3.1%
+5.4%
7.0
EMD
5.44
0.655
0.77
13.85
-91.1%
-85.9%
99.88%
5.3
SG filter 21
4.35
0.767
0.79
12.03
-85.0%
-86.3%
-90.0%
6.6
CN
5.76
0.621
0.85
14.3
-62.5%
-35.9%
-79.4%
6.1
LSTM GRU
5.95
0.495
0.87
19.23
-80.8%
-85.0%
-93.1%
4.3
KNN
3.72
0.752
0.67
12.54
-85.7%
-34.3%
-47.5%
7.7
HEROS GAN
7.7
0.354
0.89
16.86
-92.8%
-51.6%
-58.3%
3.6
IMUDB 17
6.59
0.442
0.82
17.76
-85.8%
-87.8%
-93.7%
3.4
MoE-Gyro
8.29
0.325
0.92
24.19
99.0%
-94.1 %
-98.4%
100%
10¹
Moe-Cyrr HEROS-GAN Mattab
figbliguality
LSIM_GRI
KNN IMUDB
HEROS GAN
Decrease .SEEEE
Mol: Gyro
Allan Variance
10a1
40%
20%
10a
Conemne-grric Tactirak-rrde
0%
10a
10a
10
10'
10
Angular Velocity(%/s
Times(s)
Comparison of reconstruction P_MSE. We compare MoE-Gyro with rep- resentative baselines,a drop of more than 75 % (dashed reference) marks high-quality recovery.
Figure 2:
Figure 3: Allan-varianc, comparison. The red curve corresponds MoE- and shows the best Allan-variance performance cectannce-rriiinng raising the device from consumer nearly strategic grade.
of the waveform. Meanwhile, we compare MoE-Gyro with the best data-driven baseline (HEROS- GAN) and the best model-driven baseline (Matlab2023) by plotting the relative P P_MSE reduction different angular velocity thresholds (Fig- D. At 1500%/s our method still achieves high-quality peak reconstruction, whereas HEROS-GAN deteriorates noticeably beyond 900%/s; the model-driven filter ceases reconstruct peaks effectively once the angular velocity exceeds 600%/s These results further substantiate the limitations discussed above. MoE-Gyro outperforms all baselines thanks to (i) an adaptive MAE mask that keeps peak-relevant patches, (ii) Gaussian -eassy Attention that concentrates decoding the clipped region, and (iii) carefully engineered loss that restores local dynamics (see ablations).
In terms of denoising performance, classical filters lower Allan variinarance terms but also erase faint motion, so SNR barely improves. Supervised deep-learning baselines, trained as single multitask networks, likewise sacrifice SNR because the much larger reconstruction loss dominates optimisation. By routing segments to a dedicated Denoise Expert and training it with FFT-guided noise augmenta- tion, MoE-Gyro delivers the highest SNR while further reducing QN, ARW, and BI; Allan-variance curves in Fig visualise the gain.
5.2 Real-world Experiment
To intuitively demonstrate the practical capability our framework in handling severe over-range conditions, randomly select representative segment from the test set for visualization (Fig. 4

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Table 2: Cross-Device Generalization results
Table 3: Cross-Taie Task Generalization results
Device
PSNRT
ARW Reduction
Task Type
PSNRT
iPhone 14
8.29 /7.70
94.1 %/51.6%
Running Swing
8.33 7.04
Xiaomi 14
7.95 /7.51
86.5 %/48.3%
Jumping
7.70 7.73
Huawei P70
8.28/7.44 /7.41
88.9 %/45.7%
Wrist Twist
8.18 7.56
The segment includes measurements from low-range IMU (IM900, =450%ss, the corresponding ground truth, and the enhanced output from our MoE-Gyro. At the highlighted peak, the true angular velocity reaches -1731.8% significantly exceeding the measurement limit of the IM900 sensor. Despite this substantial clipping, MoE-Gyro effectively reconstructs the peak to -1453.7%s accurately capturing key signal dynamies beyond the nominal range. By contrast, the best com- peting method we tested lifts the same peak only to -1287 "/s and exhibits pronounced waveform distortion around the apex, detailed traces are provided in Appendix C This capability suggests substantial potential for expanding the practical utility of low-cost, limited-range inertial sensors.
1500
5.3 Generalization and Robustness
1000
range High range Reconstraction
To be practical, signal enhancement framework must generalize across different hardware and dy- namic conditions. We evaluated MoE-Gyro' zero- shot generalization capability and its performance on distinct motion types. (MoE-Gyro's results are boldfaced.)
500
Angular velucitt
-500
-1000
-1500
2200
Cross-Device Generalization. Our model trained on data from the iPhone 14, was tested directly on new data collected from Huawei P70 and Xiaomi 14 without any fine-tuning. For new devices, signals only require resampling 100Hz input rate and unit conversion to rad/s. As shown in the Table 2 MoE-Gyro demonstrates strong zero-shot performance, with minimal degradation in over-range reconstruction and robust noise reduction compared the SEROS-GAN baseline. The slight decline denoising expected. as baseline noise characteristics differ between sensors.
1.0
2.0
2.5
Time (S)
Figure 4: Range-extension visualisation. At an actual angular rate of 17731.8%s. our method reconstructs the signal clipped at the 450% sensor limit to -1433.7%
Cross-Task Generalization. We further analyzed over-range reconstruction performance across different motion dynamics present in our dataset: periodic swings (c.g., running), high- amplitdde impacts (.g...jumiing) and high-frequency twists. As shown in Table results confirm that MoE- Gyro maintains stable, high-level performance across these distinct tasks, indicating that it learns general principles of signal dynamics rather than overfitting specific motion patterns.
5.4 Efficiency and Real-Time Performance
For real- applications like robotics and UAVs, computational efficiency is critical. We assessed MoE-Gyro's performance from the perspectives of PC-based real-time processing and embedded deployment feasibility.
Table 4: Performance and Efficiency comparison
Model
PSNRT
SNRt
Inf Time
Ours (Full)
8.29
24.19
117ms
Ours (Comp.)
7.89
21.60
41ms
The full MoE-Gyro model processes 2.56 second data segment in 117 ms on an NVIDIA RTX 4060 GPU. This allows for an overlapping sliding-window approach with a 0.5-second step size, achieving a 2Hz update rate suitable for many mid-level state estimation tasks. The framework acts as Navigation Co-processor, providing high-quality motion updates to supplement system's main navigation filter, rather than operating the low-level, high- high-frequency control loop.
Heros_GAN
7.70
16.86
39ms

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Table 5: MoE ablation results.
Table 6: Impact of GD-Attn Placement
Model
PSNR
SNR
Mem.
Setting
PSNR
P_ P_MSEJ
Corrt
ORE+DE
8.19
24.58
129 MB
No GD-Attn
8.08
0.345
0.87
SingleNet
7.23
12.9
64.7 MB
Encoder-only
8.03
0.345
0.88
MoE-Gyro
8.29
24.19
71.3 MB
Enc.+Dec.
8.27
0.335
0.90
Decoder-only 8.29
0.324
0.92
To evaluate embedded deployment potential, we compressed the model via pruning, reducing its pa- rameter count by 12x 1.85M, comparable to lightweight architectures like MobileNetV2. The com- pressed model significantly improves inference speed with only a minor drop in performance(Tate ( making it viable candidate for deployment on edge AI platforms like NVIDIA Jetson.
5.5 Ablation Studies
In this section, we conduct ablation experiments on the components of our method. By systematically enabling disabling each component, substituting it with simpler counterparts, we quantify how much performance each element contributes to the final system.
Ablation on the MoE. To assess the impact of the MoE architecture itself, we compare alternative expert-invocation schemes with a single multi-task network of equal size. Table (ublee)shon shows that the full MoE-Gyro achieves virtually identical enhancement to calling both the ORE and DE, indicating that the router and concatenation do not degrade either task. A single multi-task network of identical size trails behind on both metries, confirming the advantage of explicit task decoupling, Since most of the time the MoE architecture calls only single expert to process a segment, MoE-Gyro requires roughly half GPU memory consumed when both experts are run unconditionally, while matching their combined quality, demonstrating a clear efficiency gain.
Ablation on the Over-range Reconstruction Expert. We systematically evaluate the in- dividual contributions of GD-Attn, the corre- lation loss, and the PINN regularizer in our Over-range Reconstruction Expert. First, we investigate the optimal placement of the GD- Attn module (Tab, (6. Results show decoder- only integration of GD-Attn achieves the largest improvement. This demonstrates GD-Attn's critical role refining latent representations specifically at the decoding stage, effectively focusing recon- struction capacity clipped regions.
Table 7: PINN vs. Second Smoothness.
Loss
PSNR
P_MSEJ
Corrt
Smoothness
8.02
0.354
0.88
PINN (x=1)
8.29
0.324
0.92
Second, we compare our proposed physics- informed energy loss (PINN) against con- ventional second-order smoothness prior (Tab.
Table 8: Component ablation results.
Model
PSNR1
P_MSEJ
Corr
7
35 3
When evaluated on unseen
No Components
7.68
0.369
0.88
data, our PINN consistently outperforms the smoothness regularizer, improving PSNR by 0.27 dB and reducing P_MSE by 8%, high- lighting the strong generalization ability pro- vided by the physics-basee based constraint.
GD-Attn
7.96
0.364
0.90
Corr
7.83
0.354
0.91
PINN
7.95
0.345
0.90
GD+CoTT
8.21
0.350
0.91
GD+PINN
8.19
0.339
0.91
Corr+PINN
8.08
0.340
0.91
Finally, we comprehensively explore all com- binations quantify their cumulative and complementary effects (Tab. (8. Individually, GD-Attn significantly improves peak restoration, correlation loss notably enhances waveform fidelity, and PINN markedly stabilizes signal reconstruction. Jointly, these components interact positively, resulting in the best overall trade-off reconstruction quality and stability.
All
8.29
0.324
0.92
Ablation on the Denoise Expert. We isolate and analyze three key design choices within the denoising expert: mask strategy, weight sharing, and augmentation strategy. First, we optimize the complementary mask ratio from 0% to 50% (Fig. 5ap, finding that dual-branch architecture with

---

143%
Mask 0%
140%
Block Randiott Cross
arga
Faluuement ratio
131%
Mark 33%
Mark 25%
ratio
Enhinement ratio
120%
FFT FFT-guide
Guass
Markk 50%
100%
100%
100%
30%
48%
40%
20%
30%
SNR
ON
ARW
5NR
0N
ABW
88
5N.
4NN
ARW
11
(a) Mask-ratio comparison
(b) Mask-pattern comparison
(c) FFT augmentation ablation
Figure 5: Ablation studies for the Denoise Expert. (a) Mask ratio: a 50 % mask yields the strongest denoising effect; (b) Mask pattern: the cross mask outperforms block and random patterns; (c) FFT
augmentation: FFT-guided noise injection gives the largest performance gain.
50% mask ratio consistently yields superior noise suppression performance. Next, holding this ratio fixed, we compare different mask patterns (Fig. (b). block mask removes large contiguous regions and thus underperforms significantly, while random masking shows improvements on Allan metrics but still exhibits suboptimal SNR due to residual noise leakage. Our deterministic cross mask achieves the best balance, matching random masking Allan metrics while outperforming in SNR, attributed to complete temporal coverage and minimal information gaps.
We then examine the effectiveness of parame- ter sharing between branches (Tab. 19. While independent branches double model capac- ity, full encoder-decoder weight sharing re- duces parameters by 50% and GPU memory usage by 45% with negligible impact on de- noising quality. Partial sharing variants either reduce efficiency gains or degrade signal qual- ity. Thus, full weight sharing represents the optimal
Table 9: Weight-Sharing study
Weight sharing
SNRt
GPU mem
Params
No share
24.51
116.8
27.8
E share
24.35
76.2
17.15
share
24.27
105.0
24.64
E+D share
24.19
64.4
13.9
trade-off and is adopted.
Finally, we evaluates the impact of our FFT-guided augmentation strategy(Fig, 5ch. Compared to baseline without augmentation, Gaussian noise injection modestly improves SNR but leaves Allan metries largely unaffected. Our FFT-guided augmentation introducing spectrally matched synthetic noise, achieves comprehensive gains across all metrics. These results validate the superiority of using realistic spectral characteristics train a more robust denoiser.
6 Conclusion
In this work, we introduced MoE-Gyro, a novel self-supervised Mixture-of-Expeee framework tailored simultaneously address the long-standing trade-off between measurement range and noise performance in MEMS gyroscopes. MoE-Gyro leverages masked autoencoder (MAE) architectures to independently optimize dedicated experts: an Over-Range Reconstruction Expert (ORE), enhanced by Gaussian-Decay Attention and physics-informed constraints for accurate reconstruction of saturated signals; and Denoise Expert (DE), utilizing complementary masking and FFT-guided augmentation to significantly reduce noise without requiring labeled data. Additionally, we introduced ISEBench, the first open- soen-s evaluation benchmark designed for fair and comprehensive assess- ment of IMU ignall-nhaanemmet methods. Experiments on ISEBench demonstrated that MoE-Gyro extends the measurable range from +450 % +1500 % and reduces Bias Instability by 98. 98.4%, significantly surpassing existing baselines. Despite these advancements, the relatively large size of our proposed architecture may pose challenges for resource-constrriine embedded deployments; future work could thus explore model compression techniques to enable more efficient deployment. Our study opens a promising path to deep learning-bast performance upgrades for MEMS inertial sensors and establishes solid baseline for future research in inertial signal enhancement.
10

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Acknowledgements
The authors would like to express their sincere gratitude to Ph.D. candidate Yongchao Li and Master's student Tao Chen from Southeast University for their invaluable support and thoughtful guidance. This work was supported by the School of Integrated Circuits, Southeast University.
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A Metric Definitions in ISEBENCH
For completeness we list the analytical forms of the seven evaluation metrics used throughout ISEBENCH. Let y - {ye LV the ground-truth sequence, {ūr)-11 the reconstructed (or denoised) sequence, and P (I....,,N) .N the set of local peaks valleys indices.
A.1 Over-range reconstruction metrics
Peak-averaged PSNR. For each test segment s we first locate its maximum absolute in-range value Peak max maxte= Mr and then compute the dataset-level mean peak
Peakmax
Peak Cakkmax
Let Clip denote the sensor's full-scale range (e.g. +450 /s). The peak-averaged PSNR is defined as
(Peakaax Clip)
PSNR 10 logıo
(8)
Σ (v- 02)²
N
Here the numerator reflects the average recoverable headroom between the sensor's clip level and the typical (mean) peak amplitude, yielding a scale that consistent across all segments.
Correlation (Corr). Cor measures the linear similarity between the reconstructed signal and the ground truth y, serving as an indicator of reconstruction linearity. defined as:
Σn (yc (ū: 9)
Corr
(9)
V EE (v: 7) EN 7
where y 1 Ee Yt and sequences, respectively, over N samples.
N ΣN it are the mean values of the true and reconstructed
Peak Mean Squared Error (P (P_MSE). P MSE directly measures the average reconstruction error at the clipped-peak locations, quantifying the fidelity of peak recovery. Let P be the set of time indices where the true signal exceeds the sensor's 's range (i.e. the clipped samples). Then
P MSE
(ve
11)²
(10)
P
where is the ground truth and Or the reconstructed value at sample t.
A.2 Weak Signal Enhancement Metric
Signal-to-Noise Ratio (SNR). SNR quantifies the relative power of the desired signal versus
background noise. Let J.N be the segment of interest and {n+ I the corresponding noise-only sequence. We define
N N
P Psignal
P Phoise
(11)
N
1=1
==1
Then
SNR = 10 log
Pesemal Phoiss
(12)
14

---

A.3 Weak Signal Enhancement Metric
Allan Variance Computation. Given sequence of angular-rate measurements {2s} sampled at interval To, we first form non-overlapping averages over clusters of length m To:
2:
i= i
(13)
m
(=
11
where M = [N/m]. The Allan variance at cluster time T is then
M
og(()) = 2(M - 1)
((n(())=((TT)
(14)
and the Allan deviation u, (T) = vog(T).
From (T) derive three standard performance parameters:
QN (11(1)
(slope 1 at 7
(15)
v3
ARW = o (1) (slope - at = 1)
(16)
/2 22 2
BI min
(17)
extrapolated along the slope -1 region, and (1) denotes the analogous intercept for the slope 1/2 region. Within the testbench, QN and ARW are extracted from the log-log slopes of the raw signal's 's Allan deviation curve and Jy.min is the minimum deviation used to compute bias instability.
Here, 1-1(1) (1) denotes the value of (T)
B Derivation of the Physics-Informed Energy Loss
Mechanical background. For MEMS proof mass of unit mass (m=1) moving along one axis,
the instantaneous mechanical energy (t) =t) + (t),(t), where x(t) and v(t) = =())
displacement and velocity, and & is the effective spring constant. The specific power(time rate of change of energy per unit mass)
de dt
P(t)
vtt,,
a()) = #(t).
(18)
Discrete approximation. Our network reconstructs a discrete angular-rate acceleration) se- quence (ætheez with unit sample period (At=1). We approximate the first and second derivatives by
A A = I4+1 Substituting (16) into (17) and centring the acceleration term yields a discrete specific power
Au = 0 - I1-1,
2x, + Tt-1-
(19)
et
{ ætー + a
Ar.
(20)
acc. at
Mask-aver aver-aee normalised energy. take the mean specific power
Given the set M of masked (lo-be-reeoosstnuted)) indices, we
E
Σ Et
(21)
M
teM
and pass through sigmoid Fnorm = (F.) E (0, to bound the value and allow symmetrical penalties both extremes.
15

---

1.70
and Inck
8.00
-09
8.0
/00
1.52
.003
270.
459
640
750
500
8.1
0.5
Threshold
Tlaveo)
(a)
(b)
(c)
Analysis. MoE-Gyro maintains the best performance across all tested saturation, model-driven methods improve in relative ranking the threshold rises. (b) Sensitivity analysis of À in loss; (c) Reconstruction by HEROS-GAN.
Figure 6: Additional Experiments. (a)
Barrier formulation. reconstruction, whereas values near one indicate unphysical high-frequency ringing. We therefore introduce the barrier
Very small Emorm corresponds to an over-damped (excessively smooth)
Cpinn log( knorm) x. log(1 Enorm).
(22)
where и. balances the penalty on the high-energy side (x=1 in our experiments). Minimising (20) drives Eporm toward moderate value, enforcing a physically plausible energy level while remaining fully differentiable.
C Supplementary Experiments and Data
Analysis on clipping threshold. In the main text we report results for clipping threshold of +4400 /s. To evaluate robustness under more severe saturation, we additionally clip all test signals +600 /s.0 #750 #700% /s and =9000 /s and repeat the reconstruction experiments. For each clipping range, the corrupted signals are processed by our Over-Range Expert and the PSNR computed.
As depicted Figure 6al increasing the clipping threshold naturally reduces the average recoverable headroom Peakmax Clip, leading to lower absolute PSNR values. Crucially, however, our Over- Range Expert still delivers substantial PSNR gains over the raw clipped signals at every tested threshold, demonstrating its robustness across sensors with varying measurement ranges.
weight sensitivity. The total reconstruction loss C L2 + A Leorr + Xp Lpion We fix Ap = 0.5 and vary A₂ from 0.1 to 0.5, then fix A. = 0.5 and vary Ap over the same range. As shown in Figure 5(b), the highest PSNR is achieved (Az, Ap) = (0.5, 0.2). We also evaluated the symmetric setting (Xe Ap 0.2), which underperformed the asymmetric combination. Therefore, we adopt 7₁,2 A 0.5, and Ap 0.2 for all over-range reconstruction experiments.
Real- Real-World World Over- Range Reconstruction with HEROS-GAN. To benchmark against the current state of the art, we applied HEROS-GA GANN succeeds at reconstructing the overall waveform shape, it systematically underestimates extreme values-red halues-recovering recovering the highlighted peak to only -1287.3% and introduces spurious oscillations. This behavior underscores its limited capacity for precise peak recovery under severe clipping.
to the same real-world test segment (Fig [c). While
Supplementary Data for Table reported here in Table I0
For completeness, all numerical entries omitted from Table
16

---

Table 10: Full benchmark results corresponding to Table
Peak Rec. (T = 450% /s)
Allan Variance
ModelLMetric
MSEE
QN +
ARW +
B1 +
(*/²)²
(%/s)
(%/v))
(9/
RAW
181456
0.0004
0.32
10,03
Matlab 2023
93371
0.0002956
0.31
+5.4%
EMD
118916
0.0000357
0.045
0.32
SG filter
139175
0,00006
0.044
1.0
CNN
112750
0.00015
0.205
2.07
LSTM GRU
89847
0.0000767
0.048
0.69
KNN
136533
0.0000573
0.21
5.27
HEROS GAN
64302
0.0000287
0.155
4.18
IMUDB
80158
0.0000567
0.039
0.63
MoE-Gyro
59017
0.000008
0.019
0.157
D More Discussions and Future Directions
D.1 Synergistic Effects of Over-Range Signals and Noise
Noise in MEMS gyroscopes can categorized as either internal device noise Sthermo-mechanicee electronic) or undesired external inputs (e.g.. mechanical shocks). Internal noise defines the sensor's baseline noise floor and amplitude insufficient to cause saturation. contrast, high-amplitude external inputs are legitimate physical signals that cause saturation, resulting in complex mixed signal containing both clipped peaks and potential post-shock ringing.
Our MoE architecture is explicitly designed to handle both scenarios. The Denoise Expert (DE) filters aow-ampltudde internal noise, while the Over-Range Reconstruction Expert (ORE) recovers the waveform of saturated segments caused by external inputs. The gate mechanism routes segments appropriately, allowing the framework to decouple the distinct mathematical objectives of reconstruc- tion and denoising. This design ensures the delivery of high-quality, wide-range, and low-noise signal, forming a reliable foundation for downstream navigation and control tasks.
D.2 Ablation Study on Gating Mechanism
Our choice of a rule-based heuristic gate was moti- vated by its near-zero computational overhead and pre- dictable behavior. To explore alternatives, we trained a lightweight MLP signal segments. We compared its performance against the heuristic gate on the mixed-signal dataset. The MLP gate showed stronger ability to identify noise, leading improved SNR, but was sometimes overly conservative and failed trigger the ORE when needed, slightly reducing PSNR. (Tab While the heuristic gate provided the best overall balance for our current needs, exploring more advanced neural gate architectures remains a key direction for future work.
Table 11: Gate Ablation
Gate Type
PSNR
SNRt
learned gate for classifying
Heuristic gate
7.92
22.89
MLP
7.65
23.91
D.3 Downstream Impact of PINN Regularization
To provide stronger evidence for the role of the Physics-Informed Neural Network (PINN) loss regularizer, we conducted an ablation study assessing its impact across diverse dynamic tasks. We compared the performance of the full model (with PINN) against version without it.
While the unconstrained model achieves a slightly higher PSNR on simpler, periodic Running Swing task, the PINN-constrained model demonstrates far more stable and consistent performance across all tasks. Its performance does not fluctuate drastically with changes in signal dynamies. This highlights the core function of PINN: it trades small amount of specialization simple tasks
17

---

for significantly improved robustness and generalization on complex and varied motion patterns by enforcing physical plausibility.
Table 12: Downstream Impact of PINN
Task Type
PSNR(with PINNY1
PSNR(without PINN)
Running Swing
8.33
8,48
Jumping
7.70
7.39
Wrist Twist
8.18
8.01
D.4 Sensor Fusion Applications
Beyond single-sensor signal enhancement, the methodologies presented in this work, particularly the Denoise Expert (DE), hold significant promise for multi-sensor systems such as Visual-Inertinn Odometry (VIO) and SL.MM. The DE can serve powerful front-end IMU data calibrator, providing a high-quality, low-noise angular velocity and acceleration stream to the main navigation estimator.
A primary challenge in IMU-based navigation is the rapid accumulation of orientation error, especially the unobservable drift in the yaw angle, which severely degrades long-term trajectory accuracy. By effectively suppressing Angle Random Walk (ARW) and Bias Instability (BI), our framework can provide a more stable and reliable inertial input. This corrected IMU data can be pre-integrated and tightly coupled with visual features from a camera, forming a nigh-precision VIO system. Alternatively, for applications where computational efficiency paramount, our method enables an IMU-dominant fusion scheme. In this configuration, the high-quality inertial data drives the state propagation, with camera observations providing periodic corrections, resulting robust and efficient VIO pipeline. This positions our work as a valuable preprocessing step to enhance the accuracy and robustness of downstream multi-sensor fusion tasks.
D.5 Discussion Iterative Denoising
One potential limitation of our current self-supervised training paradigm is that the "low-noise" weak motion signals, used training targets not perfectly noise-free. While they represent significant improvement over the synthetically corrupted inputs, they inherently contain some level of residual noise from the sensor's baseline noise floor. This suggests that the model's performance ceiling is tied to the quality of the training repository.
This observation opens promising avenue for future work: iterative self-purification training scheme. The core idea is to leverage the currently trained MoE-Gyro model to further refine its own training data. The process would involve two stages: 1. Dataset Purification: Use the trained Denoise Expert to perform an initial denoising pass on the entire repository of weak motion signals, creating a "cleaner" set of signals. 2. Model Retraining: Retrain the Denoise Expert from scratch, using this purified dataset as a more ideal training target.
This loop could theoretically be repeated, allowing the model to progressively improve its understand- ing of the underlying signal characteristics by iteratively reducing the noise in its training targets. This concept of iterative refinement to enhance signal estimation shares conceptual similarities with advanced techniques in other signal processing domains, such as learning to smooth in partially known state space models(37). Exploring this self- oel-oinpooiing training strategy presents valuable direction for pushing the performance boundaries of IMU signal enhancement.
E Broader Impacts
This work aims to improve inertial-sensor signal quality through self-supervised Mixture-of- Experts framework. Enhanced MEMS gyroscopes can benefit wide spectrum of applications from consumer electronics and robotics to autonomous navigation-ba enabling higher accuracy without added hardware complexity. While better motion sensing may indirectly influence downstream systems (e.g., drones, vehicles, or defense technologies). we do not foresee any immediate, unique societal risks posed by the algorithm itself beyond those already associated with general improvements in sensor signal processing.
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NeurIPS Paper Checklist
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Reviews:
[{"review_id": "eBERV2Ovvh", "reviewer": "Reviewer_gDzY", "summary": "This paper introduces MoE-Gyro, a self-supervised Mixture of Experts (MoE) framework, for simultaneous over-range signal reconstruction and noise suppression in MEMS gyroscopes. It features an Over-Range Reconstruction Expert (ORE) utilizing Gaussian-Decay Attention and physics-informed constraints, and a Denoise Expert (DE) with dual-branch complementary masking and FFT-guided augmentation. The paper conducts experiments on three public datasets and introduced a benchmark named ISEBench.", "questions": "1. While task decoupling indeed resolves the gradient conflict, it might also mean that subtle synergistic effects between certain tasks are overlooked. For example, it's worth considering whether very high noise levels might change the nature of an over-range signal, or if certain over-range signals are, in fact, noise-induced.\n\n2. It's questionable whether the \"a gate then applies a simple heuristic to route each segment to...\" approach can adequately handle complex noise scenarios. For instance, how would it perform when a signal segment simultaneously contains both over-range signals and noise?\n\n3. The paper's \"FFT-guided training augmentation\" method, designed to enhance data by combining noise PSD with weak motion signals, lacks a discussion of its limitations in synthesizing data that accurately reflects complex real-world noise conditions.\n\n4. The paper contains several typographical errors. For instance, on line 54, \"Over-Range Reconstruction Expert (DE)\" should be corrected to \"Denoise Expert (DE).\"", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\nThe paper proposes a novel approach to IMU precise navigation by decoupling over-range signal reconstruction and noise elimination into two self-supervised frameworks. The method seems novel. Additionally, the experimental design and provided code are comprehensive. The writing is clear, with no major issues.\n\nWeaknesses:\n\n1. The problem studied might be important for MEMS Gyroscopes. But the topic may have limited attention and influence in the NeurIPS community. It would be more appropriate to submit the paper to a conference in more relevant field.\n\n2. Some details of the proposed system framework are not discussed in sufficient depth. The method may exhibit anomalous behavior when encountering complex or unexpected IMU signals, and the paper lacks analysis and experimental validation in this regard.", "was_revised": true, "final_justification": "I would like to thank the authors for their detailed response to my questions. My major concerns have been satisfactorily addressed. Therefore, I decide to raise my rating to weak accept.", "rebuttal": "Thank you for your constructive comments and suggestions. Next is our response.\n\n## Weakness1: Relevance and Impact within the NeurIPS Community.\n\n**A1.** Thank you for your thoughtful feedback. We believe our paper exemplifies the growing field of AI for Science (AI4Sci), which is gaining momentum within the NeurIPS community. Our key contributions include:\n- **AI Empowerment for Overcoming Fundamental Scientific Bottlenecks:** Our work tackles a long-standing challenge in sensor physics, namely the trade-off between measurement range and noise in MEMS gyroscopes. Traditional hardware approaches are constrained by the high cost and complexity of manufacturing and fabrication. We show that AI can overcome these physical limitations through a software-based approach, providing a novel solution for scientific instrument design and expanding AI's role in scientific applications.\n- **Creating New Tools for Scientific Exploration:** Our MoE-Gyro framework boosts low-cost consumer-grade sensors to near tactical-grade performance by AI, making high-precision motion sensing accessible to resource-limited labs, startups, and researchers. This enables scientific exploration in fields such as robotics, autonomous driving, and motion tracking, which previously required expensive equipment.\n- **Building an Open Benchmark to Drive Field-Wide Progress:** We recognize that progress in AI4Sci depends on open and reproducible research. To support this, we introduce ISEBench, the first open-source benchmark for IMU signal enhancement, providing a fair evaluation platform to advance AI-driven inertial sensing research.\n\nIn conclusion, our study falls within the AI4Sci domain and aligns well with NeurIPS’s research focus. We believe it offers meaningful contributions both to the MEMS field and to the broader development of AI methodologies.\n\n\n## Weakness2: Performance under complex or unexpected IMU signals.\n**A2.** Thank you for raising this question. We have addressed it in A3 and A4 of this rebuttal. A more in-depth analysis and additional experiments will be included in the next version of the paper.\n\n## Question1: On the Synergistic Effects of Over-Range Signals and Noise.\n**A3.** Thank you for this insightful question. We would first like to characterize the physical origins of noise. In our context, noise can be classified into two categories: internal device noise and undesired external inputs from the perspective of a downstream task[1].\n- **Internal Device Noise:** This noise primarily originates from thermo-mechanical and electronic sources within the sensor, defining its baseline noise floor. Its amplitude is typically far below the sensor's full-scale range and thus cannot induce an over-range event on its own. Our Denoise Expert (DE) is specifically trained to efficiently filter this type of noise and output a clean signal.\n- **Undesired High-Amplitude External Inputs:** As you rightly pointed out, some over-range signals can indeed be considered as being caused by task-level noise, such as a mechanical shock experienced by a UAV or severe jolts in a vehicle. To the sensor, these external disturbances are legitimate physical inputs with amplitudes sufficient to cause saturation. This results in a complex mixed signal, which contains both clipped peaks that need reconstruction and potentially post-shock ringing noise that needs to be filtered. Our MoE architecture is designed to decouple and process this signal: the Over-Range Reconstruction Expert (ORE) is responsible for precisely recovering the waveform of the saturated parts. The Denoise Expert (DE) is responsible for cleaning up the noise in the non-saturated parts, and a Gate mechanism to route signals to the appropriate expert.\n  \nTherefore, whether handling low-level internal noise or complex mixed signals caused by high-intensity external disturbances, our MoE framework demonstrates the feasibility and superiority of its design. By decoupling the tasks of reconstruction and denoising, which have vastly different mathematical objectives. This provides high-quality, wide-range, low-noise signals that form a reliable foundation for improving downstream tasks, including single-sensor and multi-sensor fusion applications.\n\n## Question2: Performance on Handling Complex Signals.\n\n**A4.** We thank you for your concern regarding the robustness of our gating mechanism. To comprehensively address your doubts, we will first elaborate on our gating design philosophy and then present the results of a supplementary experiment specifically conducted to validate its performance on complex signals.\n\nOur gating is designed to balance efficiency and practicality by using a lightweight, rule-based heuristic with minimal computational cost, suitable for real-time processing. Its main role is to quickly and accurately decide whether a signal segment requires reconstruction, denoising, or both.\nSpecifically, according to Algorithm 1, when consecutive saturation points are detected, a peak flag is set; if the amplitude remains below a preset threshold $\\tau$ for a continuous period, a noise flag is also set. If both flags are true, the segment is sent to both the Over-Range Reconstruction Expert (ORE) and the Denoise Expert (DE) simultaneously, enabling region-specific processing. The final output fuses both experts’ results: ORE’s reconstruction is used for saturated parts, while DE’s denoised output is used for non-saturated parts, ensuring fine-grained handling of complex signals.\n\nTo further validate our gating and fusion strategy, we conducted a supplementary experiment focusing on complex signal segments with both over-range and noise components, as you mentioned, confirming the effectiveness of our approach.\n- Experimental Setup: We created 1,000 mixed-signal test samples by combining real over-range events from the GyroPeak-100 dataset with realistic noise segments spliced into non-saturated regions, ensuring complex and authentic test data.\n- Evaluation Metrics: For mixed signals, we used two metrics: Peak Signal-to-Noise Ratio(PSNR) to assess reconstruction accuracy in saturated parts and Signal-to-Noise Ratio(SNR) to evaluate denoising effectiveness in non-saturated noisy parts.\n  \n| Signal Type | PSNR (↑) | SNR (↑) |\n| :--- | :--- | :--- |\n| Over-range Only | 8.29 dB | N/A |\n| Noise Only | N/A | 24.19 dB |\n| Mixed Signal | 7.92 dB | 22.89 dB |\n\nThe experimental results clearly show that even when processing mixed signals, the reconstruction and denoising performance of our MoE-Gyro framework experiences only a slight decrease.  This provides strong evidence that our gating mechanism and subsequent fusion strategy are both robust and efficient. We will add this supplementary experiment and its analysis to the appendix of our final manuscript to enhance the rigor of our work.\n\n## Question3:  The Limitations of Synthetic Noise.\n\n**A5.** Thank you for your concern about the authenticity Tof our data augmentation. In fact, the types of noise present in gyroscopes are known. We start by defining key MEMS gyroscope noise types based on IEEE standards[2] and Allan Variance analysis[3], which identifies distinct spectral noise components through slope fitting on Allan Variance plots, including: Quantization Noise (QN): Primarily affects the high-frequency band and corresponds to white noise in the frequency domain. Angle Random Walk (ARW): The dominant noise in the mid-frequency band, corresponding to white noise in the angular rate domain.Bias Instability (BI): The dominant noise in the low-frequency band, typically caused by flicker noise (1/f noise), which has a higher power spectral density at lower frequencies.\n\nIn other words, even the most complex noise can be decomposed into a combination of these types. Then, the core idea of our proposed FFT-guided training augmentation is to specifically synthesize these key noise components, rather than simply injecting generic Gaussian white noise. Our specific steps are as follows:\n1. Analyze the Real Noise Spectrum: We first perform a Fast Fourier Transform (FFT) on static data segments collected from the real sensor to obtain its Power Spectral Density (PSD). From the PSD curve, we identify the frequency bands that reflect the different noise components such as QN, ARW, and BI.\n2. Synthesize Noise with Matched Power in Key Bands: We synthesize noise segments with frequency distributions adjusted to closely match the PSD of real noise, ensuring key characteristics like QN, ARW, and BI are well replicated.\n3. Injection and Training: We inject the realistic synthetic noise into training data, enabling the Denoise Expert (DE) to learn a robust model that handles real sensor noise. As shown in Figure 5c, this approach significantly outperforms no augmentation or simple Gaussian noise.\nModeling more complex noise sources remains a valuable direction for future research, and we will add a discussion of this to our revised manuscript to make our work's description more comprehensive.\n\n## Question4:  Typographical Error.\n\n**A6.** Thank you for your careful review. We will correct this issue and ensure typos are eliminated in the next version. We apologize for the oversight.\n\nWe hope the revised version better meets your expectations, if you can improve the score then we appreciate it.\n\n**Reference:**\n\n[1]Fraden,Jacob.Handbook of Modern Sensors[J].Springer New York, 2010, 10.1007/978-1-4419-6466-3.\n\n[2]IEEE Standard Specification Format Guide and Test Procedure for Single-Axis Laser Gyros,\" in IEEE Std 647-2006 (Revision of IEEE Std 647-1995) , vol., no., pp.1-96, 18 Sept. 2006.\n\n[3]D. Allan, “Statistics of atomic frequency standards,” Proceedings of the IEEE, vol. 54, no. 2, pp.  221–230, 1966."}, {"review_id": "XprV1mD2W9", "reviewer": "Reviewer_io28", "summary": "This paper investigates the fundamental trade-off between measurement range and noise performance in MEMS gyroscopes: a high measurement range often comes with high noise, while low noise usually limits the range. The authors propose MoE-Gyro, which simultaneously achieves over-range signal reconstruction and noise suppression without adding extra hardware complexity. They insightfully recognize that directly using a single network to learn both “reconstructing saturated signals” and “signal denoising” would encounter gradient imbalance problems, and thus cleverly incorporate task decoupling, designing loss functions and data augmentation strategies specifically for the two modules. Experimental results demonstrate the advantages of this method over existing technologies, notably achieving substantial sensor performance improvements under unsupervised conditions. Additionally, by releasing datasets and benchmark tools, the authors make a positive contribution to advancing research in this field.", "questions": "NA.", "limitations": "Yes.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. This paper proposes a novel unified framework that simultaneously addresses the problems of over-range reconstruction and denoising for MEMS gyroscopes. The authors introduce a mixture-of-experts model into the domain of IMU signal enhancement. Each module is well designed to align with the task characteristics, effectively tackling these challenges.\n2. The overall architecture follows a decoupling philosophy, employing two dedicated models to separately handle the reconstruction and denoising tasks, thus avoiding mutual interference between the multitasks. The gated routing strategy is simple and efficient. The overall algorithm is solidly designed and works smoothly.\n3. On the ISEBench benchmark constructed by the authors, MoE-Gyro achieves state-of-the-art performance across the metrics, showing significant improvements over traditional filtering and existing deep learning methods.\n4. The authors have also released a high-quality dataset and evaluation toolkit: the IMU Signal Enhancement Benchmark, which I believe will benefit the community.\n5. Additionally, the paper is clearly written and provides detailed methodological descriptions, from which I could effectively gain information.\n\nWeaknesses:\n1. The paper targets applications such as unmanned aerial vehicles and robotics. Thus, algorithm efficiency should also be an important evaluation metric. However, the experiments seem to lack efficiency comparisons. Is it real-time on a PC (RTX4060)? And can it achieve real-time performance on embedded platforms for real-world applications?\n2. More of a question than a weakness: the paper has been thoroughly tested on ISEBench, which includes three datasets. I would like to know how MoE-Gyro generalizes to IMU devices beyond ISEBench. Does it require fine-tuning for specific IMUs?", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive comments and suggestions. Next is our response.\n\n\n## Weakness1: Efficiency and Real-Time Performance.\n\n\n**A1.** We completely agree that for applications such as UAVs and robotics, efficiency is a core metric of equal importance to accuracy.  To address this, we evaluated our method in terms of real-time PC performance, embedded deployment feasibility, and its impact on downstream systems.\n\nFirst, it is important to note that a key innovation of our work is decoupling denoising and reconstruction using an MoE framework, allowing flexible, pluggable expert models. In theory, all lightweight architectures like CNNs or MLPs can be used to adapt the framework for edge deployment.\n\n**Real-time Performance on PC:** Our full MoE-Gyro model, tested on an NVIDIA RTX 4060, processes 2.56 seconds of IMU data (256 samples @ 100Hz) in just 0.117 seconds. In a practical application, this means we can use an overlapping sliding window strategy with a 0.5-second step size to achieve a 2Hz (0.5s) data update rate, which meets the requirements of many online applications that demand high refresh rates.Theoretically, the maximum update rate of the model is 8Hz, and the maximum update rate of the compressed model is 24Hz.\n\n**Analysis for Embedded Deployment:** To address embedded deployment concerns, we compressed our model to about 1.85M, reducing parameters by 12×. This size is comparable to lightweight models like MobileNetV2, showing strong potential for deployment on embedded AI platforms such as NVIDIA Jetson after standard optimization. Then, we compared the performance and efficiency of our full and compressed models with baselines to illustrate trade-offs intuitively.（Inference time measured on RTX4060）\n  \n| Model | PSNR (dB) (↑) | SNR (dB) (↑) | Inference Time (ms) (↓) |\n| :--- | :--- | :--- | :--- |\n| MoE-Gyro (Full) | 8.29 | 24.19 | 117 |\n| MoE-Gyro (Comp.) | 7.89 | 21.60 | 41 |\n| Heros_GAN | 7.70 | 16.86 | 39 |\n| IMUDB | 6.59 | 17.76 | 173 |\n\n\nThe table shows our compressed model greatly improves efficiency with only a slight performance drop, outperforming other methods in the performance-efficiency trade-off. Smaller models can also be used by replacing Transformer backbones with CNNs or MLPs for specific tasks.\n\n**Role in Downstream Systems:** Finally, we wish to clarify the precise role of our algorithm within a robotic or UAV system. It is not intended to replace the low-level attitude control loop that runs at several hundred Hertz. Instead, MoE-Gyro acts as a Navigation Co-processor. At a moderate frequency (e.g., 2Hz), it provides the system's mid-level state estimator with a motion update that has been denoised and over-range reconstructed. This is crucial for ensuring long-term navigation accuracy in GPS-denied environments.\n  \n## Weakness2:  Generalization Capability.\n\n\n**A2.** This important question highlights our model’s practical utility. We will clarify how our framework adapts to different IMUs and present two supplementary experiments demonstrating its generalization across devices and tasks.\n\n**Device:**  We only need to resample the signal frequency to adapt to any IMU device. Our framework accepts signals at a 100Hz input rate. Therefore, for any new IMU, the user simply needs to adjust the signal to 100Hz via standard downsampling or interpolation before feeding it to the model. Attention must also be paid to the units of the angular velocity signal; if the device's output is in deg/s, a unit conversion to rad/s (by multiplying by π/180) is required. The framework has a built-in Z-score normalization module, so users do not need to manually handle data scaling issues.\n\nTo quantitatively evaluate the model's generalization to different hardware, we conducted a cross-device experiment. We used the model trained on the ISEBench dataset and performed zero-shot generalization testing on new data collected from a Huawei Pura 70 and a Xiaomi 14.\n\n| Device | PSNR (MoE-Gyro) (↑) | PSNR (HerosGAN) (↑) | ARW Red. (MoE-Gyro) (↑) | ARW Red. (HerosGAN) (↑) |\n| :--- | :--- | :--- | :--- | :--- |\n| Training Device (iPhone14/Bosch BMI160) | 8.29 dB | 7.70 dB | 94.10% | 51.60% |\n| Xiaomi 14 (Zero-shot) | 7.95 dB | 7.51 dB | 86.50% | 48.30% |\n| Huawei Pura 70 (Zero-shot) | 8.28 dB | 7.41 dB | 88.90% | 45.70% |\n\nThe results show our model generalizes well to new devices, with minimal drop in over-range reconstruction and slight decline in denoising. More experiments will be included in the final manuscript.\n\n**Task:**  To verify whether the model can generalize to different types of dynamic tasks, we performed a simple classification of the over-range signals in our data based on their motion cause and evaluated the model's performance on each. The main categories include: periodic swings (running), impacts (jumping), and high-frequency twists. The performance is as follows:\n\n| Task Type | PSNR (MoE-Gyro) (↑) | PSNR (HerosGAN) (↑) |\n| :--- | :--- | :--- |\n| Running Swing | 8.33 dB | 7.04 dB |\n| Jumping Impact | 7.70 dB | 7.73 dB |\n| Wrist Twist | 8.18 dB | 7.56 dB |\n\nThe experimental results show that our model's performance is stable and remains at a high level when processing these distinctly different dynamic tasks. This proves that it has learned the general principles of signal reconstruction, rather than memorizing specific motion patterns.\n\nTherefore, based on the strong zero-shot cross-device performance and the stable cross-task performance, we are confident that the MoE-Gyro framework possesses excellent generalization capabilities and can adapt to diverse real-world application scenarios.\n\nWe hope the revised version better meets your expectations, if you can improve the score then we appreciate it."}, {"review_id": "7YHpGBXF9T", "reviewer": "Reviewer_TRuX", "summary": "This paper aims to achieve long-range measurement and denoising performance at the same time. It adopts a Mixture of Expert (MoE) structure consisting of two experts, one for long range reconstruction and one for denoising. This method achieves state of the art (SoTA) performance on their proposed dataset called ISEBench.", "questions": "1 During training of denoise expert (DE), why can we assume that the randomly sample real recording clip s(t) is noise-free? If not, how can you make sure that DE cancels the noise in s(t)?\n\n2 From Table 5, we can see that the contribution of PINN is relatively small. Is it because the ideal mass–spring dynamics may not be valid in practical cases?", "limitations": "See weaknesses.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1 The paper is in general well written, with easy-to-follow language.\n2 The first self-supervised method to tackle both over range measurement and denoising together.\n3 Provide an open source IMU signal enhancement test bench.\n\nWeaknesses:\n1 The paper mentioned that the main weaknesses of traditional model-based methods is on the increased power draw and manufacturing costs. However, the proposed self-supervised architecture is also relatively complex and computationally heavy.\n2 The training and test split across datasets isn’t clearly described in terms of temporal or domain diversity. Namely, there’s no cross-device or cross-domain generalization test.\n3 The paper claims that it is doing label-free self supervised learning. However, when training the denoise expert (DE), it make use of synthetically generated noise, which may introduce implicit supervision from the noise assumptions.", "was_revised": true, "final_justification": "During rebuttal discussions, the authors satisfactorily addressed my main concerns about the following issues.\n1. the tradeoff between computation cost and effectiveness, through additional experiments on PSNR, SNR against inference time compared with other baselines.\n2. Across device and across task generalization, through additional experiments.\n3. the realism of the synthetic noise clarified my concerns on the implicit supervision.\nThat's why I raised my score from 4 to 5.", "rebuttal": "Thank you for your constructive comments and suggestions. Next is our response.\n\n## Weakness1. On the Issue of Cost-Effectiveness.\n**A1.** We fully agree that computational cost is a critical factor for software solutions addressing hardware limitations. We explain below, from three perspectives, why our method offers strong cost-effectiveness.\n\n**Algorithmic Efficiency Optimization and Trade-offs.** Through pruning, we have successfully compressed our model to approximately 1.85M, a size that is well within the capacity of modern embedded AI platforms. To intuitively demonstrate its benefits, we provide the following performance-efficiency table（Inference time measured on RTX4060）:\n\n| Model | PSNR (dB) (↑) | SNR (dB) (↑) | Inference Time (ms) (↓) |\n| :--- | :--- | :--- | :--- |\n| MoE-Gyro (Full) | 8.29 | 24.19 | 117 |\n| MoE-Gyro (Comp.) | 7.89 | 21.60 | 41 |\n| Heros_GAN | 7.70 | 16.86 | 39 |\n| IMUDB | 6.59 | 17.76 | 173 |\n\n\nThe table shows our compressed model greatly improves efficiency with minimal performance loss, supporting low-cost deployment. Theoretically, our proposed MoE decoupling framework can accommodate models of any size, allowing smaller models to be used for edge deployment.\n\n**Synergy with Hardware Process Improvements.**  Our framework complements hardware advances; its decoupling design supports all sensor levels and delivers better results as sensor quality improves.\n\n**System-Level Computational Cost(Reusing Existing Compute Units).**  Our method offers a substantial advantage in overall system cost by eliminating the need for dedicated compute hardware. Traditional solutions often depend on complex ASICs and high-precision manufacturing, which increase hardware expenses. In contrast, our algorithm can be deployed on existing compute units already integrated into platforms such as UAVs and robots, where they are typically used for tasks like vision, planning, and control. By running as an additional task, our method introduces minimal computational overhead, requiring no extra hardware or power consumption.\n\nIn summary, through its own algorithmic optimization, synergy with hardware advancements, and the reuse of computational resources at the system level, our method provides a more flexible and cost-effective solution than the traditional hardware upgrade path.\n\n## Weakness2: Generalization Capability.\n\n**A2.** This important question highlights our model’s practical utility. We will clarify how our framework adapts to different IMUs and present two experiments demonstrating its generalization across devices and tasks.\n\n**Device:** Before presenting the experimental results, we would like to briefly clarify how our framework adapts to different IMU models. The process is straightforward: the user only needs to adjust the input signal to 100Hz via standard downsampling or interpolation and ensure the units are in rad/s.\n\nTo quantitatively evaluate the model's generalization to different hardware, we used the model trained on ISEBench (with data primarily from an iPhone 14) to perform zero-shot generalization testing on new data from a Huawei Pura 70 and a Xiaomi 14. The results are as follows:\n\n| Device | PSNR (MoE-Gyro) (↑) | PSNR (HerosGAN) (↑) | ARW Red. (MoE-Gyro) (↑) | ARW Red. (HerosGAN) (↑) |\n| :--- | :--- | :--- | :--- | :--- |\n| Training Device (iPhone14/Bosch BMI160) | 8.29 dB | 7.70 dB | 94.10% | 51.60% |\n| Xiaomi 14 (Zero-shot) | 7.95 dB | 7.51 dB | 86.50% | 48.30% |\n| Huawei Pura 70 (Zero-shot) | 8.28 dB | 7.41 dB | 88.90% | 45.70% |\n\nThe results clearly indicate that on the over-range reconstruction task (measured by PSNR), our model exhibits excellent zero-shot generalization capabilities, with almost no performance loss on the Huawei device and maintaining a high standard on the Xiaomi device. On the denoising task (measured by the ARW reduction percentage), the zero-shot performance shows a slight decrease. This is expected, as the baseline noise characteristics differ across devices. Further results after fast fine-tuning will be included in the final manuscript.\n\n**Task:**  To validate the model's generalization to different types of dynamic tasks, we categorized and evaluated its performance on over-range signals from our dataset based on their motion cause, including periodic swings (running), impacts (jumping), and high-frequency twists.\n\n| Task Type | PSNR (MoE-Gyro) (↑) | PSNR (HerosGAN) (↑) |\n| :--- | :--- | :--- |\n| Running Swing | 8.33 dB | 7.04 dB |\n| Jumping Impact | 7.70 dB | 7.73 dB |\n| Wrist Twist | 8.18 dB | 7.56 dB |\n\nThe results confirm our model's stable, high performance on diverse dynamic tasks, suggesting it captures general reconstruction principles rather than overfitting to motion patterns.\n\nTherefore, the strong cross-device and cross-task results suggest that the MoE-Gyro framework has robust generalization and broad applicability in real-world scenarios.\n\n## Weakness3: On the Issue of Implicit Supervision.\n**A3.** We thank you for your insightful point regarding implicit supervision. Although data augmentation introduces prior knowledge, our approach retains key advantages over supervised methods, and we provide justification for using predefined noise types.\n\n**Advantage:** Traditional supervised learning needs costly, high-precision sensors with perfect synchronization for ground-truth data. Our self-supervised method avoids these expenses, which is why we call it label-free self-supervised learning.\n\nWe want to emphasize that for sensors like MEMS gyroscopes, the primary random noise processes are not infinitely unknown. Based on decades of research and industry standards such as those from the IEEE, the noise characteristics are dominated by a finite set of key components with well-defined physical models[1]. In other words, any real-world noise is a combination of these noise types.\n\nAs described in Section 4.2 of our paper, these noise components can be precisely identified and quantified using Allan Variance, and they primarily include Quantization Noise (QN), Angle Random Walk (ARW), and Bias Instability (BI). These noises have distinct spectral characteristics. Therefore, our generation method uses combinations of these noise types to simulate real-world noise. This makes our synthesis task both reasonable and bounded.\n\nIn short, our FFT-guided noise synthesis uses real sensor PSD data instead of assuming simple Gaussian noise, providing a data-driven weak prior rather than relying on labeled signals from external devices.\n\n\n## Question1: On the Noise within the Real Signal $s(t)$ during DE Training\n\n**A1.** Thank you for the insightful question. We do not assume that $s(t)$ is noise-free. Our design focuses on enabling the model to learn a denoising mapping by training it to remove the extra synthetic noise $x_{noise}^{\\prime}(t)$ that we inject. This comparative training approach allows effective denoising even when $s(t)$ contains noise.\n\n* **Training Input :**\n    $$x_{mix} = (x_{noise}(t) + \\alpha s(t)) + x_{noise}^{\\prime}(t) $$\n* **Training Target :**\n    $$x_{clean} = x_{noise}(t) + \\alpha s(t)$$\n\nThe model preserves the original noise because it is included in the training target $x_{clean}$. To minimize loss, the model must fully reproduce the target signal, including baseline noise from both $x_{noise}(t)$ and $s(t)$.\n\nAt a practical level, we use the scaling factor $\\alpha$ to adjust the scale of $s(t)$ to be just slightly above the baseline noise level. This ensures that the absolute energy of the noise contained within $s(t)$ is kept at a low level (much lower than the synthetic noise $x_{noise}^{\\prime}(t)$), preventing it from becoming a dominant interference in the training process.\n\n## Question2: The Impact of the PINN.\n**A5.** We thank you for your detailed analysis of our ablation study. The addition of PINN to the final model does bring a certain level of improvement. Furthermore, regarding the positioning of PINN, we see it primarily as a physics-based regularizer. We hope to use it to:\n- **Ensure physical plausibility:** making sure the reconstructed signal waveform adheres to basic dynamic principles and avoids unrealistic, overly-oscillatory, or overly-smoothed pseudo-signals.\n- **Enhance generalization capability:** by incorporating universal physical laws, it guides the model to learn more general features, thus making it more robust when encountering new motion patterns not seen in the training set.\n\nOur PINN loss is based on an idealized physical model. As described in Appendix B of our paper, we calculate the discrete specific power, $e_t=(\\Delta^{2}x_{t-1}+\\Delta^{2}x_{t})\\Delta x_t$, and then use a barrier loss function to penalize physically implausible reconstructions that have either excessively high (oscillatory) or low (overly-smoothed) energy.\n\nHowever, real-world sensors show complex effects beyond our ideal mass-spring model, which may limit PINN’s performance gains. Nonetheless, PINN helps ensure physical plausibility and improves generalization.\n\nWe hope the revised version better meets your expectations, if you can improve the score then we appreciate it.\n\n**Reference：**\n\n[1]IEEE Standard Specification Format Guide and Test Procedure for Single-Axis Laser Gyros,\" in IEEE Std 647-2006 (Revision of IEEE Std 647-1995) , vol., no., pp.1-96, 18 Sept. 2006."}, {"review_id": "FVCtzgavGx", "reviewer": "Reviewer_Ztva", "summary": "This paper proposes a novel self-supervised framework, MoE-Gyro, to simultaneously address over-range signal reconstruction and noise reduction in MEMS gyroscopes which commonly used in inertial navigation but limited by a trade-off between range and noise. The architecture uses a Mixture-of-Experts (MoE) approach with two specialized branches: an Over-Range Reconstruction Expert (ORE) enhanced by Gaussian-Decay Attention and physics-informed loss, and a Denoise Expert (DE) equipped with dual-branch masking and FFT-guided augmentation. A lightweight gating mechanism dynamically routes signal segments to the appropriate expert. The authors also introduce ISEBench, a new benchmark, and show that MoE-Gyro significantly outperforms existing methods.", "questions": "See weaknesses 1-4.", "limitations": "See weakness 1.\n\nThe reviewer believes that a discussion of alternative MoE architectures (such as multipath or non-exclusive routing) and their implications on training dynamics, as well as the potential modifications required in other components of the design, would strengthen the paper (interests a wider audience and followup work).", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1. The paper is motivated by a practical real-world challenge, i.e., the inherent limitations of current MEMS gyroscope systems, particularly the trade-off between extending measurement range and achieving effective noise reduction.\n2. Motivated by the observation that naively unifying denoising and over-range reconstruction leads to reconstruction loss dominating while the denoising loss is largely ignored, the paper proposes a unified self-supervised framework based on a Mixture-of-Experts (MoE) architecture. Both the Over-Range Reconstruction Expert (ORE) and the Denoise Expert (DE) are thoughtfully and appropriately designed for their respective tasks.\n3. The paper introduces a new benchmark, ISEBench, which comprises two publicly available datasets along with a newly collected dataset by the authors. The benchmark also features a set of thoughtfully designed evaluation metrics to enable comprehensive assessment of IMU signal enhancement methods.\n4. The evaluation is thorough, including both baseline comparisons and ablation studies, as well as a real-world experiment which the reviewer finds commendable and appreciates.\n\nWeaknesses\n\n1. While the design of the MoE architecture and routing logic is well motivated by the observation that naively combining denoising and over-range reconstruction leads to training imbalance, it remains unclear to the reviewer whether the strict either-or routing choice is the most appropriate or only viable solution. It is plausible that a signal segment could be both clipped and noisy. In fact, when a sensor experiences repeated clipping events, the resulting signal may exhibit increased noise or instability, suggesting that simultaneous application of both experts could be beneficial in some cases.\n2. Although the router is lightweight, it is based on hard-coded heuristics rather than a learned gating mechanism, and it does not provide any form of confidence estimation for its expert selection.\n3. The PINN constraint employed is a simplified energy-based loss that does not explicitly enforce the true physical dynamics of the system. This simplicity could be considered a strength, provided stronger empirical evidence (particularly in demonstrating its effectiveness across diverse applications and its impact on downstream task performance). The reviewer does not find the evaluation conclusive for this point.\n4. The evaluation effectively demonstrates the superiority of the proposed method in both denoising and reconstructing clipped peaks compared to baseline approaches. However, the practical implications for real-world applications remain unclear. Specifically, it is uncertain how much improvement in downstream performance (.e.g, in navigation, localization, or sensor fusion) denoising+reconstruction actually delivers. Evaluating the method within such end-to-end pipelines would strengthen the paper's claims and its practical utility.", "was_revised": true, "final_justification": "Accept.", "rebuttal": "Thank you for your constructive comments and suggestions. Next is our response.\n\n## Weakness1: On the Either-Or Routing Choice.\n\n**A1.** We thank you for your in-depth thinking and professional questions regarding our routing logic. This seems to be due to our unclear wording. In fact, our routing mechanism can ensure the use of two experts simultaneously, the use of a single expert, or even no expert at all.\n\nOur framework is designed to handle mixed signals effectively. According to Algorithm 1, when a signal segment meets both clipping and noise conditions, it is routed to both the Over-Range Reconstruction Expert and the Denoise Expert. The final output is then constructed through an intelligent fusion strategy: reconstructed results from the Over-Range Reconstruction Expert are used for the clipped, saturated parts of the signal, while denoised results from the Denoise Expert are applied to the non-saturated, noisy parts. This region-specific processing approach allows efficient handling of mixed-signal scenarios as described.\n\nWe conducted a supplementary experiment using mixed-signal test samples, created by combining real over-range events with real noise segments, to quantitatively evaluate our framework’s performance on complex signals.\n\n| Signal Type     | PSNR (↑) | SNR (↑)  |\n| :-------------- | :------- | :------- |\n| Over-range Only | 8.29 dB  | N/A      |\n| Noise Only      | N/A      | 24.19 dB |\n| Mixed Signal    | 7.92 dB  | 22.89 dB |\n\nThe results show our MoE-Gyro framework maintains high reconstruction and denoising performance on mixed signals. We will include this experiment and analysis in the appendix and improve the explanation of our MoE approach in the final manuscript.\n\n## Weakness2: On the Heuristic-based Gating Mechanism.\n\n**A2.** We thank you for your professional feedback on our gating mechanism design. Your points regarding a learned gate and confidence estimation are indeed important directions for improving the system's robustness and intelligence. Our choice of a rule-based heuristic gate was a trade-off, with its main advantages being: near-zero computational overhead, as well as clear and predictable behavior, which greatly facilitates system debugging, validation, and deployment.\n\nWe considered using a lightweight MLP as a learned gate for classifying pure noise, pure over-range, and mixed signals. However, since these signal types have distinct features like amplitude and saturation duration, a simple heuristic gate sufficed for current needs. We supplemented the training with an MLP as a pre-classification gate and conducted comparative experiments on mixed signals. The experimental results show that MLP has a strong ability to identify noise in mixed signals, while overrange experts are sometimes not called upon.\n\n| Gate Type      | PSNR(↑) | SNR(↑)   |\n| :------------- | :------ | :------- |\n| Heuristic gate | 7.92 dB | 22.89 dB |\n| MLP gate       | 7.65 dB | 23.91 dB |\n\nWe agree that for more complex cases, a learned gate would be better, and we plan to explore such neural network gate architectures as a key focus in future work.\n\n## Weakness3: On the Downstream Impact of PINN.\n\n**A3.** Thank you for your insightful comments and request for stronger evidence on our PINN design. We agree that its value requires robust cross-scenario validation and have conducted an ablation study to quantitatively assess PINN’s role across diverse dynamic tasks.\n\nWe selected three representative tasks with distinctly different dynamic characteristics from our dataset and compared the performance of our full model (with PINN) against a version with the PINN module removed (without PINN). The selected task categories include periodic swings (running), impacts (jumping), and high-frequency twists (wrist).\n\n| Task Type | PSNR (with PINN)(↑) | PSNR(without PINN)(↑) |\n| :--- | :--- | :--- |\n| Running Swing | 8.33 dB | 8.48 dB |\n| Jumping Impact | 7.70 dB | 7.39 dB |\n| Wrist Twist | 8.18 dB | 8.01 dB |\n\nFor the simple Running Swing task, the unconstrained model might achieve a slightly higher score, potentially through overfitting. However, looking at the overall picture, the performance of the PINN-constrained model is far more stable and consistent than the unconstrained one. Its performance does not fluctuate drastically with significant changes in task dynamics.\n\nThis precisely demonstrates the core role of PINN as a regularizer: by introducing a physical prior, it trades a small amount of overfitting capability on simple tasks for significantly stronger robustness and generalization capability on complex and diverse tasks.\n\n## Weakness4： On the Improvement in Downstream Tasks.\n\n**A4.** Thank you for highlighting this important limitation. We fully agree that end-to-end downstream evaluation is the ultimate validation of our work. The absence of such studies in our current paper is primarily because our focus has been on tackling the foundational challenge of enhancing MEMS gyroscope performance at the signal-source level. Investigating downstream tasks will be one of our key directions for future research.\n\nFurthermore, we would like to clarify that the core metrics we improved, especially the Allan Variance indicators, are mathematically and empirically linked to downstream navigation performance[1]. In the field of inertial navigation, established theory and extensive literature have proven that a sensor's Bias Instability (BI) is the primary cause of integrated position error that grows quadratically or cubically with time [2]. Meanwhile, Angle Random Walk (ARW) leads to error growth proportional to time to the power of 1.5 [2]. Therefore, the substantial reduction of these metrics in our work will, in theory, necessarily suppress long-term navigation drift, leading to significant accuracy improvements in downstream tasks such as navigation and localization.\n\nThank you for your valuable suggestion. Integrating our framework into a full navigation system and evaluating its impact on final trajectory accuracy is a key direction of our future work. Your feedback has reinforced our commitment to this goal, and we will highlight it clearly in the future work section of our paper.\n\n## Limitation1： Discussion of Alternative MoE Architectures.\n\n**A5.** We wholeheartedly agree that including a discussion of alternative MoE architectures would greatly enrich our paper, offer valuable insights for future researchers, and broaden its overall impact. While some related points are touched on in A2 of the rebuttal, we will add a dedicated subsection in the final manuscript to explore this topic in more depth.\n\nWe hope the revised version better meets your expectations, if you can improve the score then we appreciate it.\n\n**Reference：**\n\n[1] K. Yuan and Z. J. Wang, “A simple self-supervised imu denoising method for inertial aided\n navigation,” IEEE Robotics and Automation Letters, vol. 8, no. 2, pp. 944–950, 2023.\n\n[2] Woodman O J , Woodman C O J .An introduction to inertial navigation.Journal of Navigation, 2007, 9(3)."}]

Author rebuttal:

Meta-review: This paper introduces MoE-Gyro, a self-supervised Mixture-of-Experts framework that addresses both over-range reconstruction and denoising for MEMS gyroscopes. The method is well motivated, technically solid, and supported by a thorough evaluation, including a new benchmark (ISEBench) that will be useful to the community. The authors responded well to reviewer concerns, providing results on efficiency, cross-device generalization, and clarifying details on noise modeling and gating. Overall, the paper makes a clear contribution to AI for sensor enhancement and meets the bar for acceptance.
Decision: Accept (poster)