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Uncertainty-Guided Edge Learning for Deep Image Regression in Remote Sensing

Conference: CVPR2026
arXiv: 2605.05590
Code: https://github.com/anh-vunguyen/UGEL
Area: Remote Sensing
Keywords: Edge learning, uncertainty estimation, deep Beta regression, active learning, semi-supervised learning

TL;DR

Addressing the "edge learning" scenario with limited computational power on orbiting satellites, this paper proposes the UGEL algorithm: it utilizes "deep Beta regression" uncertainty, which can be calculated in a single forward pass, to select the most uncertain samples for manual labeling and the most certain samples for pseudo-labeling. This allows the onboard regression model to converge and retrain faster than traditional active learning or semi-supervised learning approaches.

Background & Motivation

Background: Remote sensing satellites are increasingly equipped with neural network accelerators for direct onboard inference (e.g., predicting scalar regressions like cloud or land cover where \(y\in[0,1]\)). This enables space-based decision-making and avoids the cost of massive data downlink. However, deployed models suffer performance degradation due to sensor drift and domain gaps (mismatches between training and real-time data distribution), requiring periodic retraining—a process known as "Edge Learning" (EL).

Limitations of Prior Work: Onboard computational and power resources are severely constrained, limiting retraining to a tiny subset \(\mathcal{T}\subset\mathcal{I}\) of the unlabeled data \(\mathcal{I}\). Selecting the right samples and extracting supervisory signals from unlabeled data depends on "predictive uncertainty" estimation. Since \(|\mathcal{I}|\gg|\mathcal{T}|\), the overhead of calculating uncertainty for the entire \(\mathcal{I}\) can exceed the cost of the retraining itself. Current uncertainty methods are inefficient: MC Dropout requires 10~30 forward passes per sample, consuming significant power; Deep Evidential Regression (DER) works in one forward pass but assumes an unbounded Gaussian distribution, which is biased for cloud/land cover data constrained to \([0,1]\) with many samples clustered at the boundaries.

Key Challenge: Active Learning (AL, selecting uncertain samples for manual labeling) and Semi-Supervised Learning (SSL, using pseudo-labels for unlabeled data) both have merits. However, balancing their contributions is difficult when the model has not adapted to new environments and initial labels are extremely scarce (e.g., \(M=12\)). Furthermore, a precise, efficient, and boundary-respecting uncertainty estimator for \([0,1]\) is missing.

Goal: (1) Design an edge learning algorithm that unifies AL and SSL through a principled uncertainty framework; (2) provide a single-forward uncertainty estimator supporting bounded distributions.

Key Insight: Use the differential entropy of "Deep Beta Regression (DBR)" as a unified uncertainty measure. This allows partitioning samples into the "most uncertain" (for AL) and "most certain" (for SSL), enabling complementary supervisory signals to accelerate convergence with minimal labeling budget.

Method

Overall Architecture

UGEL addresses the problem of retraining a regression model \(f_{\hat{\mathbf{w}}}\) to convergence using onboard unlabeled data \(\mathcal{I}\) under a minimal labeling budget. It is an iterative process: in each round, the current model's uncertainty estimator \(h_{\hat{\mathbf{w}}}\) scans \(\mathcal{I}\) to select two disjoint subsets—the most uncertain \(\mathcal{T}_U\) (size \(B_U\), sent for manual labeling) and the most certain \(\mathcal{T}_C\) (size \(B_C\), labeled with pseudo-labels). The main model and a twin model are then updated using ground truth loss and pseudo-label consistency loss. Finally, the newly labeled \(\mathcal{T}_U\) is merged into the labeled set \(\mathcal{D}\) and removed from \(\mathcal{I}\) before the next round.

The core of the pipeline is the uncertainty estimator provided by "Deep Beta Regression (DBR)", where the network outputs parameters for a Beta distribution, and the differential entropy serves as the uncertainty measure, calculable in a single forward pass. UGEL is uncertainty-agnostic, though DBR is the optimal choice for bounded \([0,1]\) remote sensing regression.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Unlabeled onboard data I<br/>+ Initial labels D (minimal)"] --> B["Deep Beta Regression DBR<br/>Single forward pass for entropy"]
    B --> C["Uncertainty-stratified sampling<br/>Most uncertain T_U / Most certain T_C"]
    C -->|T_U for manual labeling| D1["GT Labels Y_U"]
    C -->|T_C for pseudo-labeling| D2["Twin pseudo-labels<br/>Main + Twin model"]
    D1 --> E["Twin cross-supervised retraining<br/>GT loss + consistency loss"]
    D2 --> E
    E -->|Merge T_U into D, remove from I| F{"I remains?"}
    F -->|Yes| B
    F -->|No| G["Converged onboard model"]

Key Designs

1. UGEL: Unifying AL and SSL with a Single Uncertainty Metric

To address the difficulty of balancing AL and SSL when labels are scarce, UGEL uses a single uncertainty measure \(h_{\hat{\mathbf{w}}}\) to partition data. Each round, the subset \(\mathcal{T}=\mathcal{T}_U\cup\mathcal{T}_C\) is formed: \(\mathcal{T}_U\) contains the \(B_U\) most uncertain samples:

\[\mathcal{T}_U=\underset{\mathcal{S}\subset\mathcal{I},\,|\mathcal{S}|=B_U}{\arg\max}\sum_{x_i\in\mathcal{S}}h_{\hat{\mathbf{w}}}(x_i)\]

These are sent for manual labeling (acting as AL). \(\mathcal{T}_C\) contains the \(B_C\) most certain samples:

\[\mathcal{T}_C=\underset{\mathcal{S}\subset\mathcal{I},\,|\mathcal{S}|=B_C}{\arg\min}\sum_{x_i\in\mathcal{S}}h_{\hat{\mathbf{w}}}(x_i)\]

These are pseudo-labeled by the model (acting as SSL), ensuring \(\mathcal{T}_U\cap\mathcal{T}_C=\emptyset\). This design provides a unified framework: setting \(B_U>0, B_C=0\) reduces it to uncertainty-based AL; \(B_U=0, B_C=N\) reduces it to cross-supervised SSL; and \(B_U>0, B_C=N-B_U\) resembles standard ASSL. UGEL's benefit comes from selecting only the most certain samples for pseudo-labeling, preventing noise from diluting ground truth signals.

2. Deep Beta Regression (DBR): Efficient Bounded Uncertainty

Instead of expensive MC Dropout or unbounded DER, DBR forces the network \(f_{\mathbf{w}}\) to output parameters for a Beta distribution, whose support is naturally \([0,1]\). Using mean-precision parameterization \(\mu=\alpha/(\alpha+\beta)\in(0,1)\) and \(\nu=\alpha+\beta>0\), the network outputs \((\hat{\mu},\hat{\nu})=f_{\mathbf{w}}(x)\). The prediction is \(\hat{y} = \hat{\mu}\), and uncertainty is the differential entropy of the Beta distribution:

\[h_{\mathbf{w}}(x)=\log\frac{\Gamma(\hat{\mu}\hat{\nu})\Gamma((1-\hat{\mu})\hat{\nu})}{\Gamma(\hat{\nu})}+(\hat{\nu}-2)\psi(\hat{\nu})-(\hat{\mu}\hat{\nu}-1)\psi(\hat{\mu}\hat{\nu})-((1-\hat{\mu})\hat{\nu}-1)\psi((1-\hat{\mu})\hat{\nu})\]

where \(\psi(\cdot)\) is the digamma function. Higher entropy indicates uncertainty, while lower indicates certainty. Unlike MC Dropout, \(h_{\mathbf{w}}(x)\) requires only one pass. Unlike DER, the Beta density is strictly within \([0,1]\), crucial for remote sensing data with values clustered at 0 and 1.

3. Twin Models and Cross-Supervision: Safe Exploitation of Pseudo-labels

To utilize the certain subset \(\mathcal{T}_C\) while avoiding self-reinforcement bias, UGEL maintains a twin model \(f_{\mathring{\mathbf{w}}}\) on the edge. It shares the same architecture as \(f_{\hat{\mathbf{w}}}\) and is pre-trained on the same \(\mathcal{D}\), but with different initialization (\(\hat{\mathbf{w}}\neq\mathring{\mathbf{w}}\)). During retraining, a consistency term \(\mathcal{L}_{RMSE}\) measures the disagreement between the two models on all samples. Minimizing this forces the models to "cross-supervise," utilizing unlabeled data more robustly than single-model self-training.

4. Adaptive \(B_C=|\mathcal{D}|\): Scaling Pseudo-labels with the Labeled Set

Initially, both the labeled set \(\mathcal{D}\) and the model accuracy are low. Incorporating a large number of pseudo-labels (e.g., \(N=10k\)) would cause divergence due to excessive noise. The authors set \(B_C=|\mathcal{D}|\), ensuring the pseudo-label subset grows in sync with the ground truth. This coupling ensures pseudo-labels never overwhelm the ground truth, preventing the collapse seen in some ASSL methods.

Loss & Training

DBR pre-training optimizes regression error and negative log-likelihood:

\[\mathcal{L}_s=\mathcal{L}_{RMSE}(\hat{\mathcal{U}},\mathcal{Y})+\lambda\,\mathcal{L}_{NLL}(\hat{\mathcal{U}},\hat{\mathcal{V}},\mathcal{Y})\]

The overall UGEL loss per round includes twin cross-supervision:

\[L=\mathcal{L}_s(\hat{\mathcal{Y}},\mathcal{Y})+\mathcal{L}_s(\mathring{\mathcal{Y}},\mathcal{Y})+\tau\,\mathcal{L}_{RMSE}(\hat{\mathcal{Y}}\cup\hat{\mathcal{Y}}_C,\mathring{\mathcal{Y}}\cup\mathring{\mathcal{Y}}_C)\]

The model uses \(B_U=6\), \(B_C=|\mathcal{D}|\), \(\tau=2\), initial \(M=12\), and light backbones (ResNet18 / MobileNetV3 / MobileNetV4). Adam optimizer (lr=0.001) is used to retrain from random initialization for 12 epochs each round to avoid catastrophic forgetting.

Key Experimental Results

Main Results

UGEL+DBR was compared with AL (Random, BALD), SSL, and ASSL on three remote sensing datasets. Metrics are RMSE (lower is better) with Wilcoxon p-values (< 0.05 indicates UGEL is significantly better):

Dataset Comparison Rd.2/5 Rd.4/10 Rd.6/15 Rd.8/20
RSRC-S2 UGEL vs Rand 0.019 0.001 0.005 0.002
RSRC-S2 UGEL vs BALD 0.042 0.002 0.053 0.002
RSRC-S2 UGEL vs SSL 0.014 0.001 0.005 0.001
RSRC-S2 UGEL vs ASSL 0.016 0.008 0.008 0.008
RSRC-L8 UGEL vs SSL 0.001 0.001 0.001 0.001
RSRC-L8 UGEL vs ASSL 0.001 0.001 0.001 0.001
RSLC UGEL vs BALD 0.002 0.001 0.001 0.001

Key Findings: AL reduces RMSE but fluctuates, and BALD is not consistently better than random sampling. ASSL shows early gains but plateaus quickly due to pseudo-label noise. UGEL+DBR maintains the lowest RMSE and variance by selecting only the most certain pseudo-labels.

Ablation Study

T1: Uncertainty Estimators in UGEL (DBR vs Random / MCD P=10 / DER): DBR significantly outperforms others in early rounds.

T3 Runtime (Jetson Orin NX, RSRC-S2, seconds, min–max over 10 rounds):

Method Uncertainty Est. ↓ Retraining ↓
UGEL w. MCD 495.84–514.18 7.18–12.54
UGEL w. DER 82.01–85.47 7.23–13.29
UGEL w. DBR 68.04–74.53 7.43–12.02

Uncertainty estimation is the dominant cost, being much slower than the actual retraining. DBR is significantly more efficient than MC Dropout and DER.

Highlights & Insights

  • Leveraging both ends of uncertainty: While traditional AL uses "most uncertain" samples, UGEL also utilizes "most certain" samples for SSL, unifying both approaches via a single metric.
  • Beta distribution for bounded regression: It effectively handles \(y\in[0,1]\) constraints where Gaussian assumptions fail, especially with data concentrated at boundaries.
  • Adaptive Pseudo-labeling: The \(B_C=|\mathcal{D}|\) rule prevents the training divergence common in semi-supervised learning when initial labels are scarce.

Limitations & Future Work

  • Target Diversity: Performance gains are less significant on datasets with high target variety (e.g., RSLC).
  • Twin Model Overhead: Maintaining two models increases compute and memory usage on power-constrained satellites.
  • Scalar \([0,1]\) Constraint: Currently limited to scalar bounded regression.
  • vs MC Dropout: DBR is ~7x faster while maintaining better accuracy.
  • vs DER: DBR respects the boundaries of the target space, avoiding the biased uncertainty of Gaussian assumptions in DER.
  • vs ASSL: UGEL avoids "noise dilution" by selecting pseudo-labels selectively rather than using all available unlabeled data.

Rating

  • Novelty: ⭐⭐⭐⭐ Integrated AL/SSL via Beta entropy for edge learning.
  • Experimental Thoroughness: ⭐⭐⭐⭐ Solid testing across datasets and real hardware, though absolute RMSE tables are partially in supplementary.
  • Writing Quality: ⭐⭐⭐⭐ Clear motivation and well-explained unified framework.
  • Value: ⭐⭐⭐⭐ Highly practical for onboard remote sensing and transferable to other bounded regression tasks.