SNM-Net: Universal Open-Set Gas Recognition

• SNM-Net is a universal deep learning framework for open-set gas recognition, addressing sensor drift and unknown gas interference through geometric decoupling.
• It integrates cascaded batch normalization and ℓ₂-normalization with class-wise Mahalanobis distance scoring to create adaptive ellipsoidal decision boundaries suitable for anisotropic sensor data.
• Experimental results on the Vergara dataset reveal near-perfect AUROC and exceptional unknown detection rates, outperforming state-of-the-art methods in stability and accuracy.

SNM-Net is a universal deep learning framework designed to address the critical challenges of open-set gas recognition in electronic nose (E-nose) systems, particularly those affected by distribution shifts (such as signal drift) and decision errors caused by unknown interfering gases. The framework is based on geometric decoupling of feature magnitude and direction through cascaded batch normalization and ℓ₂-normalization, followed by class-wise Mahalanobis distance scoring, which yields adaptive ellipsoidal decision boundaries suited for the anisotropic nature of gas sensor data. SNM-Net is architecture-agnostic and can be deployed as a post-processing module atop any deep feature extractor, including CNN, LSTM (RNN), or Transformer backbones. Extensive evaluation on the public Vergara dataset demonstrates that SNM-Net delivers near-perfect open-set AUROC, outstanding unknown detection rates, and substantial improvements in stability compared to state-of-the-art methods (Chen et al., 28 Dec 2025).

1. Architectural Principles and Workflow

SNM-Net is structurally modular and designed for ease of integration with existing deep feature extractors. The typical data flow comprises five main stages:

1. Input Data Processing: Raw E-nose signals, typically in a spatiotemporal feature map (e.g., 260 × 72 sensors).
2. Feature Extraction: Backbone deep network (CNN, LSTM, or Transformer) generates high-dimensional representations $Z_{\text{raw}}\in\mathbb{R}^{d}$.
3. Geometric Refinement: Cascaded batch normalization and ℓ₂-normalization project features onto the unit hypersphere, yielding direction-only representations $f\in S^{d-1}$.
4. Statistical Scoring: Class-wise Mahalanobis distance calculation utilizes class means and covariances to derive adaptive ellipsoidal decision boundaries.
5. Decision Layer: An open-set rejection threshold $t$ splits the inference between known-class assignment and unknown-class rejection.

This architecture is explicitly backbone-agnostic; SNM-Net can be combined in a plug-and-play manner with any suitable feature extractor.

2. Spherical Normalization Mechanism

The geometric refinement stage consists of two sequential normalization operations:

• Batch Normalization: Per-dimension centering and scaling,

$$\hat{z}_i = \frac{Z_{\text{raw},i} - \mu_{B,i}}{\sqrt{\sigma_{B,i}^2 + \epsilon}},$$

where $\mu_{B,i}$ and $\sigma_{B,i}^2$ are the mean and variance over the mini-batch, and $\epsilon$ is a small numerical stabilizer.

• ℓ₂-Normalization: Projection of the batch-normalized features onto the unit sphere,

$$f = \frac{\hat{z}}{\|\hat{z}\|_2}, \qquad \|\hat{z}\|_2 = \sqrt{\sum_{i=1}^{d} (\hat{z}_i)^2},$$

ensuring $\|f\|_2=1$.

This transformation fully decouples the direction (chemical identity) from signal magnitude (concentration, sensor drift), thus rendering classification boundaries invariant to fluctuating sensor conditions such as environmental variations, sensor aging, and changes in proximity.

3. Mahalanobis Distance-Based Open-Set Recognition

After spherical normalization, class-specific statistics are computed:

• Class Mean:

$\mu_c = \frac{1}{N_c} \sum_{i:y_i=c} f_i$

• Class Covariance (with regularization for invertibility):

$$\Sigma_c = \frac{1}{N_c-1}\sum_{i:y_i=c}(f_i-\mu_c)(f_i-\mu_c)^T + \lambda I,\quad \lambda=10^{-4}.$$

• Mahalanobis Distance:

$$d_c(f) = \sqrt{(f - \mu_c)^T \Sigma_c^{-1} (f - \mu_c)}$$

Decision boundaries thus form ellipsoids conformal to the scatter of class training data (i.e., principal axes of $\Sigma_c$), in contrast to isotropic boundaries induced by Euclidean distance. For prediction, the framework computes the minimum Mahalanobis distance $s(f)$ among all known classes:

$s(f) = \min_{c=1\ldots K} d_c(f)$

The sample is assigned label $\hat{y}(f) = \arg\min_c d_c(f)$ if $s(f)<t$; otherwise, it is rejected as unknown. Threshold $t$ is empirically set as the 95th percentile of known-class scores on validation data.

4. Training Protocol and Inference Workflow

Backbone network training employs the Class-Anchor Clustering (CAC) loss,

$$\mathcal{L} = \mathcal{L}_{\rm CE} + \lambda_{\rm anchor} \mathcal{L}_{\rm anchor}, \qquad \lambda_{\rm anchor} = 10^{-5}$$

with Adam optimizer (learning rate $4\times10^{-5}$), weight decay ($1\times10^{-4}$), batch size 64, dropout 0.1, and early stopping (patience 10 epochs). At inference, extracted features undergo geometric refinement, then Mahalanobis scores are computed, compared to the global threshold $t$, and predictions are made accordingly.

5. Experimental Results and Comparative Analysis

Experiments utilize the Vergara dataset (10 gases, 18,000 samples, 260 s × 72 sensors, five sensor positions). Protocol involves 10-fold cross-validation across positions (50 experiments), with random splitting into 6 known and 4 unknown classes.

Main Results (Transformer Backbone)

Method	Acc_known	TPR@FPR=5%	AUROC
Softmax+Transformer	1.0000±0.0002	0.8120±0.1378	0.9557±0.0406
EVM+Transformer	0.9999±0.0004	0.8227±0.1339	0.9514±0.0424
CAC+Transformer	0.9998±0.0009	0.8376±0.1529	0.9675±0.0311
SNM-Net+Transformer	1.0000±0.0002	0.9957±0.0138	0.9977±0.0028

• SNM-Net achieves AUROC 0.9977 ± 0.0028 and TPR (unknown gas detection rate) of 99.57% at 5% FPR.
• SNM-Net provides a +3.02% AUROC improvement over CAC and reduces AUROC standard deviation by 91.0%.
• Even at the lowest signal position (L5), TPR remains at 98.3%, and AUROC std. across positions is reduced to 0.0013.

Ablation Analysis (CNN Backbone)

Configuration	Acc_known	TPR@5%	AUROC
BASE-CNN (CAC only)	0.9993±0.0024	0.8246±0.1492	0.9504±0.0474
+ Mahalanobis (M)	0.9974±0.0062	0.9045±0.0837	0.9785±0.0192
+ M + BatchNorm (BN)	0.9991±0.0026	0.9347±0.0732	0.9847±0.0169
+ M + ℓ₂-Norm (L2N)	0.9986±0.0052	0.9270±0.0811	0.9829±0.0168
Full (+M+BN+L2N)	0.9988±0.0042	0.9370±0.0683	0.9846±0.0148

Key findings:

• Mahalanobis scoring increases AUROC by +2.81%, reducing AUROC standard deviation by −59.5% relative to CAC baseline.
• Both BatchNorm and ℓ₂-Norm individually improve AUROC by ~+1%.
• The full cascade yields maximal stability (AUROC std.=0.0148).

6. Deployment Considerations and Computational Efficiency

SNM-Net is designed for real-time, industrial-scale E-nose deployment:

• Requires only a single BatchNorm layer, vector ℓ₂-normalization, K class means, and class covariance matrices.
• Mahalanobis computation can pre-store matrix inverses or Cholesky factors per class.
• A single global threshold $t$ suffices for all operational sensor sites and drift conditions, negating need for site-specific tuning.
• Inference overhead is minimal: BN and ℓ₂-norm are $O(d)$ per sample; Mahalanobis scoring is $O(d^2)$ per class. For typical $d=128$, added latency is <$5$ ms on GPU and <$1$ ms on embedded DSPs. End-to-end throughput is dominated by backbone computation.

7. Context and Technical Significance

SNM-Net resolves the longstanding trade-off between decision accuracy and stability in open-set gas recognition for E-nose systems. By utilizing spherical normalization to suppress magnitude drift and Mahalanobis scoring to adaptively model anisotropic class distributions, it achieves robust, near-theoretical limit performance for both known and unknown class detection. Its modularity, computational footprint, and backbone-agnostic design establish a solid basis for practical, scalable deployment in variable industrial environments (Chen et al., 28 Dec 2025). A plausible implication is that SNM-Net methodology may generalize to other domains characterized by high-dimensional, drift-prone sensor data requiring open-set or anomaly detection.