LDAC-Net: A Learnable Multi-Lag Differencing Attention-Convolution Network for Drift-Robust Recognition with Low-Cost MOX Gas Sensors

Xin Zhang; Liangxiu Han; Yue Shi; Tam Sobeih

cs.LGAug 26, 2026

LDAC-Net: A Learnable Multi-Lag Differencing Attention-Convolution Network for Drift-Robust Recognition with Low-Cost MOX Gas Sensors

Authors: Xin Zhang, Liangxiu Han, Yue Shi, Tam Sobeih

Organizations: Department of Computing and Mathematics, Manchester Metropolitan University, Manchester, M1 5GD, U.K.

Abstract

Portable electronic-nose systems based on low-cost metal-oxide (MOX) gas sensors offer a practical solution for gas and odour recognition, but their signals are affected by slow chemical transients, drifting sensor offsets, scale variation, and cross-channel correlations. Existing pipelines commonly use fixed first-order temporal differencing (FOTD), which requires a manually selected lag and may discard useful response information. We propose LDAC-Net, an end-to-end learnable multi-lag differencing attention-convolution network that operates directly on multi-channel MOX signals. Its learnable differential feature enhancement front-end combines window-conditioned statistical affine normalisation, which compensates for window-specific offset and scale variation, with learnable multi-lag differencing, which weights and combines temporal differences across multiple lags. A compact attention-convolution backbone subsequently models local transients and longer-range temporal dependencies. On the 50-class SmellNet-Base task, LDAC-Net achieves 68.2% top-1 accuracy, exceeding the best FOTD-preprocessed comparison model by approximately 14 percentage points and the raw-input Transformer by more than 30 points. Ablation studies confirm the contributions of both proposed components. The representation also transfers to SmellNet-Mixtures, improving accuracy from 45.4% to 50.5%, and generalises to the 62-channel eNose-Drift benchmark under strong long-term drift, achieving 70.6% top-1 accuracy and 69.6% macro-F1. These results outperform the best comparison model with dataset-retuned FOTD preprocessing by 8.0 and 3.0 points, respectively, demonstrating that learnable, sensor-aware preprocessing is more effective than fixed handcrafted differencing for low-cost MOX gas-sensor recognition.

Figures & tables

Figure 1: The LDAC-Net architecture. A raw window $\mathbf{x}$ first passes through the LDFE front module (WSAN normalisation and LMLD differencing), is then processed by three AC blocks, and is finally read out by the Attention-Pooling head into the 50-way logits.

Figure 2: The WSAN module. For each multi-channel window, the per-channel mean and standard deviation feed a small MLP that emits per-channel affine offsets $(1{+}\Delta\boldsymbol{\gamma},\Delta\boldsymbol{\beta})$ , which are applied to the standardised window to produce the normalised output.

Figure 3: The LMLD module. The WSAN-normalised window is differenced at a bank of lags $P=\{5,10,25,50\}$ (only $5,25,50$ drawn); each difference is scaled by a learnable per-channel weight, concatenated with the identity stream, mixed by a $1{\times}1$ convolution, layer-normalised, and gated by a squeeze-excitation block.

Figure 4: The AC block: two half-step macaron feed-forward layers around a multi-head self-attention and a ConvModule, with per-step residual connections (dashed) and a final LayerNorm. A whole-block identity bypass realises stochastic depth, and the inset expands the ConvModule.

Figure 5: Example sensor time curves from the three tasks. (a) SmellNet-Base ( Feng et al., 2026 ) : one representative substance per category across the six MOX channels. (b) SmellNet-Mixtures ( Feng et al., 2026 ) : a pure substance and two- and three-component blends across the four mixture channels. (c) eNose-Drift ( Wörner et al., 2025 ) : raw log-resistance of one channel (R46) for the three analytes on six measurement days spanning the year.

Setting	Value
Data / windowing
Channels $C$ / classes	6 / 50
Window length $T$ / stride	300 (swept 100 to 400) / 50
Train / test windows	about 1 650 / about 330
Architecture
Model width $d$	128

Table 1: LDAC-Net configuration and training recipe used throughout, unless a row states otherwise. All values are fixed across seeds.

	Raw input			FOTD input
Model	Acc@1	Acc@5	F1	Acc@1	Acc@5	F1
MLP	$21.09\pm 2.64$	$56.05\pm 1.85$	$16.79\pm 2.67$	$18.92\pm 2.97$	$49.80\pm 5.85$	$16.17\pm 3.37$
CNN	$26.82\pm 1.44$	$67.31\pm 0.65$	$22.80\pm 1.99$	$49.56\pm 7.80$	$83.19\pm 4.03$	$48.12\pm 7.20$
LSTM	$27.72\pm 2.40$	$66.74\pm 1.17$	$25.31\pm 1.73$	$53.78\pm 1.81$	$85.90\pm 1.14$	$52.40\pm 1.99$
Transformer	$37.29\pm 2.34$	$73.22\pm 1.73$	$33.49\pm 1.99$	$53.55\pm 0.83$	$85.58\pm 1.86$	$52.08\pm 0.77$
LDAC-Net (ours)	$\mathbf{68.2\pm 1.6}$	$\mathbf{89.4\pm 0.3}$	$\mathbf{65.2\pm 4.5}$	N/A	N/A	N/A

Table 2: Model performance on SmellNet-Base (50-way; Top-1 / Top-5 accuracy and macro-F1, %, mean

\pm

std). Mainstream baselines (MLP, CNN, LSTM, Transformer) are trained on raw and lag-25 FOTD-preprocessed inputs. LDAC-Net operates end-to-end on raw windows with no external preprocessing. All models use the same analysis window length

T=300

at stride

50

. Best per metric in bold.

Panel of Figure 6 — Figure 6: Model performance across analysis window lengths on SmellNet-Base (50-way, Top-1 %, mean $\pm$ std). Solid: LDAC-Net; dashed: LDAC-Net w/o LMLD. LDAC-Net rises by more than ten points from the default $T=100$ to a peak at $T=300$ , then falls at $T=400$ as each session yields too few windows. LMLD is neutral at $T=100$ , where a lag- $50$ difference is half boundary, and its benefit grows with the window, reaching $+5.9$ points at $T=300$ .

Configuration	Acc. (%)	$\Delta$
LDAC-Net	$\mathbf{68.2\pm 1.6}$	(ref.)
$-$ WSAN (plain InstanceNorm)	$54.2\pm 0.9$	$-14.0^{\ast}$
$-$ LMLD	$62.3\pm 1.2$	$-5.8^{\ast}$
$-$ squeeze-excitation gate	$61.9\pm 1.3$	$-6.2^{\ast}$
$-$ channel mixing	$63.2\pm 0.4$	$-4.9^{\ast}$
$-$ multi-lag bank (single lag $25$ )	$63.6\pm 2.5$	$-4.6^{\ast}$

Table 3: Component ablation of LDAC-Net at

T=300

(Top-1 %, mean

\pm

std over five seeds). Each row removes one part of LDAC-Net. All accuracy drops are statistically significant against the full model (

{}^{\ast}p<0.05

, two-sided paired

t

-test over the five shared seeds).

Model	Top-1 Acc. (%)
Transformer (raw)	$37.29\pm 2.34$
Transformer (FOTD)	$53.55\pm 0.83$
Non-stationary Transformer ( Liu et al., 2022 )	$52.61\pm 2.50$
Autoformer ( Wu et al., 2021 )	$50.28\pm 1.22$
TCN ( Bai et al., 2018 )	$43.63\pm 2.62$
Neural ODE ( Chen et al., 2018 )	$50.47\pm 1.51$

Table 4: Comparison of LDAC-Net against the Transformer backbone (on raw and lag-25 FOTD input) and four published time-series methods (the Non-stationary Transformer, Autoformer, TCN, and Neural-ODE) on SmellNet-Base (Top-1 %, mean

\pm

std).

Model	[email protected] $\uparrow$	MAE $\downarrow$	Top- $K$ $\uparrow$
MLP	$43.0\pm 1.5$	$0.056\pm 0.001$	$76.2\pm 1.2$
CNN	$43.1\pm 1.3$	$0.059\pm 0.000$	$75.1\pm 0.8$
LSTM	$41.0\pm 2.3$	$0.056\pm 0.001$	$80.8\pm 1.5$
Transformer	$45.4\pm 3.1$	$0.054\pm 0.002$	$78.3\pm 0.3$
LDAC-Net (ours)	$\mathbf{50.5\pm 2.0}$	$\mathbf{0.050\pm 0.001}$	$\mathbf{81.1\pm 0.2}$

Table 5: Model performance on the SmellNet-Mixtures task ( Feng et al., 2026 ) (12-component ratio prediction). [email protected] and Top-

K

in %, higher is better; MAE lower is better. Best per metric in bold.

	Raw		FOTD (lag $100$ )
Model	Acc@1	F1	Acc@1	F1
MLP	$56.3{\pm}4.3$	$55.6{\pm}4.5$	$53.4{\pm}1.4$	$52.4{\pm}1.2$
CNN	$59.2{\pm}5.3$	$58.1{\pm}6.7$	$62.6{\pm}3.1$	$66.6{\pm}3.2$
LSTM	$43.4{\pm}3.4$	$38.9{\pm}3.1$	$52.7{\pm}1.8$	$47.8{\pm}2.3$
Transformer	$56.3{\pm}3.5$	$55.3{\pm}3.9$	$61.2{\pm}3.8$	$58.5{\pm}5.4$
LDAC-Net (ours)	$\mathbf{70.6{\pm}4.8}$	$\mathbf{69.6{\pm}3.9}$	N/A	N/A

Table 6: Cross-dataset generalisation on the eNose-Drift benchmark ( Wörner et al., 2025 ) (

62

-channel MOX array, chronological drift split, raw drift-affected input). Acc@1 / macro-F1 (%, mean

\pm

std; ten seeds for LDAC-Net, the Transformer, and the FOTD CNN, five seeds otherwise); FOTD uses the dataset-retuned lag-

100

difference. Best per column in bold.

Lag bank $P$	Top-1 Acc. (%)
$\{25\}$	$63.6\pm 2.5$
$\{25,50\}$	$64.4\pm 5.0$
$\{5,10,25\}$	$64.9\pm 1.5$
$\{10,25,50\}$	$64.6\pm 3.3$
$\{15,25,50\}$	$64.0\pm 0.6$
$\{25,50,100\}$	$64.5\pm 3.0$

Table 7: Effect of the LMLD lag bank on SmellNet-Base (50-way,

T=300

, Top-1 %, mean

\pm

std). The bank used by LDAC-Net is in bold.

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