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

• Low-cost MOX sensors are practical but difficult to use because their signals combine slow transients, session drift, scale variation, and cross-channel correlations.Source: §1 · p. 1
• Fixed first-order temporal differencing suppresses slow drift and exposes dynamics but requires a hand-picked lag and may discard absolute response information.Source: §1 · p. 1
• LDAC-Net learns drift compensation, dynamics extraction, and classification jointly from raw multi-channel windows without external preprocessing or recalibration.Source: §1 · p. 2
• The compact attention-convolution backbone is designed to capture both local transients and longer-range temporal dependencies in sensor windows.Source: §1 · p. 2
• LDFE combines window-conditioned affine corrections from per-window statistics with learnable multi-lag differences, channel mixing, weighting, and gating.Source: §1 · p. 2
• A longer analysis window provides sufficient temporal context for in-model differences to expose response dynamics rather than noise.Source: §1 · p. 2

• Earlier electronic-nose systems commonly extracted response-curve descriptors for shallow classifiers, while later approaches applied fixed preprocessing before classification.Source: §2.1 · p. 2
• FOTD suppresses slow drift and exposes transient dynamics, but its fixed lag applies uniformly across substances, channels, and sessions while discarding absolute signal level.Source: §2.2 · p. 3
• Deep-learning alternatives for multivariate time-series recognition include convolutional, recurrent, and attention-based models that capture temporal patterns in different ways.Source: §2.3 · p. 3
• Two gaps remain: preprocessing is often external and fixed, while non-stationarity methods may normalise statistics without learning multi-scale differencing for slow MOX dynamics.Source: §2.3 · p. 3
• LDAC-Net combines window-conditioned affine correction with learnable multi-lag differencing, unlike methods using only statistical rescaling or predefined difference kernels.Source: §2.3 · p. 3

Overview

• LDAC-Net predicts substance labels directly from raw fixed-length multi-channel windows without external drift correction or handcrafted temporal differencing.Source: §3.1 · p. 3

Learnable Differential Feature Enhancement

• LDFE combines WSAN, which learns per-window affine corrections from channel statistics, with LMLD, which learns weighted multi-lag differences and channel interactions.Source: §3.1 · p. 3

Attention-Convolution Backbone

• The AC backbone pairs depthwise convolution for local structure with self-attention for longer-range context, while attention pooling weights informative timesteps during readout.Source: §3.1 · p. 4, §3.3 · p. 5

End-to-End Architecture

• The LDFE output is projected into a T × d token sequence, processed by three AC blocks, and mapped to 50-way logits.Source: §3.2 · p. 4, Figure 1 · p. 4, §3.2.3 · p. 5

Window-conditioned Statistical Affine Normalisation

• WSAN starts as instance normalisation, then learns residual affine corrections that remove drift while retaining a route for discriminative absolute response levels.Source: §3.2.1 · pp. 4–5

Learnable Multi-Lag Differencing

• LMLD computes differences at lags 5, 10, 25, and 50, concatenates them with the identity stream, and applies learned mixing, normalisation, and channel gating.Source: Figure 3 · p. 5, §3.2.2 · p. 5

Dataset

• SmellNet-Base is the primary 50-way substance-recognition benchmark using six-channel low-cost MOX recordings.Source: §4.1 · p. 6
• SmellNet-Mixtures evaluates compositional ratio prediction over twelve odorants using four sensor channels, while eNose-Drift tests cross-array recognition under strong long-term drift.Source: §4.1 · p. 6

Protocol

• The eNose-Drift analysis uses an initial calibration, chronological training-to-testing splits, and Acc@1 plus macro-F1 reporting across repeated seeds.Source: §4.1 · p. 8, §4.2 · p. 9
• Raw-input configurations receive no external drift correction, smoothing, or handcrafted temporal differencing unless explicitly stated otherwise.Source: §4.2 · p. 8

Experimental Design

• The study evaluates primary performance against mainstream temporal baselines, component contributions through leave-one-out ablations, and comparisons with popular multivariate time-series models.Source: §4.2 · p. 8
• Generalisation experiments test both transfer to a different task on the same array and transfer to an independent 62-channel MOX array with a different drift regime.Source: §4.1 · p. 6, §4.2 · p. 8

• 68.2% Top-1, 89.4% Top-5, and 65.2 macro-F1 make LDAC-Net the best model on every reported metric.Source: §5.1.1 · p. 9
• 14.4 points on Top-1 and 12.8 on F1 separate LDAC-Net from the strongest FOTD-preprocessed baseline despite no external preprocessing.Source: §5.1.1 · p. 9
• 57.8% at T = 100 rises to 68.2% at T = 300, then falls to 64.8% at T = 400.Source: §5.1.2 · p. 9
• At T = 300, LMLD contributes +5.9 points over LDAC-Net without LMLD, compared with −0.3 points at T = 100.Source: §5.1.2 · p. 10, Figure 6 · p. 10
• Longer windows provide sufficient context for slow MOX transients, while T = 400 yields too few windows per session for training.Source: §5.1.2 · p. 10

• 14.0 points are lost when WSAN is replaced by plain InstanceNorm, falling from 68.2% to 54.2% Top-1.Source: §5.2 · p. 10
• 5.8 points are lost when the LMLD differencing front is removed, reducing Top-1 accuracy to 62.3%.Source: §5.2 · p. 10
• 6.2 points are lost by removing squeeze-excitation, while removing learnable channel mixing costs 4.9 points.Source: §5.2 · p. 10
• 4.6 points are lost when the multi-lag bank is collapsed to the single lag {25}, confirming the value of multiple lags.Source: §5.2 · p. 10

• 52.61% is the strongest competing accuracy, achieved by the Non-stationary Transformer, which still trails LDAC-Net by more than 15 points.Source: §5.3 · pp. 10–11
• 68.2% Top-1 makes LDAC-Net more than 14 points better than Transformer-FOTD and over 15 points better than the best raw-input alternative.Source: §5.3 · p. 11
• 50.28% for Autoformer and 50.47% for Neural-ODE indicate that their added capacity does not match LDAC-Net on this small training set.Source: §5.3 · p. 11
• 43.63% makes the dilated TCN the weakest published-method transplant, while the raw Transformer reaches 37.29%.Source: §5.3 · p. 11

Compositional Generalisation

• 50.5% Top-1@0.1 exceeds the Transformer’s 45.4% on SmellNet-Mixtures, a 5.1-point gain.LDAC-Net also achieves the lowest MAE (0.050) and highest Top-K presence score (81.1%).Source: §5.4.1 · p. 11

Cross-Dataset Generalisation

• 70.6 ± 4.8 Acc@1 and 69.6 ± 3.9 macro-F1 are achieved on the 62-channel eNose-Drift benchmark.The benchmark differs in hardware and channel count and exhibits strong long-term drift over twelve months.Source: §5.4.2 · p. 11
• LDAC-Net exceeds the strongest dataset-retuned FOTD baseline by 8.0 Acc@1 points and 3.0 macro-F1 points.The model operates end-to-end on raw signals after scaling the analysis window and lag-bank range to the slower transient.Source: §5.4.2 · p. 11

6.1. Window-Conditioned Affine versus Fixed Differencing

• Fixed differencing can under- or over-compensate drift and discard discriminative absolute response levels.WSAN preserves such information, while LMLD replaces FOTD’s fixed lag with a learnable multi-lag bank.Source: §6.1 · pp. 11–12
• 63.6% is the weakest lag-bank choice, and multi-lag benefits require coverage across a wide range of time scales.Banks restricted to only long or short lags are less effective than the broader bank used by LDAC-Net.Source: §6.1 · p. 12, Table 7 · p. 12

6.2. Window Length as a Key Accuracy Factor

• Increasing T from 100 to 300 raises Top-1 accuracy from 57.8% to 68.2%.Longer windows provide more temporal context for in-model differencing, while overlap can act as augmentation and regularisation.Source: §6.2 · p. 12
• LMLD’s benefit grows from +2.3 points at T = 200 to +5.9 at T = 300 and +7.2 at T = 400.The accuracy curve is unimodal because longer windows eventually reduce the number of windows; T = 300 is the peak.Source: §6.2 · p. 12

6.3. Limitations

• Both evaluated corpora remain modest in size, so larger and more varied datasets are needed to confirm that the gains hold.SmellNet-Base has about 2,650 training windows at T = 100 and about 1,650 at T = 300.Source: §6.3 · p. 12
• The global T = 300 window is fixed by offline grid search even though the best length may vary by substance, channel, and response speed.The paper proposes input-adaptive or multi-scale windows as a next step.Source: §6.3 · p. 12
• Transfer has been tested only under controlled offline conditions, and on-device latency and power remain unmeasured.This includes the extra cost of the per-window WSAN pass.Source: §6.3 · p. 13

Architecture

• LDAC-Net classifies raw low-cost MOX sensor windows end to end using learnable drift compensation and temporal dynamics extraction.Its LDFE front end combines WSAN and LMLD, while the AC backbone uses convolution and self-attention.Source: §7 · p. 13

Main Results

• 68.2% Top-1 is achieved on the 50-way SmellNet-Base task, with 89.4% Top-5 and 65.2 macro-F1.Top-1 is more than 14 points above the strongest FOTD-preprocessed baseline and over 30 points above the raw-input Transformer.Source: §7 · p. 13
• Increasing T from 100 to 300 improves Top-1 accuracy by 10.4 points, from 57.8% to 68.2%.The ablation study reports that each evaluated component contributes to classification accuracy.Source: §7 · p. 13

Generalisation

• Generalisation experiments show transfer across tasks and sensor arrays.The conclusion identifies SmellNet-Mixtures and eNose-Drift as the two transfer settings.Source: §7 · p. 13