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Multi-task Disentangling Fusion Mamba-CNN for MODIS Spectral-Temporal Unmixing with Endmember Variability Modeling

Motasem Alkayid, Yimin Zhu, Naser El-Sheimy, Lincoln Linlin Xu

arXiv:2610.36750v1cs.CV

TL;DR

MODIS spectral-temporal unmixing is challenged by coupled channel and temporal information, endmember variability, and unstable fusion. MDF-Mamba combines channel-specialized CNN experts, a temporal Mamba branch, constrained fusion, and multi-task learning. Across Alberta and Saskatchewan, it ranks best on 12 of 14 evaluation metrics and second on the rest.

  • Problem

    MODIS unmixing must address coupled spectral-temporal information, intra-class endmember variability, and unstable fusion of multiple expert representations.

    Source: §I · pp. 1–2

  • Method

    MDF-Mamba pairs channel-specialized CNN experts with a bidirectional temporal Mamba branch and constrained fusion, while jointly training abundance estimation and spectral reconstruction.

    Source: §I · p. 2, C. Mixture of Experts for Remote Sensing · p. 4, §V · p. 25

  • Results

    MDF-Mamba ranks best on 12 of 14 evaluation metrics across Alberta and Saskatchewan and second on the remaining two.

    Source: §I · p. 3

  • Takeaways & Limitations

    The framework grounds regional-scale abundance estimates in physical spectral reconstruction while modeling endmember variability pixel by pixel.

    Source: §V · p. 25

    The study evaluates one calendar year, 2010, across two adjacent Canadian provinces, so its temporal models are optimized for a specific seasonal cycle.

    Source: §V · p. 26

Abstract

from arXiv · show

Spectral-temporal unmixing of MODIS time series is essential for applications such as abundance mapping and spectral library construction, yet it remains challenging due to (i) spectral-temporal information coupling in MODIS data, (ii) intra-class endmember spectral variability and inter-class signature ambiguity, and (iii) the instability of naively fusing multiple expert representations. This paper presents the Multi- task Disentangling Fusion Mamba (MDF-Mamba) to address these limitations. To resolve spectral-temporal coupling, we design a disentangling architecture that pairs per-channel spectral experts with a dedicated bidirectional state-space (Mamba) temporal branch. Convolutional modules each process a single spectral channel, while the Mamba branch encodes the cross-channel seasonal trajectory, forming a multi-branch expert ensemble with soft inter-expert reweighting based on squeeze-and-excitation. For the integration of these spectral and temporal expert outputs, we introduce mHCFusion, adapting the manifold-constrained hyper-connection framework to merge the outputs in a stable and interpretable manner. Endmember variability is addressed by extending the linear mixing model with pixel-wise learnable spectral variability weights that capture intra-class endmember variation. Finally, we design a multi-task training objective that combines supervised abundance estimation with self-supervised spectral reconstruction and endmember regularization terms on the same training data, yielding a highly efficient framework for spectral-temporal unmixing. Experiments on MODIS time series covering the Alberta and Saskatchewan provinces show that MDF-Mamba achieves the best performance on 12 of 14 evaluation metrics across both datasets (7 of 7 on Alberta; 5 of 7 on Saskatchewan), ranking second on the remaining two.

I. INTRODUCTION

MODIS unmixing must separate channel-specific spectral cues from temporal phenology while accommodating variable endmembers and stable feature fusion. MDF-Mamba combines specialized CNN branches, a temporal Mamba branch, constrained fusion, and multi-task training; it ranks first on 12 of 14 metrics across Alberta and Saskatchewan.

I. INTRODUCTION

  • Existing approaches often share parameters across spectral-temporal bands, retain fixed or weakly regularized endmembers, and fuse streams without geometric stability guarantees.MODIS unmixing matters for fractional abundance mapping in applications including crop monitoring, forest disturbance mapping, and land-cover change detection.Source: §I · pp. 1–2
  • MDF-Mamba assigns spectral-spatial encoding to fixed, channel-specialized CNN experts and temporal sequence encoding to a dedicated bidirectional Mamba branch.The six spectral streams are modulated by temporal features and reweighted through cross-branch squeeze-and-excitation.Source: §I · p. 2
  • The model groups expert streams by physical domain and uses mHCFusion to combine them through doubly stochastic mixing in a shared representation space.The three groups are vegetation indices, optical reflectance, and moisture; a scene-adaptive FiLM head conditions the fused representation on global context.Source: §I · p. 2
  • MDF-Mamba models endmember variability with pixel-wise weights over learnable spectral variants and jointly trains abundance estimation with spectral reconstruction and regularization.Its reconstruction module blends an attention-based spectrum with the extended linear mixing model, while curriculum training emphasizes reconstruction early to stabilize the endmember dictionary.Source: §I · p. 2
  • MDF-Mamba achieves the best performance on 12 of 14 evaluation metrics across Alberta and Saskatchewan, ranking second on the remaining two.The metrics cover abundance estimation, spectral reconstruction, and classification accuracy.Source: §I · p. 3

B. Endmember Variability Modeling

Prior approaches address endmember variability and sequence modeling separately, while multi-stream feature fusion remains difficult to stabilize. MDF-Mamba adapts constrained fusion and applies Mamba to temporal sequences alongside per-channel CNN experts.

B. Endmember Variability Modeling

  • The fixed-endmember assumption is problematic for regional studies because soil moisture, topography, and seasonal phenology drive intra-class spectral variation.Existing variability approaches include pixel-wise scaling and spectral-variant libraries, while some newer generative methods are computationally intensive and do not jointly couple variability with multi-task sequence reconstruction.Source: B. Endmember Variability Modeling · p. 3

C. Mixture of Experts for Remote Sensing

  • MDF-Mamba uses fixed channel-determined expert assignment with learned soft reweighting, rather than the dynamic routing of a strict mixture-of-experts model.Its mHC-based fusion projects connection weights onto doubly stochastic matrices, preserving equal total signal throughput across streams and the identity-mapping property.Source: C. Mixture of Experts for Remote Sensing · pp. 3–4

D. State Space Models and Mamba for Remote Sensing Temporal Sequences

  • Mamba offers linear-time sequence modeling through input-dependent state updates, with ∆t controlling how much past information is retained or forgotten at each timestep.The paper motivates temporal SSMs through ordered phenological transitions and contrasts them with static 3D convolution kernels; prior unmixing Mamba scans spectral bands rather than time.Source: D. State Space Models and Mamba for… · p. 4

III. PROPOSED MDF-MAMBA ARCHITECTURE

  • MDF-Mamba addresses the temporal-unmixing gap by applying its SSM to time while per-channel CNN experts handle spectral-spatial structure, with the streams fused by mHCFusion.The described pipeline takes MODIS patches with 6 spectral channels across 23 time steps and produces abundance maps for 14 land-cover classes plus a physics-constrained spectral reconstruction.Source: D. State Space Models and Mamba for… · p. 4, §III · p. 4

A. Spectral-Temporal Disentangling via Multi-Branch Architecture

MDF-Mamba separates spectral-spatial processing into six channel-specific CNN experts while a parallel bidirectional Mamba branch encodes cross-channel seasonal trajectories. Gates and hierarchical grouping then prepare the expert streams for fusion.

A. Spectral-Temporal Disentangling via Multi-Branch Architecture

  • Each spectral expert exchanges gated information between its pixel-wise spectral path and local spatial path without replacing either path’s features.The spectral path uses 1×1 convolutions and the spatial path uses 3×3 convolutions; gates near zero preserve a path, while gates near one add the other path’s features.Source: A. Spectral-Temporal Disentangling via… · pp. 4–5
  • Six fixed-assignment BandBranch experts process separate spectral channels, while a bidirectional Mamba branch models cross-channel phenology across 23 seasonal steps.Each CNN expert has spectral and spatial paths; temporal states use input-dependent transitions whose memory length adapts to phenological change.Source: A. Spectral-Temporal Disentangling via… · p. 5
  • Cross-branch squeeze-and-excitation and spatially adaptive phenology gates modulate the spectral streams before grouping them into vegetation, optical, and moisture representations.The phenology gate can give transitional pixels stronger temporal context than homogeneous interiors.Source: A. Spectral-Temporal Disentangling via… · p. 6
  • A preliminary rough abundance map averages the six branch logits, while each branch also supplies independently supervised abundance outputs.The band-specific paths begin after a cross-band stem calibrates scales and captures first-order inter-channel correlations.Source: A. Spectral-Temporal Disentangling via… · pp. 4, 6

B. Manifold-Constrained Hyper-Connection Fusion

The model fuses three semantically grouped streams with manifold-constrained mixing, then conditions abundance prediction on scene context. It also models endmember variability and blends physics-driven and attention-based spectral reconstructions.

B. Manifold-Constrained Hyper-Connection Fusion

  • mHCFusion integrates three semantic streams through Sinkhorn-projected doubly stochastic mixing, followed by feed-forward processing and gated residual aggregation.The fusion operates in a 64-dimensional space; the mixing constrains each stream to send and receive equal total weight without collapsing.Source: B. Manifold-Constrained… · p. 6
  • A scene-conditioned FiLM head produces class logits whose softmax enforces nonnegative abundances that sum to one at each pixel.The head derives per-channel scale and shift from global average pooled fused features; pixel-wise argmax yields the hard-classification map.Source: B. Manifold-Constrained… · p. 6
  • The ELMM represents each class with 10 learnable spectral variants and uses pixel-wise mixing weights to adapt variant combinations.The variant bank is generated from a learnable embedding with ReLU non-negativity; its initialization uses high-purity pixels or a geographic-grid fallback.Source: B. Manifold-Constrained… · p. 6
  • A top-two-class-constrained cross-attention reconstruction is blended with the ELMM reconstruction according to predicted pixel purity.High-purity pixels favor the ELMM output, while highly mixed pixels incorporate more attention output; linear mixing across vegetation indices is treated as an approximation, not a strict physical law.Source: B. Manifold-Constrained… · pp. 6–7
  • Blended reconstruction error measures overall representation quality, not the physical ELMM alone, so independent validation of abundances requires pure ELMM reconstruction.Mean endmembers are also anchored to their initialization and regularized for temporal smoothness within each physical channel.Source: B. Manifold-Constrained… · p. 7

C. Multi-Task Supervised-Unsupervised Learning

Training combines supervised abundance estimation with reconstruction and regularization objectives. A two-phase curriculum first emphasizes reconstruction while endmembers stabilize, then shifts toward abundance refinement.

C. Multi-Task Supervised-Unsupervised Learning

  • The multi-task objective combines supervised abundance losses with spectral reconstruction, per-expert, spatial-coherence, and endmember regularization terms.Abundance supervision uses L1 magnitude and KL shape penalties for refined abundances, rough abundances, and individual branch outputs, so experts are supervised before phenology gating.Source: C. Multi-Task Supervised-Unsupervised… · p. 7
  • A two-phase curriculum emphasizes reconstruction fidelity while the endmember dictionary stabilizes, then shifts optimization toward abundance accuracy.Endmember anchoring is annealed over training; reconstruction losses receive an early curriculum boost, while correlation preservation is weighted independently.Source: C. Multi-Task Supervised-Unsupervised… · p. 7
  • Reconstruction terms include whitened Mahalanobis error, spectral-angle losses, inverse-variance-weighted MSE, and covariance-matrix MSE for inter-band correlation.A spectral-affinity-weighted spatial stiffness term penalizes abundance discontinuities between similar neighboring pixels, and endmember smoothness regularizes spectral continuity.Source: C. Multi-Task Supervised-Unsupervised… · p. 7

A. Datasets

The study evaluates 2010 MODIS observations over Alberta and Saskatchewan using fractional land-cover labels and spatially blocked data splits. Dataset exploration documents class imbalance, spectral confusability, and class-specific variability that inform endmember initialization and model design.

A. Datasets

  • The dataset contains 23 observations for each of six MODIS channels at 250 m resolution, spanning the 2010 calendar year over Alberta and Saskatchewan.Fractional labels are derived from 30 m NALCMS data aggregated within each MODIS pixel; 12 active classes are evaluated after excluding two spectrally inseparable lichen-moss classes.Source: A. Datasets · pp. 7–8
  • A geographically blocked 70/15/15 train-validation-test split uses 2,731, 585, and 585 patches, with exclusion buffers to prevent patches crossing split boundaries.Patches are 64 × 64 pixels, and bands are normalized using training-set min-max statistics.Source: A. Datasets · p. 8

B. Data Exploration and Purity Analysis

  • At 80% purity, class sample counts span nearly four orders of magnitude, while some nominally pure lichen-moss pixels remain spectrally indistinguishable from mixed background.Needleleaf Forest has over 3.8 million pure pixels; Urban and Broadleaf Forest each have fewer than 400,000, and both lichen-moss classes have spectral range below 0.08 normalized units.Source: B. Data Exploration and Purity Analysis · p. 8, Figure 2 · p. 9
  • Several class pairs have SAD below 0.30 rad, including Needleleaf–Mixed Forest at 0.18 rad and Wetland–Grassland at 0.22 rad.These pairs correspond to classes with high per-class abundance MAE; the analysis adopts 0.30 rad as its spectral-confusability threshold.Source: B. Data Exploration and Purity Analysis · p. 8, Figure 2 · p. 9
  • No single spectral branch fully separates the classes: NDVI distinguishes cropland from evergreen forest, NIR differentiates coniferous from deciduous phenology, and MIR separates wetland from grassland.Purity analysis also reports near-zero lichen-moss spectral range at all thresholds and informs 80% endmember extraction, geographic fallback initialization, and 10 learnable variants.Source: B. Data Exploration and Purity Analysis · p. 8, Figure 3 · p. 9

C. Implementation Details

MDF-Mamba is trained with a staged multi-task curriculum and evaluated on abundance estimation, spectral reconstruction, and classification against eleven representative unmixing baselines.

C. Implementation Details

  • Training uses Adam for 100 epochs with batch size 8, gradient clipping at 1.0, and separate learning rates of 10^-3 and 5 × 10^-4 for the model and endmember parameters.The endmember embedding Q and temperature τ use the lower learning rate; training runs on one NVIDIA A6000 GPU.Source: C. Implementation Details · p. 9
  • During the first 30 epochs, reconstruction losses are weighted 3.0× to stabilize endmembers; afterward, reconstruction penalties return to base weights while covariance, smoothness, and anchoring are annealed.The endmember anchor penalty decreases from 1.0 to 0.1 over 100 epochs.Source: C. Implementation Details · p. 9

D. Evaluation Metrics

  • Evaluation covers abundance error, reconstruction fidelity, and classification, with classification assigned by the highest predicted abundance and per-class F1 added for class-stratified analysis.Abundance metrics are SAE and RMSE; reconstruction metrics are MSE and SAD, while classification metrics include OA, AA, and Cohen’s Kappa.Source: D. Evaluation Metrics · p. 10

E. Baseline Methods

  • MDF-Mamba is compared with eleven methods spanning traditional, NMF-based, autoencoder, CNN, attention, transformer, and state-space approaches under a shared evaluation protocol.Deep-learning baselines share data splits, 64 × 64 patches, VCA endmembers, and supervised L1 abundance loss; MDF-Mamba instead uses GT-derived high-purity endmember initialization.Source: E. Baseline Methods · pp. 10–11

F. Quantitative Results

Across Alberta and Saskatchewan, MDF-Mamba is best or second-best on every reported evaluation metric, with the strongest overall showing on Alberta. On Saskatchewan, the model is evaluated as a zero-shot transfer from Alberta.

F. Quantitative Results

  • MDF-Mamba is best or second-best across all metrics on both datasets, with the reported overall result best on 12 of 14 metrics; Alberta leads on all seven and Saskatchewan on five.The Alberta and Saskatchewan comparisons are reported in Tables I and II, respectively.Source: F. Quantitative Results · p. 11, Table I · p. 12, Table II · p. 13
  • On Alberta, MDF-Mamba achieves the best abundance MAE (0.0255) and RMSE (0.0654), reconstruction SAD (0.1843 rad) and MSE (0.0067), and classification OA (0.7122), AA (0.4721), and κ (0.6575).The reported MAE is 15.3% below SSAF-Net’s 0.0301; reconstruction SAD is 17.4% below UNMamba’s 0.2232 rad, and MSE is 35.6% below SUnSAL’s 0.0104.Source: F. Quantitative Results · p. 11, Table I · p. 12
  • On Saskatchewan, MDF-Mamba leads on OA (0.7485), AA (0.4779), κ (0.6881), abundance MAE (0.0492), and RMSE (0.1575), and ranks second on reconstruction MSE (0.0093) and SAD (0.2081 rad).The second-best reconstruction results are SSAF-Net’s MSE (0.0063) and SAD (0.1823 rad).Source: F. Quantitative Results · p. 12, Table II · p. 13
  • Saskatchewan is a zero-shot transfer using Alberta training and normalization; its higher OA and κ coexist with higher abundance MAE (0.0492 versus 0.0255), which the paper relates to class-composition differences.Cropland and Water together account for 38.6% of Saskatchewan abundance versus 21.4% in Alberta, while Mixed Forest falls from 15.1% to 3.4%.Source: F. Quantitative Results · p. 12
  • The full-scene Saskatchewan abundance errors are evaluated against one-hot class references, unlike Alberta Table I’s fractional references, so those abundance errors are not directly comparable.The Saskatchewan full-scene comparison uses all valid pixels against the 250 m reference map.Source: F. Quantitative Results · p. 13

G. Quantitative Results on Filtered High-Purity Datasets

On the 80%-purity Saskatchewan subset, MDF-Mamba leads all seven evaluation metrics. Additional analyses report Alberta spectral reconstruction fidelity and qualitative spatial comparisons across both provinces.

G. Quantitative Results on Filtered High-Purity Datasets

  • On the filtered Saskatchewan dataset, MDF-Mamba achieves the best result on all seven metrics, including abundance MAE (0.0250), reconstruction MSE (0.0119), and classification OA (0.8972).It reduces reconstruction MSE by 29.2% relative to DeepTrans-HSU’s 0.0168; the comparison uses pixels with dominant-class purity ≥80%.Source: G. Quantitative Results on Filtered… · p. 13, Table IV · p. 14
  • Filtered Saskatchewan OA and κ (0.8972 and 0.8633) are below filtered Alberta values (0.9340 and 0.9167); the paper attributes the remaining 3.7-point OA gap to zero-shot cross-provincial domain shift.The filtered subsets have similar class-distribution entropy, and Saskatchewan retains proportionally more Cropland.Source: G. Quantitative Results on Filtered… · p. 13

H. Spectral Reconstruction Analysis

  • On Alberta, pixel-level reconstruction RMSE is 0.0819 and SAD is 0.1843 rad, while per-band analysis shows consistent fidelity across the 23-step temporal sequence.Patch-mean reconstructed spectra closely follow the original signals across the six optical bands, including transition months.Source: H. Spectral Reconstruction Analysis · p. 13, Figure 5 · p. 15

I. High-Resolution Spatial Comparison

  • Across the twelve selected Alberta classification regions, MDF-Mamba is reported to preserve class boundaries where baselines show confusion, fragmentation, or spatial artifacts.The examples include forest transitions, grassland, urban, wetland, taiga, snow, cropland, water, and shrub regions.Source: §I · p. 15, Figure 6 · p. 16
  • In zoomed abundance comparisons, MDF-Mamba’s fractional patches more closely match ground truth than traditional baselines’ near-zero or diffuse predictions, and retain sharper gradients in Saskatchewan mixtures.The comparisons cover all evaluated models in diagnostically selected sub-regions on both provinces.Source: §I · pp. 13, 19, Figure 7 · p. 17, Figure 8 · p. 18

J. Per-Class Abundance Analysis

Abundance errors are concentrated in spectrally overlapping, structurally complex classes, while seasonal trajectories provide class-discriminating cues. Endmember agreement varies with pure-pixel availability, and pixel-wise variants represent intra-class variability.

J. Per-Class Abundance Analysis

  • Water (MAE: 0.0152) and Urban (MAE: 0.0158) have low abundance errors, while Needleleaf Forest (0.0786) and Wetland (0.0555) have higher errors.The largest pixel-wise errors occur in mixed transition zones involving dense vegetation, whereas spatially homogeneous Water and Temperate Grassland regions are most accurate.Source: J. Per-Class Abundance Analysis · p. 19

K. Temporal Phenology as a Disentangling Cue

  • Cropland’s July NDVI green-up contrasts with the gradual, plateaued trajectory of Temperate Needleleaf Forest across the 23-step seasonal series.The TemporalMambaBranch scans trajectories across all six channels; these phenological differences correspond to spatial disentanglement of spectrally similar classes.Source: K. Temporal Phenology as a… · p. 19

L. Endmember Analysis and Shift Justification

  • Needleleaf Forest has the highest endmember concordance (CCC = 0.770), while Taiga Forest has the lowest (CCC = 0.000).Rich-pixel classes such as Cropland also show high concordance (CCC = 0.740); classes lacking spectrally distinguishable pure pixels at 250 m show weak correspondence. In Fig. 10, displacement from the GT reference visually indicates lower CCC; Fig. 11 shows learned variants and their average pixel-wise mixing weights.Source: L. Endmember Analysis and Shift… · pp. 19–20, Figure 10 · p. 21, Figure 11 · p. 22
  • Wetland (CCC = 0.158) and Water (CCC = 0.126) retain lower concordance where band-level offsets are larger as the anchor loss relaxes.For Needleleaf Forest, abundance difficulty is attributed to scene-level spectral ambiguity despite its high endmember concordance; lower concordance may also contribute for Mixed Forest, Grassland, and Wetland.Source: L. Endmember Analysis and Shift… · pp. 20, 22
  • Needleleaf Forest, Mixed Forest, Wetland, and Grassland have the highest abundance errors, with overlapping signatures linked to similar vegetation phenology.The NIR and MIR experts learn moisture-specific features, the NDVI expert captures green-up timing, and the temporal branch encodes seasonal trajectories across channels.Source: L. Endmember Analysis and Shift… · pp. 20, 22

M. Feature Space Disentanglement

Training changes fused features from mixed, scattered representations to separated pure-endmember clusters. Ablations show that learned fusion weighting most affects abundance and classification, while reconstruction objectives and variable endmembers strongly affect spectral fidelity.

M. Feature Space Disentanglement

  • After training, fused features project pure endmembers into well-separated land-cover clusters, unlike the mixed, scattered features before training.The t-SNE visualization presents this separation before final abundance estimation.Source: M. Feature Space Disentanglement · p. 22, Figure 12 · p. 22

N. Ablation Study

  • Uniform stream weighting raises abundance MAE by 46% (0.0255 →0.0372), drops OA by 3.6 percentage points (71.22%→67.59%), and lowers κ from 0.658 to 0.601.The component lesion study disables modules at inference using the same trained weights.Source: N. Ablation Study · p. 22, Table V · p. 22
  • Removing the temporal branch raises abundance MAE by 20% (0.0255→0.0305) and reduces OA from 71.22% to 70.36%.The authors describe this as a measurable, complementary phenological contribution to the fused representation.Source: N. Ablation Study · pp. 22–23
  • Collapsing pixel-wise endmember variants to their class mean raises reconstruction MSE 7.1× (0.0067→0.0474) and SAD 2.6× (0.1843→0.481 rad).Abundance and classification metrics remain unchanged; the variant module acts on the reconstruction pathway.Source: N. Ablation Study · p. 22
  • Using one endmember signature per class raises reconstruction MSE 8.5× (0.0067→0.0568), while random seeding raises it 12× (0.0067→0.0798).Both changes modestly increase abundance MAE from 0.0290 to 0.0294; the reported reconstruction degradation is substantially larger.Source: N. Ablation Study · p. 23
  • Removing the reconstruction objective raises reconstruction MSE 4.2× (0.0067→0.0281), while abundance MAE (0.0264) and classification OA (71.01%) remain comparable to the full model.The result indicates that the objective primarily constrains the endmember dictionary and spectral fidelity, rather than directly boosting classification accuracy on the training domain.Source: N. Ablation Study · p. 23

O. Statistical Reproducibility and Variance Analysis

Across three Alberta training seeds, classification and reconstruction metrics vary little, while abundance MAE and κ show modest spread. MDF-Mamba combines a 3.33M-parameter, 14.93-GFLOP profile with reported high accuracy and throughput.

O. Statistical Reproducibility and Variance Analysis

  • Across three seeds, OA is 0.7118 ± 0.0004, reconstruction MSE varies by 0.0004, abundance MAE ranges from 0.0255 to 0.0268, and κ is 0.6522 ± 0.0038.The runs use identical Alberta splits and training conditions; the authors characterize the κ and abundance variation as small but measurable.Source: O. Statistical Reproducibility and… · p. 23, Table VII · p. 24

P. Computational Efficiency

  • MDF-Mamba uses 3.33M parameters and 14.93 GFLOPs per patch, achieving 48.8 patches per second throughput and a peak inference memory footprint of 180.9 MB.The computational profile was measured on input shape (1, 138, 64, 64); throughput is reported at batch size 1.Source: P. Computational Efficiency · p. 23, Table VIII · p. 24, Table IX · p. 24
  • The six CNN BandBranches account for 82.9% of parameters (2.761M) and 75.8% of FLOPs (11.32 GFLOPs), while Temporal Mamba accounts for 3.8% and 16.5%, respectively.The mHC fusion gate and ELMM reconstruction head together account for less than 6% of total cost.Source: P. Computational Efficiency · pp. 23–24, Table IX · p. 24

Q. Cross-Provincial Class-Level Transfer Analysis

Alberta-trained MDF-Mamba transfers to Saskatchewan, but class-level transfer varies with spectral-temporal signatures and training representation. The paper also reports limits from its single-year, two-province evaluation and contrasts the model with generic Mamba architectures lacking physics-constrained reconstruction.

Q. Cross-Provincial Class-Level Transfer Analysis

  • In Alberta-to-Saskatchewan transfer, classes governed by universal physical processes—water absorptance, sparse bare-soil reflectance, and stable crop phenology—transfer consistently (F1 > 0.70), whereas classes with regionally distinct phenology exhibit poor transfer.Taiga reaches F1 = 0.432 despite accounting for only 0.16% of Alberta training abundance.Source: Q. Cross-Provincial Class-Level… · p. 24
  • Saskatchewan OA is 0.7485 and κ is 0.6881, above Alberta’s 0.7122 and 0.6575; abundance MAE rises from 0.0255 to 0.0492.The text attributes higher Saskatchewan abundance error to domain shift for phenologically sensitive classes and the use of one reference for the full scene.Source: Q. Cross-Provincial Class-Level… · p. 25
  • Needleleaf Forest, Cropland, and Grassland have low endmember RMSEs (0.136, 0.161, and 0.258) and transfer with F1 > 0.60; Broadleaf Forest has F1 = 0.065.The analysis links weaker minority-class transfer to insufficient pure-pixel representation and regionally bound phenological signatures in the training data.Source: Q. Cross-Provincial Class-Level… · p. 25

R. Evaluation Against Generic Mamba Architectures

  • Generic Mamba models lack a physics-constrained decoder, so their spectral reconstruction outputs are zero-vectors with SAD = 1.5708 rad (π/2).The evaluation describes this as a limitation for full physics-based unmixing, despite their ability to estimate fractional abundances.Source: R. Evaluation Against Generic Mamba… · p. 25, Table XI · p. 25

V. CONCLUSION

  • The conclusion reports Alberta state-of-the-art results and strong Saskatchewan transfer without retraining, with the greatest gains in complex agricultural transition zones.It also reports 150-fold lower spectral angle errors than single-variant models and a 14.93-GFLOP footprint.Source: §V · pp. 25–26
  • Evaluation covers one calendar year (2010) across Alberta and Saskatchewan, so the temporal models are optimized for a specific seasonal cycle.The authors identify multi-year stacks and a wider range of global biomes as future work.Source: §V · p. 26

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