LIMODENet: Attention-Free Compact Encoders for Information-Preserving Onboard Satellite Image Restoration

Thanh-Dung Le; Vu Nguyen Ha; Ti Ti Nguyen; Symeon Chatzinotas

Figure 2: LIMODENet integrates three ODE stages at constant width, and sends only the latent onward. (a) The tiny restoration variant: a strided stem lifts

3{\times}128{\times}128

to

128

channels, then one Euler LargeKernelBlock at

64^{2}

(

\alpha{=}0.5

), a depthwise stride-

2

downsample, and four Euler FocalBlocks (

\alpha{=}0.7

) plus one RK-2 LargeKernelBlock (

\alpha{=}0.5

) at

32^{2}

; the

64^{2}

-input classifier halves each figure. Every block integrates ( 1 ) through

x\!\leftarrow\!x+\alpha f

: the FocalBlock adds a pooled global branch to the local one, which is how the network mixes globally without attention, and the RK-2 stage evaluates the same field twice, at

x

and at the midpoint. (b) What each stage is for, illustrated rather than measured. The downlink box is the setting the design targets, not the experiment we ran: every reported result degrades pixels before the encoder and the autoencoder never sees a channel, so

z\to\tilde{z}

is an interface sketch ( Sec. P ).

Scale	$C$	$s_{1}/s_{2}/s_{3}$	$r$	$k$	Params	MACs
Width ladder: shape held fixed, only $C$ varies
nano	96	1/4/1	3.0	5	0.39M	149M
tiny	128	1/4/1	3.0	5	0.69M	262M
small	192	1/4/1	3.0	5	1.55M	581M
base	256	1/4/1	3.0	5	2.73M	1027M
Off-ladder: four hyper-parameters change at once

Table 1: The LIMODENet family scales width alone, except for big .

C

is the constant channel width,

s_{i}

the number of blocks in stage

i

,

r

the pointwise-MLP expansion ratio,

k

the depthwise kernel. Parameters/mult-adds for a

10

-class head at

64{\times}64

; residual scales

\alpha{=}(0.5,0.7,0.5)

and the Euler/Euler/midpoint assignment are identical at every scale.

Reconstructor	Params	PSNR (dB)	SSIM	Top-1 (%) ∗	bs1 ms / img/s †
U-Net (skips)	0.75M	36.32 $\pm$ 0.33	0.9591 $\pm$ 0.0027	77.17 $\pm$ 0.89	—
CNN-AE	0.75M	35.64 $\pm$ 0.18	0.9531 $\pm$ 0.0017	71.89 $\pm$ 0.77	—
LIMODENet-AE	0.77M	37.39 $\pm$ 0.14	0.9672 $\pm$ 0.0010	78.50 $\pm$ 0.83	2.54 / 898
LIMODENet-skip	0.78M	38.07 $\pm$ 0.26	0.9716 $\pm$ 0.0014	80.66 $\pm$ 0.54	2.74 / 830
LIMODENet-depth4	1.02M	37.18 $\pm$ 0.21	0.9663 $\pm$ 0.0013	76.96 $\pm$ 0.60	3.04 / 882
LIMODENet-skip-depth4	1.03M	37.93 $\pm$ 0.05	0.9706 $\pm$ 0.0003	80.34 $\pm$ 0.57	3.13 / 813

Table 2: Encoder-controlled restoration, iso-parameter, top to bottom: baselines, LIMODENet and its kill-test variants, and two modern restorers.

1

dB/

100

q,

3

seeds,

60

epochs, val-selected. LIMODENet leads the top block (U-Net/CNN-AE, its deployment-constrained peers) but trails the bottom block (NAFNet-lite/Restormer-lite), which additionally carry spiking-illegal gating/attention; every LIMODENet variant nonetheless beats both modern restorers on batched throughput (

813

–

898

vs.

518

/

203

img/s). ∗ Reconstruct-then-classify accuracy under a fixed Spiking-CNN judge, the least favourable of two neutral judges tried. † Batch

32

, FP32 + cuDNN autotune, one RTX 4070 Laptop GPU; full ablation and judge-control detail in Secs. M and G .

Reconstructor	PSNR (dB)	SSIM	Top-1 (%)	bs1 ms / img/s
LIMODENet-skip (ANN)	38.07 $\pm$ 0.26	0.9716 $\pm$ 0.0014	80.66 $\pm$ 0.54	2.74 / 830
LIMODENet-skip (spiking, $T{=}8$ )	35.95 $\pm$ 0.05	0.9519 $\pm$ 0.0004	80.22 $\pm$ 0.20 ∗	53.44 / 33 †

Table 3: Full spiking conversion costs measurable fidelity but not measurable downstream accuracy. Three seeds,

60

epochs,

T{=}8

, same protocol and judge as Table 2 ; PSNR/SSIM are non-overlapping between rows, Top-1 is not. ∗ Indistinguishable from the ANN row. † GPU-simulated latency, not a neuromorphic-hardware measurement: every timestep is a full dense forward pass here. See the energy analysis below.

Reconstructor	PSS $\uparrow$	$D_{\mathrm{sem}}$ $\downarrow$	CKA $\uparrow$
LIMODENet-AE	0.796 $\pm$ 0.010	0.611 $\pm$ 0.016	0.799 $\pm$ 0.011
U-Net (skips)	0.746 $\pm$ 0.010	0.685 $\pm$ 0.015	0.757 $\pm$ 0.013
CNN-AE	0.694 $\pm$ 0.014	0.756 $\pm$ 0.018	0.681 $\pm$ 0.011

Table 4: A self-supervised, label-free judge reproduces the exact restoration ranking. DINOv2 ViT-S/14 embeddings,

1

dB/

100

q, three seeds; all three metrics separate non-overlapping. Full neutral-judge, judge-free and certified-bound tables in Sec. G .

Dataset	Nano	Tiny	Small	Base	$\Delta_{\mathrm{ladder}}$	Big	IN $\to$ FT †
	Width ladder (3 seeds)					Off-ladder
EuroSAT	95.65 $\pm$ 0.23	96.54 $\pm$ 0.17	96.93 $\pm$ 0.16	97.26 $\pm$ 0.17	$+0.7$	97.54 $\pm$ 0.14	98.26 †a
RSICB128	96.38 $\pm$ 0.05	97.18 $\pm$ 0.19	97.76 $\pm$ 0.03	97.91 $\pm$ 0.09	$+0.7$	98.23 $\pm$ 0.06	99.09 †
PatternNet	94.90 $\pm$ 0.17	95.82 $\pm$ 0.31	96.90 $\pm$ 0.28	97.43 $\pm$ 0.10	$+1.6$	97.69 $\pm$ 0.05	98.98 †
NWPU45	74.82 $\pm$ 0.41	78.81 $\pm$ 0.72	81.82 $\pm$ 0.14	82.94 $\pm$ 0.40	$+4.1$	85.01 $\pm$ 0.33	90.54 †
UCMerced	56.24 $\pm$ 1.70	60.26 $\pm$ 0.51	68.36 $\pm$ 2.01	72.70 $\pm$ 1.20	$+12.4$	79.31 $\pm$ 1.35	95.87 †b

Table 5: RS classification top-1 (%), uniform

64

px protocol, full width ladder. Nano/Tiny/Small/Base vary only

C{\in}\{96,128,192,256\}

(Sec. 3.3 ); Big is off-ladder. All columns are

3

-seed mean

\pm

std, val-selected epoch.

\Delta_{\mathrm{ladder}}

is the Tiny

\to

Base gain from a controlled

4\times

width increase:

{\leq}1.6

pp wherever accuracy exceeds

95\%

,

4.1

/

12.4

pp on the two benchmarks with real headroom. † Legacy single-seed IN

\to

FT runs under the earlier protocol, not directly comparable. a Best checkpoint reports

98.45\%

. b

256

px input, unlike the other

\dagger

entries.

Figure 3: Layer-wise probing: label information is preserved through the ODE blocks and only compressed at the head. Linear- and kNN-probe top-1 accuracy read off the representation after each block. Accuracy rises monotonically through the six ODE blocks (

79.9\!\to\!98.4\%

linear) and dips only at the strided downsample (

91.5\!\to\!90.9\%

): the opposite of early compression.

Figure 4: Why a smaller step and one second-order stage: the motivation, on a model problem. A forward-Euler discretization of a damped spiral

\dot{x}=Ax

leaves the true trajectory

x(t)

by a per-step error of order

\mathcal{O}(\alpha^{2})

(dotted segments) that accumulates to

\mathcal{O}(N\alpha^{2})

over

N

steps (Prop. 1 ). Halving

\alpha

quarters the leading term at no extra cost, and replacing one Euler step with a two-stage RK-2 step removes it entirely up to

\mathcal{O}(\alpha^{3})

; LIMODENet therefore uses

\alpha\!\leq\!0.7

at every stage and one RK-2 stage at the coarsest resolution (Thm. 1 ). This is a schematic of the numerical argument, not a measurement of the trained network.

Figure 5: What the FocalBlock right-hand side is built to do, and the expected effect. The block field is the GELU-gated sum of a local branch (

\mathrm{DWConv}_{3\times 3}

, which by itself drives features only toward neighborhood structure, with no long-range term) and a global branch (

\mathrm{Conv}_{1\times 1}

on a spatial average, a single position-independent vector broadcast everywhere, i.e. the first moment

\mu_{h}

of Prop. 2 ). Adding the mean-field term makes every output position depend on every input in one step (Prop. 6 ), which pure stacked

3\times 3

convolutions reach only after

{\geq}15

layers at this resolution; the additive (not multiplicative) form keeps the combined field bounded and gradient-friendly. The panels plot analytic branch models on a

2

-D cartoon domain to isolate the construction; they are not activations of a trained model.

Figure 6: The same local/global split, measured on a trained model. Per-position channel-

\ell_{2}

norm of the two branches of the first Stage-2 FocalBlock of a trained tiny LIMODENet (EuroSAT, Tiny-ImageNet pretraining then fine-tuning, seed 0), on one held-out EuroSAT patch; panels 2–4 share a color scale. The local (DWConv) branch carries spatially varying structure (coefficient of variation

0.17

); the global branch is exactly spatially constant, a single pooled vector

W_{g}\mu_{h}

broadcast to every position (Prop. 2 ), with norm

0.35\times

the combined field, and it points partly against the mean local direction (

\cos=-0.28

), i.e. it acts as a scene-level corrective offset rather than a copy of the local response. This is the behavior Fig. 5 sketches, now on real activations.

	Reconstructor	PSNR (dB)	SSIM	Top-1 (%)
$3$ dB	LIMODENet-AE	46.42 $\pm$ 0.01	0.9974 $\pm$ 0.0000	87.60 $\pm$ 0.09
	U-Net	46.45 $\pm$ 0.05	0.9975 $\pm$ 0.0001	87.66 $\pm$ 0.10
	CNN-AE	46.07 $\pm$ 0.06	0.9969 $\pm$ 0.0001	87.54 $\pm$ 0.05
$4$ dB	LIMODENet-AE	39.60 $\pm$ 0.00	0.9966 $\pm$ 0.0000	87.31 $\pm$ 0.06
	U-Net	39.60 $\pm$ 0.00	0.9967 $\pm$ 0.0001	87.50 $\pm$ 0.07
	CNN-AE	39.55 $\pm$ 0.00	0.9963 $\pm$ 0.0001	87.45 $\pm$ 0.08

Table 6: Above the decoding threshold no architecture leads. Three seeds, iso-parameter,

60

epochs, val-selected, neutral judge. A formal equivalence test calibrated against independent controls (TOST, see below) confirms all four comparisons (LIMODENet versus the U-Net and versus the CNN-AE, at both

3

and

4

dB) as ties. Compare with the sub-threshold margins of up to

+1.53

dB and

+9.8

pp in Tabs. 10 and 9 .

		failed frames		remaining frames
	Reconstructor	in $\to$ out	gain	in $\to$ out	gain
$3$ dB	LIMODENet-AE	$22.10\to 29.25$	$+7.15$	$50.48\to 52.25$	$+1.77$
	U-Net	$22.10\to 29.27$	$+7.16$	$50.48\to 52.39$	$+1.91$
	CNN-AE	$22.10\to 26.34$	$+4.24$	$50.48\to 51.55$	$+1.07$
$4$ dB	LIMODENet-AE	$14.04\to 14.04$	$-0.00$	$50.78\to 52.11$	$+1.33$
	U-Net	$14.04\to 14.04$	$-0.00$	$50.78\to 52.08$	$+1.31$

Table 7: Stratified by received quality: input

\to

output PSNR (dB), seed 0. “Failed frames” are received images below

30

dB (

8

of

8090

at

3

dB,

16

at

4

dB); the remainder arrive essentially lossless. At

4

dB the failed frames are not recovered at all by any of the three architectures.

Figure 7: The injectivity condition fails everywhere in the trained model, holds everywhere when enforced, and costs

3.22

dB to enforce. Left: per-block

\alpha L_{g}

, estimated by JVP/VJP power iteration at real operating points (

8

points per block,

22

iterations); the axis is logarithmic because the trained values exceed the bound by one to two orders of magnitude. Right: i-ResNet fixed-point inversion of each block. The trained model’s error is flat or growing, because the iteration is not a contraction and so has no fixed point to reach, whereas the constrained variant falls geometrically to machine precision in every block.

LIMODENet-AE (as trained)
Block	Disc.	$\alpha$	$\hat{L}_{g}$	$\alpha L_{g}$	inverts?
stage1	euler	0.5	58.84	29.42	✗
stage2.0	focal	0.7	9.12	6.39	✗
stage2.1	focal	0.7	4.94	3.46	✗
stage2.2	focal	0.7	5.87	4.11	✗
stage2.3	focal	0.7	9.71	6.79	✗

Table 8: Per-block injectivity measurements for the trained reconstructor and for the spectral-normalized variant.

\hat{L}_{g}

is the estimated local Lipschitz constant of the residual field; the condition is

\alpha L_{g}<1

for Euler and focal blocks and

\alpha L_{g}(1+\tfrac{\alpha}{2}L_{g})<1

for the midpoint block. Auto-generated by theory/theory_recon_plot.py .

	Reconstructor	PSNR (dB)	SSIM	Top-1 (%)
$100$ q	LIMODENet-AE	37.39 $\pm$ 0.14	0.9672 $\pm$ 0.0010	78.50 $\pm$ 0.83
	U-Net	36.32 $\pm$ 0.33	0.9591 $\pm$ 0.0027	77.17 $\pm$ 0.89
	CNN-AE	35.64 $\pm$ 0.18	0.9531 $\pm$ 0.0017	71.89 $\pm$ 0.77
$50$ q	LIMODENet-AE	33.92 $\pm$ 0.05	0.9426 $\pm$ 0.0006	67.14 $\pm$ 0.18
	U-Net	33.43 $\pm$ 0.16	0.9358 $\pm$ 0.0027	66.33 $\pm$ 1.15
	CNN-AE	32.93 $\pm$ 0.05	0.9301 $\pm$ 0.0006	62.78 $\pm$ 0.22

Table 9: The fidelity ranking is preserved across the whole quality axis. The same iso-parameter three-seed comparison at

1

dB, run at JPEG quality

100

,

50

and

10

; all models trained to convergence (

60

epochs), epochs val-selected. Top-1 uses the neutral Spiking-CNN judge; LIMODENet beats the CNN-AE at all three settings but is tied with the U-Net at all three, which is why the main text scopes the U-Net claim to fidelity.

Figure 8: The link has a decoding threshold, and the encoder comparison lives entirely below it. Left: received-image PSNR before any model, measured over the full

8{,}090

-image test split at the

128

px working resolution. Right: restored PSNR for the three iso-parameter reconstructors,

3

seeds,

60

epochs, val-selected. Margins exist only below the threshold and vanish above it, which is what the bottleneck reading predicts: routing detail around a bottleneck costs nothing when the input still contains that detail.

	Reconstructor	PSNR (dB)	SSIM	Top-1 (%)
$1$ dB	LIMODENet-AE	37.39 $\pm$ 0.14	0.9672 $\pm$ 0.0010	78.50 $\pm$ 0.83
	U-Net	36.32 $\pm$ 0.33	0.9591 $\pm$ 0.0027	77.17 $\pm$ 0.89
	CNN-AE	35.64 $\pm$ 0.18	0.9531 $\pm$ 0.0017	71.89 $\pm$ 0.77
$2$ dB	LIMODENet-AE	35.61 $\pm$ 0.11	0.9738 $\pm$ 0.0011	81.72 $\pm$ 0.68
	U-Net	34.89 $\pm$ 0.27	0.9652 $\pm$ 0.0030	78.43 $\pm$ 1.01
	CNN-AE	34.08 $\pm$ 0.06	0.9552 $\pm$ 0.0008	71.90 $\pm$ 0.21

Table 10: The ranking also holds when the channel, rather than the compression, is varied. Iso-parameter three-seed comparison at JPEG quality

100

and two

E_{s}/N_{0}

settings;

60

epochs, val-selected epochs, neutral Spiking-CNN judge. Absolute values are comparable within a row block only.

LIMODENet margin (LIMODENet-ANN / Sp.-CNN / SEW)
	recon $\to$ clf Top-1 (%), $3$ seeds
Judge	LIMODENet-AE	U-Net	CNN-AE
LIMODENet-ANN †	76.42 $\pm$ 1.35	71.92 $\pm$ 1.91	67.98 $\pm$ 0.69
Spiking-CNN	78.50 $\pm$ 0.83	77.17 $\pm$ 0.89	71.89 $\pm$ 0.77
SEW-ResNet	81.55 $\pm$ 0.60	79.71 $\pm$ 0.58	77.35 $\pm$ 0.74
vs. U-Net	$+4.50$ / $+1.34^{\circ}$ / $+1.84$

Table 11: A negative control: the semantic margin over the U-Net is an artifact of the judge. † Confounded judge; the other two are architecturally unrelated to all three reconstructors. ∘ Under the Spiking-CNN judge the LIMODENet–U-Net difference lies within overlapping error bars.

	Reconstructor	PSS ( $\uparrow$ )	$D_{\mathrm{sem}}$ ( $\downarrow$ )	CKA ( $\uparrow$ )
$1$ dB/ $100$ q	LIMODENet-AE	0.9967 $\pm$ 0.0002	0.0675 $\pm$ 0.0026	0.9931 $\pm$ 0.0004
	U-Net	0.9949 $\pm$ 0.0007	0.0854 $\pm$ 0.0054	0.9876 $\pm$ 0.0016
	CNN-AE	0.9928 $\pm$ 0.0004	0.0998 $\pm$ 0.0026	0.9833 $\pm$ 0.0009
$1$ dB/ $50$ q	LIMODENet-AE	0.9892 $\pm$ 0.0002	0.1234 $\pm$ 0.0008	0.9707 $\pm$ 0.0006
	U-Net	0.9868 $\pm$ 0.0009	0.1366 $\pm$ 0.0047	0.9631 $\pm$ 0.0025
	CNN-AE	0.9839 $\pm$ 0.0001	0.1501 $\pm$ 0.0004	0.9562 $\pm$ 0.0001

Table 12: A judge-free re-run of the downstream comparison separates cleanly on all three metrics, at every sub-threshold condition. Frozen Tiny-ImageNet-pretrained LIMODENet backbone, never fine-tuned on EuroSAT; three seeds, mean

\pm

std. LIMODENet leads on all three metrics with non-overlapping error bars at all four conditions,

24/24

comparisons in total.

Reconstructor	PSS ( $\uparrow$ )	$D_{\mathrm{sem}}$ ( $\downarrow$ )	CKA ( $\uparrow$ )
LIMODENet-AE	0.7960 $\pm$ 0.0098	0.6108 $\pm$ 0.0157	0.7991 $\pm$ 0.0107
U-Net	0.7459 $\pm$ 0.0103	0.6848 $\pm$ 0.0151	0.7570 $\pm$ 0.0125
CNN-AE	0.6937 $\pm$ 0.0143	0.7560 $\pm$ 0.0180	0.6807 $\pm$ 0.0113

Table 13: An independent, self-supervised encoder reproduces the identical ranking. DINOv2 ViT-S/

14

;

1

dB/

100

q, three seeds, mean

\pm

std. All three metrics separate with non-overlapping error bars, same order as Table 12 . Absolute values are far lower (domain gap from natural-image pretraining) but the relative ordering is exactly reproduced.

Nano	PSS $\uparrow$	$D_{\mathrm{sem}}$ $\downarrow$	CKA $\uparrow$	CSPR (%)
LIMODENet-AE	0.9955 $\pm$ 0.0001	0.0802 $\pm$ 0.0009	0.9902 $\pm$ 0.0001	7.36 $\pm$ 0.32
U-Net	0.9911 $\pm$ 0.0019	0.1111 $\pm$ 0.0111	0.9776 $\pm$ 0.0055	5.93 $\pm$ 0.48
CNN-AE	0.9920 $\pm$ 0.0004	0.1052 $\pm$ 0.0030	0.9812 $\pm$ 0.0011	6.27 $\pm$ 0.20

Table 14: The judge-free and certified-guarantee advantages both survive at half the parameter budget. Nano band (

0.44

M for the full autoencoder),

1

dB/

100

q, three seeds, mean

\pm

std; frozen Tiny-ImageNet encoder, same protocol as Table 12 . The

D_{\mathrm{sem}}

margin over the U-Net grows relative to the tiny band (

0.0179\!\to\!0.0309

), echoing the fidelity finding ( Sec. 4.8 ) that the U-Net margin strengthens rather than shrinks at half budget. As in Table 28 , the two baselines swap at this budget: the CNN-AE edges the U-Net on all four metrics here, having trailed it on all three in the tiny band (Table 12 ). Only LIMODENet’s first place is stable across bands.

	PSNR (dB)		recon $\to$ clf (%) ‡
	$25$ ep †	$60$ ep	$25$ ep †	$60$ ep
LIMODENet-AE	35.49 $\pm$ 0.18	37.39 $\pm$ 0.14	67.08 $\pm$ 0.63	76.42 $\pm$ 1.35
U-Net	34.85 $\pm$ 0.33	36.32 $\pm$ 0.33	64.61 $\pm$ 1.00	71.92 $\pm$ 1.91
CNN-AE	34.05 $\pm$ 0.17	35.64 $\pm$ 0.18	61.03 $\pm$ 0.73	67.98 $\pm$ 0.69
margin vs. U-Net	$+0.64$	$\mathbf{+1.07}$	$+2.47$	$\mathbf{+4.50}$
margin vs. CNN-AE	$+1.44$	$\mathbf{+1.75}$	$+6.05$	$\mathbf{+8.44}$

Table 15: Training to convergence widens LIMODENet’s margin rather than closing it. † The

25

-epoch columns predate the validation-split protocol and select the epoch on test. ‡ Both recon

\to

clf columns use the LIMODENet-ANN judge so the two budgets remain comparable to each other; the PSNR columns need no judge at all.

Method	EuroSAT top-1	Input	Params	Protocol note
LIMODENet (tiny, scratch)	$96.54$ $\pm$ 0.17	$64$	$0.69$ M	3 seeds, val-selected
LIMODENet (IN $\to$ FT) †	$98.45$	$64$	$0.69$ M	single seed, best ckpt
SceneMixer [ 1 ]	$93.90$	$64$	low	native res., same DW+PW family
KCN / KonvNeXt [ 8 ]	${\sim}96$	$224$	${\geq}28$ M	ConvNeXt+KAN head, upsampled
STConvNeXt [ 36 ]	– ∗	$224$	${\sim}13$ M	reports NWPU/AID/UCM, not EuroSAT
FocalNet-T [ 53 ]	– ∗	$224$	$28.6$ M	ImageNet backbone, no EuroSAT eval

Table 16: LIMODENet against recent lightweight / efficient RS classifiers on EuroSAT. Not a controlled comparison: entries differ in input resolution, pre-training, split, and augmentation. † Legacy single-seed protocol, not comparable to the 3-seed rows. ∗ No EuroSAT number in the source; the method targets other RS benchmarks or ImageNet. Included for positioning only; the paper’s claims rest on Sec. 4.2 .

Scale	Params	Tiny-ImageNet top-1 (%)	GPU-h
nano	0.41M	46.64	0.9
tiny	0.72M	47.29	1.1
small	1.58M	50.85	1.3
base	2.78M	51.61	1.7
big ∗	5.85M	51.06	3.5

Table 17: Tiny-ImageNet pre-training ,

60

epochs at

64{\times}64

, single seed. These checkpoints initialize the IN

\to

FT arm of the scaling study. Parameter counts exceed those of Table 1 because the head here is

200

-way rather than

10

-way. ∗ big is off the width ladder: it changes depth, MLP ratio and kernel as well as width, and despite

2.1\times

the parameters of base it does not exceed it.

$\Delta_{\mathrm{TinyIN}}$	EuroSAT	NWPU	PatternNet	RSICB	UCMerced
nano	$+1.9$	$+11.4$	$+3.5$	$+2.2$	$\mathbf{+36.3}$
tiny	$+1.2$	$+8.1$	$+2.7$	$+1.5$	$+31.9$
small	$+0.5$	$+6.7$	$+1.7$	$+1.2$	$+25.9$
base	$+0.5$	$+5.7$	$+1.3$	$+1.0$	$+21.8$
big	$+0.2$	$+3.1$	$+1.0$	$+0.5$	$+15.5$

Table 18: The pretraining benefit decays monotonically with capacity on every one of the five RS benchmarks.

\Delta_{\mathrm{TinyIN}}

is TinyIN

\to

FT minus from-scratch, same cell, both

3

-seed means. Every one of the

20

scale transitions is non-increasing, with a single tie (EuroSAT, small

\to

base).

Benchmark	Base	Big	disjoint?
EuroSAT (saturated)	97.26 $\pm$ 0.17	97.54 $\pm$ 0.14	no
NWPU (headroom)	82.94 $\pm$ 0.40	85.01 $\pm$ 0.33	yes, $+2.07$

Table 19: Whether the off-ladder big configuration beats base depends on headroom, not on a fixed capacity budget.

3

seeds, mean

\pm

std, epochs selected on a held-out split.

System	Metric	$10$ q	$50$ q	$100$ q
Recon. $\to$ clf.	PSNR (dB)	30.63	33.98	38.25
	SSIM	0.8585	0.9340	0.9681
	Top-1 (%)	47.44	66.87	85.96
Degraded- trained clf.	PSNR (dB)	n/a — emits no image
	SSIM	n/a — emits no image
	Top-1 (%)	81.81 $\pm$ 0.22	87.89 $\pm$ 0.11	88.31 $\pm$ 0.23

Table 20: The two systems are not comparable on the same axes, and that is the point.

3

seeds, mean

\pm

std. The classifier has no PSNR or SSIM to report, because it discards the scene, whereas restoration returns the image. This bounds the label-accuracy claim rather than ranking the systems: the bound is local, and reverses off the training operating point. The reconstruct-then-classify row is the original pipeline reconstructor; the iso-parameter model of Table 2 scores

76.42\%

at

100

q under the LIMODENet-ANN judge (Table 21 ) and loses to the classifier by more.

Figure 9: Reconstruction recovers most of the label information a DVB-S2X channel destroys (EuroSAT). The left panel plots three-way top-1 accuracy against JPEG quality at

1

dB for (A) classifying the degraded image (a clean-trained classifier applied zero-shot,

11.1\%

), (B) reconstruct-then-classify, and (C) the clean oracle. Note: pipeline (A) is a clean-trained classifier applied zero-shot and is a weak baseline; the gain over it is not our claim (see Table 20 ).

Figure 10: The backbone recovers both the image and its label (classes River , Highway , Industrial ;

1

dB,

100

q). The DVB-S2X-degraded input (left) is noise, and the frozen clean classifier does not merely err on it but collapses to a constant : it predicts Residential for

400/400

test images spanning all ten classes, and likewise at

1

dB/q10 and

2

dB (it recovers only at

3

dB,

95.0\%

). The backbone’s reconstruction (middle) restores both the image and the correct label against the clean reference (right). Because pipeline (A) is a constant function below the channel cliff, the label flip is reported as a qualitative illustration only, not as evidence of semantic gain (cf. Table 20 ).

Evaluated at ( $100$ q)	$1$ dB ∗	$2$ dB	$3$ dB	$4$ dB
Degraded-trained classifier	88.31	78.52	47.88	47.77
( $\pm$ over $3$ seeds)	$\pm$ 0.23	$\pm$ 0.48	$\pm$ 2.05	$\pm$ 2.05
change vs. own point	—	$-9.8$	$-40.4$	$-40.5$
Frozen restorer $\to$ classify	76.42	74.29	71.54	71.41
( $\pm$ over $3$ seeds)	$\pm$ 1.35	$\pm$ 2.34	$\pm$ 1.01	$\pm$ 1.01
change vs. own point	—	$-2.1$	$-4.9$	$-5.0$

Table 21: The classifier’s advantage is local; the restorer’s is not. Both systems are trained at

1

dB/

100

q and applied unchanged at higher

E_{s}/N_{0}

. ∗ their common training point, where the classifier wins by

+11.9

pp. The crossover lies between

2

and

3

dB.

Spiking model	Top-1 (%)	Energy ( $\mu$ J)	AC-share
Spiking-CNN	92.57 $\pm$ 0.56	43.9 $\pm$ 0.1	64.1%
SEW-ResNet	92.59 $\pm$ 0.42	152.5 $\pm$ 2.7	92.9%
LIMODENet (scratch)	91.86 $\pm$ 0.28	482.7 $\pm$ 12.1	62.8%
LIMODENet (ANN init)	93.55 $\pm$ 0.54	477.7 $\pm$ 3.1	61.9%
Spiking-MLP	50.62 $\pm$ 0.71	25.3 $\pm$ 0.0	0.3%

Table 22: A plain Spiking-CNN Pareto-dominates LIMODENet on clean EuroSAT classification. All models hold

{\sim}0.69

M parameters, run at

T{=}8

from scratch,

3

seeds, mean

\pm

std, scored with a

45

nm SynOps proxy. LIMODENet (ANN init) and Spiking-CNN are statistically indistinguishable on accuracy while Spiking-CNN spends

{\sim}11\times

less energy. Where the architecture pays off is reconstruction (Table 2 ).

Figure 11: Spiking LIMODENet traces an accuracy–energy Pareto front on EuroSAT (representative run). The knee is at

T{=}6

–

8

(

93.6\%

3-seed mean at

2.44\times

lower energy than the ANN,

\star

);

T{\geq}10

is dominated. Energy is a

45

nm SynOps proxy that credits every spike-driven operation; on matched silicon with the measured firing rate, the spiking reconstructor is

3.34\times

more expensive than its ANN ( Sec. 4.2 ), so the

2.44\times

here is an optimistic bound for the classifier, not a measured saving.

Model	$T$	Top-1 (%)	Energy (mJ)	Eff. vs ANN
ANN	–	98.47	1.203	$1.0\times$
SNN	4	82.03	0.239	$5.03\times$
SNN	6	92.18	0.366	$3.29\times$
SNN	8	94.18	0.493	$2.44\times$
SNN	10	93.89	0.619	$1.95\times$
SNN	12	92.99	0.745	$1.62\times$

Table 23: Accuracy, SynOps energy, and efficiency of spiking LIMODENet on EuroSAT relative to the ANN across time steps

T

, for a single representative run that is not one of the three reported seeds (its

T{=}8

value,

94.18\%

, sits above the best seed’s

94.07\%

). At

T{=}8

the 3-seed mean is

93.55{\pm}0.54\%

. The ANN row is the fine-tuned checkpoint re-evaluated in the spiking pipeline; the classification log reports

98.45\%

for the same run.

Spiking classifier	q10	q50	q100
SEW-ResNet	55.30 $\pm$ 3.84	71.43 $\pm$ 3.68	82.10 $\pm$ 1.17
Spiking-CNN	48.63 $\pm$ 1.07	66.94 $\pm$ 2.23	79.44 $\pm$ 1.47
LIMODENet (scratch)	39.44 $\pm$ 1.95	59.97 $\pm$ 1.40	74.80 $\pm$ 0.58
LIMODENet ( $+$ ANN init)	39.84 $\pm$ 1.35	59.37 $\pm$ 1.26	75.68 $\pm$ 2.37
Spiking-MLP	50.39 $\pm$ 0.69	50.12 $\pm$ 1.65	50.96 $\pm$ 0.70

Table 24: Swapping the classifier on a fixed LIMODENet reconstructor improves accuracy. Reconstruct-then-classify top-1 accuracy (%) at

1

dB DVB-S2X across JPEG quality,

3

seeds, mean

\pm

std. Cross-family SEW-ResNet and Spiking-CNN classify LIMODENet’s reconstructions better than either LIMODENet classifier does at every quality, non-overlapping in

11

of

12

cross-family-vs-LIMODENet comparisons.

Figure 12: Most spiking energy goes to the graded-residual path (

T{=}8

). The depthwise convolutions and the stem consume

67\%

of LIMODENet’s spiking-inference energy, because they see a graded residual stream and therefore run dense MACs; only the pointwise MLP is event-driven (AC).

Method	Params	ANN	SNN	Loihi (mJ)
VGG-16 [ 31 ]	${>}14$ M	95.07	85.11	4.44
LIMODENet ( $T{=}6$ )	0.69M	98.47	92.18	4.70
LIMODENet ( $T{=}8$ )	0.69M	98.47	93.55	6.27

Table 25: Apples-to-apples comparison with the ESA on-board SNN baseline (energy from the same KerasSpiking ModelEnergy tool on Loihi). ANN-on-GPU energy is comparable (

79

vs

70

mJ). LIMODENet’s SNN top-1 is a

3

-seed mean in the

T{=}8

row and the single representative run of Table 23 in the

T{=}6

row; test splits differ between the two studies.

Encoder variant	Params	GMac	PSNR	$\Delta$	Top-1 ‡
LIMODENet (ours)	0.77M	1.21	37.39 $\pm$ 0.14	—	78.50 $\pm$ 0.83
ODE-specific choices
$\alpha{=}1$ (all stages)	0.77M	1.21	37.23 $\pm$ 0.11	$-0.16$	77.92 $\pm$ 0.32
$\alpha$ learned per block	0.77M	1.21	37.43 $\pm$ 0.15	$+0.04$	78.54 $\pm$ 1.08
Euler at Stage 3	0.77M	1.11	37.30 $\pm$ 0.21	$-0.09$	78.40 $\pm$ 0.90
Architectural choices

Table 26: Ablating the design on the restoration task shows that the advantage is architectural rather than a consequence of the ODE discretization. Each variant changes one axis, within

0.03\%

of the reference parameter count; protocol matches Table 2 . The three ODE cells overlap the reference and are negative results; only the global branch separates, on both metrics. Its replacement is iso-parameter but costs more compute (

1.28

vs.

1.21

GMac), so the loss is not bought with a smaller budget; conversely the Euler cell is cheaper (

1.11

), so its null is not bought with extra compute. ‡ Top-1 is reconstruct-then-classify accuracy under the neutral Spiking-CNN judge; only the spectral-normalized row separates from the reference on this metric.

Test	Condition	variant	reference	$\Delta$	sep.?
Is the global branch necessary? (remove it from LIMODENet)
necessity	$1$ dB/ $q100$	36.97 $\pm$ 0.13	37.39 $\pm$ 0.14	$-0.42$	yes
necessity	$1$ dB/ $q10$	30.43 $\pm$ 0.06	30.56 $\pm$ 0.03	$-0.13$	yes
necessity	$2$ dB/ $q100$	35.53 $\pm$ 0.20	35.61 $\pm$ 0.11	$-0.08$	no
Is it sufficient? (add it to the CNN-AE encoder)
sufficiency	$1$ dB/ $q100$	35.66 $\pm$ 0.18	35.64 $\pm$ 0.18	$+0.02$	no

Table 27: The global branch is necessary in the harshest condition but neither condition-general nor transferable. PSNR in dB,

3

seeds per cell. The sufficiency null is the informative one.

Reconstructor	Params	PSNR (dB)	SSIM	Top-1 ‡
LIMODENet-AE	0.44M	36.65 $\pm$ 0.08	0.9619 $\pm$ 0.0003	75.96 $\pm$ 0.31
CNN-AE	0.43M	35.34 $\pm$ 0.12	0.9506 $\pm$ 0.0016	70.85 $\pm$ 0.89
U-Net (skips)	0.43M	34.96 $\pm$ 0.48	0.9464 $\pm$ 0.0053	71.85 $\pm$ 1.40

Table 28: At half the parameter budget the encoder advantage grows rather than shrinks. The nano iso-parameter band, same protocol as Table 2 . ‡ Top-1 uses the neutral Spiking-CNN judge. Never compare figures across bands.

Reconstructor	Params	PSNR (dB)	$\Delta$	% of gain
additive noise : ImageNet-C gaussian_noise , input $15.52$ dB
LIMODENet-AE	0.77M	29.112 $\pm$ 0.003	—	—
U-Net (skips)	0.75M	29.107 $\pm$ 0.005	$+0.005$	$0.03\%$
CNN-AE	0.75M	28.901 $\pm$ 0.005	$+0.211$	$1.55\%$
information-destroying : pixelate $4\times$ , input $24.63$ dB
LIMODENet-AE	0.77M	26.288 $\pm$ 0.005	—	—

Table 29: On a second corpus, the advantage over a skip architecture tracks whether the corruption destroys information or merely adds noise. PatternNet at

128

px,

3

seeds,

60

epochs, val-selected. “% of gain” normalises the margin by LIMODENet’s own PSNR improvement over its input, since absolute margins are not comparable when the amount of recoverable signal differs by an order of magnitude. Seed deviations are

0.003

–

0.005

dB under both corruptions, which makes non-overlap trivially easy to achieve, so read the table on effect size rather than on separation.

LIMODENet family (ours)
Model	In.	Params	MACs	Lat.	Top-1
nano	$64^{2}$	0.39M	149M	2.23	95.65
tiny	$64^{2}$	0.69M	262M	2.41	96.54
small	$64^{2}$	1.55M	581M	2.23	96.93
base	$64^{2}$	2.73M	1027M	2.37	97.26
big	$64^{2}$	5.80M	2466M	3.58	97.54

Table 30: Complexity in context. Latency is single-image (batch 1) on one RTX 4070 Laptop, FP32, median of 200 timed runs; the tiny-AE value is the measurement of Table 2 . Below about

1

GMac this GPU is launch-bound at batch 1, which is why the width ladder is nearly flat (

2.2

–

2.4

ms) and only big separates. Our restoration model (

1.21

G MACs) sits between two networks that have flown, i.e.

{\sim}3.9\times

below flight-proven demand. Note the honest reading of the top block: at

64^{2}

LIMODENet-tiny already spends more MACs than EfficientViT-M2 [ 34 ] does at

224^{2}

, so we claim parameter efficiency and a viable absolute budget, not compute efficiency. Input resolutions, training protocols and accuracy sources differ across blocks; rows are for order-of-magnitude context, not a controlled comparison.

Figure 13: The deployment setting our restoration experiments stand in for. Satellite A encodes an observation with the LIMODENet encoder

E_{\theta}

, quantises and entropy-codes the latent, and either crosslinks it to a better-provisioned satellite B or downlinks it; B decodes with

D_{\varphi}

, cross-checks the restored scene, and forwards EO products with quality flags. The figure is a proposal. Measured in this paper: only the

x\!\to\!E_{\theta}\!\to\!D_{\varphi}\!\to\!\hat{x}

path, with degradation applied to pixels before the encoder. Not measured: the latent quantiser and entropy coder, the crosslink, the effect of channel noise applied to

z

rather than to

x

, and any cross-checking logic.

LIMODENet: Attention-Free Compact Encoders for Information-Preserving Onboard Satellite Image Restoration

Abstract

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