Hardware-Aware Functional Kolmogorov-Arnold Networks for Efficient Medical Image Enhancement and Segmentation

I. INTRODUCTION

• FunKANLite targets edge deployment because FunKAN’s 11.6 M parameters and 8.7 GFLOPs exceed the memory and power limits of portable and bedside hardware.MRI Gibbs artifact removal and medical image segmentation are the two tasks motivating deployment at the point of care.Source: §I · p. 1
• FunKANLite retains FunKAN’s spatially aware representation for medical-image enhancement and segmentation on edge devices.Fig. 1 presents the network as processing medical images and running on an edge device.Source: §I · p. 1, Figure 1 · p. 1
• FunKANLite-ST, using a lower Hermite rank, low-rank prior, and halved widths, has 5.6× fewer parameters and 3.7× fewer GFLOPs than FunKAN, while staying within 1.4 pp IoU and 1.1 dB PSNR of FunKAN.Source: §I · pp. 1–2
• FunKANLite-TR uses a compact spatial prior and depthwise-separable offset predictor, with 1.9× fewer parameters than FunKAN and no accuracy loss.The spatial prior is reduced from 145 × 145 to 110 × 110.Source: §I · p. 1
• On Jetson Orin Nano and Raspberry Pi 5, FunKANLite-ST reduces energy per inference by up to 68% and raises throughput by 2.9×.The evaluation covers IXI, BUSI, GlaS, and CVC-ClinicDB.Source: §I · p. 2

A. Architecture Design

• FunKANLite retains FunKAN’s U-Net-style outer shell, changing only the operator block; MRI enhancement removes skips and uses a 5 × 5 embedding, while segmentation uses a 3 × 3 embedding and encoder-decoder skips.The shared shell comprises embedding, lifting, operator, projection, and restoration stages.Source: A. Architecture Design · p. 2

1) FunKAN Operator:

• Each FunKAN layer combines learned inner functions with a bank of six 2D Hermite basis functions, then uses a 1 × 1 mixing convolution.The inner products between inner functions and basis functions form an attention matrix selecting relevant Hermite modes at each spatial location.Source: 1) FunKAN Operator · p. 2
• The operator-block figure shows a BN-ReLU-DW3×3-PW1×1 offset predictor and a 110×110 spatial prior interpolated at runtime.This predictor replaces FunKAN’s ResBlock offset predictor.Source: Figure 3 · p. 2
• Hermite functions are evaluated on a runtime-deformed grid so they can adapt to local anatomy; FunKANLite-TR compresses both the spatial prior and offset predictor.The backbone blocks are connected residually.Source: 1) FunKAN Operator · p. 2

3) Compact Spatial Prior:

• 42% fewer spatial-prior parameters per backbone block result from reducing storage from 145×145 to 110×110.The prior is bilinearly interpolated to the current feature-map size before use.Source: 2) Compact Spatial Prior · p. 2
• Runtime interpolation preserves spatial adaptivity despite storing the prior at lower resolution.Interpolation is performed to the current H × W feature-map size at each forward pass.Source: 2) Compact Spatial Prior · p. 2
• The attention computation in Eq. (1) remains unchanged because the prior is interpolated before it is used.Source: 2) Compact Spatial Prior · p. 2

3) Depthwise-Separable Offset Predictor:

• At the 128-channel segmentation backbone stage, the ResBlock offset predictor accounts for a large share of model size.Its two full 3×3 convolutions cost O(18c^2) parameters and proportional MACs per backbone block.Source: 3) Depthwise-Separable Offset Predictor · p. 2
• The depthwise-separable predictor uses O(9c + 2c^2) parameters, about 20× fewer than the ResBlock at large c.It retains the same 3×3 receptive field for local deformation.Source: 3) Depthwise-Separable Offset Predictor · p. 2
• A depthwise 3×3 convolution operates per channel, then a pointwise 1×1 convolution mixes channels into the 2c offset maps.Fig. 3 shows the resulting operator block.Source: 3) Depthwise-Separable Offset Predictor · p. 2

1) Memory Hierarchy Analysis:

• FunKANLite-ST targets the 5.5 MB Jetson and 4.5 MB Raspberry Pi on-chip memory budgets, avoiding a main-memory transfer on every inference when the working set fits.The on-chip footprint is the stated compression target.Source: 1) Memory Hierarchy Analysis · p. 3

2) Architecture:

• Reducing the Hermite basis rank from 6 to 4 drops ψ4 and ψ5, cuts the attention matrix by 33%, and removes those Hermite evaluations.The passage explains that lower-order modes hold most signal energy for smooth anatomical structures.Source: 2) Architecture · p. 3
• FunKANLite-ST factorizes the spatial prior into learned low-rank matrices, with rank ρ = 40 for segmentation and ρ = 12 for MRI enhancement.The product UV is computed once per forward pass before the attention step.Source: 2) Architecture · p. 3
• Halving filter widths reduces the backbone channel dimension from 128 to 88 for segmentation and from 32 to 16 for MRI, lowering attention compute with quadratic effect.The stated operator complexity scales as O(c^2 · r · HW).Source: 2) Architecture · p. 3

• Training combines task, feature-level, and output-level terms, with α = 1.0, β = 0.5, and γ = 0.1.FunKANLite-ST is trained from scratch while FunKANLite-TR is held frozen.Source: 3) Knowledge Distillation Training · p. 3
• The task loss is MSE for MRI enhancement and a weighted binary cross-entropy plus Dice loss for segmentation.Ltask is the primary supervised loss.Source: 3) Knowledge Distillation Training · p. 3
• Feature-level distillation aligns intermediate backbone representations, while output-level distillation matches FunKANLite-ST’s final output to FunKANLite-TR’s at temperature T = 4.0.Only backbone stages with matching spatial sizes are included in the feature-level term.Source: 3) Knowledge Distillation Training · p. 3

A. Experimental Setup

• Accuracy values in this section use an earlier training protocol and were not regenerated under the current protocol.The current segmentation recipe and IXI schedule are described separately.Source: A. Experimental Setup · pp. 3–4
• Earlier reported accuracies are aggregated over the final 50 epochs for seeds 50, 100, and 150.Segmentation uses Dice loss weighted 1.0 plus binary cross-entropy weighted 0.1; enhancement uses mean squared error.Source: A. Experimental Setup · p. 3, Table III · p. 4
• Current segmentation runs use 400 epochs, three data-split seeds, and the checkpoint with best validation IoU, evaluated on the same held-out subset as a validation estimate.IXI retains its ordered test set and selects the checkpoint by validation loss.Source: A. Experimental Setup · p. 4
• Segmentation is evaluated on BUSI, CVC-ClinicDB, and GlaS at 256×256 using IoU and F1; IXI enhancement uses 145×145 inputs with 25% k-space truncation and PSNR and TV.Source: A. Experimental Setup · p. 4
• Deployment measurements cover a Lambda server, Jetson Orin Nano, and Raspberry Pi 5, with 200 runs after 10 warm-up iterations on each edge platform.Jetson power is sampled with its INA3221 monitor and Raspberry Pi power with an external FNB58 USB meter; the Lambda GPU is not power-instrumented.Source: A. Experimental Setup · p. 4, Table II · p. 4

B. Results

• Table IV reports IXI enhancement accuracy, and its values are kept unchanged from the earlier protocol.Source: Table IV · p. 4, B. Results · p. 4
• FunKANLite-ST has 5.6× fewer parameters and 3.7× fewer GFLOPs than FunKAN, at a cost of at most 1.4 pp IoU and 0.9 pp F1.On Jetson Orin Nano and Raspberry Pi 5, it fits in on-chip cache, with up to 2.9× higher throughput and 68% lower energy per inference than FunKAN.Source: B. Results · p. 4
• FunKANLite-TR has 1.9× fewer parameters than FunKAN, keeps segmentation accuracy, and reaches 34.80 dB PSNR on IXI.FunKANLite-TR serves as the source model for distillation because FunKAN is too costly to distill from directly.Source: B. Results · p. 4

IV. CONCLUSION

• FunKANLite-ST has 5.6× fewer parameters and 3.7× fewer GFLOPs than FunKAN, at a cost of at most 1.4 pp IoU.These reductions follow distillation from FunKANLite-TR.Source: §IV · p. 4
• FunKANLite-TR has 1.9× fewer parameters than FunKAN with no accuracy loss.Source: §IV · p. 4
• On an NVIDIA Jetson Orin Nano and a Raspberry Pi 5, FunKANLite-ST provides up to 2.9× higher throughput and 68% lower energy per inference.Source: §IV · p. 4