Lightweight medical CNNs let recurrence order set channel width: brain-MRI parameters fall up to 50.4%, with accuracy gains and losses

The number of channels in each convolutional block can be set directly by a recurrence order m, instead of being fixed layer by layer or left to architecture search. Fibonacci-Net fixed filter counts to the Fibonacci sequence (21, 34, 55, 89, 144, 233, 377), allowing only that one second-order recurrence and little adjustment of overall network width. On 15-class brain MRI, the m=3 Tribonacci-Net gained 0.67 percentage points of accuracy over Fibonacci-Net while cutting parameters by about 37.5% and FLOPs and MACs by about 40.7%; on 44-class brain MRI, the m=5 Pentanacci-Net gained 0.34 points with about 47.1% fewer parameters and about 44.5% fewer FLOPs and MACs.

The scaling coefficient comes from the dominant root, so a higher order yields a narrower network. The dominant positive root of the m-Bonacci recurrence rises from about 1.618 toward about 1.984 and approaches 2, so using raw higher-order terms as filter counts would enlarge the model. With s_m=ln ρ2/ln ρm, s_2=1 and higher orders fall below 1; scaled counts are rounded to multiples of eight, giving channel vectors for m=3 through m=6, for example (16, 24, 40, 64, 104, 160, 264) at m=6.

Depthwise separable convolutions in the final blocks push parameters and computation down further. A standard convolution's parameter count grows with the product of input and output channels, whereas a depthwise separable convolution splits it into a per-channel convolution and a 1×1 pointwise convolution. Across the 4-, 15- and 44-class brain MRI settings and the CKD ultrasound set, the scaled variants cut parameters by about 37.5%–50.4%, FLOPs and MACs by about 40.7%–45.1%, and neurons by 25.0%–25.9% relative to Fibonacci-Net.

The evaluation covers three brain-MRI classification settings (4, 15 and 44 classes) and one locally collected CKD ultrasound dataset; images were resized to 224×224, split 60:20:20 with stratification, and trained for 50 epochs without early stopping, data augmentation or extra image processing. Grad-CAM maps are qualitative explanations only, not lesion segmentation and not a substitute for review by experienced radiologists.

The scaling rule alone does not guarantee preserved accuracy: on 4-class brain MRI the scaled variants lost 0.77 to 2.11 percentage points, and on CKD ultrasound Tribonacci and Tetranacci each lost 5.00 points while Pentanacci lost 6.25. The best recurrence order is dataset-dependent, with intermediate orders balancing best across the three brain-MRI benchmarks and Hexanacci best on CKD ultrasound at 83.75% accuracy and 0.7941 macro F1.