Scaled m-BonacciNet: A Recurrence-Guided Lightweight CNN for Efficient Medical Image Classification
Habib, G.; Thakur, S.; Shaban, M.; Ahmad, R.; Malik, I. A.
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The -Bonacci weighted sequence space {ell}(,) is introduced for [≥] 2, 1 [≤] < {infty}, and > 0). It is proved to be a Banach space which is isometrically isomorphic to {ell}, with an unconditional Schauder basis. The space is also reflexive and uniformly convex. Its strict inclusion chain, continuous dual, and asymptotic truncation estimate of order - / are also established. Based on this framework, Scaled 𝑚-BonacciNet is proposed as a lightweight CNN that rescales Fibonacci-Net channels using the dominant 𝑚-Bonacci root and employs depth wise separable convolutions. Tribonacci-Net achieved 96.09% accuracy and a 0.9581 macro F1-score on the 15-class Brain MRI dataset using 0.85 million parameters and 0.366 GFLOPs. Pentanacci-Net attained 95.87% accuracy on the 44-class dataset while reducing parameters and FLOPs by 47.10% and 44.48%, respectively. On the CKD ultrasound dataset, Hexanacci-Net achieved 83.75% accuracy and a 0.7941 macro F1-score, with corresponding reductions of 50.37% and 45.10%. These findings support dominant-root scaling as a structured approach to lightweight CNN design.
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