Monotonic Rank Knowledge Distillation via Kendall Correlation

The computational and memory demands of deep neural networks for vision tasks remain a critical barrier to their deployment on resource-constrained edge devices. Although knowledge distillation (KD) effectively transfers over-parameterized models’ knowledge into compact students, its efficacy diminishes substantially when a significant capacity gap exists between them. Current approaches often impose linear mapping constraints between output distributions, an assumption that becomes prohibitively restrictive under such capacity gaps. This paper proposes a fundamental relaxation of alignment requirements. Specifically, rather than enforcing strict parametric relationships, we experimentally validate that preserving monotonic rank correlation between teacher and student outputs suffices for effective knowledge transfer. To operationalize this insight, we introduceMonotonic Rank Knowledge Distillation, a novel framework that leverages differentiable approximations of Kendall’s rank correlation coefficient to measure and optimize rank-order consistency. Our methodology further decomposes rank correlation into inter-class and intra-class components, ensuring the student network retains both global discriminative patterns and fine-grained categorical distinctions inherent to the teacher’s outputs. Extensive experiments across CIFAR-100 and ImageNet-1K benchmarks validate the effectiveness of our approach, demonstrating consistent performance gains over state-of-the-art distillation methods. The proposed framework achieves superior generalization across diverse architectures, including CNN-based, MLP-based, and ViT-based, with particular efficacy in various compression scenarios.