Leveraging Kernel Symmetry for Joint Compression and Error Mitigation in Edge Model Transfer

Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions parameterized by multiple basis coefficients. This introduces a source of redundancy that conventional neural-network compression does not directly expose. We present \textbf{SparseKAN}, a unified approach that compresses KANs along three complementary axes: basis functions, neurons/channels, and numerical precision. SparseKAN equips the base branch, nonlinear basis branch, and individual basis terms with hierarchical learnable gates trained under a differentiable active-cost objective. The learned importance structure is subsequently hardened under explicit basis and width budgets, recovered in full or low precision, and physically compacted into smaller dense tensors rather than retained as sparse masks. Experiments on MNIST, CIFAR-10, and CIFAR-100 across spline, polynomial, RBF, wavelet, and convolutional KAN variants show that the structural axes compose predictably in cost. We also find strong basis-dependent differences in term importance: coefficient-based selection outperforms matched low-order truncation by up to 15.25 accuracy points in the evaluated Gram-polynomial settings. Eight-bit quantization is broadly robust, whereas 4-bit convolutional KANs require quantization-aware adaptation. Physical compaction removes up to 73.0% of parameters without accuracy loss on MNIST and reduces large-batch CUDA latency to as little as $0.51\times$ dense execution. On a ZCU104 FPGA, the resulting sparse low-bit models achieve up to $23.63\times$ lower inference latency, demonstrating that SparseKAN converts functional redundancy into measurable software and hardware efficiency. The SparseKAN implementation is available at https://github.com/OSU-STARLAB/SparseKAN.

Scaling models has led to significant advancements in deep learning, but training these models in decentralized settings remains challenging due to communication bottlenecks. While existing compression techniques are effective in data-parallel, they do not extend to model parallelism. Unlike data-parallel training, where weight gradients are exchanged, model-parallel requires compressing activations and activation gradients as they propagate through layers, accumulating compression errors. We propose a novel compression algorithm that compresses both forward and backward passes, enabling up to 99% compression with no convergence degradation with negligible memory/compute overhead. By leveraging a recursive structure in transformer networks, we predefine a low-dimensional subspace to confine the activations and gradients, allowing full reconstruction in subsequent layers. Our method achieves up to 100x improvement in communication efficiency and enables training billion-parameter-scale models over low-end GPUs connected via consumer-grade internet speeds as low as 80Mbps, matching the convergence of centralized datacenter systems with 100Gbps connections with model parallel.

Adapting large AI models (LAMs) to personalized edge data is challenging because wireless devices have limited memory, computation, and uplink capacity. Federated fine-tuning preserves data privacy but still requires each device to host the full model, while split learning reduces device memory at the cost of heavy activation transmission. This paper proposes TSFLora, a token-compressed split fine-tuning framework for communication-efficient LAM adaptation at the edge. TSFLora combines attention-guided token selection, token merging, low-bit activation quantization, and LoRA-based adaptation within a split federated training pipeline. The key idea is to compress the intermediate token sequence before transmission so that the system reduces both uplink traffic and server-side processing without changing the frozen backbone. Experiments on ViT models over CIFAR-10, CIFAR-100, and TinyImageNet show that TSFLora achieves up to \textbf{6.8$\times$} communication reduction and \textbf{41%} memory saving while maintaining competitive accuracy.