DegreeSpar: Structured Degree Sparsity for Efficient Secure Transformer Inference

Secure Transformer inference protects sensitive inputs but incurs substantial cryptographic overhead, with nonlinear operations such as Softmax and GeLU becoming major bottlenecks. Existing compression methods reduce nonlinear complexity, sequence-dependent computation, or model structure through separately defined compression variables. Under aggressive compression, however, these independently optimized perturbations can accumulate: at a matched compression level, stacking representative approximation, token-pruning, and model-pruning methods reduces ViT-S accuracy from 80.20% to 76.41%. We introduce DegreeSpar, which formulates secure Transformer compression as structured sparsification over nonlinear polynomial degrees. Polynomial degree directly controls the cost of secure nonlinear evaluation, while computation-aligned zero-degree structures expose token-level and model-dimension computation as removable within the same optimization space. DegreeSpar further incorporates approximation-aware training for low-degree Softmax and GeLU, enabling aggressive degree reduction and creating the optimization headroom required for structured computation removal. Across vision and language Transformers, DegreeSpar consistently improves the accuracy-latency trade-off across model scales, tasks, and sequence lengths, achieving speedups from 2.29x to 6.63x over the corresponding baselines. Under the same network setting, DegreeSpar achieves 92.68% accuracy on BERT/SST-2 in 110.55 s, compared with 92.66% in 167.26 s for CipherPrune, the closest prior hybrid secure-inference approach. These results establish structured polynomial degree as an effective shared optimization space for secure Transformer compression.