Post-Training Probability Manifold Correction via Structured SVD Pruning and Self-Referential Distillation
Aaron R. Flouro, Shawn P. Chadwick
TL;DR
SparseKD introduces a post-training correction regime that combines structured SVD pruning with self-referential knowledge distillation, treating pruning as a controlled perturbation and distillation as a probability-domain projection back onto a stable manifold. The key finding is that self-referential distillation is the primary driver of quality gains, with pruning providing compression; across two model families, SparseKD achieves substantial parameter reduction (15–65%) while maintaining or improving perplexity relative to the original dense checkpoint, especially at lower sparsity. Additional results show a 1.10–1.17x speedup in batch inference attributed to reduced dense FFN/GEMM compute while attention kernels remain unchanged, highlighting a complementary relationship with attention-focused optimizations. The approach requires no external teachers, no architectural changes, and no custom inference kernels, making it readily deployable with existing infrastructure and suggesting a practical pathway for deployment-time efficiency gains in large language models.
Abstract
Large language models are expensive to deploy. We introduce Sparse Knowledge Distillation (SparseKD), a post-training method that compresses transformer models by combining structured SVD pruning with self-referential knowledge distillation. The key insight is simple: instead of using an external teacher, the model teaches itself by matching its own probability distribution from before compression. This self-referential setup enables surprisingly strong quality recovery after aggressive pruning. Our experiments reveal an unexpected finding: self-referential distillation alone, applied post-training under an identical objective and fixed calibration dataset, improves model quality by 39% relative to the original converged checkpoint. When combined with structured pruning, SparseKD achieves 15-65% parameter reduction with acceptable quality trade-offs. Kernel profiling shows that speedups arise entirely from reduced dense matrix multiplication in feed-forward layers while attention remains unchanged, making this approach complementary to attention optimizations. We validate across two model families (0.6B and 3.8B parameters) with multi-seed experiments confirming high reproducibility. SparseKD requires no external super-teacher, no architectural changes, and no custom inference kernels, making it immediately deployable with existing infrastructure.