Post-Training Probability Manifold Correction via Structured SVD Pruning and Self-Referential Distillation

TL;DR

This paper introduces SparseKD, a post-training compression method for large language models that combines structured SVD pruning with self-referential knowledge distillation, enabling significant parameter reduction with minimal quality loss.

Contribution

The paper presents a novel post-training compression technique that uses self-distillation without external teachers, achieving high compression rates while maintaining model quality.

Findings

Self-distillation alone improves model quality by 39%.

SparseKD achieves 15-65% parameter reduction with acceptable quality.

Speedups are due to reduced dense matrix multiplication in feed-forward layers.

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.