Task-Asymmetric Compression: A Spectrum Analysis from Retrieval to Generation

This paper presents the first systematic analysis of task-asymmetric compression across the NLP spectrum, revealing compression tolerance varies by over two orders of magnitude — from 100% invariant (NER at 128x) to catastrophic failure (generation at all ratios). Extends our prior work (DOI: 10.5281/zenodo.17595736), which showed PCA achieves 86–94% retrieval quality at 178x but 0% for generation. We now map the full spectrum. KEY FINDINGS Compression-Invariant Tasks: NER: 100% at 128x (6D); QA: 97–98% across all ratios Perplexity Catastrophe: Universal power law P(r) ≈ 26.1 × r^0.80 (R² = 0.98) Variance-Performance Paradox: 96.6% explained variance → 40x perplexity degradation PCA Optimality: Outperforms UMAP by 30.9% average; confirms linear ~20D semantic manifold Convergent evidence : Limits hold across quantum Hilbert projections (4,660x worse), hybrid cascades (0% gain), and UMAP EXPERIMENTS 8 tasks: NER, QA, Classification, Summarization, Sentiment, Retrieval, NLI, Generation 500–2000 samples/task; p < 2.5e-106 Models: BERT-base, GPT-2 (768D) Ratios: 2x to 128x Methods: PCA, UMAP, Quantum circuits, Hybrid cascades THEORY Task-Compression Frontier F(τ, r) Information Scaling Laws: O(1) → O(log n) → O(L log |V|) Multi-Layered Manifold: ~20D core vs. full 768D+ PRACTICAL IMPACT Enables 99%+ cost reduction in non-generative systems via task-specific compression. REPRODUCIBILITY Full code (PCA, quantum, UMAP, evaluation), configs, results, and figures in supplementary.zip. This work establishes task-asymmetric compression as a fundamental principle of language model efficiency.