On the Spectral Flattening of Quantized Embeddings
This addresses the problem of instability in low-bit LLM training for AI researchers, providing a theoretical foundation for spectral fidelity, but it is incremental as it builds on existing quantization and spectral analysis methods.
The paper tackled the instability in training Large Language Models at ultra-low precision by proving that the heavy-tailed spectral nature of linguistic data is essential for semantic encoding, and showed that uniform quantization introduces noise that flattens this spectrum, leading to representational collapse, with empirical validation across architectures like GPT-2 and TinyLlama.
Training Large Language Models (LLMs) at ultra-low precision is critically impeded by instability rooted in the conflict between discrete quantization constraints and the intrinsic heavy-tailed spectral nature of linguistic data. By formalizing the connection between Zipfian statistics and random matrix theory, we prove that the power-law decay in the singular value spectra of embeddings is a fundamental requisite for semantic encoding. We derive theoretical bounds showing that uniform quantization introduces a noise floor that disproportionately truncates this spectral tail, which induces spectral flattening and a strictly provable increase in the stable rank of representations. Empirical validation across diverse architectures including GPT-2 and TinyLlama corroborates that this geometric degradation precipitates representational collapse. This work not only quantifies the spectral sensitivity of LLMs but also establishes spectral fidelity as a necessary condition for stable low-bit optimization.