A Layer Importance Metric for Quantization Accounting for the Speed-Quality Trade-off in Autoregressive Models

Abstract

Small language models (sLLMs) are nowadays hosted on devices with limited memory and computational budget. In an autoregressive setup, inference is memory-bandwidth bound: uniform quantization is often detrimental to such models, since their architecture has limited redundancies and only a few layers are not very sensitive to lower precision. We propose a composite metric that combines two orthogonal criteria: information retention (measured in terms of a normalized SQNR-based coefficient) and throughput gains (modeled using a roofline-based latency analysis). By profiling Gemma 3 1B, we find that Feed-Forward Network blocks and the embedding matrix are the most promising targets for acceleration. For each candidate, we estimate a normalized quality score based on simulated quantization and a normalized speed score based on roofline modeling with no actual execution needed. We combine the two scores in a composite priority coefficient, allowing us to tune the trade-off between speed and quality as needed. Our metric is general and can be used to prioritize individual blocks, their projection sublayers, or transformer layers as a whole. We evaluate our approach on several model architectures, showing that our estimates have at around 4% prediction error for the accelerated speedup. We find that our method generally allocates more resources to the most expressive layers compared to evolutionary search, specialized accelerators, or Shapley-value-based approaches that require expensive approximate inference. Our analytical approach makes sLLM quantization a predictable engineering task.