We introduce GateTrim, an adaptive-rank post-training quantization method for large language models that learns matrix-specific ranks through gate optimization and threshold-based rank selection. GateTrim standardizes the low-rank factors of a quantized low-rank--residual representation, learns a separate gate vector for each target weight matrix, and uses a shared threshold to automatically determine its retained rank. The resulting ranks can differ across matrices, and the compact quantized representations are subsequently reconstructed. We evaluate GateTrim under W4A8 on Qwen3-4B/8B/14B, Llama-3.2-3B-Instruct, and Llama-3.1-8B-Instruct. Across all five models, we observe a counterintuitive finding: increasing the threshold from $τ=0.3$ to $τ=0.7$ reduces the mean retained rank by 46.60%--67.89% while simultaneously lowering WikiText-2 perplexity by 0.59%--5.17%. Threshold 0.7 achieves the lowest mean retained rank and final perplexity among the three tested thresholds, 0.3, 0.5, and 0.7, and reduces measured target-export size by 1.50%--4.25% relative to 0.3. GateTrim uses an $8\times512$-token fitting pool and a separate development pool of the same size. Its Qwen3-4B/8B/14B perplexities at $τ=0.7$ are numerically below TwinQuant's published W4A8 values, reported with a $128\times2048$-token calibration pool, in a cross-study comparison. On Qwen3-8B, the threshold-0.7 configuration already has the lowest perplexity before reconstruction under both tested initialization seeds; reconstruction improves it further without increasing retained rank or export size.

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