Abstract: Large Language Models (LLMs) have recently demonstrated a remarkable success across various tasks. However, efficiently serving LLMs has been a challenge due to its large memory bottleneck, specifically in small batch inference settings (e.g. mobile devices). Weight-only quantization can be a promising approach, but sub-4 bit quantization remains a challenge due to large-magnitude activation outliers. To mitigate the undesirable outlier effect, we first propose per-IC quantization, a simple yet effective method that creates quantization groups within each input channel (IC) rather than the conventional per-output channel (OC). Our method is motivated by the observation that activation outliers affect the input dimension of the weight matrix, so similarly grouping the weights in the IC direction can $\textit{isolate outliers to be within a group}$. We also find that activation outliers do not dictate quantization difficulty, and inherent weight sensitivities also exist. With per-IC quantization as a new outlier-friendly scheme, we then propose Adaptive Dimensions ($\textbf{AdaDim}$), a versatile quantization framework that can adapt to various weight sensitivity patterns. We demonstrate the effectiveness of AdaDim by augmenting prior methods such as Round-To-Nearest and GPTQ, showing significant improvements across various language modeling benchmarks for both base (up to $+4.7\%$ on MMLU) and instruction-tuned (up to $+10\%$ on HumanEval) LLMs.