A unified representation space in multi-modal learning is essential for effectively integrating diverse data sources, such as text, images, and audio, to enhance efficiency and performance across various downstream tasks. Recent binding methods, such as ImageBind, typically rely on a single, fixed anchor modality for aligning multi-modal data. We mathematically analyze these fixed anchor binding methods and uncover significant limitations: (1) over-reliance on the choice of the anchor modality, (2) inadequate capture of intra-modal information, and (3) failure to account for cross-modal correlation among non-anchored modalities. To address these issues, we propose the need for adaptive anchor binding methods, exemplified by our framework CentroBind. The proposed method uses adaptively adjustable centroid-based anchors generated from all available modalities, leading to a balanced and rich representation space. We theoretically demonstrate that our approach captures three critical properties of multi-modal learning -- intra-modal learning, inter-modal learning, and multi-modal alignment -- while constructing a unified representation that spans all modalities. Experiments on both synthetic and real-world datasets show that adaptive anchor methods such as CentroBind consistently outperform fixed anchor binding methods, verifying our analysis.