Multi-modal large language models (MLLMs) have emerged as a transformative approach for aligning visual and textual understanding. They typically require extremely high computational resources (e.g., thousands of GPUs) for training to achieve cross-modal alignment at multi-granularity levels. We argue that a key source of this inefficiency lies in the vision encoders they widely equip with, e.g., CLIP and SAM, which lack the alignment with language at multi-granularity levels. To address this issue, in this paper, we leverage hyperbolic space, which inherently models hierarchical levels and thus provides a principled framework for bridging the granularity gap between visual and textual modalities at an arbitrary granularity level. Concretely, we propose an efficient training paradigm for MLLMs, dubbed as \blg, which can optimize visual representations to align with their textual counterparts at an arbitrary granularity level through dynamic hyperbolic radius adjustment in hyperbolic space. \alg employs learnable matrices with M\"{o}bius multiplication operations, implemented via three effective configurations: diagonal scaling matrices, block-diagonal matrices, and banded matrices, providing a flexible yet efficient parametrization strategy. Comprehensive experiments across multiple MLLM benchmarks demonstrate that \alg consistently improves both existing pre-training and fine-tuning MLLMs clearly with less than 1\% additional parameters.