Feed-forward visual geometry models such as the Visual Geometry Grounded Transformer (VGGT) have recently enabled direct 3D reconstruction from multi-view images. Despite their promising performance, these models scale quadratically with the number of input views due to their global attention mechanism, resulting in substantial latency for long sequence inputs. There have been some recent efforts to accelerate VGGT, but they primarily focus on reducing \emph{token redundancy} through token merging or key/value sparsification. Our work resolves this bottleneck from a different perspective by investigating \emph{architectural redundancy} in visual geometry transformers. We show that the multi-head attention modules in VGGT's global-attention layers contain substantial architectural redundancy, with only a subset of heads carrying critical geometric information. In light of this observation, we propose VGGT-Prime, a compute-adaptive mixture-of-heads model that resolves this redundancy to accelerate visual geometry transformers while maintaining competitive reconstruction quality. The key idea of VGGT-Prime is to estimate the appropriate computation level for each global-attention head using a lightweight router and then dynamically assign each head to different computation modes. Extensive experiments on multiple datasets demonstrate that VGGT-Prime can achieve an {
8×} inference speedup over VGGT while maintaining competitive performance on camera pose, depth, and point-cloud predictions. We further show that VGGT-Prime is complementary to existing acceleration methods, such as token merging, further improving inference speed by up to
14× over VGGT. An overview of our work is available on our \href{https://vggt-prime.github.io}{project page}.