Unification of Identity and Difference: A Tri-Space Dual-Projection Framework for Transformer Interpretability

Research on the interpretability of large language models has long been constrained by the discreteness of neuron- and feature-centric perspectives, making it difficult to uniformly explain attention mechanisms, multi-head collaboration, and semantic emergence. Building upon our prior work on Relation Body Geometry (Wang, 2026), this paper proposes the Tri-Space Dual-Projection (TSDP) framework, which precisely aligns with the actual computational flow of Transformers (Vaswani et al., 2017). We demonstrate that: the Query, Key, and Value (Q, K, V) spaces each internally satisfy the Relation Body Unit Circle (Theorem 1); identity and difference (tong-yi) are not directional properties inherently carried by information, but rather relational properties defined by the Query-Key projection (Q-K) in the first projection; softmax normalizes the absolute intensity of QK into value shares; these shares constitute a Share Operator acting on V, allocating the proportion of each V being utilized. The boundary of identity and difference is defined by QK, while the value share is allocated by softmax; the two are decoupled but sequentially connected. The Attention-Value projection (A-V) serves as the second projection, directly acting on V due to the positional alignment between K and V. Multi-head attention consists of multiple independent TSDP modules concatenated along the feature dimension; the residual stream is the integration channel running through the layers. The architecture itself (layers, multi-head, residual) constitutes the physical skeleton of the Static Tree. Under the TSDP mechanism, semantic evolution automatically selects a path from identity to difference. Driven by semantic pressure, this evolution manifests macroscopically as a progression from a narrow-semantic Traditional Tree trunk in the shallow layers, to a broad-semantic Bush in the middle layers. In the deep layers, regardless of the macroscopic form, the demand for deep local deduction forces the attention distribution to drastically sharpen, forming a Local Petiole structure. Combined with systematic empirical evidence covering dense/sparse architectures (Mixture of Experts, MoE), causal/bidirectional architectures (Bidirectional Encoder Representations from Transformers, BERT) (Devlin et al., 2019), pre-trained base models versus instructiontuned models (Base/Chat) alignment paradigms, and multi-head ablation, this paper verifies that Theorem 3 (the No-Trunk Theorem) and the U-shaped contour are inherent architectural priors. Crucially, contrasting causal interventions reveal that severing QK routing causes severe semantic collapse, while shuffling multi-head feature dimensions yields minimal impact, proving that residual streams provide a robust integration fallback. Furthermore, within MoE architectures, the Router effectively partitions the global semantic Bush into multiple narrow-semantic Traditional Trees, while maintaining uniform orthogonality in multi-head projections. This paper provides a precise geometric framework for understanding large models, ranging from the local tangent circle to hierarchical state progression, and proposes the dual structure of the Static Tree and the Dynamic Tree. The overarching theme is the unification of identity and difference (tong-yi-gui-yi) and their evolution (tong-yi-yan-jin).