arXiv:2605.02907v1 Announce Type: cross
Abstract: Softmax attention maps every query–key interaction into a probability distribution, but the underlying structure remains largely unexplored. We define the emphenergy field, the row-centered attention logit, and show that it exhibits invariant properties across models, architectures, and inputs.
Two classes of invariants emerge. emphMechanism-level invariants follow from the algebraic structure of softmax attention. They include a per-row zero-sum constraint, a rank bound determined by the head dimension, and spectral signatures that follow from them. emphModel-level regularities are not required by the mechanism, yet hold in every autoregressive language model we test, spanning several architecture families. The energy field distributes its variance over key positions without concentrating at a few. This delocalization traces to a property of the key matrix we call emphkey incoherence.
These invariants have practical consequences. The rank bound confines the energy field to a low-dimensional subspace. Key incoherence yields a per-head training monitor. All results are verified at multiple context lengths and input texts.
Crisis support teams’ technological openness and learning attitudes toward the AI based virtual patient system crisis support VR
BackgroundAgainst the backdrop of escalating global humanitarian crises, innovative didactic simulations are becoming increasingly important. A promising alternative to traditional classroom-based didactics for learning psychological