High-dimensional geometry imposes concurrency limits on semantic directions in LLM embeddings via residual interference, with N < exp(c d_eff ε²) for coexistence and σ_int ~ √(k/d_eff) for readout noise.
The softmax function, softmax(zi) = exp(zi) CX j=1 exp(zj) ,(A5) fori= 1,
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Semantic Concurrency Limits in Large Language Models
High-dimensional geometry imposes concurrency limits on semantic directions in LLM embeddings via residual interference, with N < exp(c d_eff ε²) for coexistence and σ_int ~ √(k/d_eff) for readout noise.