Open Access Journal of Applied Science and Technology(OAJAST)

Financial Physics Lab, Finland

Publications

• Research Article   
  Structural Isomorphism Between LLM Embedding Spaces and Quantum Mechanical Systems
  Author(s): Timo Aukusti Laine*
  
  Large language models (LLMs) represent semantic information as high-dimensional embedding vectors, typically compared using cosine similarity. This paper establishes a structural isomorphism between LLM embedding spaces and quantum mechanical systems. We demonstrate that the transformed cosine similarity can be precisely mapped to a quantum mechanical measurement probability, governed by a rank-1 Hamiltonian and the Schrödinger equation, where the time parameter is identified as a gauge variable. A commutative diagram unifies four equivalent expressions for this similarity, spanning classical bilinear forms and quantum Born rule probabilities. Crucially, the quantum formulation reveals a local U(1) gauge symmetry, absent from classical descriptions, with an associated conserved semantic charge modeling contextual influence. A quantum circuit on logarithmically many qubits yields .. Read More»
  

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