On transformations of physical systems

Chen, Zeqian

The introduction of the transformer architecture in 2017 marked the most striking advancement in natural language processing. The transformer is a model architecture relying entirely on an attention mechanism to draw global dependencies between input and output. However, we believe there is a gap in our theoretical understanding of what the transformer is, and how it works physically. From a physical perspective on modern chips, such as those chips under 28nm, modern intelligent machines should be regarded as open quantum systems beyond conventional statistical systems. Thereby, in this paper, we construct physical models realizing large language models based on a transformer architecture as open quantum systems in the Fock space over the Hilbert space of tokens. Our physical models underlie the transformer architecture for large language models.

N.P. Klepikov

An active transformation of a physical system implies its motion. A passive transformation of the system is a change in the method of describing it. An analogy transformation means transition to another physical system, similar in some respect to the original one. In some cases transformations of one type may imitate those of another. The operation of particle permutation in quantum mechanics implies a passive transition to describing the same state of the system by a different method of introducing particle numbering. The problems of transitions from describing identical particles to describing different ones and that of explaining the probabilistic meaning of wave functions statistically are touched upon.

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers

Masahito Hayashi

Paul Merriam

Decoherence may not solve all of the measurement problems of quantum mechanics. It is proposed that a solution to these problems may be to allow that superpositions describe physically real systems in the following sense. Each quantum system "carries" around a local spacetime in whose terms other quantum systems may take on nonlocal states. Each quantum system forms a physically valid coordinate frame. The laws of physics should be formulated to be invariant under the group of allowed transformations among such frames. A transformation of relatively superposed spatial coordinates that allows an electron system to preserve the de Broglie Relation in describing a double-slit laboratory system-in analogy to a Minkowskian Transformation-is proposed. In general, "quantum relativity" says is invariant under transformations among quantum reference frames. Some conjectures on how this impacts gravity and gauge invariance are made.