A Born Machine Approach to Controllable Text Generation with Language Models

Controllable text generation requires estimating lookahead probabilities, i.e., the likelihood that future tokens will satisfy a given constraint. We propose using Born machines, probabilistic models from quantum mechanics that define probabilities as squared magnitudes of complex amplitudes. Born machines admit efficient marginalization, making lookahead tractable. We parameterize Born machines using Matrix Product States (MPS) and derive a backward algorithm that propagates density matrices through the tensor network. This density matrix formulation naturally captures the quadratic structure of the Born rule and summarizes constraint information. Experiments on text infilling, lexical constraints, and detoxification demonstrate that Born machine lookahead efficiently guides language models toward constraint satisfaction.