GDPR Article 20 gives data subjects the right to receive their personal data in a "structured, commonly used and machine-readable format" and transmit it to another controller without hindrance from the original controller. The right applies when processing is based on consent or contract and is carried out by automated means.
For AI systems that accumulate memory about a user — preferences, conversation history, learned context — Article 20 implies that this memory must be exportable in standardized formats. Vendor lock-in by way of un-exportable user context is incompatible with the right to data portability.