How quickly can we learn about a quantum system, and what ultimately limits that speed? I will present experiments that bring advanced analysis and decision making directly onto FPGA control hardware (OPX1000), enabling adaptation of both measurement parameters and entire quantum circuits during execution. First, we use entanglement polytopes to certify multipartite entanglement from local information, combining classical shadows with direct fidelity estimation to bound the global purity required for certification. Measurement generation, analysis, shot allocation, and selection of the next circuit all run on the FPGA, enabling entanglement certification on millisecond timescales without returning to a host computer for decisions. Second, we introduce a persistent learning protocol that combines repeated measurement with FPGA-based conditional re-excitation to reach the fundamental statistical speed limit for estimating qubit relaxation times. Operating simultaneously on five superconducting qubits over seven days, this protocol reveals rapid relaxation-time fluctuations and correlations across the processor. Together, these results show how embedded adaptive control can improve the information gained from each experiment and push learning towards the limits imposed by the quantum dynamics themselves.