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Synthetic genetic circuits enable the reprogramming of cells and has advanced the study and application of biology with greater precision. However, quantitative circuit design is hampered by the limited modularity of biological parts. Moreover, as circuit complexity increases this imposes a greater metabolic burden on chassis cells limiting circuit design capacity. Here we present a generalizable technology composed of wetware and software to enable the quantitative design of highly compressed genetic circuits for higher-state decision-making. Wetware is composed of a new set of synthetic transcription factors facilitating the full development of compressed 3-input Boolean logic. Complementary software enables the design of compressed higher-state circuits, paired with a modeling workflow for the design of prescribed performance setpoints. On average the resulting multi-state compressed circuits were ~5-times smaller than canonical inverter-based genetic circuits. Our quantitative predictions had an average error below 1.4-fold validated via >50 test cases. Additionally, we applied said technology toward the predictive design of recombinase-based memory, and flux through a metabolic pathway. 

Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Generating diverse posterior samples remains expensive, as existing methods require restarting the entire generative process for each new sample. In this work, we propose a posterior sampling approach that simulates Langevin dynamics in the noise space of a pre-trained generative model. By exploiting the mapping between the noise and data spaces which can be provided by distilled flows or consistency models, our method enables seamless exploration of the posterior without the need to re-run the full sampling chain, drastically reducing computational overhead. Theoretically, we prove a guarantee for the proposed noise-space Langevin dynamics to approximate the posterior, assuming that the generative model sufficiently approximates the prior distribution. Our framework is experimentally validated on image restoration tasks involving noisy linear and nonlinear forward operators applied to LSUN-Bedroom (256 x 256) and ImageNet (64 x 64) datasets. The results demonstrate that our approach generates high-fidelity samples with enhanced semantic diversity even under a limited number of function evaluations, offering superior efficiency and performance compared to existing diffusion-based posterior sampling techniques.