# Energy Score

When target samples are limited, conditional flow matching can borrow a covariate representation learned from a related source population. TFM-Freeze keeps the source encoder fixed and trains only a target velocity head; TFM-Adapt jointly learns the head and a representation correction under a functional anchoring penalty. In simulations with related five-dimensional representations and 10000 source samples, unpenalized TFM-Adapt lowered energy discrepancy from 0.3158 for TFM-Freeze to 0.2325, a 26.4% reduction; target validation falls back to a target-only generator when transfer does not help.

When target samples are limited, conditional flow matching can borrow a covariate representation learned from a related source population. TFM-Freeze keeps the source encoder fixed and trains only a target velocity head; TFM-Adapt jointly learns the head and a representation correction under a functional anchoring penalty. In simulations with related five-dimensional representations and 10000 source samples, unpenalized TFM-Adapt lowered energy discrepancy from 0.3158 for TFM-Freeze to 0.2325, a 26.4% reduction; target validation falls back to a target-only generator when transfer does not help.

Single-cell perturbation atlases cover only a fraction of possible experimental combinations, and existing generative models map measured control cells to perturbed cells without a reference for how good a prediction can be. GENESIS instead generates single-cell expression distributions directly from covariates such as cell line or donor, drug or cytokine, dose and batch, training a lightweight multilayer perceptron with the energy score and needing no control cells at inference. On 530 repeated Tahoe-100M plate pairs its Pearson Δ was 0.430 versus 0.432 for experimental repeats and its energy distance 0.158 versus 0.154, neither significantly different; top-100 DEG overlap was 0.289 versus 0.299, 3.4% short.

Single-cell perturbation atlases cover only a fraction of possible experimental combinations, and existing generative models map measured control cells to perturbed cells without a reference for how good a prediction can be. GENESIS instead generates single-cell expression distributions directly from covariates such as cell line or donor, drug or cytokine, dose and batch, training a lightweight multilayer perceptron with the energy score and needing no control cells at inference. On 530 repeated Tahoe-100M plate pairs its Pearson Δ was 0.430 versus 0.432 for experimental repeats and its energy distance 0.158 versus 0.154, neither significantly different; top-100 DEG overlap was 0.289 versus 0.299, 3.4% short.