Numerical labels often specify a set of possible values: a measurement is rounded, a laboratory test reports only a bound, or a program is stopped at a timeout. We introduce boundary marginalization, the first method that trains an autoregressive language model on the exact likelihood of such observations through its existing digit tokens. A fixed-width, order-preserving numeral representation groups consecutive grid values under shared digit prefixes. An interval is a union of such groups, so its exact probability and gradient follow from at most two boundary paths, the successive digit prefixes of its endpoints, each of length logarithmic in the number of grid values. The resulting objective unifies precise, rounded, bounded, and censored supervision and trains digit decisions at the resolution supplied by each observation. The same computation supports exact distributional queries and unbiased gradients for the continuous ranked probability score on exact labels. Experiments show recovery of a conditional distribution from rounded and censored reports alone, improved likelihood on naturally censored molecular measurements, and more accurate code latency distributions on two backbones. Exact interval updates remain tractable as the numerical support grows to one million values.
Yuwei Miao, Jingquan Yan, Hehuan Ma, Thao M. Dang, Lin Xu, Siyuan Zhang, Junzhou Huang
原文摘要
Predicting gene expression under perturbations from single-cell data is a fundamental task for modeling cellular responses, with applications in discovering gene function and designing therapeutics. However, existing methods often struggle to generalize across datasets due to differences in experimental protocols, biological contexts, and species. We present \textbf{CytoWave}, a perturbation-centric pretraining framework for single-cell genetic perturbation response prediction. We leverage large-scale cross-species perturbation datasets unified via orthology and train CytoWave in a two-stage manner. In the first stage, we learn reference control cell states via masked gene expression recovery on unperturbed cells. In the second stage, we pretrain the model to predict perturbed gene expression given control states and perturbation signals, together with a contrastive objective that aligns latent representations of perturbation responses with perturbation signals. We perform strict dataset-held-out evaluation across multiple condition combinations and case studies of pathway activity changes, demonstrating consistent and effective performance of CytoWave in predicting single-cell genetic perturbation responses.
Correlation metrics such as the Pearson Correlation Coefficient (PCC) and Concordance Correlation Coefficient (CCC) are standard regression metrics and learning objectives, but their non-decomposable nature poses a challenge for stochastic optimization. Since these metrics depend on dataset-level moments (mean, variance, covariance), naive mini-batch training with local statistics yields biased, high-variance gradients whose expectation does not align with the population gradient. To bridge this ``batch-to-population'' (B2P) gap, we propose \textbf{B2P-Corr}, a novel framework that transforms correlation objectives into decomposable pseudo-losses driven by lightweight global ``moment sketches''. We introduce two efficient variants: \textbf{B2P-EMA}, which utilizes exponential moving averages and stop-gradient operators to ensure asymptotic gradient tracking with $O(B)$ cost ($B$ is batch size); and \textbf{B2P-U}, which uses sampled cross-batch U-statistic estimators and a reservoir-based stabilization with an $O(B)$ implementation. Theoretically, we quantify the $O(B^{-1})$ bias of naive mini-batch optimization, prove a moving-target tracking result for B2P-EMA under a fast-sketch / slow-parameter regime, and provide an idealized control-variate analysis for B2P-U. Experiments on two synthetic and three real-world datasets demonstrate B2P-Corr achieves stable optimization and higher correlation than naive mini-batch optimization with negligible overhead.