Accurately predicting precipitation phase is critical for hydrology, weather forecasting, and climate applications, yet fixed temperature thresholds perform inconsistently across regions. We present DeepCut, a neural network that learns adaptive, context-dependent (observation-conditional) temperature thresholds conditioned on location, climate and meteorological state and applies them in a differentiable classification stage. Unlike conventional black-box models, DeepCut offers transparency by explicitly predicting observation-conditional transition cutoffs where rain transitions to snow, combining high accuracy with physical interpretability. Using 16.8 million surface reports from 11 626 stations across the Northern Hemisphere over the training period 1978–2005, our model reaches the accuracy rate of 93.34% for the independent test period 2006–2007, significantly higher than existing models. More importantly, the predicted thresholds (model outputs) exhibit spatially coherent patterns when aggregated over time and stations, generally consistent with known physical processes. Adding explicit temporal encodings (month d⁻¹) provides little incremental benefit beyond meteorological predictors in our experiments; we therefore treat them as optional. We nevertheless observe slowly varying long-term signals over the study period, which are reflected in the data and can be captured through the model’s covariates and regional context. Finally, we have considered atmospheric profiles in addition to near-surface temperature variables that have typically been included in previous studies. Although these profile predictors do not increase overall predictive accuracy in our experiments, their demonstrated relationships with the thresholds are promising in explaining the phase transition process and worth further investigation in future research.

Probabilistic artificial-intelligence (AI) models in sports are often reused across seasons despite changes in teams and context. We develop Monotone Empirical-Bayes Transport Recalibration (MEBTR), a model-agnostic maintenance layer that partially pools local calibration maps, requires a prespecified worthwhile Brier-risk improvement before updating, and monitors gains with anytime-valid e-processes. A predictable-support construction sharpens the universal Brier-difference bound using outcome-free bounds known once both forecasts are frozen. Across logistic regression, random forest, histogram gradient boosting (HGB), and multilayer perceptron learners, 400 paired replications retain Raw AI in 94.25–96.00% of exact-identity runs and select local MEBTR in 82.50–85.50% of affine-shift runs, improving guarded Brier risk by 3.27–3.47% under shift. In leakage-audited NCAA basketball, prospective HGB recalibration improves Brier from 0.224853 to 0.224395, calibration slope from 0.9489 to 0.9883, and ICI from 0.02182 to 0.02050. A 10,000-game bootstrap confirms positive average gain, but the prespecified δ = 0.0005 threshold is not anytime certified. Whole-game-disjoint and repeated-season audits show why the risk guard is necessary: candidate improvements can be small and finite-sample action selection is not oracle model selection.

Continuous dequantization embeds discrete data into a continuous space, but relaxation can alter the statistical information carried by the original categories. We study a complementary regime in which a specified weighted discrete law is the target and the dequantizer is required to be lossless under a prescribed quantizer. Any partition-respecting, parameter-independent kernel produces a continuous experiment Blackwell equivalent to the original discrete one, so likelihood ratios, maximum-likelihood estimators, score and Fisher information, Bayes posteriors, and optimal risks are unchanged before downstream approximation. We then characterize what happens after a finite-capacity continuous model is fitted. A Kullback–Leibler (KL) chain rule separates continuous approximation error into the categorical error of the requantized model plus a within-cell shape term; the information-preservation guarantee therefore does not extend automatically to an arbitrary fitted downstream model. We also provide a plug-in analysis for empirically estimated weights, showing that dequantization preserves rather than removes the discrete estimation error. Within each cell, maximizing entropy minus a displacement penalty yields a truncated Gibbs kernel. The apparent concentration and geometric-scale parameters reduce exactly to one effective concentration, $\alpha =\lambda /s_c^2$. We further derive exact transport costs, a sharp $W_1=\Theta \left(h^2\right)$ reconstruction rate for the special reconstruction-from-exact-bin-masses setting, leakage-specific and geometry-perturbation bounds, and a bounded-domain multidimensional formulation. A finite-candidate Monte Carlo selector satisfies a nonasymptotic $O\left(m^{-1/2}\right)$ oracle inequality. Experiments verify the identities and show that exact dequantization can materially reduce requantized error when a smooth continuous downstream model is imposed; this is a conditional representational advantage, not a claim that dequantization dominates an unrestricted categorical model.