Scientific machine learning often relies on proxy targets computed from known domain factors when direct observations are limited. When those same factors are used as model inputs, however, high predictive accuracy may reflect reconstruction of the proxy-generating equation rather than robustness to degraded factor information. We study this problem in RUSLE-derived soil-loss proxy prediction under controlled degradation of the soil-erodibility factor $K$. We introduce a diagnostic framework that combines degraded-formula references, classical tree-based baselines, matched direct and formula-feature predictors, contextual ablations, tail-error analysis, and degradation robustness scoring. We then propose RASPL, a formula-preserving residual framework that retains the degraded formula estimate as the prediction anchor and learns an adaptively gated contextual correction. RASPL substantially outperforms matched direct prediction and provides stronger degradation and tail robustness than treating the formula estimate as an ordinary input feature. Within RASPL, a compact statistical encoder achieves the highest macro-averaged $R^2$ and lowest computational cost, whereas a convolutional encoder achieves the strongest degradation robustness and lowest Tail95 mean absolute error (MAE). These results establish formula preservation as the central design principle for robust learning from factor-derived proxy targets.
Training target speaker extraction (TSE) models for real conversational mixtures remains challenging because large-scale training corpora and clean target speech for supervision are unavailable. We present PS4, a proxy-supervised training framework for TSE in real conversational mixtures, with two main contributions. First, we construct a large-scale corpus of 71,771 training samples derived from four public datasets, covering both Chinese and English scenarios. Each sample contains an overlapping speech mixture, per-speaker enrollment audio, a ground-truth transcript, and frame-level voice activity labels. Second, we propose a proxy-supervised joint training strategy that fine-tunes a BSRNN-based TSE model using four complementary differentiable objectives: ASR cross-entropy, speaker similarity, frame-level voice activity detection, and perceptual audio quality. Starting from a publicly available pre-trained checkpoint, only the BSRNN separator is updated during fine-tuning. On the REAL-T challenge leaderboard, PS4 ranks 2nd overall, achieving the best speaker similarity and timing F1 among all submitted systems.