The global uniform aggregation of random forests leaves conditional bias along the decision boundary uncorrected. To correct this locally, we propose exploiting the structural pattern of each tree's decision path. At inference, a random forest reaches its prediction through the root-to-leaf path the sample traverses in each tree, so path-level reliability offers a finer granularity than tree-level weighting can access. We show that reliability varies meaningfully across path patterns in the boundary region identified by the forest itself, and that using this signal yields a statistically significant accuracy improvement over RF on 36 binary classification benchmarks (Wilcoxon p < 0.0001). We further devise a way to measure the sufficiency of residual information in the fitted RF's decision boundary, providing an estimate of the expected gain before the method is applied; on the qualifying group identified this way, the method delivers a mean +0.99 pp accuracy improvement with strict wins on every dataset (7/0/0). Class-recall regression -- the typical failure mode of RF correction methods -- is measured: zero minority-recall regressions and a single majority-recall regression at the 0.2 pp threshold, indicating that the correction operates in the direction of bias reduction rather than class trade-off. Our work suggests that the structural information of decision paths, previously overlooked in random forest research, can contribute to RF performance improvement.

No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via ensemble averaging (DASH), and machine-verify it with 305 Lean 4 theorems. We characterize the complete attribution design space: exactly two families of methods exist -- faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods like DASH (stable, reporting ties for symmetric features) -- and no method lies outside this dichotomy. The impossibility is quantitative: the attribution ratio diverges as 1/(1-rho^2) for gradient boosting, is infinite for Lasso, and converges for random forests. DASH (Diversified Aggregation of SHAP) is provably Pareto-optimal among unbiased aggregations, achieving the Cramer-Rao variance bound with a tight ensemble size formula. In a survey of 77 public datasets, 68% exhibit attribution instability. Switching to conditional SHAP does not escape the impossibility when features have equal causal effects. The framework includes practical diagnostics -- a Z-test workflow and single-model screening tool -- and has direct consequences for fairness auditing: SHAP-based proxy discrimination audits are provably unreliable under collinearity. The design space theorem, diagnostics, and impossibility are mechanically verified in Lean 4 (305 theorems from 16 axioms, 0 sorry) -- to our knowledge, the first formally verified impossibility in explainable AI.

Tabular data underpins most high-value prediction problems in science and industry, and TabPFN has driven the foundation model revolution for this modality. Designed with feedback from our users, TabPFN-3 builds on this foundation to scale state-of-the-art performance to datasets with 1M training rows and substantially reduce training and inference time. Pretrained exclusively on synthetic data from our prior, TabPFN-3 dramatically pushes the frontier of tabular prediction and brings substantial gains on time series, relational, and tabular-text data. On the standard tabular benchmark TabArena, a forward pass of TabPFN-3 outperforms all other models, including tuned and ensembled baselines, by a significant margin, and pareto-dominates the speed/performance frontier. On more diverse datasets, TabPFN-3 ranks first on datasets with many classes, and beats 8-hour-tuned gradient-boosted-tree baselines on datasets up to 1M training rows and 200 features. TabPFN-3 introduces test-time compute scaling to tabular foundation models. Our API offering TabPFN-3-Plus (Thinking) exploits this to beat all non-TabPFN models by over 200 Elo on TabArena, rising to 420 Elo on the largest data subset, and outperforms AutoGluon 1.5 extreme while being 10x faster, without using LLMs, real data, internet search or any other model besides TabPFN. TabPFN-3 extends the capabilities of our models, enabling SOTA prediction on relational data (new SOTA foundation model on RelBenchV1) and tabular-text data (SOTA on TabSTAR via TabPFN-3-Plus); and improves existing integrations: a specialized checkpoint, TabPFN-TS-3, ranks 2nd on the time-series benchmark fev-bench, and SHAP-value computation is up to 120x faster. TabPFN-3 achieves this performance while being up to 20x faster than TabPFN-2.5. In addition, a reduced KV cache and row-chunking scale to 1M rows on one H100 with fast inference speed.

We study online prediction under distribution shift, where inputs arrive chronologically and outcomes are revealed only after prediction. In this setting, predictors must remain stable in quiet regimes yet adapt when regimes shift, and the right adaptation memory is unknown in advance. We propose MELO (Memory-hedged Exponentially Weighted Least-Squares Online aggregation), a model-agnostic method that hedges across adaptation scales: it wraps any non-anticipating base-predictor pool with exponentially weighted least-squares (EWLS) adaptation experts at multiple forgetting factors, and aggregates raw and EWLS-adapted forecasts with MLpol which is a parameter-free online aggregation rule. Under boundedness conditions, we establish deterministic oracle inequalities showing that it competes with both the best raw predictor and the best bounded, time-varying affine combinations of the base predictions, up to a path-length-dependent tracking cost and a sublinear aggregation overhead. We evaluate MELO on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. MELO reduces overall RMSE by 34.7%relative to base-only MLpol and achieves lower overall RMSE than a TabICL reference supplied with an external COVID policy-response covariate. MELO requires only lightweight per-step recursive updates without model retraining.

Gradient Boosting Decision Trees (GBDTs) dominate tabular machine learning, with modern implementations like XGBoost, LightGBM, and CatBoost being based on Newton boosting: a second-order descent step in the space of decision trees. Despite its empirical success, the global convergence of Newton boosting is poorly understood compared to first-order boosting. In this paper, we introduce Restricted Newton Descent, which studies convex optimization with Newton's method on Hilbert spaces with inexact iterates, based on the concepts of cosine angle and weak gradient edge. Within this framework, we recover Newton boosting with GBDTs and classical finite-dimensional theory as special cases. We first prove that vanilla Newton boosting achieves a linear rate of convergence for smooth, strongly convex losses that satisfy a Hessian-dominance condition. To handle general convex losses with Lipschitz Hessians, we extend a recent gradient regularized Newton scheme to the restricted weak learner setting. This scheme minimally modifies the classical algorithm by introducing an adaptive $\ell_2$-regularization term proportional to the square root of the gradient norm at each iteration. We establish a $\mathcal{O}(\frac{1}{k^2})$ rate for this scheme, thereby obtaining a globally convergent second-order GBDT algorithm with a rate matching that of first-order boosting with Nesterov momentum. In numerical experiments, we show that our scheme converges while vanilla Newton boosting may diverge.

Research on adversarial robustness is primarily focused on image and text data. Yet, many scenarios in which lack of robustness can result in serious risks, such as fraud detection, medical diagnosis, or recommender systems often do not rely on images or text but instead on tabular data. Adversarial robustness in tabular data poses two serious challenges. First, tabular datasets often contain categorical features, and therefore cannot be tackled directly with existing optimization procedures. Second, in the tabular domain, algorithms that are not based on deep networks are widely used and offer great performance, but algorithms to enhance robustness are tailored to neural networks (e.g.

Geographic context is often consider relevant to motor insurance risk, yet public actuarial datasets provide limited location identifiers, constraining how this information can be incorporated and evaluated in claim-frequency models. This study examines how geographic information from alternative data sources can be incorporated into actuarial models for Motor Third Party Liability (MTPL) claim prediction under such constraints. Using the BeMTPL97 dataset, we adopt a zone-level modeling framework and evaluate predictive performance on unseen postcodes. Geographic information is introduced through two channels: environmental indicators from OpenStreetMap and CORINE Land Cover, and orthoimagery released by the Belgian National Geographic Institute for academic use. We evaluate the predictive contribution of coordinates, environmental features, and image embeddings across three baseline models: generalized linear models (GLMs), regularized GLMs, and gradient-boosted trees, while raw imagery is modeled using convolutional neural networks. Our results show that augmenting actuarial variables with constructed geographic information improves accuracy. Across experiments, both linear and tree-based models benefit most from combining coordinates with environmental features extracted at 5 km scale, while smaller neighborhoods also improve baseline specifications. Generally, image embeddings do not improve performance when environmental features are available; however, when such features are absent, pretrained vision-transformer embeddings enhance accuracy and stability for regularized GLMs. Our results show that the predictive value of geographic information in zone-level MTPL frequency models depends less on model complexity than on how geography is represented, and illustrate that geographic context can be incorporated despite limited individual-level spatial information.

We propose a new conformal prediction method for time-series data with a guaranteed asymptotic conditional coverage rate, Sequential Conformalized Density Regions (SCDR), which is flexible enough to produce both prediction intervals and disconnected prediction sets, signifying the emergence of bifurcations. Our approach uses existing estimated conditional highest density predictive regions to form initial predictive regions. We then use a quantile random forest conformal adjustment to provide guaranteed coverage while adaptively changing to take the non-exchangeable nature of time-series data into account. We show that the proposed method achieves the guaranteed coverage rate asymptotically under certain regularity conditions. In particular, the method is doubly robust -- it works if the predictive density model is correctly specified and/or if the scores follow a nonlinear autoregressive model with the correct order specified. Simulations reveal that the proposed method outperforms existing methods in terms of empirical coverage rates and set sizes. We illustrate the method using two real datasets, the Old Faithful geyser dataset and the Australian electricity usage dataset. Prediction sets formed using SCDR for the geyser eruption durations include both single intervals and unions of two intervals, whereas existing methods produce wider, less informative, single-interval prediction sets.