TreeWalker: Partial Evaluation for Grouped Tree-Ensemble Inference

Sparse oblique (SPO), part of the top-ranked configuration of Google's Yggdrasil Decision Forests (YDF), improve the accuracy while maintaining interpretability of Random Forests (RF) and Gradient Boosted Trees (GBT) by scanning a sparse linear combination of features instead of a single feature. Because projections are sampled at runtime, training is significantly slower, as pre-run optimizations such as presorting cannot be used. We overhaul SPO training in YDF, first by fixing inefficiencies in the released version, achieving 2-5x speedup, then by devising two novel methods, one aimed at GBTs and the other at RFs: (1) Hierarchical AVX2 and AVX-512-vectorized histogram filling speeds up typical GBT-depth trees by up to 1.6x in SPO-GBT and 2x for SPO-RF, and (2) runtime-dynamic histograms between vectorized histograms and exact splits, speeds up deeper, RF depth-typical trees (depths 16 to purity) by up to 1.6x with no detectable effect on accuracy. Our optimizations bring SPO-RF training time on par with YDF's axis-aligned RF. We extensively evaluate on 8 natural and 11 synthetic datasets of up to 10.5 million rows and 1.6 million features, from depth 6 to purity, and open-source the implementation.

Conventional decision tree algorithms produce effective, transparent models that can be audited, communicated, and deployed independently of the training data, but require learning every new task from scratch. In contrast, tabular foundation models demonstrate that meta-learning from a synthetic prior distribution enables strong in-context prediction for previously unseen tasks, especially in small-sample regimes. However, this approach does not produce a standalone model that can be inspected in isolation. We introduce MotherTree, a tabular transformer that meta-learns decision tree induction: given a training set for a new task, it outputs a hard, axis-aligned decision tree, equivalent in form to classically trained trees, in a single forward pass. MotherTree is pre-trained on a synthetic prior using stochastic gradient descent without requiring reference trees for supervision. On established benchmarks with controlled sample size, the approach is competitive with size-matched trees from common algorithms: recursive partitioning, gradient-based tree learning, globally optimal trees, and distillation from tabular foundation models. Notably, MotherTree consistently improves over from-scratch gradient-based learning and acts as a strong initializer: task-specific tuning of the generated tree outperforms the corresponding from-scratch learner on all benchmarks and sample sizes. These results show that meta-learning can provide effective inductive biases for learning stand-alone, small decision tree classifiers.

Gradient Boosted Decision Trees (GBDT), exemplified by LightGBM, spend a dominant fraction of training time -- typically 65-70% -- constructing per-feature histograms. Existing approaches such as random feature subsampling (feature_fraction) discard features without regard for their predictive utility. We propose EMA-based Feature Screening (EMA-FS), an algorithm-level optimization that maintains an exponential moving average (EMA) of per-feature split gains across boosting iterations and, after a short warmup, restricts histogram construction to the top-K features ranked by historical gain. Unlike random subsampling, EMA-FS is informed: it retains high-gain features while screening out low-gain ones. Operating at the per-tree level, it preserves full compatibility with LightGBM's histogram subtraction trick, requiring no changes to core routines. We evaluate EMA-FS on datasets spanning financial fraud detection, advertising click-through prediction, industrial quality control, and synthetic benchmarks, with feature dimensionalities from 29 to 968. On dense, moderate-to-high-dimensional data it achieves significant speedups: 2.61x on a 500-feature synthetic benchmark and 1.45x on the 432-feature IEEE-CIS Fraud dataset at 30% retention. At 70% retention it improves AUC by 0.11 points while delivering a 1.34x speedup. On extremely sparse data (Bosch, >90% missing) it yields no speedup, as LightGBM's sparse bin optimization already bypasses empty values. We further introduce Stochastic EMA-FS (S-EMA-FS), which replaces deterministic top-K selection with gain-weighted random sampling controlled by a concentration parameter beta, unifying deterministic EMA-FS (beta -> infinity) and random subsampling (beta = 0) in one framework. Both are implemented in ~120 lines of C++ across all six LightGBM tree learners and are fully backward-compatible.