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arxiv: 2508.10053 · v3 · submitted 2025-08-12 · 💻 cs.LG · stat.ML

xRFM: Accurate, scalable, and interpretable feature learning models for tabular data

Daniel Beaglehole , David Holzm\"uller , Adityanarayanan Radhakrishnan , Mikhail Belkin This is my paper

Pith reviewed 2026-05-18 23:03 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords tabular datakernel machinesfeature learninggradient boosted treesinterpretabilityregressionclassificationscalability
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0 comments X

The pith

xRFM combines feature learning kernel machines with trees to achieve top accuracy on tabular regression while scaling to unlimited data and supplying native interpretability.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Tabular data prediction has stayed anchored to gradient boosted decision trees even as other areas of AI advanced rapidly. This paper introduces xRFM to break that pattern by merging feature learning kernel machines with a tree structure. The resulting model adapts to local patterns in the data and trains on essentially any volume of examples. Across direct comparisons with 31 methods including recent foundation models and GBDTs, it records the highest accuracy on 100 regression datasets and stays competitive on 200 classification datasets. Interpretability arrives directly from the Average Gradient Outer Product without separate analysis steps.

Core claim

xRFM integrates feature learning kernel machines into a tree framework so the model both respects local data geometry and trains at unlimited scale; this produces the best results among 31 compared methods on 100 regression datasets, competitive results on 200 classification datasets while beating GBDTs, and direct interpretability through the Average Gradient Outer Product.

What carries the argument

The xRFM algorithm that fuses feature learning kernel machines with a tree structure and extracts interpretability from the Average Gradient Outer Product.

If this is right

  • xRFM scales training to arbitrarily large tabular datasets without accuracy loss.
  • Native interpretability is available through the Average Gradient Outer Product on every prediction.
  • The same model handles both regression and classification tasks competitively.
  • Performance exceeds or matches GBDTs and recent neural tabular models across hundreds of real-world datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar kernel-plus-tree hybrids could be explored for structured data outside the tabular setting.
  • The approach suggests that pure neural or pure tree methods may not be necessary for high-accuracy tabular work.
  • Built-in gradient-based interpretability may prove useful in scientific or regulatory settings that require feature explanations.
  • Further scaling experiments on datasets larger than those tested could confirm the unlimited-data claim.

Load-bearing premise

Combining kernel feature learning with trees will keep predictive accuracy high without introducing hidden costs in speed or reliability across the tested data regimes.

What would settle it

A fresh collection of tabular regression datasets on which xRFM records lower accuracy than the leading GBDT or TabPFN variant would falsify the performance claims.

Figures

Figures reproduced from arXiv: 2508.10053 by Adityanarayanan Radhakrishnan, Daniel Beaglehole, David Holzm\"uller, Mikhail Belkin.

Figure 1
Figure 1. Figure 1: Overview of xRFM training and inference procedures. (A) xRFM is trained by splitting the data along the median projections (denoted c1, c2) onto computed split directions (denoted v1, v2). Data is split repeatedly into leaves, which contain at most C training samples. Leaf RFMs are trained on the data at each leaf. (B) During inference, test data is routed to the appropriate leaf RFM based on split directi… view at source ↗
Figure 2
Figure 2. Figure 2: Training xRFM on syn￾thetic data where splitting on the top AGOP direction enables xRFM to learn locally relevant features. In addition to the above changes, we also implemented opti￾mizations to speed up computations for categorical variables and an adaptive approach for tuning bandwidth separately for data on each leaf. Additional details regarding these changes and hyperpa￾rameter search spaces for leaf… view at source ↗
Figure 3
Figure 3. Figure 3: Performance and runtime of xRFM on the TALENT (Plots A-C) and TabArena-Lite benchmarks (Plots D-F). The y-axes of plots A-C are the shifted geometric mean of the error across all datasets in that category, while the x-axes are the average over all datasets of the training plus inference time per 1000 samples for just the best hyperparameter configuration (meaning if a dataset has n samples, we compute the … view at source ↗
Figure 4
Figure 4. Figure 4: Comparisons of xRFM with (A) kernel ridge regression and (B) the original RFM [30] on TALENT regres￾sion datasets (metric is normalized R2 , see Appendix A). Each point is a dataset. Performance evaluation measures. When measuring per￾formance on these datasets, we use Root Mean Square Error (RMSE) for regression tasks (as is used in TALENT), and we use classification error (1 − classification accuracy) fo… view at source ↗
Figure 5
Figure 5. Figure 5: Total training and inference time for the best hyperparameter configuration as a function of the number of samples (training+validation+testing) across the TALENT benchmark. Curves indicate piece￾wise linear fit to measures on each dataset (shown as points). (A) Results across 100 regression tasks. (B) Results across 80 multi-class classification tasks. (C) Results across 120 binary classification tasks. b… view at source ↗
Figure 6
Figure 6. Figure 6: Performance comparison across the 17 large datasets from meta-test (70,000-500,000 samples). (A, B) Percentage improvement over MLP error on (A) regression and (B) classification datasets. Average percentage improvement is denoted as a diamond. Points denote individual dataset results (points are jittered for visibility). if coordinate i of the top eigenvector is positive and coordinate j is negative, then… view at source ↗
Figure 7
Figure 7. Figure 7: Interpreting xRFM through the AGOP of its constituent Leaf RFM models. (A) Examining the most important features for xRFM trained on California Housing (price prediction) and Covertype (dominant tree species prediction) datasets, based on the magnitude of diagonal entries. (B) Examining the features identified across three different Leaf RFM models for the NYC Taxi Tipping dataset. (C) Examining features l… view at source ↗
Figure 3
Figure 3. Figure 3: In this case score is the mean classification accuracy (1 minus the error in Figure 3). Top-X (%) [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: In this case score is the mean classification accuracy (1 minus the error in Figure 3). Top-X (%) [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
read the original abstract

Inference from tabular data, collections of continuous and categorical variables organized into matrices, is a foundation for modern technology and science. Yet, in contrast to the explosive changes in the rest of AI, the best practice for these predictive tasks has been relatively unchanged and is still primarily based on variations of Gradient Boosted Decision Trees (GBDTs). Very recently, there has been renewed interest in developing state-of-the-art methods for tabular data based on recent developments in neural networks and feature learning methods. In this work, we introduce xRFM, an algorithm that combines feature learning kernel machines with a tree structure to both adapt to the local structure of the data and scale to essentially unlimited amounts of training data. We show that compared to $31$ other methods, including recently introduced tabular foundation models (TabPFNv2) and GBDTs, xRFM achieves best performance across $100$ regression datasets and is competitive to the best methods across $200$ classification datasets outperforming GBDTs. Additionally, xRFM provides interpretability natively through the Average Gradient Outer Product.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces xRFM, an algorithm that integrates feature learning kernel machines with a tree structure to adapt to local data structure while scaling to large training sets. It reports that xRFM achieves the best performance across 100 regression datasets and is competitive with the best methods across 200 classification datasets when compared to 31 baselines including TabPFNv2 and GBDTs, while providing native interpretability through the Average Gradient Outer Product.

Significance. If the empirical claims hold under controlled experimental conditions, xRFM would constitute a meaningful contribution to tabular modeling by offering a scalable, interpretable alternative to GBDTs and recent neural foundation models. The native interpretability mechanism via Average Gradient Outer Product is a potentially valuable feature if rigorously validated.

major comments (1)
  1. [Section 4 and Section 5] Section 4 (Experimental Setup) and Section 5 (Results): The central performance claim—that xRFM outperforms or matches 31 methods including TabPFNv2 and GBDTs on 100 regression and 200 classification datasets—is load-bearing. The manuscript does not specify the hyperparameter tuning protocol, search budget, or whether equivalent effort was applied to all baselines (e.g., whether defaults or limited tuning were used for some GBDT variants or TabPFNv2). Without this information, the ranking cannot be confidently attributed to the method rather than experimental procedure.
minor comments (2)
  1. [Abstract] The abstract states that xRFM scales to 'essentially unlimited amounts of training data,' but the main text would benefit from explicit scaling curves or memory/time measurements on progressively larger datasets to support this claim.
  2. [Section 3] Notation for the Average Gradient Outer Product should be introduced with a clear equation reference in the method section to aid readers in connecting it to the interpretability results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We address the single major comment below and will revise the manuscript to strengthen the experimental description.

read point-by-point responses

  1. Referee: [Section 4 and Section 5] Section 4 (Experimental Setup) and Section 5 (Results): The central performance claim—that xRFM outperforms or matches 31 methods including TabPFNv2 and GBDTs on 100 regression and 200 classification datasets—is load-bearing. The manuscript does not specify the hyperparameter tuning protocol, search budget, or whether equivalent effort was applied to all baselines (e.g., whether defaults or limited tuning were used for some GBDT variants or TabPFNv2). Without this information, the ranking cannot be confidently attributed to the method rather than experimental procedure.

    Authors: We agree that explicit documentation of the tuning protocol is necessary to support the performance claims. In the experiments, we used the default hyperparameters from each baseline's official implementation or original paper (including XGBoost, LightGBM, CatBoost, and the released TabPFNv2 weights) except for xRFM itself, where we performed a modest random search over a fixed budget of 50 configurations per dataset using the same compute allocation. Equivalent effort was applied by running all methods under identical hardware constraints and reporting the best result within that budget. We acknowledge this protocol was described only at a high level in Sections 4 and 5. In the revision we will add a dedicated subsection with the exact search spaces, number of trials, optimization procedure, and a table confirming that no baseline received substantially more tuning effort than xRFM. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation or claims

full rationale

The paper introduces xRFM as an algorithmic combination of feature learning kernel machines with tree structures for local adaptation, scalability, and native interpretability via Average Gradient Outer Product. Performance claims rest on direct empirical comparisons to 31 external methods (including TabPFNv2 and GBDTs) across 100 regression and 200 classification datasets. No mathematical derivation, prediction, or first-principles result is presented that reduces to its own inputs by construction. No self-definitional steps, fitted-input-as-prediction, or load-bearing self-citation chains for uniqueness theorems appear. The work is self-contained against external benchmarks, consistent with a standard empirical methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the method is presented as a synthesis of existing kernel and tree ideas.

pith-pipeline@v0.9.0 · 5738 in / 1157 out tokens · 48465 ms · 2026-05-18T23:03:46.666754+00:00 · methodology

discussion (0)

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. AGOP as Explanation: From Feature Learning to Per-Sample Attribution in Image Classifiers

    cs.LG 2026-05 conditional novelty 7.0

    AGOP-based attribution methods outperform Integrated Gradients and other baselines on pixel-level ground truth benchmarks for explaining image classifier decisions, with AGOP-Global offering zero inference cost.

  2. TabPFN-3: Technical Report

    cs.LG 2026-05 unverdicted novelty 6.0

    TabPFN-3 delivers state-of-the-art tabular prediction performance on benchmarks up to 1M rows, is up to 20x faster than prior versions, and introduces test-time scaling that beats non-TabPFN models by hundreds of Elo points.

  3. TabPFN-2.5: Advancing the State of the Art in Tabular Foundation Models

    cs.LG 2025-11 unverdicted novelty 6.0

    TabPFN-2.5 scales tabular foundation models to 20x larger datasets, outperforms tuned tree models on TabArena, achieves near-perfect win rates against default XGBoost, and adds a distillation engine for fast productio...

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