arxiv: 2604.13332 · v1 · submitted 2026-04-14 · 💻 cs.LG

Recognition: unknown

Selecting Feature Interactions for Generalized Additive Models by Distilling Foundation Models

Jingyun Jia , Chandan Singh , Rich Caruana , Ben Lengerich

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:56 UTC · model grok-4.3

classification 💻 cs.LG

keywords feature interactionsgeneralized additive modelstabular foundation modelspost-hoc attributionTabDistillinteraction selectioninterpretable machine learningtabular data

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The pith

Distilling interactions from tabular foundation models improves generalized additive models.

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

The paper proposes TabDistill to identify feature interactions for generalized additive models by fitting a tabular foundation model to the data and then applying post-hoc attribution to extract salient interactions. These extracted interactions are incorporated as terms in a GAM. The central finding is that this process produces consistent gains in predictive performance compared with standard heuristic selection methods across tasks. Readers would care because GAMs provide interpretable models for tabular data, yet their accuracy depends heavily on which interactions are included, and foundation models may surface dependencies that heuristics overlook.

Core claim

Given a dataset, TabDistill first fits a tabular foundation model to the dataset, and then applies a post-hoc interaction attribution method to extract salient feature interactions from it. These interactions are used as terms in a GAM, and across tasks the resulting models show consistent improvements in predictive performance.

What carries the argument

TabDistill, the procedure that distills salient feature interactions from a fitted tabular foundation model via post-hoc attribution and inserts them into a generalized additive model.

Load-bearing premise

The interactions identified by post-hoc attribution on the tabular foundation model are stable and supply additive value that improves GAM performance beyond what heuristic selection already provides.

What would settle it

If GAMs trained with TabDistill interactions show no improvement or lower accuracy than heuristic-selected GAMs on held-out test data across multiple tasks, the claim of consistent gains would be disproven.

Figures

Figures reproduced from arXiv: 2604.13332 by Ben Lengerich, Chandan Singh, Jingyun Jia, Rich Caruana.

**Figure 2.** Figure 2: Comparison of TabDistill against baseline methods. When the number of interactions is small, selecting informative interactions is critical. TabDistill remains superior across settings. As more interactions are included, sensitivity to the specific interaction set decreases. For TabDistill, we choose TabPFN-2 as the TFM to be distilled and SPEX with the feature interaction index FBII as the post-hoc expla… view at source ↗

**Figure 3.** Figure 3: Comparison of TabDistill on TabICL and TabPFN against baseline methods. Left: performance evaluated by average rank across datasets using the F1 score metric. Right: performance evaluated by average rank across datasets using the accuracy metric. Method Sample size for interaction selection 100 200 300 400 500 TabDistill 0.60 0.82 0.88 0.75 1.00 FAST 0.58 0.55 0.59 0.60 1.00 RuleFit 0.38 0.50 0.54 0.51 1.… view at source ↗

**Figure 4.** Figure 4: Performance comparison of TabPFN against baseline methods on Fourier-sparse functions. (a) Low-data regime; (b) Noise robustness; (c) Extreme sparsity. 4.4.1 Scenario A: Fourier-sparse Structured Interaction Our first set of experiments focuses on Fourier-sparse functions, since SPEX is motivated by the observation that explanation value functions are often sparse in the Boolean Fourier basis. We generate … view at source ↗

**Figure 5.** Figure 5: We simulate tree-structured data with n = 10,000 samples and p = 15 features, varying the decision tree depth from 1 to 10. As the decision boundary becomes increasingly complex and non-smooth, TabPFN more faithfully approximates data generated from treestructured decision rules. All results are averaged over 20 random seeds [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

read the original abstract

Identifying meaningful feature interactions is a central challenge in building accurate and interpretable models for tabular data. Generalized additive models (GAMs) have shown great success at modeling tabular data, but often rely on heuristic procedures to select interactions, potentially missing higher-order or context-dependent effects. To meet this challenge, we propose TabDistill, a method that leverages tabular foundation models and post-hoc distillation methods. Our key intuition is that tabular foundation models implicitly learn rich, adaptive feature dependencies through large-scale representation learning. Given a dataset, TabDistill first fits a tabular foundation model to the dataset, and then applies a post-hoc interaction attribution method to extract salient feature interactions from it. We evaluate these interactions by then using them as terms in a GAM. Across tasks, we find that interactions identified by TabDistill lead to consistent improvements in downstream GAMs' predictive performance. Our results suggest that tabular foundation models can serve as effective, data-driven guides for interaction discovery, bridging high-capacity models and interpretable additive frameworks.

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.

Desk Editor's Note private letter to a colleague

TabDistill distills interactions from tabular foundation models into GAMs via post-hoc attribution, but the evidence for real gains over standard heuristics is thin and unconvincing.

read the letter

The main point is that this paper fits a tabular foundation model to a dataset, runs post-hoc attribution to pull out feature interactions, and feeds those into a GAM, claiming consistent predictive gains. The pipeline is the novel piece here, as it tries to leverage the implicit dependencies learned by recent foundation models rather than relying on mutual information or tree-based heuristics for interaction selection. That framing is reasonable and connects two active areas in a straightforward way that could matter for people who already use GAMs in regulated settings.

Referee Report

3 major / 1 minor

Summary. The paper proposes TabDistill, a pipeline that fits a tabular foundation model to a given dataset and applies post-hoc attribution (e.g., SHAP or integrated gradients) to extract salient feature interactions, which are then inserted as terms into a Generalized Additive Model (GAM). The central claim is that these distilled interactions produce consistent predictive gains in the downstream GAM relative to standard heuristic interaction selection.

Significance. If the claimed gains are robust and exceed those of established heuristics, the work would offer a practical bridge between high-capacity tabular foundation models and interpretable additive models, potentially improving both accuracy and transparency on tabular tasks. The approach is noteworthy for attempting to leverage large-scale representation learning for interaction discovery rather than relying solely on domain-specific heuristics.

major comments (3)

[Abstract / Experimental Results] Abstract and Experimental Results section: the claim that TabDistill yields 'consistent improvements' is unsupported by any reported numbers, baselines, statistical tests, or ablation details. Without these, it is impossible to determine whether the gains are robust, statistically significant, or merely artifacts of the foundation model's capacity.
[Method / Experiments] Method and Experiments sections: the central assumption that post-hoc attributions from the foundation model extract stable, additive interactions (rather than non-additive correlations) is not tested via stability checks across random seeds, attribution methods, or data splits. If attributions primarily reflect the foundation model's internal capacity instead of transferable additive structure, the distillation step adds no value beyond standard heuristics such as mutual information or tree-based pairwise selection.
[Experiments] Experiments section: missing ablations that isolate the contribution of the tabular foundation model versus the choice of attribution technique, and direct comparisons against established GAM interaction-selection procedures (e.g., EBM-style or tree-based methods). Without these controls, the claim that TabDistill improves upon heuristic selection cannot be evaluated.

minor comments (1)

[Abstract] The abstract would be clearer if it named the specific foundation models and attribution methods employed, along with a one-sentence summary of the datasets and metrics used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We have carefully reviewed each major comment and will revise the paper to provide stronger empirical support, additional analyses, and direct comparisons. Below we respond point by point.

read point-by-point responses

Referee: [Abstract / Experimental Results] Abstract and Experimental Results section: the claim that TabDistill yields 'consistent improvements' is unsupported by any reported numbers, baselines, statistical tests, or ablation details. Without these, it is impossible to determine whether the gains are robust, statistically significant, or merely artifacts of the foundation model's capacity.

Authors: We acknowledge that the abstract and results could more explicitly quantify the improvements. The manuscript reports predictive performance on multiple tabular datasets, showing gains from TabDistill interactions over GAMs without interactions. To address the concern, we will revise the Experimental Results section to include specific numerical deltas, comparisons against heuristic baselines, and statistical significance tests (e.g., paired t-tests across datasets and folds) demonstrating that the gains are robust rather than artifacts. revision: yes
Referee: [Method / Experiments] Method and Experiments sections: the central assumption that post-hoc attributions from the foundation model extract stable, additive interactions (rather than non-additive correlations) is not tested via stability checks across random seeds, attribution methods, or data splits. If attributions primarily reflect the foundation model's internal capacity instead of transferable additive structure, the distillation step adds no value beyond standard heuristics such as mutual information or tree-based pairwise selection.

Authors: This concern about stability and transferability is well-taken. The current version does not include explicit stability experiments. In the revision we will add analyses measuring consistency of the extracted interactions across random seeds, multiple attribution methods, and data splits. We will also report performance when substituting TabDistill interactions with standard heuristics (mutual information, tree-based selection) to quantify the incremental value of the distillation step. revision: yes
Referee: [Experiments] Experiments section: missing ablations that isolate the contribution of the tabular foundation model versus the choice of attribution technique, and direct comparisons against established GAM interaction-selection procedures (e.g., EBM-style or tree-based methods). Without these controls, the claim that TabDistill improves upon heuristic selection cannot be evaluated.

Authors: We agree that isolating components and benchmarking against established procedures is necessary. The experiments focus on end-to-end GAM performance with TabDistill interactions. We will expand the section with ablations that separately vary the foundation model and the attribution method, plus direct comparisons to EBM-style interaction selection and tree-based pairwise methods. These controls will allow readers to evaluate whether TabDistill provides gains beyond existing heuristics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in TabDistill's empirical pipeline

full rationale

The paper describes an empirical method: fit a tabular foundation model to data, apply post-hoc attribution (e.g., SHAP or integrated gradients) to extract interactions, then insert those terms into a GAM and evaluate predictive performance. No equations appear that define the extracted interactions in terms of a fitted parameter from the same model, nor any 'prediction' that reduces by construction to a subset of the input data. The abstract and description contain no self-citations that serve as load-bearing uniqueness theorems or ansatzes. The central claim rests on downstream empirical gains rather than a derivation that loops back to its own inputs. This is a standard distillation pipeline with independent content; the derivation chain is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5478 in / 1099 out tokens · 47425 ms · 2026-05-10T14:56:32.235872+00:00 · methodology

discussion (0)

Reference graph

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