Finding Multiple Interpretations in Datasets

With the rise of tabular foundation models alongside traditional models still performing well on many tasks, choosing the right model for a tabular dataset remains difficult. We investigate whether dataset meta-features can explain performance gaps between model families on tabular prediction tasks. Using the TabArena benchmark results, we analyze dataset-level performance gaps and relate them to model-agnostic meta-features. After strict statistical tests with false discovery control, we find that (1) for neural network vs. tree gaps, no meta-feature survives false discovery control, (2) for non-foundation vs. foundation model gaps, one association is robust but does not generalize when tested in leave-one-dataset-out prediction, and (3) for TabICLv2 vs. TabPFN-2.6, one robust association also improves held-out prediction. Furthermore, we conduct a leave-one-dataset-out analysis and find that meta-feature predictors fail to improve meaningfully over a simple baseline. Overall, our results show the heterogeneity of tabular datasets and that global meta-feature approaches are not robust enough to offer explanations on the 51 TabArena datasets.

Can a dataset be recognized from the spurious correlations it induces during training? We argue that datasets leave dataset-specific traces in a model's learned semantic correlation structure: incidental regularities that are predictive within a dataset, but not causal for the underlying task, can be internalized during training. We use this insight to study dataset-level membership inference, moving beyond existing methods that rely on behavioral or distributional evidence such as confidence scores, losses, margins, generated samples, or query responses. We introduce a white-box semantic fingerprinting approach based on semantic correlation descriptors (SCDs), which capture the semantic correlation structure learned by a model and make it comparable across dataset mixtures. In a controlled leave-one-dataset-out diagnostic, SCDs recover dataset-specific changes and perfectly separate matching from non-matching dataset pairs. We then propose a practical SCD-based membership score that tests whether a target dataset is part of a model's training mixture using only the model's SCD and the target dataset's standalone SCD, without requiring leave-one-dataset-out models. Across three diverse experimental settings, with dataset groups for natural language inference, emotion classification, and medical text classification, we test both the advantages and limitations of SCD-based membership inference with different degrees of semantic separation and keyword support between dataset splits. On average, the classifier based on this score achieves the highest performance and the lowest std, outperforming black-box baselines RMIA, Attack-P, and LiRA, as well as the white-box SIF baseline. These results show that dataset membership can be traced through internal semantic correlations, with the largest relative gain exceeding 60% in ROC-AUC when dataset groups expose distinct semantic particularities.

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to out-of-distribution mechanisms, or basis-dependent parameters, meaning they disregard weight-space symmetries. To address these issues for the class of tensor-based models, we introduce a weight-based metric, tensor similarity, that is invariant to such symmetries. This metric captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. Empirically, tensor similarity tracks functional training dynamics, such as grokking and backdoor insertion, with higher fidelity than existing metrics. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.