Grables: When Graph Structure Helps Tabular Prediction

The gist The paper shows that row-wise predictors rule out natural targets driven by global counts, overlaps, and relational patterns in tabular learning This finding motivates the introduction of grables, a modular interface separating table lifting from node prediction to pinpoint where expressive power comes from.

Grables as a Modular Interface

The authors introduce grables as a way to make “using structure” precise across architectures by separating how a table is lifted to a graph (constructor) from how predictions are computed on that graph (node predictor). A grable consists of two parts: a graph constructor, which maps a table to a graph while preserving a canonical correspondence between rows and nodes, and a node predictor, which operates on the resulting graph. This abstraction makes explicit where structural inductive bias enters and provides a common language to compare row-wise tabular models, message-passing neural networks, and transformer-style tabular methods whose structure is implicit in attention.

Expressiveness Framework

The authors formalize grabular expressibility as a framework that characterizes which row-level prediction functions can be realized by a given family of constructors and predictors. This framework quantifies the families of graph views induced from the same underlying table, rather than fixing the input graph as in standard neural network analyses. They show that row-local predictors are exactly those that are invariant under table extensions and therefore incapable of representing natural inter-row targets driven by counts, overlaps, or shared witnesses.

Separations in Predictors

The analysis fixes the predictor side to be k-layer MPNNs and asks how the choice of constructor family shapes Expr(Γ,P(k)MPNN). On the trivial constructor γtriv, MPNNs are row-wise, meaning any k-layer MPNN reduces to an independent per-row classifier. To expose inter-row dependencies, they use the schemadriven incidence constructor γinc. This allows them to show that targets like UNIQUE and COUNTN fall within graded modal logic GML(≤k) for small k, implying realizability by constant-depth MPNNs.

Empirical Validation

Experiments confirm the predicted separations on synthetic and real transactional data, showing that apparent gains by row-local models can arise from row-local cues rather than genuine relational reasoning. The case study on the RelBench clinical-trials data demonstrates that explicitly exposing inter-row structure and combining it with strong tabular representations yields consistent improvements, confirming that tabular and graph-based representations are complementary rather than competing. This is shown by hybrid models achieving consistent performance gains over purely tabular models when cross-row aware information is combined with a strong tabular predictor.

Structural Insights from Experiments

The experiments isolate two sources of inductive bias: (i) the representation induced by the table-to-graph constructor, and (ii) the downstream predictor class. They test whether row-local representations are structurally misaligned with the target, and whether exposing cross-row structure via explicit constructions and message passing resolves that mismatch. The results confirm that models with access to explicit inter-row structure capture extensionsensitive dependencies that row-local predictors miss. Furthermore, the analysis of feature importance in hybrid models shows that GNN-derived embeddings dominate the top-ranked features, indicating that tabular learners rely on message-passing representations even when strong row-local features are present.

Conclusion

The paper concludes that while strong tabular models capture most of the predictive signal for relational datasets, they can be lifted to access inter-row structure through hybrid methods, confirming that tabular and graph-based representations are complementary rather than competing. This motivates the use of structure-aware tabular learning as a principled way to overcome row-local limitations. The work provides a principled framework for reasoning about when and why modeling inter-row structure is beneficial. The techniques and analyses presented here do not introduce new data sources, new deployment scenarios, or new mechanisms for decision-making about individuals. This work may help practitioners avoid inappropriate model choices in settings such as transactional, temporal, or relational data. The techniques and analyses presented here do not raise novel ethical concerns beyond those commonly associated with machine learning research on tabular data. This work is methodological and theoretical in nature, focusing on expressiveness, inductive bias, and experimental diagnosis rather than on deploying new predictive systems. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness. This work is complementary to literature on transformer-based tabular models by introducing an explicit abstraction separating table-to-structure construction from prediction. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness. The paper's primary goal is to advance the understanding of representational limitations in tabular machine learning and to provide a principled framework for reasoning about when and why modeling inter-row structure is beneficial. This work may help practitioners avoid inappropriate model choices in settings such as transactional, temporal, or relational data. The techniques and analyses presented here do not raise novel ethical concerns beyond those commonly associated with machine learning research on tabular data. This work is methodological and theoretical in nature, focusing on expressiveness, inductive bias, and experimental diagnosis rather than on deploying new predictive systems. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness. This work is complementary to literature on transformer-based tabular models by introducing an explicit abstraction separating table-to-structure construction from prediction. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness. This work is complementary to literature on transformer-based tabular models by introducing an explicit abstraction separating table-to-structure construction from prediction. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness. This work is complementary to literature on transformer-based tabular models by introducing an explicit abstraction separating table-to-structure construction from prediction. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness. This work is complementary to literature on transformer-based tabular models by introducing an explicit abstraction separating table-to-structure construction from prediction. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness. This work is complementary to literature on transformer-based tabular models by introducing an explicit abstraction separating table-to-structure construction from prediction. The authors do not propose new graph learning methods or graph constructions; instead, they provide a formalization of the graph-to-table process and introduce a framework and vocabulary for studying expressiveness.

1. Improved system can capture extension-sensitive dependencies by utilizing graph structures, as message passing captures inter-row dependencies that row-local models miss. This allows for learning targets such as global counts, overlaps, and relational patterns which are otherwise inaccessible to row-local predictors.

2. Improved system can leverage explicit structural information via a modular interface called grables to separate how a table is lifted to a graph (constructor) from how predictions are computed on that graph (node predictor). This allows researchers to pinpoint where expressive power comes from and compare different architectures transparently through the metric of (Γ,P)-expressibility.

3. Improved system can achieve superior performance on complex relational tasks by employing hybrid approaches, as hybrid approaches that explicitly extracts inter-row structure and feeds it to strong tabular learners yield consistent gains. This is demonstrated by combining strong tabular representations with structural features derived from graph constructions like the incidence grable or learned message-passing representations.

4. Improved system can be designed for specific relational data types by selecting appropriate graph constructors, such as using the incidence grable for tasks that fall within graded modal logic, which allows expression of targets like UNIQUE, COUNTN, and DOUBLE via k-layer MPNNs.

5. Improved system can overcome the limitations of purely relational models on certain datasets by implementing hybrid structures that combine tabular learning with inter-row signals, as shown by the result that explicitly exposing structure—whether through fixed aggregations or learned message passing—can lift the structural limitations of row-local learning when combined with a strong tabular predictor.

Simple row-wise predictors that score each row independently remain competitive with far more expressive architectures on tabular benchmarks, which are i.i.d. by construction. They cannot, however, represent natural targets on transactional, temporal, and relational tables, where labels depend on other rows. We show that row-wise prediction provably rules out targets driven by global counts, overlaps, and relational patterns. To make ``using structure'' precise across architectures, we introduce grables: a modular interface that separates how a table is lifted to a graph (constructor) from how predictions are computed on that graph (node predictor), placing gradient-boosted trees, neighbourhood aggregation, transformer-style tabular models, and relational GNNs on a single axis and pinpointing where expressive power comes from. The framework yields a hierarchy that answers when structure is needed: row-local models suffice for extension-invariant targets, lightweight neighbourhood aggregation captures shallow inter-row signals, and explicit graph construction is needed for compositional patterns that fixed aggregations cannot express without exponential feature blow-up. Experiments on synthetic, transactional, and relational data confirm the predicted separations, but also show that benchmark performance is a poor proxy for structural capability: row-local models score well on tasks they provably cannot represent, and a stress-test that suppresses row-local cues is needed to expose the gap. Conversely, access to cross-row context does not imply a model uses it. Feeding explicitly extracted inter-row structure to strong tabular learners yields gains exactly where the hierarchy predicts. The practical recipe is to add structure incrementally, and only where the target is extension-sensitive.