Compositionality you can check, not hope for.

In 1988, Fodor & Pylyshyn argued that neural networks cannot support systematic compositionality — the ability to represent structure and run structure-sensitive operations, so that understanding “A loves B” entails understanding “B loves A.” Without it, they argued, a network is not a model of thought.

The bar is precise, and it is easy to mistake. It is not “can vectors add.” Vector arithmetic has produced “king − man + woman ≈ queen” since word2vec, and vector symbolic architectures have offered compose / invert / decompose algebra for decades. The real bar is generalization to novel combinations the system was never trained on, with undiminished competence.

The field's most-cited answer came from Lake & Baroni in 2023: meta-train a network on a stream of compositional tasks until human-like generalization emerges. It became the reference point for the claim that networks can learn to compose.

In 2025, Woydt et al. took that claim apart. They show the result holds “only … under a very narrow and restricted definition of a meta-learning setup” — widen the setup and the failure returns. Their verdict: “Fodor and Pylyshyn's legacy persists … to date, there is no human-like systematic compositionality learned in neural networks.”

That is the opening. If the strongest learned approach still falls short, the fix is not a bigger training curriculum — it is dropping the assumption that compositionality should emerge from training at all. Our research drops that assumption.

The 2023–2025 exchange is about compositionality learned by a sequence model. We do not claim to have won that argument, or to surpass it. We take a different road: we do not ask a network to approximate compositional behavior and hope it emerges. We treat composition as a property of the representation space that either holds or does not — and we measure it.

If the critique is right about anything, it is this: behavior you have to hope emerges from training is fragile. Structure you can verify is not. That is the bet.

A fair skeptic asks the right question: is this structure a property of the representation, or of the operators we train on top of it? Closure on familiar pairs is a low bar — many representations clear it. The bar that matters is Fodor & Pylyshyn's own: generalization to novel combinations the operators never saw.

That is the evaluation we measure against, and we report it honestly as the standard the work is held to — not a claim we wave away. A representation that earns its compositional structure should generalize systematically where weaker substrates do not. Demonstrating that cleanly, against controls, is the frontier — and we would rather state it plainly than overclaim.