If AI reasons by combining reusable building blocks, skills should transfer between domains — but the evidence says that's not what's happening.

This explores why compositional reasoning — the appealing story that a model learns reusable primitives and recombines them, so a skill learned in one area should snap together in another — keeps falling short as an explanation for cross-domain transfer. The short version the corpus points to: models mostly aren't composing in the first place. When you look under the hood, what looks like compositional reasoning turns out to be Do transformers actually learn systematic compositional reasoning? — transformers succeed in-distribution by matching memorized computation subgraphs, not by applying systematic rules, and they fall apart on genuinely novel combinations with errors compounding across steps. If the mechanism is pattern-matching dressed as composition, it can't be the thing that transports skills to a new domain.

A second thread explains why. The reasoning models actually do is bound to meaning, not form: Do large language models reason symbolically or semantically? shows that when you strip semantic content away and give a model correct rules in context, performance collapses. So-called reasoning is riding on parametric commonsense and token associations tied to the training distribution — exactly the associations that don't survive a domain change. This is reinforced by the finding that Do language models fail at reasoning due to complexity or novelty?: models break at instance novelty, not task complexity, because they fit instance-specific patterns rather than the general algorithm a true compositional account would predict. Compositional reasoning predicts smooth transfer across novel instances; what we observe is failure precisely at the novelty boundary.

The chain-of-thought work closes the loop. Does chain-of-thought reasoning reveal genuine inference or pattern matching? and What makes chain-of-thought reasoning fail in language models? find that visible reasoning steps reproduce familiar schemata from training rather than performing fresh symbolic inference — invalid prompts work about as well as valid ones, and performance degrades predictably under distribution shift. If the reasoning trace is imitation of a form, there's no portable abstract structure inside it to carry across domains.

So what does transfer, if not composition? The corpus quietly reframes the question. How do transformers perform analogical reasoning across domains? finds that cross-domain analogy works through geometric alignment of relational structure in embedding space plus a learned mapping — transfer as spatial correspondence, not symbol recombination. And Can discrete codes transfer better than text embeddings? shows discrete codes transfer across domains better than raw text embeddings precisely because they strip out domain-specific surface bias. Both suggest that transfer, where it happens, rides on shared representational geometry — not on the assembly-of-primitives picture compositional reasoning assumes.

The honest tension worth sitting with: Do neural networks naturally learn modular compositional structure? finds networks genuinely do develop isolated modular subroutines, and pretraining makes them more reliable. So composition isn't a myth — it's just local. Modules form within the training distribution but don't generalize as clean, transportable operators. Compositional reasoning fails to explain transfer not because models never compose, but because their composition is memorized and semantics-bound, while whatever carries across domains lives one level down, in the shape of the representation space itself.