Much of the patterned use of language occupies a poorly charted middle ground of usages that are neither frozen, one-off items listable in dictionaries nor products of maximally general rules found in grammars. Similarly, these usages fly below the radar of modular theories of language that make a strict distinction between items in a lexicon and the rules of syntax for combining them. Early constructionist approaches showed this neglected territory to be teeming with conventional form-meaning pairings, i.e., lexico-grammatical constructions. While corpora have been seen as a source for investigating these constructions, they entail a fundamental but seldom-noted limitation: constructions are constituted by both syntagmatic and paradigmatic relations, but corpora lack the paradigmatic dimension. Thus corpora can reveal multiword items but not the relations among them that constitute constructions. We elaborate on an alternative, illustrating how the design of an existing machine-readable language model affords discovery of lexico-grammatical constructions by capturing bottom up the relations they contract with other patterns. The network is noise-ridden, but we exploit the noise as the necessary background against which constructions can be set into relief and thus made discoverable.