Search papers, labs, and topics across Lattice.
This paper critiques the conventional endpoint measurement of statistical watermarks in language models, arguing that it fails to account for the inner geometry of meaning-preserving transformations. By employing the formalism of linguistic loops, the authors demonstrate that the invariant of these transformations can be decomposed into an endpoint component and a holonomy that is overlooked by traditional semantic similarity measures. Their findings reveal that the retention of meaning can vary dramatically based on the positions of edits, leading to significant implications for watermark detection efficacy.
The retention of meaning in language models can vary from half to zero based solely on the positions of edits, challenging existing assumptions about watermark robustness.
Statistical watermarks for language models live in the freedom of the signifier: they choose among tokens that are nearly equivalent in meaning, and they are therefore eroded by exactly those transformations which move the form of a text while leaving its content in place. The literature measures such transformations by their endpoint, through the semantic similarity between the original and the rewritten text. We show that the endpoint is the wrong statistic. Adapting the formalism of linguistic loops, we prove that the invariant of a chain of meaning-preserving transformations factorises canonically into an endpoint part and a holonomy in the stabiliser of the initial state, the second of which the semantic deficit cannot see; the loop rotation is parallel transport on the unit sphere of the embedding space, so that the analogy with the Wilson loop becomes a theorem rather than a figure of speech. On the side of the detector we prove an exact identity: the residual statistic is proportional to the number of positions whose seeding window survived intact, from which the decay law $\rho^{h+1}$ follows as the independent-edit corollary. The identity has a disconcerting consequence, which we confirm to three decimal places: at one and the same retention rate the surviving signal may be one half of the original, one quarter of it, or exactly nothing, according only to where the edits fall.
