RSD: Moving Local Triangular Charts for Auditing Language-Model Hidden States

A researcher has proposed Relational Semantic Decomposition (RSD), a method that uses moving local triangular charts to audit the hidden states of language models, according to a preprint posted on arXiv [1]. The work, authored by Seungmin Jin, was submitted on 17 May 2026 and revised through 25 June 2026 [1]. RSD fits a shared three-anchor membership chart at a given layer or token-time for repeated occurrences of a target word [2]. The hidden-state channel is approximated as Xt ≈ StCt, and the invariant readout Mt = StSt⊤ captures the induced occurrence co-membership relation [2]. The residual Rt = Xt − StCt records what the fitted root chart leaves outside the chart [2]. A broader joint audit reuses the same membership chart for relation data, expressed as At ≈ StBtSt⊤, which can incorporate an attention-derived occurrence relation [2]. The current evidence uses GPT-2 hidden states with Word-in-Context labels as an external same-sense versus different-sense reference relation [2]. On the full WiC training set, the root chart passes 16 of 53 eligible target words; the paper describes this as audit coverage, not GPT-2 task accuracy [2]. Token-time and pair-level diagnostics reveal distinct regimes: the words “make” and “break” align at the target state, while “drive” and “stay” improve after right context in small-count exploratory cases [2]. The word “play” remains a localized root-chart failure where final same-sense pairs are not closer and exhibit larger residual discrepancy [2]. The preprint appeared on arXiv, an open-access repository of electronic preprints that is moderated but not peer-reviewed [6]. Founded in 1991, arXiv passed the two-million-article milestone by the end of 2021 and now receives about 24,000 submissions per month [6]. The paper’s submission history shows three versions: the initial v1 weighed 90 KB, v2 dropped to 59 KB, and v3 settled at 35 KB [1]. The diagnostic claim of the work is that RSD reports where a sense relation is visible in root co-membership and which failures become residual branch candidates or attention-channel obligations [2].