HSGM: Hierarchical Segment-Graph Memory for Scalable Long-Text Semantics

Semantic parsing of long documents remains challenging due to quadratic growth in pairwise composition and memory requirements. We introduce \textbf{Hierarchical Segment-Graph Memory (HSGM)}, a novel framework that decomposes an input of length $N$ into $M$ meaningful segments, constructs \emph{Local Semantic Graphs} on each segment, and extracts compact \emph{summary nodes} to form a \emph{Global Graph Memory}. HSGM supports \emph{incremental updates} -- only newly arrived segments incur local graph construction and summary-node integration -- while \emph{Hierarchical Query Processing} locates relevant segments via top-$K$ retrieval over summary nodes and then performs fine-grained reasoning within their local graphs. Theoretically, HSGM reduces worst-case complexity from $O(N^2)$ to $O\!\left(N\,k + (N/k)^2\right)$, with segment size $k \ll N$, and we derive Frobenius-norm bounds on the approximation error introduced by node summarization and sparsification thresholds. Empirically, on three benchmarks -- long-document AMR parsing, segment-level semantic role labeling (OntoNotes), and legal event extraction -- HSGM achieves \emph{2--4$\times$ inference speedup}, \emph{$>60\%$ reduction} in peak memory, and \emph{$\ge 95\%$} of baseline accuracy. Our approach unlocks scalable, accurate semantic modeling for ultra-long texts, enabling real-time and resource-constrained NLP applications.