Graph State Networks (GSNs): Persistent Nodewise Selective State Space Models

Arijit Dey, Bahman Gharesifard

Abstract: Temporal graphs are often observed as streams of timestamped interactions, where accurate prediction requires retaining and selectively using historical information nodes. Existing temporal graph models either (i) recompute representations from a sliding neighborhood/history at query time, or (ii) maintain a memory module but offer limited control and limited theory for what is retained over long horizons. We propose Graph State Networks (GSNs), a bucketed temporal-graph framework that maintains a persistent hidden state per node and updates it online using a content- and time-dependent selective state space update. Concretely, GSNs store node states in an explicit id-indexed state table and for each bucket, read the current state, update it with a time-aware Mamba-like mechanism, and commit the state back via an exponential moving average controlled by a commit-rate. This commit mechanism provides an explicit "retention dial'' and enables a tractable analysis of forgetting. We develop a capacity/recall theory for persistent node memory and show that, under incremental-stability assumptions on blank-bucket dynamics, the influence of a single past event admits a geometric forgetting bound, with the effective decay governed by the contraction of the blank dynamics and the commit mechanism. Empirically, GSNs are competitive on standard dynamic link prediction benchmarks under Average Precision (AP), with the strongest gains appearing in several inductive settings, while AUC-ROC remains more mixed. We validate these ideas with controlled synthetic write-wait-read probes. Under shared later blank sequences and a small nonzero state-noise blank update, the measured write-vs-zero-write relative influence exhibits near-exponential decay over the main operating regime. Our simulation studies verify this overall trend, including the nonzero floor at larger commit rates. We provide an extended implementation of GSNs.

Submission Type: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=zMEuBQfeT6

Changes Since Last Submission: N/A

Code: https://github.com/arijitcodespace/GSN

Assigned Action Editor: ~Nicolas_THOME2

Submission Number: 7155