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

TMLR Paper7155 Authors

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 commit-rate $\alpha$. This commit mechanism provides an explicit "retention dial'' and enables a clean analysis of forgetting. We develop a capacity/recall theory for persistent node memory and show that, under an affine approximation of blank-bucket dynamics, the influence of a single past event decays geometrically at a rate governed by $\alpha$ and the induced linearized update. Empirically, GSNs are competitive on standard dynamic link prediction benchmarks. We validate the theory with controlled synthetic write--wait--read probes: measured influence is close to exponential in delay, and fitting short-delay dynamics predicts long horizon recall across commit rates.

Submission Type: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=uo5BBCYaQV

Changes Since Last Submission:

Fixed template compliance issues flagged by the desk rejection. Now the header section is visible.

Reformatted the abstract to be a single paragraph (per TMLR instructions).

Regenerated the PDF using the official TMLR style without layout-altering modifications.

No changes to technical content; only formatting/template compliance fixes.

Assigned Action Editor: ~Nicolas_THOME2

Submission Number: 7155