TIDESTEMPORAL GRAPH FM
TIME, THEN SPACE

TIDES

Temporal Injection of Decoupled Encodings into Static GNNs

A compositional framework that decouples time from space to build transferable temporal graph foundation models.

De Castelli, Gravina, Bacciu, Eliasof
Graph Foundation Models Workshop · ICML 2026 · Seoul
HERO
OVERVIEW

The tide moves over a seabed that stays still.

Learning general representations for temporal graphs is challenging because temporal dynamics and structural changes are often intertwined, causing models to capture domain-specific patterns over generalizable ones. This acts as a barrier to foundation models for temporal graphs.

TIDES decouples the two. It relies on a one-time, parallel extraction of three domain-agnostic priors, temporal embeddings from a frozen time-series foundation model, deterministic summaries of local temporal contexts, and supra-Laplacian positional encodings of the changing graph structure. These features are computed once and used as node inputs for a static GNN, so the same spatial reasoning transfers across domains while the temporal component adapts.

01 / MOTIVATION

Time and space are entangled in temporal graphs.

When sequence models and GNNs are trained jointly, every shared parameter is exposed to conflicting spatio-temporal patterns and is forced to encode domain identity to fit them. This produces a leakage channel that scales poorly with corpus diversity and leads to negative transfer under heterogeneous domain shifts. We argue that this failure is in part structural, and that the two sources of variation should be treated as separable.

FIG 1 · ENTANGLED DYNAMICS
time space SHARED PARAMETERS entangled
02 / METHOD

Decouple the tide from the seabed.

TIDES formulates representation learning as a composition of three structured operators that encode the temporal signal, the structural topology, and positional information independently, then integrate them into a unified space. Following the time-then-graph paradigm, the representation map \(\Phi\) concatenates a temporal operator \(\Phi_{\mathrm f}\), a statistical operator \(\Phi_{\mathrm s}\), and a positional operator \(\Phi_{\mathrm p}\). This decomposition induces a partition of the representation space, so each subspace captures a distinct source of variation.

FIG 2 · DECOUPLED ENCODING
time space Φ_f Φ_s Φ_p H
COMPOSITIONAL ENCODING
\[ \Phi(\mathcal{X}, \mathcal{G}_{1:T}) = \big[\, \Phi_{\mathrm f}(\mathcal{X}) \;\Vert\; \Phi_{\mathrm s}(\mathcal{X}) \;\Vert\; \Phi_{\mathrm p}(\mathcal{G}_{1:T}) \,\big], \qquad \mathbb{R}^{d} = \mathcal{H}_{\mathrm f} \oplus \mathcal{H}_{\mathrm s} \oplus \mathcal{H}_{\mathrm p} \]
Three complementary operators are concatenated into a single node representation, and the representation space splits into a temporal, a statistical, and a structural subspace.
03 / PRIORS

Three frozen, domain-agnostic priors.

The temporal operator \(\Phi_{\mathrm f}\) maps each node trajectory to embeddings through a frozen time-series foundation model over a sliding context. The statistical operator \(\Phi_{\mathrm s}\) summarizes the recent local signal, grounding the deep temporal representation in the immediate state of the network. The positional operator \(\Phi_{\mathrm p}\) lifts a sliding window of snapshots into a multilayer graph and reads the smallest eigenpairs of its supra-Laplacian. The parameters of all three are precomputed once and never updated during downstream training.

FIG 3 · FROZEN PRIORS
Φ_f frozen TS model Φ_s local statistics Φ_p supra-Laplacian
FROZEN PRIORS
\[ \Phi_{\mathrm f}(\mathcal{X})_t = f_\theta\big(\mathcal{X}_{t-w_f+1:t}\big) \in \mathbb{R}^{n \times d_f}, \qquad \mathbf{L}_{\mathrm{supra}} = \mathbf{D}_{\mathrm{supra}} - \mathbf{A}_{\mathrm{supra}} \in \mathbb{R}^{n w_p \times n w_p} \]
A frozen time-series foundation model encodes each node trajectory over a window \(w_f\), while the supra-Laplacian of a sliding multilayer graph supplies positional structure through its smallest eigenpairs.
04 / ARCHITECTURE

Fixed inputs to a trajectory-aware static GNN.

The three precomputed features are treated as fixed inputs to a static GNN with \(L\) residual layers, trained only to model spatial dependencies. Rather than reading the final layer alone, the full residual trajectory is pooled across depth and refined by node-wise multi-head self-attention, so every layer scale contributes to the representation. Because sequence modeling is handled in a one-time preprocessing stage, the temporal dimension is factored out, avoiding backpropagation through time and keeping training parallelizable.

FIG 4 · ARCHITECTURE
Φ_f Φ_s Φ_p Gate GNNx L (res) HistoricalAggregation MHSA residual
TRAJECTORY-AWARE AGGREGATION
\[ \mathbf{Z} = \sum_{l=0}^{L} \alpha_l\, \hat{\mathbf{H}}_l, \qquad \tilde{\mathbf{H}} = \mathrm{MHSA}(\mathbf{Z}, \mathbf{Z}, \mathbf{Z}) \]
The full residual trajectory of the static GNN is pooled across depth with signed weights, then refined by multi-head self-attention to restore inter-node mixing.
05 / TRANSFER

One framework, many temporal graphs.

Because the priors are domain-agnostic and the backbone reasons over precomputed temporal and structural representations without encoding node identities or dataset-specific memory, TIDES transfers to unseen temporal graphs by simply recomputing the same priors. This reduces negative transfer and improves cross-graph transferability, outperforming state-of-the-art temporal graph baselines on the 20 unseen networks of the MiNT zero-shot benchmark.

FIG 5 · CROSS-DOMAIN TRANSFER
no transfer (y = x) single-network AUC zero-shot AUC

Per-network zero-shot transfer on the 20 MiNT test networks (Table 5). Each marker compares single-network AUC (x) with multi-network, zero-shot AUC (y); markers above the dashed diagonal indicate positive transfer. TIDES (squares) sits above the line far more often than MiNT (circles).

RESULTS · ZERO-SHOT

Transfer without relearning structure.

We evaluate zero-shot transfer on the MiNT benchmark. TIDES is pre-trained on 64 token networks and evaluated directly on 20 unseen networks, with no target-specific training. The task is binary graph property prediction at weekly resolution. Higher AUC and a lower average rank are better.

Average rank over 20 unseen networks
ModelAvg. rank ↓
HTGN2.45
MiNT-642.05
TIDES-sup2.60
TIDES-64 (ours)1.45
Transfer gain of the pre-trained models
StatisticMiNT-64TIDES-64
Mean transfer gain Δ ↑+0.024+0.107
Median Δ ↑+0.043+0.075
Negative transfer (Δ<0) ↓7 / 202 / 20
Strong transfer (Δ>+0.1) ↑5 / 209 / 20

Zero-shot AUC averaged over 20 unseen MiNT test networks and 3 seeds. TIDES-64 achieves the best average rank, ranking first on 12 of 20 networks and outperforming MiNT-64 despite using identical training data. Its mean transfer gain is more than four times that of MiNT-64, with negative transfer on only 2 of 20 networks.

SCALING WITH PRETRAINING SIZE

Mean zero-shot AUC as the number of pretraining token networks grows. TIDES outperforms the largest MiNT competitor using as few as four token networks, and its performance saturates early. Error bands show standard deviation across the test networks.