GFMate: Test-Time Prompt Tuning for GFMs

• GFMate is a test-time prompt tuning framework that adjusts frozen Graph Foundation Models using few-shot labeled data and unlabeled target data for cross-domain adaptation.
• It employs centroid prompts and layer prompts to refine class representations and balance multi-layer contributions for improved node and graph classification.
• The method integrates a complementary learning objective on unlabeled data to mitigate distribution shifts, achieving significant gains over baseline approaches.

GFMate is a test-time prompt-tuning framework for Graph Foundation Models (GFMs) that is designed for cross-domain adaptation on a target graph using both few-shot labels and abundant unlabeled target-domain data. In the formulation introduced in "GFMate: Empowering Graph Foundation Models with Test-time Prompt Tuning" (Jiang et al., 14 May 2026), the underlying GFM is pre-trained in a label-free manner and then frozen; adaptation occurs only through prompts introduced after pre-training. The method combines centroid prompts, layer prompts, and a complementary learning objective, with the stated aim of avoiding prompt entanglement with specific source domains or pre-training strategies while exploiting unlabeled target nodes during test-time tuning (Jiang et al., 14 May 2026).

1. Problem setting and motivation

GFMate is defined in a setting where a Graph Foundation Model $f_\theta$ has been pre-trained in a label-free manner, for example via link prediction or contrastive learning, on a set of source-domain graphs $\mathcal{G}_{pre}$. At downstream time, one observes a single target graph $G_{tar}=(V,A,X)$, where $V$ is the node set, $A\in\{0,1\}^{|V|\times |V|}$ is the adjacency matrix, and $X\in\mathbb{R}^{|V|\times d}$ contains node features. A few-shot subset $V_{FS}\subset V$ has labels $y_i$, while the remaining nodes form the unlabeled set $V_{UL}=V\setminus V_{FS}$ (Jiang et al., 14 May 2026).

The paper places GFMate against earlier graph prompt tuning methods that tune prompts learned during source pre-training. In that standard few-shot setting, one tunes a prompt set $B_{pre}$ by solving

$\mathcal{G}_{pre}$0

Two limitations are identified. First, there is pre-training entanglement: prompts specialized to a source domain or to a particular pre-training objective may not generalize to unseen target domains or to GFMs pre-trained by different objectives. Second, there is neglect of unlabeled data: abundant unlabeled nodes in the target graph are not actively used, leaving a substantial train-test distribution shift unaddressed (Jiang et al., 14 May 2026).

GFMate addresses these issues by introducing prompts only after pre-training is fixed. The test-time objective is written as

$\mathcal{G}_{pre}$1

with $\mathcal{G}_{pre}$2 frozen. In the terminology of the paper, this makes the prompts pre-training-agnostic, because they do not participate in source pre-training and therefore are not tied to a particular source-domain set or self-supervised pre-training loss (Jiang et al., 14 May 2026).

2. Prompt parameterization: centroid prompts and layer prompts

The method assumes that the pre-trained GFM consists of $\mathcal{G}_{pre}$3 layers of a GNN backbone, such as GCN or GAT. Layer-wise embeddings are denoted

$\mathcal{G}_{pre}$4

where the row $\mathcal{G}_{pre}$5 is the embedding of node $\mathcal{G}_{pre}$6 at layer $\mathcal{G}_{pre}$7 (Jiang et al., 14 May 2026).

For each class $\mathcal{G}_{pre}$8, GFMate first computes a few-shot centroid at each layer: $\mathcal{G}_{pre}$9 where $G_{tar}=(V,A,X)$0. A learnable additive prompt $G_{tar}=(V,A,X)$1 is then introduced, yielding the refined centroid

$G_{tar}=(V,A,X)$2

The collection of centroid prompts is

$G_{tar}=(V,A,X)$3

These centroid prompts alter the class representatives directly in embedding space rather than modifying the pre-training process or encoding source-domain-specific prompt parameters (Jiang et al., 14 May 2026).

In parallel, GFMate introduces a layer prompt in the form of a learnable scalar weight $G_{tar}=(V,A,X)$4 for each layer. The vector

$G_{tar}=(V,A,X)$5

controls how strongly each layer contributes to final classification. The paper describes these weights as adapting automatically to the “hop-aggregation” patterns of the target graph (Jiang et al., 14 May 2026).

Prediction is performed by a multi-layer ensemble score. For any node $G_{tar}=(V,A,X)$6 and class $G_{tar}=(V,A,X)$7,

$G_{tar}=(V,A,X)$8

where cosine similarity is used: $G_{tar}=(V,A,X)$9 Class probabilities are then obtained through a temperature-scaled softmax,

$V$0

with $V$1 (Jiang et al., 14 May 2026).

3. Complementary learning at test time

The optimization objective combines ordinary few-shot supervision with an unlabeled-data term derived from complementary labels. On the labeled set $V$2, GFMate uses the standard cross-entropy

$V$3

This term anchors the prompt tuning to the observed few-shot labels (Jiang et al., 14 May 2026).

For unlabeled nodes, the method first computes a per-layer confidence statistic. For each layer $V$4, the average entropy over $V$5 is

$V$6

where $V$7 is defined using only layer $V$8 in the score. The pivot layer is then selected as

$V$9

that is, the layer with highest confidence on the unlabeled target nodes (Jiang et al., 14 May 2026).

Using that pivot layer, each unlabeled node $A\in\{0,1\}^{|V|\times |V|}$0 is assigned a complementary label

$A\in\{0,1\}^{|V|\times |V|}$1

namely the class least similar to the node representation at the pivot layer. The corresponding loss is

$A\in\{0,1\}^{|V|\times |V|}$2

This explicitly pushes the probability of the complementary class toward zero (Jiang et al., 14 May 2026).

The full objective is a convex combination: $A\in\{0,1\}^{|V|\times |V|}$3 Only $A\in\{0,1\}^{|V|\times |V|}$4 and $A\in\{0,1\}^{|V|\times |V|}$5 are learnable; the GFM parameters $A\in\{0,1\}^{|V|\times |V|}$6 remain fixed. Updates are performed by gradient descent,

$A\in\{0,1\}^{|V|\times |V|}$7

with learning rate $A\in\{0,1\}^{|V|\times |V|}$8, and optimization stops when the validation loss on a small held-out part of $A\in\{0,1\}^{|V|\times |V|}$9 converges or after a fixed number of steps (Jiang et al., 14 May 2026).

4. Algorithmic workflow and computational profile

The test-time procedure begins by computing layer embeddings $X\in\mathbb{R}^{|V|\times d}$0 on the target graph. Centroid prompts $X\in\mathbb{R}^{|V|\times d}$1 and layer prompts $X\in\mathbb{R}^{|V|\times d}$2 are initialized randomly, and the few-shot centroids $X\in\mathbb{R}^{|V|\times d}$3 are computed for all layers and classes. Each optimization step then refines the centroids, computes per-layer probabilities and entropies on unlabeled nodes, selects the pivot layer, determines complementary labels, evaluates $X\in\mathbb{R}^{|V|\times d}$4 and $X\in\mathbb{R}^{|V|\times d}$5, forms the total loss, and updates $X\in\mathbb{R}^{|V|\times d}$6 and $X\in\mathbb{R}^{|V|\times d}$7 by SGD. Final predictions on $X\in\mathbb{R}^{|V|\times d}$8 are given by

$X\in\mathbb{R}^{|V|\times d}$9

This is the complete workflow described as the GFMate test-time prompt tuning algorithm (Jiang et al., 14 May 2026).

The paper gives the per-step complexity as

$V_{FS}\subset V$0

which is stated to be linear in graph size. It also emphasizes parameter efficiency: GFMate tunes only $V_{FS}\subset V$1 parameters, in contrast to $V_{FS}\subset V$2 parameters in instance-level prompt methods (Jiang et al., 14 May 2026).

A practical consequence is reported in downstream adaptation on Arxiv-year. SAMGPT requires $V_{FS}\subset V$3 s, $V_{FS}\subset V$4 M tunable parameters, and $V_{FS}\subset V$5 GB GPU memory, while GFMate requires $V_{FS}\subset V$6 s, $V_{FS}\subset V$7 k parameters, and $V_{FS}\subset V$8 GB GPU memory, corresponding to 98% faster adaptation and 97% less memory in that experiment (Jiang et al., 14 May 2026).

5. Experimental evaluation

GFMate is evaluated on 12 benchmarks across node and graph classification. The node-classification portion includes Cornell, Texas, Wisconsin, Chameleon, Squirrel, Cora, Citeseer, Arxiv-year, and Amazon-Photo in a one-versus-all cross-domain setting; the graph-classification portion includes BZR, COX2, and PROTEINS. The task range is from one-shot to full-shot classification with 5 random runs (Jiang et al., 14 May 2026).

The baseline suite spans several categories. Supervised GNNs include GCN, GAT, GraphSAGE, H2GCN, and GPR. Self-supervised pre-train plus fine-tune baselines include LP+FT, DGI+FT, and GCL+FT. Single-domain prompt-tuning baselines include GPPT, ProNoG, GraphPrompt, GPF, DAGPrompt, and All-In-One. Cross-domain GFM baselines include GCOPE, MDGPT, SAMGPT, MDGFM, BRIDGE, and RiemannGFM, while GraphAny and GTrans are considered in the full-shot setting (Jiang et al., 14 May 2026).

For one-shot node classification, the paper reports the following accuracies in a representative table: GFMate attains $V_{FS}\subset V$9 on Cora, $y_i$0 on Cite, $y_i$1 on Chameleon, and $y_i$2 on Squirrel. The stated average improvement over the best baseline is up to +30.63% (relative) on Chameleon (Jiang et al., 14 May 2026). Across varying few-shot sizes $y_i$3, GFMate is reported to consistently outperform GFMs. When plugged into different pre-training strategies—LP, DGI, and GCL—and different backbones—GCN, SAGE, GAT, and H2GCN—the method is reported to yield always +10–30% gain (Jiang et al., 14 May 2026).

Ablation studies attribute the performance to all three main components. On one- versus three-shot node classification averaged over five graphs, removing centroid prompts causes a $y_i$4 drop, removing layer prompts causes a $y_i$5 drop, and removing complementary learning so that only few-shot supervision remains causes a $y_i$6 drop (Jiang et al., 14 May 2026). In the binary classification setting, the paper reports even larger relative gains, described as being in line with the $y_i$7 risk bound in Proposition 1 (Jiang et al., 14 May 2026).

6. Scope, interpretation, and limitations

The central claim about generalization is that GFMate’s prompts are agnostic to both the source pre-training domain set and the GFM’s self-supervised loss. The method is said to plug seamlessly into any GNN-based GFM backbone and pre-training objective, and the active use of unlabeled testing data through complementary labels is presented as a mechanism for mitigating train-test distribution shifts (Jiang et al., 14 May 2026).

The term pre-training-agnostic has a precise meaning in this framework. It does not denote adaptation without optimization; rather, it denotes that prompt parameters are introduced only after the source pre-training stage and are therefore not entangled with a particular source-domain prompt design. The learnable objects are the centroid prompts $y_i$8 and layer prompts $y_i$9, while the foundation model parameters $V_{UL}=V\setminus V_{FS}$0 remain fixed (Jiang et al., 14 May 2026).

The paper also identifies clear limitations. GFMate is designed for GNN-based GFMs on text-free graphs and does not immediately extend to LLM-based GFMs on text-attributed graphs. Its test-time tuning protocol requires access to the full target graph, so the setting is transductive; inductive test-time tuning is explicitly left as an open direction. In addition, the complementary labeling mechanism is characterized as heuristic, and the authors suggest that more robust uncertainty-based or self-training mechanisms could be investigated in future work (Jiang et al., 14 May 2026).

Within the graph prompt-tuning literature, GFMate is therefore best understood as a target-domain adaptation mechanism that relocates prompt optimization from pre-training or source-domain transfer into inference-time adjustment on the target graph itself. This suggests a distinct design principle for GFMs: rather than encoding source-domain knowledge into prompt parameters in advance, one can leave the foundation model frozen and use structurally lightweight prompts plus unlabeled target-domain signals to specialize predictions at test time (Jiang et al., 14 May 2026).