Competing Infection-Removal Graph Layer
Implementation & benchmark of arXiv:2607.29409 — The Zombie Infection Model
Source paper: The Zombie Infection Model arXiv:2607.29409 ⓘ · analyzed Aug 31, 2026
AI-generated research hypothesis, automatically tested. Not peer-reviewed.
Idea description
Replace a conventional graph message-passing layer with a finite-horizon stochastic propagation process containing susceptible, infected, and removed feature states. Messages spread along active infected-to-susceptible edges, while infected nodes are simultaneously deleted at a rate proportional to their susceptible-neighbor count. This provides explicit propagation control and anti-oversmoothing dynamics instead of repeatedly averaging over every neighbor.
Formulas
Mathematical statement
The paper defines the Zombie Infection Model generator as $$L_{\lambda,\mu}^{\mathrm{ZIM}}f(\omega)=\sum_{x:\omega(x)=I}\left(\mu\sum_{y:\omega(y)=S,\,x\sim y}[f(\omega^{x\leftarrow R})-f(\omega)]+\lambda\sum_{y:\omega(y)=S,\,x\sim y}[f(\omega^{y\leftarrow I})-f(\omega)]\right).$$ Here $G=(V,E)$ is a graph, $\omega:V o\{S,I,R\}$ is the node-state configuration, $x\sim y$ means that $x$ and $y$ are adjacent, $\lambda>0$ is infection intensity per active SI edge, $\mu>0$ is removal intensity per susceptible neighbor, and $\omega^{z\leftarrow i}$ changes node $z$ to state $i$. The active boundary is $$\partial_{SI}(\omega)=\{(x,y)\in\overrightarrow E:\omega(x)=I,\ \omega(y)=S\}.$$ The total event rate is $(\lambda+\mu)|\partial_{SI}(\omega)|$, and an infection-versus-removal event has relative probabilities $\lambda/(\lambda+\mu)$ and $\mu/(\lambda+\mu)$. For neural use, let $h_i,s_i,r_i\geq0$ denote infected, susceptible, and removed masses with $h_i+s_i+r_i=1$. Define $$F_j=\lambda s_j\sum_iA_{ij}h_i,\qquad D_i=\mu h_i\sum_jA_{ij}s_j,$$ and update $$h_j^{t+1}=h_j^t+\Delta t F_j^t-\Delta t D_j^t,\quad r_j^{t+1}=r_j^t+\Delta t D_j^t,\quad s_j^{t+1}=1-h_j^{t+1}-r_j^{t+1}.$$ The key property is explicit competition: high susceptible degree increases both incoming propagation and removal of the source.
Implementation notes
Integrate this as an optional propagation block before the graph encoder's usual MLP or residual update. First compute node embeddings $x_i$ using a linear projection. Produce initial infected mass $h_i^0=\operatorname{sigmoid}(w_h^Tx_i)$, set $r_i^0=0$, and set $s_i^0=1-h_i^0$. For each of $K$ propagation steps, compute active edge mass $a_{ij}=A_{ij}h_i s_j$, incoming infection flux $F_j=\lambda\sum_i a_{ij}$, and source removal flux $D_i=\mu\sum_j a_{ij}$. Update h = h + dt * (F - D), r = r + dt * D, and s = 1 - h - r; clamp all states to nonnegative values and renormalize each node's three states to sum to one. Use the accumulated flux to gate learned messages: m_j = sum_t sum_i a_ij * Wv(x_i), followed by x_out = x + MLP(m). Parameterize $\lambda$ and $\mu$ with softplus to keep them positive. The paper supplies the competing-event rates; the neural model learns the states and rates. Choose $\Delta t$ so that $\Delta t(\lambda+\mu)\max_i\deg(i)<0.25$. Start with a two-layer GCN or GraphSAGE on Cora, PubMed, and a synthetic tree task, matching parameter counts. Compare $K=2,4,8$ and $\mu/\lambda=0,0.1,0.3,1$. Success is higher accuracy on noisy or heterophilous graphs, lower cosine-similarity collapse across layers, and less degradation after adding irrelevant edges.
Verification
This idea has not been verified yet.
Verification happens in two stages: Stage 1 — a mechanism check on a toy system confirms the claimed mathematical phenomenon reproduces; Stage 2 — a benchmark implements the idea on a real (small) neural network task and compares it against a tuned baseline over 8 paired seeds with a permutation test.
Artifacts
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