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Stability and Diversity of Networked Self-Consuming Generative Ecosystems

NeurIPS 2026 · Graph learning › Graph self-supervised learning · approach: Diffusion-based graph generation

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Proposes a graph-based theoretical framework for networked self-consuming generative models, deriving local stability conditions via a spectral-radius criterion and topology-dependent diversity bounds, validated with diffusion/flow-matching experiments on CIFAR-10.

Problem

Self-consuming training loops have been studied mostly for isolated models or two-model pairs; the long-term stability and diversity of large networks of generative models that consume each other's synthetic data are not well understood.

Approach

Model the ecosystem as a directed weighted graph of retraining models with row-stochastic synthetic-data flow weights; show local stability around any fixed point is governed by the spectral radius of a topology-aware comparison matrix diag(beta)W, and that diversity contracts via a graph-Laplacian smoothing operator (I + Lambda L)^{-1}.

Key results

• Local asymptotic stability holds when rho(D) < 1, with linear convergence rate bounded by rho(D); the norm-based condition lambda_i < alpha_i/(M_i||W||_2 - (alpha_i - L_i eps_i)) is sufficient.
• Diversity bound under symmetric undirected graphs: D_out <= D_data / (1 + lambda mu_2)^2, so higher algebraic connectivity yields faster diversity collapse.
• Experiments on CIFAR-10 show increasing synthetic mixing ratio alpha and denser graphs reduce diversity; System 1 (isolated) diversity does not decrease with alpha because it reflects instability rather than differentiation.

Surprising findings

• Shorter interaction cycles mitigated FID degradation when real data are present, contrasting with synthetic-only settings where short cycles accelerated instability.
• Increases in diversity can stem from instability rather than meaningful specialization, complicating diversity interpretation.

Limitations

• Results are local, around an assumed fixed point; global existence and uniqueness are not established.
• Analysis assumes exact MLE-style updates with strong concavity and Hessian stability; ignores finite-sample and stochastic optimization effects.
• Diversity upper bound is worst-case and cannot separate specialization from instability-induced diversity.

Experimental setup

Datasets: CIFAR-10 Synthetic 8-Gaussian mixture

Benchmarks: CIFAR-10

Metrics: FID precision recall system diversity (variance of ResNet-18 features)

Baselines: isolated retraining (System 1)

Builds on: model collapse analysis (single-model self-consuming loops) implicit function theorem Gelfand's formula

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