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Optimizing Social Network Interventions via Hypergradient-Based Recommender System Design
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Proposes BeeRS, a gradient-based bilevel method that optimizes social network edge weights under Friedkin-Johnsen opinion dynamics using hypergradients computed via implicit differentiation, scaling to ~3M variables.
Problem
Mitigating polarization and disagreement in social networks by modifying interaction weights when user opinions evolve under Friedkin-Johnsen dynamics; existing methods are heuristic or solve bilevel problems that are NP-hard or non-convex and do not scale.
Approach
Treat the FJ equilibrium as an implicit mapping of network weights and run projected gradient descent with momentum on the weights, using hypergradients obtained by solving one linear system (adjoint/implicit differentiation), so the intervention accounts for how weight changes shift equilibrium opinions.
Key results
- On full DBLP (3,079,007 nodes, ~3M variables), BeeRS reduces polarization by 38.6% with mean runtime 664.5 s on GPU.
- BeeRS is up to three orders of magnitude faster than IPOPT on smaller instances while reaching ~4e-3 lower relative cost than IPOPT.
- On the Reddit network, BeeRS reduces polarization by 40.2% and disagreement by 21.5%, whereas default NAD increases polarization by 128.7% and disagreement by 41.4%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BeeRS instead of NAD | Network intervention on Reddit · Reddit | change in polarization P: $+128.7\%$ -> $-40.2\%$ | Helped |
| Use BeeRS instead of NAD | Network intervention on Reddit · Reddit | change in disagreement D: $+41.4\%$ -> $-21.5\%$ | Helped |
| Use BeeRS instead of NAD* (λ = 0.2) | Network intervention on Reddit · Reddit | change in polarization P: $-0.7\%$ -> $-40.2\%$ | Helped |
| Use BeeRS instead of NAD* (λ = 0.2) | Network intervention on Reddit · Reddit | change in disagreement D: $+0.3\%$ -> $-21.5\%$ | Helped |
| Use BeeRS instead of NAD | Network intervention on Reddit · Reddit | mean runtime (s): 35.9 -> 82.9 | Hurt |
| Use BeeRS instead of IPOPT | DBLP network intervention · DBLP, 100–2000 users | relative suboptimality: IPOPT: $4.63\mathrm{e}\text{-3}$, $4.42\mathrm{e}\text{-3}$, $4.67\mathrm{e}\text{-3}$, $4.87\mathrm{e}\text{-3}$, $4.72 | Helped |
| Increase momentum γ for small step sizes (ablation) | BeeRS · DBLP, 1000 users | iterations until convergence | Helped |
| Set γ = 0.95 rather than lower momentum at small step sizes (ablation) | BeeRS · DBLP, 1000 users | minimum cost | Helped |
| Use a medium step size with low γ rather than γ = 0.95 (ablation) | BeeRS · DBLP, 1000 users | minimum cost | Helped |
| Use larger step sizes (ablation) | BeeRS · DBLP, 1000 users | minimum cost | Hurt |
| Scale α proportional to n rather than use a constant step size (ablation) | BeeRS · DBLP, varying number of users | iterations until convergence | Helped |
| Use α = 30,000 and γ = 0.95 instead of α = 10,000 and γ = 0.9 (ablation) | BeeRS · DBLP, 3,079,007 nodes | objective stability near convergence | Hurt |
Surprising findings
- The default NAD baseline increases both polarization and disagreement on the Reddit network, and BeeRS increases the weight on a toy edge (to 1.2) where NAD decreases it, despite NAD's objective targeting disagreement.
Limitations
- Convexity assumption on the constraint set precludes binary decisions (whether an edge exists).
- On Reddit, BeeRS runtime (~83 s) is higher than NAD baselines (~27-36 s), and the Frobenius-norm constraint is not supported on GPU.
Experimental setup
Datasets: DBLP citation network Reddit network dataset
Benchmarks: DBLP (3,079,007 nodes) Reddit (553 users)
Metrics: runtime (s) polarization reduction (%) disagreement reduction (%) relative suboptimality
Baselines: IPOPT NAD NAD with regularization
Builds on: Friedkin-Johnsen model implicit function theorem Network Administrator Dynamics (NAD) projected gradient descent with momentum
Closest papers by meaning
- Minimizing Polarization and Disagreement in Social Networks via Link Recommendation (NeurIPS 2021 · similarity 0.90)
- Optimizing Long-term Social Welfare in Recommender Systems: A Constrained Matching Approach (ICML 2020 · similarity 0.86)
- Opinion Maximization in Social Networks by Modifying Internal Opinions (NeurIPS 2025 · similarity 0.86)
- User-Creator Feature Polarization in Recommender Systems with Dual Influence (NeurIPS 2024 · similarity 0.85)
- Disentangled Modeling of Preferences and Social Influence for Group Recommendation (AAAI 2025 · similarity 0.85)
- DiffIM: Differentiable Influence Minimization with Surrogate Modeling and Continuous Relaxation (AAAI 2025 · similarity 0.85)
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