Predicting Channel Closures in the Lightning Network with Machine Learning

We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity? We cast this as a budget-constrained combinatorial optimization problem on graphs, selecting $k$ edge additions that maximize $s$--$t$ max-flow, a theory-grounded measure of routing capacity, and solve it with graph reinforcement learning. Our lightweight agent combines a message-passing policy network with proximal policy optimization (PPO) and action masking, and is trained under a hub-exclusion curriculum: the network's top hubs are removed from training subgraphs, forcing the policy to learn capacity-aware placement rather than hub attachment. In extensive experiments on real Lightning Network snapshots, our method consistently outperforms strong heuristic baselines on the max-flow objective across multiple seeds and unseen graphs. The agent has been deployed in production for peer recommendations, executing 4640 channel-open decisions that cumulatively allocate 267.3 BTC over $16 million across 30 managed nodes.

The consensus that GCN, GraphSAGE, GAT, and EvolveGCN outperform feature-only baselines on the Elliptic Bitcoin Dataset is widely cited but has not been rigorously stress-tested under a leakage-free evaluation protocol. We perform a seed-matched inductive-versus-transductive comparison and find that this consensus does not hold. Under a strictly inductive protocol, Random Forest on raw features achieves F1 = 0.821 and outperforms all evaluated GNNs, while GraphSAGE reaches F1 = 0.689 +/- 0.017. A paired controlled experiment reveals a 39.5-point F1 gap attributable to training-time exposure to test-period adjacency. Additionally, edge-shuffle ablations show that randomly wired graphs outperform the real transaction graph, indicating that the dataset's topology can be misleading under temporal distribution shift. Hybrid models combining GNN embeddings with raw features provide only marginal gains and remain substantially below feature-only baselines. We release code, checkpoints, and a strict-inductive protocol to enable reproducible, leakage-free evaluation.

Graph neural networks for node classification are typically trained by gradient descent over hundreds or thousands of epochs. Recent work has shown that, when properly tuned, classic GCN/SAGE/GAT architectures can match graph transformers on many node-classification benchmarks. We ask a complementary question: how much of this performance can be recovered by deterministic closed-form solvers, and what guarantees does this enable? We introduce a routed closed-form framework selected by adjusted homophily. For assortative graphs, we use SGC-style propagation followed by Ridge regression; for heterophilous graphs, we introduce LCF-Net, a layer-wise closed-form graph feature-refinement network whose per-layer Ridge solves are capped by a Gaussian kernel-Ridge head. Across 14 benchmarks, including ogbn-arxiv and ogbn-proteins, our closed-form predictors match or beat the best vanilla 2-layer GCN/SAGE/GAT on 9 of 9 measured datasets, tie tuned deep recipes within one standard deviation on 9 of 12 small benchmarks, and exceed the OGB-leaderboard plain GCN on both large graphs. The remaining heterophilous gap closely tracks the gain from vanilla 2-layer to deep SAGE, suggesting that the residual difference is primarily architectural. Because our predictors are explicit solutions of deterministic linear systems, modified graph inputs can be re-solved to obtain retrain-equivalent parameters. We formalize exact graph-object unlearning for label, feature, edge, node, and subgraph modifications, prove K-hop locality for Ridge components, and verify exactness across 109 configurations. On ogbn-arxiv, localized updates give $21$--$45\times$ speedups over full re-solving and roughly $10^{6}\times$ speedups over gradient retraining. Structural-inversion experiments further quantify the privacy floor of exact retraining and the additional leakage of approximate graph-unlearning methods.