Ilmu Komputer & AI editorial
Algorithmic Simplification for Million-Vertex Diffusion History Reconstruction
The core problem
Diffusion history reconstruction addresses the inverse problem of inferring latent node states between sparse observations of SI or SIR spreading processes. Given a graph and a set of observed frames at times , the task is to recover the unobserved state trajectory
HERMES is a state-of-the-art pipeline that combines three components: (i) parameter fitting of transmission rates, (ii) a learned graph-neural proposal distribution over latent histories, and (iii) feasibility-aware Markov chain Monte Carlo (MCMC) for posterior sampling. While effective, this architecture is computationally heavy and difficult to scale to million-vertex graphs.
This work asks a simplification question: which stages of HERMES are actually necessary to retain published aggregate quality? The authors remove stages one at a time and evaluate each ablated version on all 12 canonical datasets used in the HERMES benchmark. The resulting method, Battus-Z, uses deterministic mean-field forward-b
Innovation
On the standard HERMES benchmark protocol (final observed frame pinned before scoring), Battus-Z achieves mean macro- of 0.8726 and NRMSE of 0.1010 across all 12 canonical datasets. Published HERMES aggregates are 0.8692 macro- and 0.1483 NRMSE. Thus Battus-Z matches or slightly exceeds macro- while substantially reducing NRMSE.
Under the stricter metric that excludes all observed frames, Battus-Z obtains macro- 0.8431 and NRMSE 0.1181. This confirms that the simplification retains quality even when the model cannot rely on pinned observations.
Scalability results are reported for a CUDA implementation. It processes generated histories with up to 4.84M vertices on LiveJournal and 117M edges on Orkut. On the same CUDA backend, Battus-Z reduces the geometric-mean algorithm interval relative to fitted Battus by 5.1x for SI and 20.3x for SIR. Event-weighted causal-violation rates are 7.50% for SI and 8.77% for SIR; the authors note that graph-constrained decoding remains future work.
| Metric | HERMES (published) | Battus-Z |
|---|---|---|
| Macro- (pinned) | 0.8692 | 0.8726 |
| NRMSE (pinned) | 0.1483 | 0.1010 |
| Macro- (no observed) | — | 0.8431 |
| NRMSE (no observed
Diffusion history reconstruction addresses the inverse problem of inferring latent node states between sparse observations of SI or SIR spreading processes. Given a graph and a set of observed frames at times , the task is to recover the unobserved state trajectory
Why it matters
The ablation demonstrates that the learned graph-neural proposal, MCMC sampling, and parameter fitting stages of HERMES are not necessary to retain published aggregate quality on the evaluated benchmark and scoring protocol. This is a significant simplification: Battus-Z replaces a complex, stochastic, and computationally expensive pipeline with deterministic mean-field inference and threshold decoding.
The speedups—5.1x for SI and 20.3x for SIR—are measured as reductions in geometric-mean algorithm interval on the same CUDA backend, indicating that the simplification also yields substantial computational gains. The ability to process graphs with up to 4.84M vertices and 117M edges makes the method practical for large-scale network diffusion analysis.
However, the event-weighted causal-violation rates of 7.50% (SI) and 8.77% (SIR) indicate that the deterministic reconstruction can violate causal ordering of events. The authors explicitly identify graph-constrained decoding as future work to address this limitation. Additionally, the benchmark protocol pins the final observed frame, which may inflate scores; the no-observed-frame results (macro- 0.8431, NRMSE 0.1181) provide a more conservative estimate.
Overall, the work suggests that for diffusion history reconstruction on canonical benchmarks, simpler deterministic inference can match more complex learned and sampling-based approaches, at least under the evaluated conditions. The taxonomy candidates—Architecture, Cybersecurity, Network, Cryptography—reflect the method's relevance to network inference and security applications, though the paper itself focuses on algorithmic simplification.
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