Replication package for Flows and Rounds: benchmark and retrieval scripts for distributed neurodynamic optimization and federated learning

Abstract

This package contains the code and generated data behind the quantitative results of the survey "Flows and Rounds: A Survey of Distributed Neurodynamic Optimization and Federated Learning", submitted to Neurocomputing. It reproduces every number, table, and figure in Sections 2.3 and 8 of the article. No third-party, proprietary, or personal data is involved: all data is synthetic and generated at run time from fixed random seeds, so the package is self-contained and deterministic. Two scripts are included. The first, toy_benchmark.py, runs a controlled experiment on a synthetic distributed optimization problem with five nodes, twenty dimensions, and a closed-form optimum, averaged over ten seeds. It measures two things. Experiment one measures consensus drift as a function of the number of local steps per communication round, holding total local work fixed, and tests the prediction that drift grows with the dwell interval and vanishes when the agents hold identical objectives. Drift is found to be identically zero without gradient dissimilarity and to grow as E^0.88 and E^0.84 at the two heterogeneity levels tested. Experiment two measures whether an integral-enhanced flow, of the kind used in the zeroing neural network literature to reject persistent disturbance, also attenuates the Gaussian noise that a differential privacy mechanism deliberately injects. Both flows are driven by an identical noise stream and the noise response is isolated by differencing each noisy run against its own noise-free run. The integral term is found to remove steady-state bias almost entirely while leaving injected-noise energy unchanged, a ratio of 1.007. This second result contradicted the authors' expectation when the experiment was designed, and it is reported as measured. The second script, search_protocol.py, records a structured literature retrieval executed on 31 August 2026 and computes the deduplication and overlap counts reported in Section 2.3 of the article. It also emits a screening sheet listing all eighty-five retrieved records with their query provenance. The package is intended for readers who wish to verify the article's numerical claims, and for anyone extending the benchmark to other flows, noise models, or heterogeneity regimes. It requires only Python, NumPy, and Matplotlib.