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

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.本套件包含提交至《Neurocomputing》的综述论文《Flows and Rounds：分布式神经动态优化与联邦学习综述》（Flows and Rounds: A Survey of Distributed Neurodynamic Optimization and Federated Learning）的定量结果所依托的代码与生成数据集。本套件可复现该论文第2.3节与第8节中的全部数值、表格与图像。本套件未涉及任何第三方专有数据或个人隐私数据：所有数据均为合成数据，通过固定随机种子在运行时生成，因此该套件无需依赖外部资源且运行结果具有确定性。 套件包含两个脚本文件。第一个脚本为`toy_benchmark.py`，针对含5个节点、20维且存在闭式最优解的合成分布式优化问题开展受控实验，实验结果基于10个随机种子取平均。该脚本开展两项测试： 测试1：在总本地计算量固定的前提下，测量共识漂移（consensus drift）随每轮通信的本地迭代步数的变化关系，并验证如下假说：共识漂移随驻留间隔（dwell interval）增长，且当智能体目标完全一致时漂移消失。实验结果显示，无梯度差异时共识漂移严格为零；在本次测试的两种异质性水平下，漂移分别随$E^{0.88}$与$E^{0.84}$的规律增长。 测试2：验证积分增强流（integral-enhanced flow，该类流曾在零化神经网络（zeroing neural network）领域用于抑制持续扰动）是否同样可以削弱差分隐私（differential privacy）机制刻意注入的高斯噪声。两种流均使用同一噪声流驱动，通过将带噪运行结果与其对应的无噪运行结果做差分，可分离出噪声响应。实验结果表明，积分项可几乎完全消除稳态偏差，同时保持注入噪声的能量基本不变，二者比值为1.007。该结果与实验设计时作者的预期相悖，因此如实记录了实测结果。 第二个脚本为`search_protocol.py`，记录了2026年8月31日执行的结构化文献检索任务，并计算了论文第2.3节中提及的去重与重叠计数。该脚本还会生成一份筛查表，列出全部85条检索到的文献记录及其查询溯源信息。 本套件面向两类用户：一是希望验证论文数值结论的读者，二是希望将该基准测试拓展至其他流模型、噪声模型或异质性场景的研究者。本套件仅依赖Python、NumPy与Matplotlib三个库。