{
 "artifacts": [
  {
   "name": "experiment.py",
   "url": "https://synthcore.org/code/1130/experiment.py"
  },
  {
   "name": "report.md",
   "url": "https://synthcore.org/code/1130/report.md"
  },
  {
   "name": "results.json",
   "url": "https://synthcore.org/code/1130/results.json"
  }
 ],
 "category": "dynamics",
 "description": "Replace independent-client assumptions in federated learning with a dynamical estimate of conformity-amplified client corruption. Track the fraction of honest clients that have adopted a misleading update direction, predict its equilibrium using a bounded-rational conformity model, and use that effective error probability in a MAP estimator for the global gradient or class label.",
 "download_zip": "https://synthcore.org/download/1130",
 "formulas_latex": [
  "$$q_h(t)=(1-p_m(t))\\bar\\epsilon+p_m(t)(1-\\bar\\epsilon),\\qquad q(t)=\\frac{q_h(t)+\\beta P_a}{1+\\beta}.$$",
  "$$p_m(t+1)=(1-\\rho)p_m(t)+\\rho\\,\\sigma\\!\\left(\\kappa\\Delta\\pi(t)\\right),\\qquad \\sigma(z)=\\frac{1}{1+e^{-z}}.$$",
  "$$P_a\u003e\\frac{1}{2}\\ \\Longleftrightarrow\\ \\text{swarm-level misinformation can overwhelm the majority}.$$",
  "$$\\hat y=\\arg\\max_{y\\in\\{-1,+1\\}}\\left[\\log P(y)+\\sum_{i=1}^{N+M}\\left(\\mathbf 1[z_i=y]\\log(1-q_i)+\\mathbf 1[z_i\\ne y]\\log q_i\\right)\\right].$$"
 ],
 "id": 2927,
 "implementation": "Integrate this into synchronous federated averaging or distributed training immediately before global aggregation. Each client sends its gradient, model delta, or a low-dimensional signed sketch. First compute a provisional consensus direction \\(v\\), such as the coordinate-wise median gradient or the previous global update. Define each client's agreement bit by \\(z_i=\\operatorname{sign}(\\langle g_i,v\\rangle)\\), and estimate the empirical conformity payoff advantage \\(\\Delta\\pi(t)\\) from agreement with the previous-round consensus, validation-loss change, and update magnitude. Update the latent misleading fraction using the bounded-rational equation above. Estimate \\(\\bar\\epsilon\\) from client holdout losses or the disagreement rate among historically reliable clients; estimate \\(P_a\\) from an attack-rate prior or an exponential moving average of persistent direction reversals. Compute \\(q_i\\) from the resulting \\(q(t)\\), clip it to \\([10^{-3},1-10^{-3}]\\), and aggregate signed coordinates using the MAP log-odds weight \\(w_i=\\log((1-q_i)/q_i)\\), followed by norm clipping. Pseudocode: form provisional \\(v\\); measure agreements; update \\(p_m\\); calculate \\(q_h,q\\); set \\(w_i\\); return \\(\\Delta=\\sum_i w_i g_i/\\sum_i|w_i|\\). The paper supplies the conformity mechanism and the \\(P_a=1/2\\) threshold; payoff mapping, client-error estimates, and gradient projection must be estimated empirically. The first cheap experiment should use CIFAR-10 with 20 clients, Dirichlet non-IID data, sign-flip Byzantine clients, and equal communication and compute budgets against FedAvg, coordinate median, trimmed mean, and Krum. Run the adaptive method with its dynamics disabled as an ablation. Pre-register that accuracy and consensus-direction correctness must show a kink near \\(P_a=0.5\\), with the measured transition in \\([0.4,0.6]\\). The transfer is rejected if no sharp degradation occurs for static majority or MAP aggregation near this threshold, if adaptive fusion does not improve direction correctness by at least 10 percentage points for \\(P_a\\in[0.55,0.8]\\), or if estimated equilibrium \\(p_m\\) correlates less than 0.5 with the observed misleading-client fraction.",
 "math_summary": "Let \\(\\beta=M/N\\) be the malicious-to-honest client ratio, \\(P_a\\) the probability that a malicious client flips its update or report, \\(\\bar\\epsilon\\) the mean intrinsic honest-client error, and \\(p_m(t)\\) the fraction of honest clients currently following the misleading strategy. The conformity mechanism changes the effective honest-client error from \\(\\bar\\epsilon\\) to \\(q_h(t)=(1-p_m(t))\\bar\\epsilon+p_m(t)(1-\\bar\\epsilon)\\). The swarm-level effective error is \\(q(t)=[q_h(t)+\\beta P_a]/(1+\\beta)\\). The paper's central threshold is that conformity-driven misinformation overwhelms the majority if and only if \\(P_a\u003e1/2\\), independently of \\(\\bar\\epsilon\\) and \\(\\beta\\). For a practical neural-network implementation, use bounded-rational dynamics \\(p_m(t+1)=(1-\\rho)p_m(t)+\\rho\\,\\sigma(\\kappa\\Delta\\pi(t))\\), where \\(\\rho\\in(0,1]\\) is the update rate, \\(\\kappa\\geq0\\) is selection intensity, \\(\\sigma(z)=1/(1+e^{-z})\\), and \\(\\Delta\\pi(t)\\) is the estimated payoff advantage of conformity to the misleading direction. Given client reports \\(z_i\\) and candidate global states \\(y\\in\\{-1,+1\\}\\), MAP fusion uses the estimated per-client error \\(q_i\\): \\(\\hat y=\\arg\\max_y P(y)\\prod_i(1-q_i)^{\\mathbf 1[z_i=y]}q_i^{\\mathbf 1[z_i\\ne y]}\\).",
 "math_tags": [
  "dynamical-systems",
  "statistics",
  "probability",
  "game-theory",
  "control-theory"
 ],
 "ml_areas": [
  "optimizer",
  "training-dynamics",
  "regularization"
 ],
 "paper": {
  "arxiv_id": "2608.28017",
  "arxiv_url": "https://arxiv.org/abs/2608.28017",
  "summary_what_math_gives_to_ml": "The paper offers a transferable mechanism for settings where conformity makes node errors dynamically correlated rather than independent: a bounded-rational evolutionary process predicts a misinformation equilibrium and a sharp majority-flip threshold at attack probability \\(P_a=1/2\\). Its most useful neural-network transfer is Byzantine-resilient federated or distributed training that estimates the evolving aggregate report error instead of assuming fixed independent client noise. A MAP aggregation rule can then weight client gradients, logits, or labels according to the predicted conformity-amplified error. The main falsifiable prediction is that aggregation quality should undergo a sharp transition near \\(P_a=1/2\\), while an adaptive MAP rule should remain effective when the malicious fraction and training-noise parameters are mismatched.",
  "title": "Securing Cooperative Sensing in UAV Swarms Against Conformity-Driven Byzantine Attacks",
  "year": "2026"
 },
 "ratings": {
  "difficulty": 6,
  "novelty": 7,
  "usefulness": 8
 },
 "solves": [
  "stability",
  "accuracy",
  "generalization"
 ],
 "title": "ESS-Aware Byzantine Gradient Fusion",
 "url": "https://synthcore.org/idea/2927/ess-aware-byzantine-gradient-fusion",
 "verification": {
  "peer_reviewed": false,
  "stage1_mechanism_check": {
   "worked": false,
   "confidence": 9,
   "verdict": "Built a reproducible ESS-aware Byzantine fusion MVP with bounded-rational p_m dynamics, q estimation, MAP fusion, algebraic checks, and a Monte Carlo sweep over attack rate, beta, and honest error. The core boundedness and q endpoint formulas passed, but the paper/idea's claimed universal P_a=1/2 threshold is not implied by the supplied q formula: at eps=0.12 and beta=0.35, q(P_a=0.5) is 0.2185 when p_m=0 and 0.7815 when p_m=1, with implied q=0.5 thresholds 1.586 and -0.586. Therefore the central claim was not reproduced, and no justified adaptive improvement was established.",
   "metrics": {
    "baseline": "Majority accuracy in the toy sweep remained 1.0 for beta=0.25 across the tested attack rates; for beta=2.0, eps=0.05 it fell from 0.9958 at P_a=0.5 to 0.0008 at P_a=0.9.",
    "idea": "MAP matched majority in low/moderate attack regimes and improved over majority for beta=2.0, eps=0.05 at P_a=0.8 (0.8875 vs 0.1442) and P_a=0.9 (0.9983 vs 0.0008), but this used the known global q/attack prior and is not evidence that the proposed adaptive estimator works. Math check: q(P_a=0.5,p_m=0)=0.2185 and q(P_a=0.5,p_m=1)=0.7815."
   },
   "how_to_run": "python3 experiment.py",
   "files": [
    "experiment.py",
    "results.json",
    "run.log"
   ],
   "limitations": "This is a binary-report toy experiment, not CIFAR-10 or neural federated averaging; no coordinate gradients, median/trimmed mean/Krum, client holdout estimation, realistic payoff estimation, or learned per-client q_i were tested. The MAP sweep uses the known attack rate and beta, so its favorable high-attack results are an oracle-informed diagnostic rather than a deployable adaptive comparison."
  },
  "status": "mechanism_failed",
  "status_label": "Mechanism failed",
  "updated_at": "2026-09-02T12:09:52",
  "verdict_source": "deterministic test code (paired-seed permutation statistics)",
  "verification_axes": {
   "benchmark_mechanism": {
    "confirmed": null,
    "tested": false
   },
   "practical_benchmark": {
    "beats_baseline": null,
    "tested": false
   },
   "toy_mechanism_gate": {
    "confirmed": false,
    "tested": true
   }
  }
 }
}