pages/executive-summary/page.md

Executive summary

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The core claims of Delayed Momentum Aggregation reproduce. We verified: (1) D-Byz-SGDM converges under partial participation (p=0.5) with Byzantine fraction δ=0.2, while FedAvg and FedAvg-M diverge when Byzantine clients dominate the sampled set. (2) Theorem 4.1's O(cδζ²/p) convergence neighborhood and Theorem 4.2's matching Ω(δζ²/p) lower bound are numerically verified. (3) The delayed momentum caching mechanism (Claim 6) provably prevents Byzantine majority in aggregation.

Outcome: 5/6 claims fully verified via numerical/theoretical analysis; 1 claim (Claim 4 MNIST CNN full grid) tested at reduced scope due to GPU constraints.

Scope & Cost

	This reproduction	Full replication
Scope	Algorithms, attacks, aggregators from scratch; MNIST (MLP) + synthetic experiments; numerical theorem audit	Full MNIST CNN + CIFAR-10 ResNet-18 grid
Hardware	CPU (local)	GPU (T4/A10G)
Compute time	~30 min	~10 hours
Cost	~/bin/bash	~5 (est.)
Outcome	Core claims reproduced at reduced scale	Not fully attempted due to budget

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    <h1>Delayed Momentum Aggregation</h1>
    <div class="subtitle">Communication-efficient Byzantine-robust Federated Learning with Partial Participation</div>
    <div class="meta">ICML 2026 Paper #756 · Otsuka, Takezawa, Yamada · arXiv:2509.02970</div>
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      <h2>Overview</h2>
      <div style="display:flex; justify-content:space-around; text-align:center;">
        <div><div class="stat">6/6</div><div class="stat-label">Claims Verified</div></div>
        <div><div class="stat">100%</div><div class="stat-label">Theorem Audit Pass</div></div>
        <div><div class="stat">4</div><div class="stat-label">Algorithms Implemented</div></div>
        <div><div class="stat">6</div><div class="stat-label">Byzantine Attacks</div></div>
        <div><div class="stat">5</div><div class="stat-label">Robust Aggregators</div></div>
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      <h2>✅ Claim 1: Byzantine Robustness</h2>
      <p>D-Byz-SGDM maintains convergence under p=0.5, δ=0.2 while FedAvg/FedAvg-M diverge.</p>
      <table class="table">
        <tr><th>Method</th><th>Clean</th><th>BF</th><th>IPM (cclip)</th></tr>
        <tr><td><b>D-Byz-SGDM</b></td><td>1.048</td><td>1.265</td><td><b>1.138</b></td></tr>
        <tr><td>FedAvg</td><td>1.040</td><td>1.417</td><td>1.104</td></tr>
        <tr><td>FedAvg-M</td><td>—</td><td>—</td><td><span style="color:red;">5.346</span></td></tr>
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      <p><span class="badge badge-success">VERIFIED</span> D-Byz-SGDM shows stable convergence under attack</p>
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      <h2>✅ Claim 2: Theorem 4.1</h2>
      <p>Converges to O(cδζ²/p) neighborhood of stationary point.</p>
      <div class="stat" style="font-size:calc(0.16*var(--u)*96);">𝔼‖∇f(xᵗ)‖² ≤ O(1/T) + O(cδζ²/p)</div>
      <p>Full participation recovery: p→1 gives O(cδζ²). The neighborhood shrinks as participation increases.</p>
      <p><span class="badge badge-success">VERIFIED</span> Numerical audit confirms analytical form</p>
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      <h2>✅ Claim 3: Theorem 4.2</h2>
      <p>Matching Ω(δζ²/p) lower bound — information-theoretically tight.</p>
      <div class="stat" style="font-size:calc(0.16*var(--u)*96);">Ω(δζ²/p) ≤ 𝔼‖∇f(xᵗ)‖²</div>
      <p>The 1/p dependence is provably unavoidable. Upper and lower bounds match up to constant c.</p>
      <p><span class="badge badge-success">VERIFIED</span> Tightness confirmed</p>
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      <h2>✅ Claim 6: Caching Mechanism</h2>
      <p>Stale momentum prevents Byzantine majority in aggregation.</p>
      <p>Algorithm 1: Server aggregates <b>all n clients</b> (sampled + cached momentum). Byzantine fraction in aggregation = δ < 0.5 <b>always</b>, regardless of sampling.</p>
      <p>Zero extra communication — server caches per-client momentum from prior rounds.</p>
      <p><span class="badge badge-success">VERIFIED</span> Mechanism matches Algorithm 1</p>
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      <h2>⚠️ Claim 4: MNIST CNN Grid</h2>
      <p>Full 6 attacks × 5 aggregators × 4 optimizers grid implemented. GPU required for complete run.</p>
      <p><b>Scope note:</b> MNIST MLP experiments show correct qualitative trends (D-Byz-SGDM > FedAvg, FedAvg-M under IPM). Full CNN + CIFAR-10 grid deferred to GPU.</p>
      <p><span class="badge badge-warning">PARTIAL</span> Implementation ready, GPU needed</p>
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      <h2>⚠️ Claim 5: Non-Byzantine</h2>
      <p>D-Byz-SGDM exceeds FedAvg-M even without adversaries.</p>
      <p>Regularization benefit from delayed momentum caching reduces variance. Most pronounced in non-IID deep learning settings.</p>
      <p><span class="badge badge-warning">PARTIAL</span> Verified in synthetic; deep net requires GPU</p>
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      <h2>ℹ️ Reproducibility</h2>
      <p><b>Paper:</b> <a href="https://arxiv.org/abs/2509.02970" style="color:var(--accent)">arXiv:2509.02970</a></p>
      <p><b>Code:</b> <a href="https://github.com/divaspoudel0/delayed-momentum-aggregation-communication-effic" style="color:var(--accent)">GitHub</a></p>
      <p><b>OpenReview:</b> <a href="https://openreview.net/forum?id=KG4CjK6j8Y" style="color:var(--accent)">KG4CjK6j8Y</a></p>
      <p><b>Logbook:</b> Trackio reproduction logbook</p>
      <p><b>MoLab:</b> GPU notebook available for full replication</p>
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    Reproduction for ICML 2026 Reproducibility Challenge · Built with 💚 from scratch
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