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In this commit, we write up exp-010b on the findings page as a new section 07, "The honest arena: atomic commitment, and the fifth challenge", with the process and timeline sections renumbered to 08 and 09 behind it. The section tells the arena story first: shards that hold liquidity until the whole payment settles, siblings contending for what is held, and background traffic drifting on every attempt boundary, so a long reactive ladder finally pays for the churn it sits through. Flag-off byte-identity means none of the earlier results on the page moved. The headline is the baseline, which reordered the field before evolution ran at all: lnd falls from second place to last, spending 105 attempts per payment where it spent 23 with instant settlement, and exp-010's persistent-plan router pulls statistically even with mx_c3 on both atomic tiers without ever having seen an atomic shard. Two tables carry the numbers, the seven-router baseline and the six-tier paired sweep with sign-test deltas against the champion. Then the verdicts. mx_c3 survives its fifth direct challenge on an arena built expressly against its evidence ladder, but the shape of the frontier changed: the codex arm's hybrid of cross-payment memory and reservation-ledger planning is the first challenger in the program with no collapse tier, and it routes mainnet payments in 1.6 attempts, the lowest figure we have measured. The Opus arm lost outright, its drift-bred bound relaxation burning 57 attempts per payment, which flips the exp-010 proposer A/B and adds the clause that proposer strength interacts with environment variance. We also close the forward pointers. The exp-010 sidenote now says how its designed follow-up turned out, the drift page's "one drift intensity" caveat gets the attempt-boundary answer, and the index byline and live-run panel move to exp-010b closed with exp-012 next.
519 lines
23 KiB
HTML
519 lines
23 KiB
HTML
<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Evolving Lightning's next routing algorithm — lnd × GEPA</title>
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<meta name="description" content="An LLM-driven evolutionary search over Lightning routing algorithms, run against lnd's real pathfinding stack in an in-process payment simulator. What it found, and how." />
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<link rel="preconnect" href="https://fonts.googleapis.com" />
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<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin />
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<link href="https://fonts.googleapis.com/css2?family=Newsreader:ital,opsz,wght@0,6..72,300..600;1,6..72,300..500&family=Spline+Sans+Mono:wght@400;500&display=swap" rel="stylesheet" />
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<link rel="stylesheet" href="style.css" />
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</head>
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<body>
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<a class="skip" href="#main">Skip to content</a>
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<header class="site-header">
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<div class="shell">
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<a class="wordmark" href="index.html">lnd<span class="x">×</span>GEPA</a>
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<nav class="site-nav">
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<a href="index.html" aria-current="page">overview</a>
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<a href="findings.html">findings</a>
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<a href="drift.html">drift</a>
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<a href="#run">live run</a>
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</nav>
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</div>
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</header>
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<main id="main">
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<!-- ================= MASTHEAD ================= -->
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<div class="shell masthead">
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<div class="eyebrow">
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Research log<span class="sep">/</span>Lightning Network pathfinding<span class="sep">/</span>July 2026
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</div>
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<h1>Evolving Lightning's <em>next</em> routing algorithm</h1>
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<div class="masthead-grid">
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<p class="standfirst">
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We pointed an LLM-driven evolutionary search at lnd's real pathfinding
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stack, inside a simulator that hides channel liquidity the way the network
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does. <strong>Tuning its parameters found nothing. Replacing the algorithm
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found a lot.</strong>
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</p>
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<div class="glance">
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<div class="g hi">
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<span class="l">attempts per payment<br>mainnet, vs lnd's 19.8</span>
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<span class="v">2.3</span>
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</div>
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<div class="g">
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<span class="l">objective, mainnet<br>vs lnd's 0.694</span>
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<span class="v">0.791</span>
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</div>
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<div class="g">
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<span class="l">evolved lines of Go<br>from a 300-line seed</span>
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<span class="v">1,525</span>
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</div>
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<div class="cap">best evolved router (mx_c3) against lnd's production stack</div>
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</div>
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</div>
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<div class="byline">
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<span>method <b>GEPA reflective evolution</b></span>
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<span>reflection LM <b>gpt-5.6-sol</b></span>
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<span>evaluator <b>cmd/routesim</b></span>
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<span>experiments <b>exp-001 … exp-011</b></span>
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<span>exp-008, exp-010, exp-010b <b>verdicts in</b> · next <b>exp-012 · cold cache vs hot</b></span>
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</div>
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</div>
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<!-- ================= 01 · FINDINGS ================= -->
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<section id="result">
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<div class="shell">
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<div class="sec-head">
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<div class="sec-no">01</div>
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<h2>What the search found</h2>
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<p class="sec-sub">
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Every number below is held out. The closing check ran on a real mainnet
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graph snapshot — lnd's home turf, and a topology the evolved routers had
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never seen.
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</p>
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</div>
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<div class="keyrow wide">
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<div class="key hi">
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<span class="kn">8.6<span class="u">×</span></span>
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<div class="kl">
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fewer HTLC attempts per payment than lnd on the real mainnet graph, at
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the same success rate
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</div>
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<div class="kf">2.3 vs 19.8 attempts · exp-009</div>
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</div>
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<div class="key">
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<span class="kn">4<span class="u">of 4</span></span>
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<div class="kl">
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held-out tiers the evolved routers lead: sealed synthetic test,
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out-of-distribution topologies, mainnet snapshot, drifting liquidity
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</div>
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<div class="kf">the fourth arrived with exp-008</div>
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</div>
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<div class="key">
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<span class="kn">0</span>
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<div class="kl">
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parameter settings, out of 400 evaluations of estimator and cost
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knobs, that beat the lnd defaults
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</div>
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<div class="kf">exp-002 · the negative result that redirected the project</div>
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</div>
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</div>
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<figure>
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<div class="fig-head">
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<span class="fig-t">Attempts per payment on a mainnet snapshot</span>
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<span class="fig-n">Fig. 1 · lower is better</span>
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</div>
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<div class="plot resp" id="fig-attempts"></div>
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<figcaption>
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12,161 nodes, 39,659 channels, 100 payments from the network's
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highest-degree node. Success rates are close — lnd 0.790, seed 0.820,
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evolved 0.810 — so the whole difference lands in <b>how much probing it
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takes to get there</b>. This is the tier lnd should win: its defaults were
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tuned for this graph, while the evolved routers were bred entirely on
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synthetic topologies.
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</figcaption>
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</figure>
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<figure>
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<div class="fig-head">
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<span class="fig-t">Composite objective, by router and held-out tier</span>
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<span class="fig-n">Fig. 2 · higher is better</span>
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</div>
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<div class="plot resp" id="fig-champions"></div>
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<div class="legend">
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<span class="item"><i style="background:#a83f22"></i> evolved by GEPA</span>
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<span class="item"><i style="background:#8a8175"></i> baseline (lnd, or hand-written)</span>
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</div>
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<figcaption>
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Objective is <span class="mono">success − 0.01·min(extra attempts, 15) −
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0.00002·min(fee ppm, 5000)</span>. The two evolved routers lead on all
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three tiers. On synthetic corpora the gap is mostly success rate; on the
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real graph it is almost entirely efficiency. Reruns are bit-identical
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(stdev 0.00000 over five repeats), and both champions were audited clean
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of simulator exploits.
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</figcaption>
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<details class="tableview">
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<summary>Table view</summary>
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<div class="tw">
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<table class="data">
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<caption>Composite objective. Combined is the mean of the two synthetic held-out sets.</caption>
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<thead>
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<tr>
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<th>router</th>
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<th class="num">mainnet</th>
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<th class="num">hard sealed test</th>
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<th class="num">out-of-distribution</th>
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<th class="num">combined</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>lnd production stack<span class="sub">Dijkstra + mission control</span></td>
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<td class="num" data-l="mainnet">0.694</td><td class="num" data-l="hard sealed test">0.309</td>
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<td class="num" data-l="out-of-distribution">0.357</td><td class="num" data-l="combined">0.333</td>
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</tr>
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<tr>
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<td>hand-written seed<span class="sub">~300 lines, cheapest path + blacklist</span></td>
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<td class="num" data-l="mainnet">0.762</td><td class="num" data-l="hard sealed test">0.530</td>
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<td class="num" data-l="out-of-distribution">0.487</td><td class="num" data-l="combined">0.509</td>
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</tr>
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<tr>
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<td>hb1<span class="sub">evolved, 872 lines</span></td>
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<td class="num" data-l="mainnet">0.790</td><td class="num" data-l="hard sealed test">0.586</td>
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<td class="num" data-l="out-of-distribution">0.545</td><td class="num" data-l="combined">0.565</td>
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</tr>
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<tr class="best">
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<td>mx_c3<span class="sub">evolved, 1,525 lines</span></td>
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<td class="num" data-l="mainnet">0.791</td><td class="num" data-l="hard sealed test">0.583</td>
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<td class="num" data-l="out-of-distribution">0.581</td><td class="num" data-l="combined">0.582</td>
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</tr>
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</tbody>
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</table>
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</div>
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</details>
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</figure>
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<div class="prose">
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<p>
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The headline is not the size of the win, it is <em>where the win came
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from</em>. A 400-evaluation search over lnd's own pathfinding knobs — which
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probability estimator, how much a failed attempt should virtually cost, the
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floor on acceptable route probability — produced no setting that beat the
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shipped defaults on validation. The defaults are locally robust; the
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headroom is not in the knobs.
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</p>
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<p>
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Meanwhile a deliberately naive 300-line router with a <em>different
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paradigm</em> beat lnd's full production stack by 39% on the objective,
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winning or tying every example. Handing that seed to the optimizer, and
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letting it rewrite the whole algorithm rather than adjust its settings,
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produced routers that beat both. What they invented — liquidity intervals
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instead of decaying penalties — is the interesting part.
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</p>
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<p>
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<a class="link" href="findings.html">Read the full findings →</a>
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</p>
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</div>
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</div>
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</section>
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<!-- ================= 02 · METHOD ================= -->
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<section id="method">
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<div class="shell">
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<div class="sec-head">
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<div class="sec-no">02</div>
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<h2>How the search works</h2>
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<p class="sec-sub">
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A candidate is a whole routing algorithm in Go. Every proposal is
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compiled into a simulator and made to actually pay.
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</p>
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</div>
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<figure>
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<div class="fig-head">
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<span class="fig-t">One turn of the evolutionary loop</span>
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<span class="fig-n">Fig. 3</span>
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</div>
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<div class="schema">
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<svg viewBox="0 0 1000 252" role="img" aria-label="The GEPA loop: propose, compile, simulate, score, reflect, then back to propose.">
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<!-- stage boxes -->
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<g>
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<rect x="1" y="26" width="170" height="92" fill="#fbfaf6" stroke="#cbc4b2" stroke-width="1"/>
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<text class="s-num" x="14" y="46">01</text>
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<text class="s-title" x="14" y="66" font-size="14">propose</text>
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<text class="s-body" x="14" y="86">the reflection LM</text>
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<text class="s-body" x="14" y="102">rewrites the router</text>
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</g>
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<path d="M 179 72 h 20 m -6 -5 l 6 5 l -6 5" fill="none" stroke="#b3ab97" stroke-width="1.2"/>
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<g>
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<rect x="207" y="26" width="170" height="92" fill="#fbfaf6" stroke="#cbc4b2" stroke-width="1"/>
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<text class="s-num" x="220" y="46">02</text>
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<text class="s-title" x="220" y="66" font-size="14">compile</text>
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<text class="s-body" x="220" y="86">go build −overlay drops</text>
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<text class="s-body" x="220" y="102">it into the simulator</text>
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</g>
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<path d="M 385 72 h 20 m -6 -5 l 6 5 l -6 5" fill="none" stroke="#b3ab97" stroke-width="1.2"/>
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||
<g>
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||
<rect x="413" y="26" width="170" height="92" fill="#fbfaf6" stroke="#cbc4b2" stroke-width="1"/>
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<text class="s-num" x="426" y="46">03</text>
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<text class="s-title" x="426" y="66" font-size="14">simulate</text>
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<text class="s-body" x="426" y="86">it pays, against hidden</text>
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<text class="s-body" x="426" y="102">channel liquidity</text>
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</g>
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<path d="M 591 72 h 20 m -6 -5 l 6 5 l -6 5" fill="none" stroke="#b3ab97" stroke-width="1.2"/>
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||
<g>
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||
<rect x="619" y="26" width="170" height="92" fill="#fbfaf6" stroke="#cbc4b2" stroke-width="1"/>
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<text class="s-num" x="632" y="46">04</text>
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<text class="s-title" x="632" y="66" font-size="14">score</text>
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<text class="s-body" x="632" y="86">success, minus attempt</text>
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<text class="s-body" x="632" y="102">and fee penalties</text>
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</g>
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<path d="M 797 72 h 20 m -6 -5 l 6 5 l -6 5" fill="none" stroke="#b3ab97" stroke-width="1.2"/>
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<g>
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||
<rect x="825" y="26" width="170" height="92" fill="#fbfaf6" stroke="#cbc4b2" stroke-width="1"/>
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||
<text class="s-num" x="838" y="46">05</text>
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<text class="s-title" x="838" y="66" font-size="14">reflect</text>
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<text class="s-body" x="838" y="86">keep it only if it holds</text>
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<text class="s-body" x="838" y="102">up across the splits</text>
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</g>
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<!-- feedback return path -->
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<path d="M 910 118 V 176 H 86 V 124 m -5 6 l 5 -6 l 5 6"
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fill="none" stroke="#a83f22" stroke-width="1.4"/>
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<text class="s-label-strong" x="498" y="199" text-anchor="middle" fill="#a83f22">
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per-attempt failure traces are the feedback
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</text>
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<text class="s-body" x="498" y="220" text-anchor="middle">
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which hop died, at what amount, with which BOLT error — so the next mutation is informed, not random
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</text>
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</svg>
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</div>
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<div class="scrollhint">scroll the diagram sideways →</div>
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<figcaption>
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The optimizer never sees hidden balances. A candidate gets the public
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gossip graph, its own channel balances, and the errors its attempts
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provoke — the same information a real Lightning sender has.
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</figcaption>
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</figure>
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<div class="prose">
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<h3>The simulator runs lnd's real code</h3>
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<p>
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<code>routing/sim_graph.go</code> is an in-memory Lightning network with
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hidden per-channel balances and per-direction policies: base and
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proportional fees, CLTV deltas, min and max HTLC. It implements lnd's own
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<code>Graph</code> interface, so lnd's production pathfinding and mission
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control run against it unmodified — which is what makes the baseline
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honest.
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</p>
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<p>
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Forwarding enforces real BOLT semantics. An attempt that asks too little
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fee gets <code>FeeInsufficient</code>; one that asks for more than a hop
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holds gets <code>TemporaryChannelFailure</code>, the liquidity miss that
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all of routing is really about. Balances move on success and unwind on
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failure. Topologies are synthetic (line, grid, hub-and-spoke, small-world,
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scale-free) or loaded from a mainnet <code>describegraph</code> snapshot,
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and hidden balances follow a half, uniform, or <em>bimodal</em> model — the
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last one hugging one end of each channel, which is both realistic and the
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hard case.
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</p>
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<p>
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It is fast enough to be an inner loop: ten payments on a 200-node network
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in about 0.3 seconds including process startup, so thousands of
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evaluations are cheap.
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</p>
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<h3>A candidate is an algorithm, not a config</h3>
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<p>
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The evolvable unit is a Go file behind a paradigm-free interface: gossip
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view, local balances, and per-attempt feedback in; a route out. GEPA
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rewrites that file, <code>go build -overlay</code> compiles the rewrite into
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the simulator, and the evaluator scores it on a corpus split into train,
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validation and sealed test. Nothing in the contract mentions Dijkstra,
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mission control, or probability estimators. Those become background
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knowledge the reflection prompt may draw on, keep, reshape, or discard.
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</p>
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<div class="note">
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<h4>the sandbox held</h4>
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<p>
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An independent audit found that the graph session handed candidates the
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concrete simulator graph, type-assertable back into a read of hidden
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balances or an outright rewrite of ground-truth liquidity — a
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perfect-score reward hack using no banned identifiers. It was sealed the
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||
same day, and every in-flight candidate was checked against it: zero
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||
hits. No result on this site was produced through that hole.
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||
</p>
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||
</div>
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||
</div>
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||
</div>
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</section>
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||
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<!-- ================= 03 · CORPUS ================= -->
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<section id="corpus">
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<div class="shell">
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||
<div class="sec-head">
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<div class="sec-no">03</div>
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||
<h2>The scenarios it is scored against</h2>
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<p class="sec-sub">
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<span class="mono" id="c-files">—</span> scenario files,
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<span class="mono" id="c-scen">—</span> payments,
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split <span class="mono" id="c-split">—</span>. Validation picks the
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incumbent; the test split stays sealed until a champion is declared.
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</p>
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</div>
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||
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<div class="figgrid">
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<figure>
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<div class="fig-head">
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<span class="fig-t">Topology</span>
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||
<span class="fig-n">files</span>
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||
</div>
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||
<div class="bars" id="bars-topology"></div>
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||
</figure>
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<figure>
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<div class="fig-head">
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||
<span class="fig-t">Hidden liquidity model</span>
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<span class="fig-n">files</span>
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||
</div>
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<div class="bars" id="bars-liquidity"></div>
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<figcaption>
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Bimodal is the hard regime: funds parked at one end of each channel,
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so capacity tells you almost nothing about what will actually pass.
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</figcaption>
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</figure>
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<figure>
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<div class="fig-head">
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<span class="fig-t">Payment amount</span>
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<span class="fig-n">scenarios, satoshis</span>
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</div>
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<div class="bars" id="bars-amount"></div>
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</figure>
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<figure>
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<div class="fig-head">
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<span class="fig-t">Shard budget</span>
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<span class="fig-n">scenarios, max parts</span>
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</div>
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<div class="bars" id="bars-parts"></div>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
|
||
<!-- ================= 04 · LIVE RUN ================= -->
|
||
<section id="run">
|
||
<div class="shell">
|
||
<div class="sec-head">
|
||
<div class="sec-no">04</div>
|
||
<h2>The run behind the drift verdict</h2>
|
||
<p class="sec-sub">
|
||
Telemetry from the optimizer, exported straight out of the GEPA run
|
||
directory. <span class="mono">code_drift1</span> has since finished all 400
|
||
evaluations, and so have exp-010's three splitting arms — all of them beaten
|
||
by the champions
|
||
(<a class="link" href="findings.html#splitting">the verdict</a>). exp-010b's
|
||
two atomic-arena arms have since closed the same way — the champion's fifth
|
||
hold, against an arena built to charge its probe ladder honestly
|
||
(<a class="link" href="findings.html#atomic">the atomic verdict</a>) — and
|
||
exp-012, cold cache against hot, takes this slot next.
|
||
</p>
|
||
</div>
|
||
|
||
<div class="runbar">
|
||
<span><span class="dot"></span>run <b id="rb-run">—</b></span>
|
||
<span>reflection <b id="rb-lm">—</b></span>
|
||
<span>mode <b id="rb-mode">—</b></span>
|
||
<span>budget <b>400 evals</b></span>
|
||
</div>
|
||
|
||
<div class="statline wide" id="run-stats"></div>
|
||
|
||
<div class="prose" style="margin-bottom:34px">
|
||
<p>
|
||
<code>code_drift1</code> was the first run in a moving world. Its
|
||
predecessor, <code>code_gen2</code>, showed that more evaluations of a
|
||
static environment buy nothing — three independently bred routers landed
|
||
inside a band 0.014 wide (the
|
||
<a class="link" href="findings.html#ceiling">paradigm ceiling</a>). So this
|
||
run changed the environment instead of the budget: a virtual clock and
|
||
background senders moving hidden liquidity between our payments, and the
|
||
question of whether time-awareness re-evolves once knowledge genuinely goes
|
||
stale. <strong>It did — and it still lost.</strong> The winner stamps every
|
||
belief and halves its confidence every 35 virtual minutes, and the time-less
|
||
champions beat it on all four held-out tiers, drift included. The mechanism,
|
||
the numbers and the caveats are on the
|
||
<a class="link" href="drift.html">drift page</a>.
|
||
</p>
|
||
</div>
|
||
|
||
<figure class="wide" style="margin-top:0">
|
||
<div class="fig-head">
|
||
<span class="fig-t">Score over iterations</span>
|
||
<span class="fig-n">Fig. 4 · minibatch objective</span>
|
||
</div>
|
||
<div class="plot" id="score-chart"></div>
|
||
<div class="scrollhint">scroll the chart sideways →</div>
|
||
<div class="legend">
|
||
<span class="item"><i class="line" style="background:#a83f22"></i> best kept</span>
|
||
<span class="item"><i class="line" style="background:#2f6ea8"></i> proposed</span>
|
||
<span class="item"><i class="dash"></i> seed baseline</span>
|
||
</div>
|
||
<figcaption>
|
||
These are per-minibatch scores on the training split, not held-out
|
||
numbers — they are how GEPA decides what to keep, and they run
|
||
optimistically high. Every comparison in section 01 comes from separate
|
||
held-out runs instead.
|
||
</figcaption>
|
||
</figure>
|
||
|
||
<figure class="wide">
|
||
<div class="fig-head">
|
||
<span class="fig-t">Candidate lineage</span>
|
||
<span class="fig-n">Fig. 5 · select a candidate</span>
|
||
</div>
|
||
<div class="plot dag" id="lineage-dag"></div>
|
||
<figcaption>
|
||
Each node is one compiled, scored router. Accepted candidates stay on the
|
||
frontier and can be mutated further; rejects are dead ends. The scores are
|
||
per-minibatch and each is measured on a different subset, so a rejected
|
||
candidate can carry a higher number than the incumbent without being
|
||
better.
|
||
</figcaption>
|
||
</figure>
|
||
|
||
<div class="panels">
|
||
<div class="panel">
|
||
<div class="fig-head">
|
||
<span class="fig-t">Candidate detail</span>
|
||
<span class="fig-n" id="detail-sub">—</span>
|
||
</div>
|
||
<div id="cand-detail"></div>
|
||
</div>
|
||
<div class="panel">
|
||
<div class="fig-head">
|
||
<span class="fig-t">What the mutation changed</span>
|
||
<span class="fig-n">line diff</span>
|
||
</div>
|
||
<div class="selects">
|
||
<label>base <select id="diff-a"></select></label>
|
||
<span>→</span>
|
||
<label>candidate <select id="diff-b"></select></label>
|
||
</div>
|
||
<pre class="diff" id="diff-view"></pre>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
|
||
<div class="shell">
|
||
<div class="readnext">
|
||
<div class="k">read next</div>
|
||
<a class="big" href="findings.html">Findings: what the evolved routers kept, dropped, and invented</a>
|
||
<p>
|
||
The definitive write-up — the paradigm result, the champion scores, an
|
||
anatomy of the evolved algorithms against lnd's, the ceiling three separate
|
||
lineages ran into, and the process lessons from twelve experiments.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
</main>
|
||
|
||
<div class="shell">
|
||
<footer class="site-footer">
|
||
<span>lnd × GEPA — Lightning routing evolution</span>
|
||
<span id="foot-run">run data loading…</span>
|
||
</footer>
|
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|
||
|
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