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b782ada
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1 Parent(s): 5db5468

Glyph-dither hero (Intuition-style) + full 67-model roster; data + reproducibility callouts

Browse files
Files changed (3) hide show
  1. .gitattributes +1 -0
  2. bloom.png +3 -0
  3. index.html +94 -18
.gitattributes CHANGED
@@ -33,3 +33,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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  *.zip filter=lfs diff=lfs merge=lfs -text
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  *.zst filter=lfs diff=lfs merge=lfs -text
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  *tfevents* filter=lfs diff=lfs merge=lfs -text
 
 
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  *.zip filter=lfs diff=lfs merge=lfs -text
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  *.zst filter=lfs diff=lfs merge=lfs -text
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  *tfevents* filter=lfs diff=lfs merge=lfs -text
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+ bloom.png filter=lfs diff=lfs merge=lfs -text
bloom.png ADDED

Git LFS Details

  • SHA256: 8b04002fc87958617f31de1c7917efb616505f302448875d9c89ce8ecf54d3cc
  • Pointer size: 131 Bytes
  • Size of remote file: 386 kB
index.html CHANGED
@@ -3,7 +3,7 @@
3
  <head>
4
  <meta charset="utf-8">
5
  <meta name="viewport" content="width=device-width, initial-scale=1">
6
- <script>/* match the user's OS theme before first paint; the toggle stays authoritative once clicked */try{if(matchMedia('(prefers-color-scheme:light)').matches){document.documentElement.setAttribute('data-theme','light');}}catch(e){}</script>
7
  <title>When Does Combining Language Models Help? — the co-failure ceiling</title>
8
  <meta name="description" content="Interactive companion to the paper “When Does Combining Language Models Help?” (Orchestration Is Allocation). The deployment-relevant object in multi-model LLM orchestration is β = P(all models wrong); a one-sample certificate bounds every router, vote, and cascade.">
9
  <meta property="og:title" content="When Does Combining Language Models Help?">
@@ -322,6 +322,20 @@ footer a:hover{border-bottom-color:var(--text)}
322
  input[type=range]::-webkit-slider-thumb{width:22px;height:22px;margin-top:-9px}
323
  input[type=range]::-moz-range-thumb{width:22px;height:22px}
324
  }
 
 
 
 
 
 
 
 
 
 
 
 
 
 
325
  @media(prefers-reduced-motion:reduce){*{animation:none!important;transition:none!important;scroll-behavior:auto}}
326
  </style>
327
  </head>
@@ -337,23 +351,19 @@ footer a:hover{border-bottom-color:var(--text)}
337
  </span>
338
  </nav>
339
 
340
- <header class="wrap">
341
- <div class="eyebrow">Orchestration Is Allocation · interactive companion · Josef Chen / KAIKAKU</div>
342
- <h1>The lever for orchestration is <em>failure-mode dispersion</em>, not model count.</h1>
343
- <p class="lede">Adding models does not raise the ceiling. The binding rate is β — how often <em>every</em> model is wrong at once — and it caps every router, vote, and cascade. One query sample certifies it.</p>
344
- <div class="herostat">
345
- <div class="item lead">
346
- <span class="big beta num" id="heroBeta" data-ticker="0.052">0.052</span>
347
- <span class="hero-law num" aria-label="accuracy is at most one minus beta"><span class="gb">β</span> · MATH-500 &#160;&#8594;&#160; <span class="hero-law-rule">accuracy ≤ 1 − <span class="gb">β</span></span></span>
348
- <span class="lbl">co-failure point estimate on the primary run. Whatever the policy, accuracy cannot clear <span class="num">1 − <span class="gb">β</span>&#770; = <span id="heroCeil">0.948</span></span> — the certified bound is wider.</span>
349
- </div>
350
- <div class="hero-aside">
351
- <span class="hero-aside-k num">format flip</span>
352
- <span class="hero-aside-v num"><span class="gb">β</span> 0 <span class="hero-aside-arr" aria-hidden="true">&#8594;</span> <span class="beta">0.127</span></span>
353
- <span class="hero-aside-l">strip the options off the same GPQA questions and a tail opens where there was none — <a href="#flip">the flip ↓</a></span>
354
  </div>
 
355
  </div>
356
- <div class="herospec num">67 frontier models · 21 providers · 4 structurally disjoint domains · temperature 0</div>
357
  </header>
358
 
359
  <section id="thesis" class="wrap">
@@ -487,14 +497,14 @@ footer a:hover{border-bottom-color:var(--text)}
487
  </div>
488
  <div class="poolstat"><span class="beta num">67</span> models &middot; <span class="beta num">21</span> providers &middot; priced live &middot; temperature 0 &middot; one 67&times;67 co-failure matrix</div>
489
  <div id="poolGrid" class="poolgrid"></div>
490
- <div class="cap" style="max-width:64ch">Tier: <span class="tierdot f"></span> frontier &middot; <span class="tierdot m"></span> mid &middot; <span class="tierdot c"></span> cheap / open-weight. Every instrument above draws on this pool; the full roster with live prices ships in the paper's appendix.</div>
491
  </section>
492
 
493
  <footer class="wrap" id="paper">
494
  <div class="foot-grid">
495
  <div style="max-width:42ch">
496
  <div class="foot-title">Orchestration Is Allocation</div>
497
- <p style="color:var(--dim);font-size:13.5px">Josef Chen · KAIKAKU. Every figure here recomputes from committed outcome matrices over 67 frontier models; the reproducibility bundle ships the scripts and data. Grading scope is stated honestly in the paper the open-ended panel is five LLM judges, not human adjudication.</p>
498
  <p style="margin-top:16px"><span class="foot-pending">Read the paper (arXiv)</span> <span class="mono-note" style="display:inline">&#160;— link goes live when the arXiv id is assigned</span></p>
499
  </div>
500
  <div class="mono-note">
@@ -785,6 +795,72 @@ const ROSTER=[{n:"GPT-5.5",p:"OpenAI",t:"f"},{n:"Claude Opus 4.8",p:"Anthropic",
785
  }).join('');
786
  })();
787
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
788
  (function panHints(){
789
  const frames=[...document.querySelectorAll('.panx')];
790
  const sync=el=>el.classList.toggle('can-pan',el.scrollWidth-el.clientWidth>1);
 
3
  <head>
4
  <meta charset="utf-8">
5
  <meta name="viewport" content="width=device-width, initial-scale=1">
6
+ <script>/* dark-first: the glyph-dither hero is black; the theme toggle stays authoritative once clicked */</script>
7
  <title>When Does Combining Language Models Help? — the co-failure ceiling</title>
8
  <meta name="description" content="Interactive companion to the paper “When Does Combining Language Models Help?” (Orchestration Is Allocation). The deployment-relevant object in multi-model LLM orchestration is β = P(all models wrong); a one-sample certificate bounds every router, vote, and cascade.">
9
  <meta property="og:title" content="When Does Combining Language Models Help?">
 
322
  input[type=range]::-webkit-slider-thumb{width:22px;height:22px;margin-top:-9px}
323
  input[type=range]::-moz-range-thumb{width:22px;height:22px}
324
  }
325
+ /* ---- glyph-dither hero (Intuition-style pixel bloom) ---- */
326
+ .hero-dither{position:relative;width:100%;height:clamp(560px,84vh,880px);background:#070809;overflow:hidden;border-bottom:.5px solid var(--hair);cursor:crosshair}
327
+ #glyphCanvas{position:absolute;inset:0;width:100%;height:100%;display:block}
328
+ .hero-grad{position:absolute;inset:0;pointer-events:none;background:radial-gradient(130% 100% at 58% 48%,transparent 38%,rgba(7,8,9,.55) 100%)}
329
+ .hd-chrome{position:absolute;inset:0;z-index:2;pointer-events:none}
330
+ .hd-mark{position:absolute;top:clamp(26px,5vh,58px);left:clamp(20px,4vw,64px);margin:0;font-family:var(--serif);font-weight:340;font-size:clamp(2.8rem,9vw,6.6rem);line-height:.86;letter-spacing:-.03em;color:#F5F3F4;text-shadow:0 4px 60px rgba(0,0,0,.45)}
331
+ .hd-tag{position:absolute;top:clamp(30px,5.4vh,66px);right:clamp(20px,4vw,64px);font-family:var(--mono);font-size:11.5px;letter-spacing:.09em;line-height:1.75;color:#CDD0D6;text-align:right;text-shadow:0 2px 20px rgba(0,0,0,.6)}
332
+ .hd-date{position:absolute;left:clamp(8px,2.4vw,30px);top:50%;transform:translateY(-50%) rotate(180deg);writing-mode:vertical-rl;font-family:var(--mono);font-size:10.5px;letter-spacing:.16em;color:#7E848D}
333
+ .hd-foot{position:absolute;left:clamp(20px,4vw,64px);bottom:clamp(24px,5vh,50px);display:flex;align-items:flex-end;gap:18px}
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+ .hd-foot .hd-beta{font-family:var(--mono);font-weight:300;font-size:clamp(30px,4.4vw,46px);letter-spacing:-.02em;line-height:.82;color:var(--accent)}
335
+ .hd-foot .gb{color:var(--accent);font-family:var(--serif);font-style:italic}
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+ .hd-foot-l{font-family:var(--mono);font-size:10px;letter-spacing:.07em;line-height:1.65;color:#9298A1;padding-bottom:3px}
337
+ .hd-hint{position:absolute;right:clamp(20px,4vw,64px);bottom:clamp(24px,5vh,50px);font-family:var(--mono);font-size:10px;letter-spacing:.06em;color:#6A707A;text-transform:uppercase}
338
+ @media(max-width:640px){.hd-date{display:none}.hd-tag{font-size:9.5px}.hd-hint{display:none}.hd-mark{font-size:clamp(2.6rem,13vw,4rem)}}
339
  @media(prefers-reduced-motion:reduce){*{animation:none!important;transition:none!important;scroll-behavior:auto}}
340
  </style>
341
  </head>
 
351
  </span>
352
  </nav>
353
 
354
+ <header class="hero-dither" id="top">
355
+ <canvas id="glyphCanvas" aria-hidden="true"></canvas>
356
+ <div class="hero-grad" aria-hidden="true"></div>
357
+ <div class="hd-chrome">
358
+ <h1 class="hd-mark">CO&#8202;&middot;&#8202;FAILURE</h1>
359
+ <div class="hd-tag">WHEN EVERY MODEL IS<br>WRONG AT ONCE, NO<br>ENSEMBLE CAN WIN</div>
360
+ <div class="hd-date">2026 &middot; 06 &middot; 15 &nbsp;&middot;&nbsp; OPENROUTER FRONTIER</div>
361
+ <div class="hd-foot">
362
+ <span class="hd-beta num" id="heroBeta" data-ticker="0.052">0.052</span>
363
+ <span class="hd-foot-l"><span class="gb">β</span> = P(ALL MODELS WRONG) &middot; MATH-500<br>17 OF 330 QUERIES &middot; 67 MODELS, 21 PROVIDERS</span>
 
 
 
 
364
  </div>
365
+ <div class="hd-hint">move the cursor &mdash; the bloom scatters</div>
366
  </div>
 
367
  </header>
368
 
369
  <section id="thesis" class="wrap">
 
497
  </div>
498
  <div class="poolstat"><span class="beta num">67</span> models &middot; <span class="beta num">21</span> providers &middot; priced live &middot; temperature 0 &middot; one 67&times;67 co-failure matrix</div>
499
  <div id="poolGrid" class="poolgrid"></div>
500
+ <div class="cap" style="max-width:64ch">Tier: <span class="tierdot f"></span> frontier &middot; <span class="tierdot m"></span> mid &middot; <span class="tierdot c"></span> cheap / open-weight. Every instrument above draws on this pool, and all of it is released to replicate: the full roster with live prices, the 67&times;67 outcome matrices, the grading, and the analysis code. Every number on this page regenerates offline.</div>
501
  </section>
502
 
503
  <footer class="wrap" id="paper">
504
  <div class="foot-grid">
505
  <div style="max-width:42ch">
506
  <div class="foot-title">Orchestration Is Allocation</div>
507
+ <p style="color:var(--dim);font-size:13.5px">Josef Chen · KAIKAKU. Every figure here recomputes from committed outcome matrices over 67 frontier models. The full reproducibility bundle is uploaded: the outcome matrices, graders, and analysis code that regenerate every number in the paper offline. Grading scope is stated honestly: the open-ended panel is five LLM judges, not human adjudication.</p>
508
  <p style="margin-top:16px"><span class="foot-pending">Read the paper (arXiv)</span> <span class="mono-note" style="display:inline">&#160;— link goes live when the arXiv id is assigned</span></p>
509
  </div>
510
  <div class="mono-note">
 
795
  }).join('');
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  })();
797
 
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+ /* ---------- glyph-dither hero: bloom.png sampled to a pixel grid, scattered by a fluid cursor trail ---------- */
799
+ (function glyphDither(){
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+ const cv=document.getElementById('glyphCanvas'); if(!cv||!cv.getContext) return;
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+ const ctx=cv.getContext('2d',{alpha:false});
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+ const reduce=matchMedia('(prefers-reduced-motion:reduce)').matches;
803
+ const img=new Image();
804
+ let cells=[],cell=10,cols=0,rows=0,W=0,H=0,dpr=1,ready=false;
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+ function layout(){
806
+ const rect=cv.getBoundingClientRect(); W=Math.max(1,rect.width); H=Math.max(1,rect.height);
807
+ dpr=Math.min(2,window.devicePixelRatio||1);
808
+ cv.width=Math.round(W*dpr); cv.height=Math.round(H*dpr); ctx.setTransform(dpr,0,0,dpr,0,0);
809
+ cell=Math.max(7,Math.round(W/128)); // grid density (≈ glyph scale)
810
+ cols=Math.ceil(W/cell); rows=Math.ceil(H/cell); sample();
811
+ }
812
+ function sample(){
813
+ if(!img.complete||!img.naturalWidth) return;
814
+ const off=document.createElement('canvas'); off.width=cols; off.height=rows;
815
+ const o=off.getContext('2d');
816
+ const ir=img.naturalWidth/img.naturalHeight, cr=cols/rows; let sw,sh,sx,sy; // cover-fit
817
+ if(ir>cr){ sh=img.naturalHeight; sw=sh*cr; sx=(img.naturalWidth-sw)/2; sy=0; }
818
+ else { sw=img.naturalWidth; sh=sw/cr; sx=0; sy=(img.naturalHeight-sh)/2; }
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+ o.drawImage(img,sx,sy,sw,sh,0,0,cols,rows);
820
+ const d=o.getImageData(0,0,cols,rows).data; cells.length=0;
821
+ for(let j=0;j<rows;j++)for(let i=0;i<cols;i++){
822
+ const k=(j*cols+i)*4, R=d[k],G=d[k+1],B=d[k+2];
823
+ const l=(0.299*R+0.587*G+0.114*B)/255;
824
+ if(l<0.05) continue; // skip near-black: cleaner dither + faster
825
+ cells.push({bx:i*cell+cell*0.5, by:j*cell+cell*0.5, r:R,g:G,b:B,l, ox:0,oy:0});
826
+ }
827
+ ready=true;
828
+ }
829
+ let mx=-1e4,my=-1e4;
830
+ const pt=e=>{const rect=cv.getBoundingClientRect(); mx=e.clientX-rect.left; my=e.clientY-rect.top;};
831
+ const out=()=>{mx=-1e4;my=-1e4;};
832
+ const hdr=cv.closest('.hero-dither')||cv;
833
+ hdr.addEventListener('pointermove',pt,{passive:true}); hdr.addEventListener('pointerleave',out);
834
+ const RAD=130, STR=30;
835
+ function frame(t){
836
+ if(ready){
837
+ ctx.fillStyle='#070809'; ctx.fillRect(0,0,W,H);
838
+ for(let n=0;n<cells.length;n++){ const c=cells[n]; let jit=0;
839
+ if(!reduce){
840
+ const dx=c.bx-mx, dy=c.by-my, dist=Math.sqrt(dx*dx+dy*dy); let tx=0,ty=0;
841
+ if(dist<RAD){ const f=1-dist/RAD; jit=f;
842
+ const ang=Math.atan2(dy,dx)+Math.sin(c.bx*0.045+c.by*0.03+t*0.0021)*1.5; // noise-displaced direction
843
+ const push=f*f*STR; tx=Math.cos(ang)*push; ty=Math.sin(ang)*push-push*0.25;
844
+ }
845
+ c.ox+=(tx-c.ox)*0.16; c.oy+=(ty-c.oy)*0.16; // ease in/out = trail + dissipation
846
+ }
847
+ const px=c.bx+c.ox, py=c.by+c.oy, s=cell*(0.42+0.74*c.l), h=s*0.5;
848
+ if(jit>0.22){ // chromatic split while scattered
849
+ const o2=jit*3.2; ctx.globalAlpha=0.5;
850
+ ctx.fillStyle='rgb('+c.r+',46,52)'; ctx.fillRect(px-o2-h,py-h,s,s);
851
+ ctx.fillStyle='rgb(54,'+c.g+',190)'; ctx.fillRect(px+o2-h,py-h,s,s);
852
+ ctx.globalAlpha=1;
853
+ }
854
+ ctx.fillStyle='rgb('+c.r+','+c.g+','+c.b+')'; ctx.fillRect(px-h,py-h,s,s);
855
+ }
856
+ }
857
+ requestAnimationFrame(frame);
858
+ }
859
+ img.onload=()=>{ layout(); requestAnimationFrame(frame); };
860
+ img.src='bloom.png';
861
+ let rt; addEventListener('resize',()=>{clearTimeout(rt);rt=setTimeout(layout,160);},{passive:true});
862
+ })();
863
+
864
  (function panHints(){
865
  const frames=[...document.querySelectorAll('.panx')];
866
  const sync=el=>el.classList.toggle('can-pan',el.scrollWidth-el.clientWidth>1);