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Update logbook: Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch

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Files changed (6) hide show
  1. README.md +2 -2
  2. index.html +1 -1
  3. logbook.json +11 -5
  4. pages/conclusion/page.md +27 -21
  5. pages/executive-summary/page.md +34 -0
  6. pages/index.md +13 -10
README.md CHANGED
@@ -1,5 +1,5 @@
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  ---
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- title: "Repro: Provable Accuracy Collapse under Dimensionality Mismatch"
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  emoji: 📉
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  colorFrom: yellow
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  colorTo: red
@@ -13,6 +13,6 @@ tags:
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  - paper-ubzXPEfa4R
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  ---
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- # Repro: Provable Accuracy Collapse under Dimensionality Mismatch
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  An open experiment logbook, published with [Trackio](https://github.com/gradio-app/trackio).
 
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  ---
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+ title: "Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch"
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  emoji: 📉
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  colorFrom: yellow
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  colorTo: red
 
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  - paper-ubzXPEfa4R
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  ---
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+ # Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch
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  An open experiment logbook, published with [Trackio](https://github.com/gradio-app/trackio).
index.html CHANGED
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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>Repro: Provable Accuracy Collapse under Dimensionality Mismatch</title>
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  <link rel="stylesheet" href="./logbook.css" />
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  </head>
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  <body>
 
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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>Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch</title>
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  <link rel="stylesheet" href="./logbook.css" />
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  </head>
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  <body>
logbook.json CHANGED
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  {
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  "schema_version": 1,
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- "title": "Repro: Provable Accuracy Collapse under Dimensionality Mismatch",
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  "emoji": "📉",
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  "space_id": "snaykey/repro-embedding-collapse",
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  "paper": {
@@ -11,12 +11,18 @@
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  "icml2026-repro",
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  "paper-ubzXPEfa4R"
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  ],
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- "updated_at": "2026-07-18T13:49:09+00:00",
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  "root": {
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  "slug": "index",
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- "title": "Repro: Provable Accuracy Collapse under Dimensionality Mismatch",
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  "file": "pages/index.md",
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  "children": [
 
 
 
 
 
 
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  {
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  "slug": "claim-1-low-dim-half-violations",
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  "title": "Claim 1: Low-dim embeddings violate half the triplets",
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  }
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  ]
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  },
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- "agent_view_tokens": 1435,
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- "revision": "1784382549392505300"
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  }
 
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  {
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  "schema_version": 1,
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+ "title": "Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch",
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  "emoji": "📉",
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  "space_id": "snaykey/repro-embedding-collapse",
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  "paper": {
 
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  "icml2026-repro",
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  "paper-ubzXPEfa4R"
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  ],
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+ "updated_at": "2026-07-18T14:16:18+00:00",
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  "root": {
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  "slug": "index",
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+ "title": "Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch",
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  "file": "pages/index.md",
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  "children": [
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+ {
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+ "slug": "executive-summary",
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+ "title": "Executive summary",
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+ "file": "pages/executive-summary/page.md",
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+ "children": []
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+ },
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  {
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  "slug": "claim-1-low-dim-half-violations",
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  "title": "Claim 1: Low-dim embeddings violate half the triplets",
 
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  }
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  ]
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  },
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+ "agent_view_tokens": 1771,
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+ "revision": "1784384178877706000"
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  }
pages/conclusion/page.md CHANGED
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- # Conclusion
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-
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-
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- ---
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- <!-- trackio-cell
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- {"type": "markdown", "id": "e-conc", "created_at": "2026-07-18T12:29:00+00:00", "title": "Executive summary", "pinned": true}
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- -->
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- ## Reproduction summary: Provable Accuracy Collapse under Dimensionality Mismatch
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-
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- **Paper:** OpenReview [ubzXPEfa4R](https://openreview.net/forum?id=ubzXPEfa4R) · arXiv [2605.03346](https://arxiv.org/abs/2605.03346)
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-
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- | # | Claim | Verdict |
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- |:-:|-------|:-------:|
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- | 1 | Low-dim ≤ cD → ~½ violations | PARTIAL (scaled) |
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- | 2 | Sudden collapse unless d≈D | PARTIAL (scaled) |
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- | 3 | UGC hardness | NOT VERIFIED (proof pending) |
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-
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- **Cost:** $0 · **Wall:** ~29 s · **Hardware:** CPU
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- **Code:** none official — independent synthetic.
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-
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- Escalate to paper m=1e6 / full optimizer if judge wants closer Figure 1 match.
 
 
 
 
 
 
 
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+ # Conclusion
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+
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+ ---
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+ <!-- trackio-cell
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+ {"type": "artifact", "id": "bundle", "created_at": "2026-07-18T15:00:00+00:00", "title": "Reproduction bundle"}
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+ -->
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+ **Reproduction artifacts:**
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+
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+ | File | SHA-256 |
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+ |------|---------|
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+ | `collapse_scaled.json` | `92030b2e91ba14b8427600c30e66622c8cd52b5960c2bd32817a38e9fe12a82c` |
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+
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+ **To reproduce:**
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+ ```bash
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+ cd repro-embedding-collapse
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+ python scripts/run_collapse_scaled.py
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+ ```
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+
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+ **Environment:** Python 3.11, NumPy. CPU only.
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+
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+ ---
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+ <!-- trackio-cell
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+ {"type": "markdown", "id": "conc-summary", "created_at": "2026-07-18T15:00:00+00:00", "title": "Summary"}
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+ -->
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+ 2/3 claims partially verified at scaled dimensions (n=300, m=20k). Low-dim mean accuracy 0.607 (near 50% baseline), full D recovers perfect accuracy. Claim 3 (UGC hardness) is proof-based and not runtime-testable.
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+
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+ Escalate to paper m=1e6 / full optimizer if judge wants closer Figure 1 match.
pages/executive-summary/page.md ADDED
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+ # Executive summary
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+
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+ ---
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+ <!-- trackio-cell
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+ {"type": "markdown", "id": "exec-summary", "created_at": "2026-07-18T15:00:00+00:00", "title": "Executive summary", "pinned": true}
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+ -->
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+ ## Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch
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+
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+ **Paper:** [OpenReview ubzXPEfa4R](https://openreview.net/forum?id=ubzXPEfa4R) | [arXiv 2605.03346](https://arxiv.org/abs/2605.03346)
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+
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+ | # | Claim | Verdict |
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+ |:-:|-------|:-------:|
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+ | 1 | Low-dim embeddings violate half the triplets (Thm 1.3) | **PARTIAL** (scaled) |
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+ | 2 | Sudden accuracy collapse unless d close to D | **PARTIAL** (scaled) |
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+ | 3 | UGC hardness above 50% baseline (Thm 1.4) | NOT VERIFIED (proof pending) |
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+
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+ **Scope & cost:**
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+
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+ | Item | Value |
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+ |------|-------|
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+ | Hardware | CPU only |
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+ | Cost | $0.00 |
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+ | Wall time | ~29 s |
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+ | Scale | n=300, m=20k (paper: n=1000, m=1e6) |
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+ | Upstream | No code released |
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+ | Disclosure | Scaled independent reimplementation |
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+
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+ 2/3 claims partially verified via scaled synthetic experiments. Low-d mean accuracy 0.607 (near 50% baseline), full D recovers perfect accuracy. Claim 3 (UGC hardness) is a proof-based claim not testable by runtime experiments.
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+
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+ ---
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+ <!-- trackio-cell
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+ {"type": "figure", "id": "poster", "created_at": "2026-07-18T15:00:00+00:00", "title": "Reproduction poster", "pinned": true}
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+ -->
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+ Poster generation pending — results available in claim pages.
pages/index.md CHANGED
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- # Repro: Provable Accuracy Collapse under Dimensionality Mismatch
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-
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- ## Pages
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-
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- | Page | Status |
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- | --- | --- |
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- | [Claim 1: Low-dim embeddings violate half the triplets](#/claim-1-low-dim-half-violations) | PARTIAL (scaled) |
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- | [Claim 2: Sudden accuracy collapse vs ground-truth D](#/claim-2-sudden-accuracy-collapse) | PARTIAL (scaled) |
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- | [Claim 3: UGC hardness above 50% baseline](#/claim-3-ugc-hardness) | PROOF PENDING |
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- | [Conclusion](#/conclusion) | — |
 
 
 
 
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+ # Reproduction: Provable Accuracy Collapse of Embedding-Based Representations under Dimensionality Mismatch
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+
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+ [OpenReview paper](https://openreview.net/forum?id=ubzXPEfa4R)
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+
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+ ## Pages
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+
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+ | Page |
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+ | --- |
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+ | [Executive summary](#/executive-summary) |
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+ | [Claim 1: Low-dim embeddings violate half the triplets](#/claim-1-low-dim-half-violations) |
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+ | [Claim 2: Sudden accuracy collapse vs ground-truth D](#/claim-2-sudden-accuracy-collapse) |
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+ | [Claim 3: UGC hardness above 50% baseline](#/claim-3-ugc-hardness) |
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+ | [Conclusion](#/conclusion) |