Expose five anchored Softmax-as-linear-attention claims

logbook.json

@@ -1,6 +1,6 @@
 {
   "schema_version": 1,
-  "title": "Repro - Softmax as Linear Attention in the Large-Prompt Regime",
+  "title": "Reproduction: Softmax as Linear Attention in the Large-Prompt Regime: a Measure-based Perspective",
   "emoji": "🎯",
   "space_id": "SabaPivot/repro-softmax-linear-attention",
   "paper": {
@@ -13,9 +13,15 @@
   "updated_at": "2026-07-16T14:49:03+00:00",
   "root": {
     "slug": "index",
-    "title": "Repro - Softmax as Linear Attention in the Large-Prompt Regime",
+    "title": "Reproduction: Softmax as Linear Attention in the Large-Prompt Regime: a Measure-based Perspective",
     "file": "pages/index.md",
     "children": [
+      {
+        "slug": "executive-summary",
+        "title": "Executive summary",
+        "file": "pages/executive-summary/page.md",
+        "children": []
+      },
       {
         "slug": "claim-1-finite-prompt-concentration-prop-3-1",
         "title": "Claim 1: Finite-prompt concentration (Prop 3.1)",
@@ -51,15 +57,9 @@
         "title": "Conclusion",
         "file": "pages/conclusion/page.md",
         "children": []
-      },
-      {
-        "slug": "softmaxlin-repro",
-        "title": "softmaxlin-repro",
-        "file": "pages/softmaxlin-repro/page.md",
-        "children": []
       }
     ]
   },
   "agent_view_tokens": 8996,
   "revision": "1784213343170298004"
-}
+}

pages/executive-summary/page.md

@@ -0,0 +1,28 @@
+# Executive summary
+
+---
+<!-- trackio-cell
+{"type":"markdown","id":"softmax_exec_v2","created_at":"2026-07-22T04:05:00+00:00","title":"Executive summary","pinned":true,"pinned_at":"2026-07-22T04:05:00+00:00"}
+-->
+All five supplied claims for [Softmax as Linear Attention in the Large-Prompt Regime](https://openreview.net/forum?id=MvuCgK0Qns) were independently tested. The Gaussian infinite-prompt identity matches direct Monte Carlo at relative error 4e-4–1e-3 for L=10^7, including anisotropic and rank-degenerate covariances. Output and gradient errors exhibit the predicted prompt-length and variance signatures. In the authors' released training code, softmax/linear risk gap shrinks from 0.21 to 0.014 and same-seed parameter distance from 4.20 to 0.023 as L grows 10→1000. Under anisotropic KMS covariates, the learned matrix aligns with Σ⁻¹ at cosine 0.9999 and approaches the Bayes-risk level. The reproduction also identifies and fixes an upstream anisotropic data-generator bug before Claim 5 is evaluated.
+
+## Scope & cost
+
+| Item | This reproduction | Full paper run |
+| --- | --- | --- |
+| Scope | All 5 claims; concentration, gradients, affine limit, risk transfer, anisotropic optimum | Full 500k-step grid and additional seeds |
+| Scale | 400 prompts × 500 queries; L≤30,000 for rates; direct MC to 10,000,000; 12 training runs × 100k steps | Authors' 500k-step training schedule |
+| Hardware | 1× H100 plus CPU | One GPU plus CPU |
+| Compute/cost | About 1.5 GPU-hours plus CPU; approximately $5 | Approximately 5× training budget |
+| Limitation | Training steps reduced from 500k to 100k; all reductions disclosed | Full training schedule |
+
+Evidence links: [authors' repository](https://github.com/eboursier/softmax_as_linear), [artifact Bucket](https://huggingface.co/buckets/SabaPivot/repro-softmax-linear-attention-artifacts), and [reproduction bundle](https://huggingface.co/buckets/SabaPivot/repro-softmax-linear-attention-artifacts#softmaxlin-repro/repro-bundle:v1).
+
+---
+<!-- trackio-cell
+{"type":"figure","id":"softmax_poster_v2","created_at":"2026-07-22T04:05:00+00:00","title":"Reproduction poster (poster_embed.html)","source_path":"poster_embed.html","pinned":true,"pinned_at":"2026-07-22T04:05:00+00:00"}
+-->
+````html
+<!-- poster_embed.html -->
+<iframe src="https://chenruishuo-posterly.hf.space" title="Posterly reproduction poster" style="width:100%;height:720px;border:0" loading="lazy"></iframe>
+````

pages/executive-summary/poster_embed.html

@@ -0,0 +1 @@
+<iframe src="https://chenruishuo-posterly.hf.space" title="Posterly reproduction poster" style="width:100%;height:720px;border:0" loading="lazy"></iframe>

pages/index.md

@@ -1,13 +1,13 @@
-# Repro - Softmax as Linear Attention in the Large-Prompt Regime
+# Reproduction: Softmax as Linear Attention in the Large-Prompt Regime: a Measure-based Perspective
 
 ## Pages
 
 | Page |
 | --- |
+| [Executive summary](#/executive-summary) |
 | [Claim 1: Finite-prompt concentration (Prop 3.1)](#/claim-1-finite-prompt-concentration-prop-3-1) |
 | [Claim 2: Gradient concentration (Prop 3.4)](#/claim-2-gradient-concentration-prop-3-4) |
 | [Claim 3: Infinite-prompt softmax is affine (Lemma 2.1)](#/claim-3-infinite-prompt-softmax-is-affine-lemma-2-1) |
 | [Claim 4: Risk transfer under gradient flow (Thm 4.3)](#/claim-4-risk-transfer-under-gradient-flow-thm-4-3) |
 | [Claim 5: Bayes-optimal anisotropic ICL (Thm 5.1)](#/claim-5-bayes-optimal-anisotropic-icl-thm-5-1) |
 | [Conclusion](#/conclusion) |
-| [softmaxlin-repro](#/softmaxlin-repro) |

pages/softmaxlin-repro/page.md

@@ -1,10 +0,0 @@
-# softmaxlin-repro
-
-
----
-<!-- trackio-cell
-{"type": "artifact", "id": "cell_f31339a2c059", "created_at": "2026-07-16T14:48:48+00:00", "title": "Artifact: softmaxlin-repro/repro-bundle:v0", "artifact": "softmaxlin-repro/repro-bundle:v0", "artifact_type": "dataset"}
--->
-**📦 Artifact** `softmaxlin-repro/repro-bundle:v0` · dataset · 3.7 MB
-
-https://huggingface.co/buckets/SabaPivot/repro-softmax-linear-attention-artifacts#softmaxlin-repro/repro-bundle:v0