manual-sync 2026-07-02T20:50:21Z local-atlas-guided-flow latex

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@@ -203,6 +203,15 @@ with $F_{\theta}$, and executes a candidate only when a calibrated dominance
 margin over the base action is confident; otherwise it falls back to the base
 or a safe action.
 
+The current V3 diagnostic instantiates the same idea in a deliberately compact
+form. We train a conditional flow in keyframe spline tangent space on positive
+chart interventions, then train a contrastive utility head on train-only
+positive versus negative tangents. During sampling, the flow follows the
+positive tangent density while ascending the learned utility gradient in the
+same normalized spline chart. This tests the central atlas hypothesis directly:
+positive support should come from local causal geometry and its negative
+boundary, not from replaying prototypes or increasing candidate count.
+
 \section{Current Six-Task Diagnostic}
 
 We evaluate six ManiSkill manipulation tasks with three seeds and 575
@@ -240,20 +249,27 @@ We now also export 43,095 measured tangent targets from 2,873 charts. A
 train-only positive-tangent memory diagnostic reaches 11.83\% PTR proxy at
 K=16 under a strict 0.20 RMS-L2 threshold and 41.94\% under a looser 0.40
 threshold, with positives closer than negatives in 61.33\% of covered heldout
-charts. A first raw-action CVAE improves the safety side of the proxy---0.00\%
+charts. A local-atlas retrieval diagnostic, which retrieves train-only positive
+tangents from nearby observation-language-task charts, reaches 23.66\% PTR at
+0.20 and 52.69\% at 0.40, while reducing negative-near to 5.33\%. This is the
+strongest support-proxy evidence so far: positive tangents are locally organized
+in the atlas, not merely task-level prototypes.
+
+A first raw-action CVAE improves the safety side of the proxy---0.00\%
 negative-near at the 0.20 threshold and 65.33\% positives-closer-than-negatives
 at K=16---but covers less positive support (7.53\% PTR at 0.20, 34.41\% at
 0.40). A 21D keyframe spline-CVAE decoded back to full $16\times 7$ chunks
 recovers more strict support than the raw CVAE (9.68\% PTR at 0.20) while
 keeping negative-near low (1.33\%). A vanilla spline flow-matching baseline is
-even safer (0.00\% negative-near) but collapses support (1.08\% PTR at 0.20),
-showing that flow matching must be utility- and geometry-guided rather than
-merely density matching positive keyframes. This is not yet the method result.
-It is a useful failure mode: positive support is structured, but prototypes,
-raw chunk likelihood, simple keyframe splines, and unguided flows still miss
-much of the chart. The full generator should therefore model object-centric
-positive tangent flows with utility contrast, not just replay or compress action
-chunks.
+even safer (0.00\% negative-near) but collapses support (1.08\% PTR at 0.20).
+Adding a contrastive utility head and gradient guidance keeps negative-near at
+0.00\% and improves positives-closer-than-negatives to 69.33\%, but does not
+recover support (1.08\% PTR at 0.20, 25.81\% at 0.40). This is not yet the
+method result. It is a useful failure mode: the local atlas contains positive
+support modes, but raw likelihood, spline compression, and noise-initialized
+flows miss them. The full generator should therefore learn object-centric local
+chart transport or flow initialization from atlas neighborhoods, with utility
+contrast as the boundary rather than as an afterthought.
 
 \section{Roadmap to the Full Paper}