feat(flow): flow-matching stages for the HPT head

[AnikethCheluva]

Adds the objective HPT is trained with upstream, decomposed the same way the
diffusion head already is: noising, denoiser, loss. Both trios read "condition"
and "target" and write "loss/*" in training and "pred_action" at inference, so
choosing between them is a config edit rather than a code change.

Flow matching interpolates linearly between action and noise,

x_t = t * noise + (1 - t) * action

and predicts that path's constant velocity, noise - action. Sampling integrates
the field backwards from t=1 to t=0 with plain Euler steps, so unlike the
diffusion stages there is no noise schedule and no scheduler-signature
handshake to keep in sync.

time_dist defaults to beta(1.5, 1) as upstream: it leans toward the noisy end,
spending capacity where sampling starts and errors compound. Sampled time is
kept strictly inside (0, 1) because either endpoint degenerates -- at 0 the
path carries no noise, at 1 no action.

Tests pin the interpolation identity itself rather than just shapes (action is
recovered from x_t and u_t), that beta really does skew above uniform, the
per-mode contracts, that inference runs with the noising stage absent, and a
convergence check that the whole graph fits a fixed target and samples nearer
to it than noise -- which would fail if the interpolation, the velocity target
or the loss were wrong.

Co-Authored-By: Claude Opus 5 noreply@anthropic.com

[AnikethCheluva]

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• feat(arc): arc tokenize and detokenize as graph nodes #11 : 4 dependent PRs (#12 , #63 , #68 and 1 other)
• feat(hpt): configured HPT graph for the ABC yam baseline #46
• feat(abc): ABC-130k mcap->zarr pipeline + yam_bimanual embodiment #10
• feat(hpt): Add Qwen stem and annotation prompt stage #53
• fix(data): actually honour bounds_check #45
• feat(flow): flow-matching stages for the HPT head #44 👈 (View in Graphite)
• feat(hpt): stems and trunk as graph stages #43
• feat(hpt): trunk primitives and tensor helpers #42
• feat(val): nested validation dataset groups #9
• refactor(transforms): factor rotation representation out of transform modes #8
• main

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