Decode-time stochasticity — when temperature matters for tokenized-action policies

Papers: Understanding Multimodal Failure in Action-Chunking Behavioral Cloning (2605.22493), MARS (2605.29766), Understanding Behavior Cloning with Action Quantization (2603.20538), BOKBO (2605.30660), plus Discrete Diffusion VLA’s decoding ablation (2508.20072) as a supporting data point. Read 2026-08-07, timed to the #19 T-sensitivity rungs scoring on the local GPU as this page is written. Fed: #19 — the dT diagnostic’s interpretive frame (what a temperature should do to a mean-of-draws panel number, so the record-only table lands with a prior instead of as bare digits) and a fresh caveat on the selection rung; a theory anchor for the q-token AR trunk itself (#5/#19).

The theme

Our sampled-draws program treats the AR policy’s decode temperature as a fixed, registered constant: the primary is T=1.0, and tonight’s rungs re-score the frozen checkpoint at T ∈ {0.5, 0.7, 1.3} purely to put an error bar on how sensitive the mean-of-10 numbers are to that choice. The question this cluster answers: what does the field actually know about when stochastic decoding of actions helps, when it is inert, and when it hurts? The short version — stochastic capacity matters only where the demonstrated action distribution is genuinely multimodal, and most frames of most manipulation tasks are not; where it is unimodal, deterministic (or sharpened) decoding is at least as good and often better. That is exactly the regime our draws10_t1 readout measured from the other side: Δ_AR = −0.145, mean-of-10 barely beating greedy, the pre-registered mean-collapse shape.

1. Multimodal failure in action-chunking BC (2605.22493)

The anchor read. The paper proves and then measures that the two standard ways of making a chunking policy stochastic fail for different structural reasons: latent-variable policies (CVAE-style) lose the mode information to posterior–prior KL regularization — at ACT’s default β=10 the policy is provably driven toward unimodality (their bound: preserving modes needs I(A;Z|S) above a Fano floor, while KL strength caps it at C/β) — and action-space generators (flow/diffusion heads) are geometrically capped: a smooth map from a unimodal base can only represent about 1 + L/Δ well-separated modes, so low-Lipschitz samplers either bridge between modes with invalid trajectories (bridge fraction ~0% at 2 modes → ~51% at 16) or snap discontinuously. The empirical kicker for us: on the nearly unimodal UR3 BlockPush, the deterministic baseline beats every generative variant (1.98 vs 0.82–1.78 goals), and on their 16-mode synthetic task near-complete mode coverage still yields only 0.37–0.52 success — diversity is necessary for multimodal tasks but nowhere near sufficient, and on unimodal ones it is pure overhead.

Transfers: this is the published mechanism behind our measured mean-collapse (E2 of the draws10_t1 readout): where the conditional action distribution is near-unimodal, sampling buys nothing that the mean didn’t already have, and pooling draws re-averages whatever spread the sampler added. It gives tonight’s dT table a directional prior worth writing down before the numbers land: on a mostly-unimodal panel, T<1 (sharpening toward the local mode) should move pooled chunk/first MAE little or slightly down, and T=1.3 (flattening) should hurt more than T=0.7 helps — an asymmetry, not a symmetric bump. Record-only either way; if the table comes out inverted, that is evidence the q4 subset carries more multimodality than the family baseline suggests, which would be worth knowing. Doesn’t transfer: their β/Lipschitz analysis targets CVAE and flow heads; our AR softmax over q-tokens has neither bottleneck — its capacity for multimodality is the full categorical per token, which is exactly why the draws program tests sampling on it at all.

2. MARS — stochasticity only when it matters (2605.29766)

The engineering mirror of the same claim: a policy that selectively activates stochastic multimodal generation in task phases with real behavioral diversity and runs deterministic elsewhere, reporting +16.7% real-world success with an 83% inference-latency cut over always-stochastic baselines (8 sim + 4 real tasks). The counterintuitive result they highlight: on near-deterministic tasks MARS trains more efficiently than a purely deterministic policy — modeling the small pockets of genuine diversity helps even when most of the trajectory is prescribed.

Transfers: supports the per-frame view over the per-run view — the interesting unit is the frame, not the policy. Our selection-ceiling diagnostics (dispersion-vs-gain quartiles in selection_ceiling_results.py) are already shaped to answer the MARS question on our data: if best-of-K headroom concentrates in the high-dispersion quartile, phase-adaptive stochasticity is the shape of any follow-up; if it is flat, even that is not worth building. Doesn’t transfer: MARS is closed-loop success on live rollouts; our panel is open-loop MAE against one demonstration — a mode-matching metric that structurally cannot reward picking a valid non-demonstrated mode.

3. Theory anchor — BC with action quantization (2603.20538)

First sample-complexity analysis of exactly our trunk recipe: behavior cloning with quantized actions under log-loss. Result: optimal sample complexity matching known lower bounds, with quantization error compounding only polynomially along the horizon (not exponentially) given stable dynamics plus a policy-smoothness condition; they characterize which quantization schemes satisfy the conditions and give a model-based augmentation that provably tightens the bound. Abstract-level read (no experiments to audit). Transfers: a clean citation that the q-token + CE-loss trunk is not just an engineering convenience — it is the statistically efficient estimator class for this problem. Doesn’t transfer: no decode-time content at all; it is about what training converges to.

4. BOKBO — temperature draws as a safety substrate (2605.30660)

A conformal abstention layer over VLA policies: sample K candidate actions, score them with a learned violation predictor, abstain with finite-sample distribution-free guarantees on executed-violation rate (per-task Mondrian calibration lifts the worst per-task conditional hold rate 0.71 → 0.93 on OpenVLA-OFT/LIBERO variants). Relevant to us for two reasons. First, its candidate generators are exactly our draws menu — token-level temperature sampling among them — used not to improve the mean but to expose the policy’s spread to a downstream decision layer; a use of draws the panel-MAE lens never sees. Second, its measured caveat: policy-internal confidence correlates poorly with actual violations under perturbation sampling — learned predictors were needed. That is the second independent strike against cheap probe-style selectors (after the test-time-selection page’s rollout caveat), banked on the #19 selection rung: the oracle ceiling read stays the gate, and any selector that survives it should expect to need trained scoring, not a free confidence readout.

5. Supporting data point — decode-order temperature in DDVLA (2508.20072)

Discrete Diffusion VLA’s Table 7 (LIBERO-Goal): hard argmax 96.2%, fixed T=1 96.4%, linear decay T 1→0 97.4% — mild exploration early, sharp commitment late. Weak transfer (it schedules temperature over refinement iterations of a discrete-diffusion decode, not over an AR chunk, and it is closed-loop success), but it is the one published cell we found where a temperature schedule beats both extremes — a reminder that “which fixed T” (our rung question) and “T as a schedule” are different axes, and the second is unexplored in AR-VLA decoding. Parked as a hook, not an arm: nothing opens unless the dT table shows sensitivity worth chasing.

Where this leaves #19

The dT rungs land tonight with a written prior: near-flat response with mild asymmetry against T=1.3 says the panel is unimodal-dominated and the T=1.0 registration was safe (the expected outcome); a monotone win for T=0.7/0.5 says greedy-adjacent decoding is simply better on this metric and the mean-collapse story deepens; sensitivity concentrated in high-dispersion frames says MARS-shaped phase-adaptivity is the only version of this worth ever building. All three readings are record-only against the frozen T=1.0 primary — the rung exists to put an error bar on the leaderboard’s mean-of-10 rows, and this cluster says that error bar should be small.