To Route or to Adapt? Multi-Expert Diffusion Planners in Unseen Regions

Introduction

Deploying a trajectory planner in an unseen region presents a challenge for models trained with domain-specific experts. One approach is to select the most suitable expert for each new scene, reusing what the planner has already learned. Another is to update the model using data from the new region. The former avoids additional training but is limited by the available experts; the latter can change the planner’s predictions but risks degrading performance on the original training domains. How much can expert selection actually achieve before adaptation becomes necessary?

We investigate this question using a reward-fine-tuned diffusion trajectory planner [1, 2] with a shared adapter and four per-ODD expert adapters. The four training ODDs are ODD-Hongo (the University of Tokyo’s Hongo campus), ODD-Kashiwa (suburban Kashiwa), ODD-Shulan (a controlled test site), and ODD-Nagoya (Nagoya University campus). The three held-out maps are Knowledge Hub (a research campus), Ishiodai (a suburban district), and Morikoro (an open park), all in Aichi Prefecture, Japan. Within the Generator–Selector framework of the Autoware end-to-end reference architecture [3], we compare methods that select among existing expert trajectories with methods that modify the planner’s adapter weights, as shown in Figure 1.

We first examine whether routing can make better use of the existing experts. Across the three held-out maps, none of eight routing schemes improves the fleet-mean lateral offset over the static default, which uses the geographically nearest training expert (ODD-Nagoya on all three maps). More importantly, an oracle that selects the lowest-offset expert trajectory for each scene improves the mean offset by only 0.9 m. Even perfect selection among the four existing trajectories therefore offers little additional benefit. We next examine whether updating the planner can overcome this limitation.

Fine-tuning the shared adapter on geometrically perturbed training scenes improves performance on the open-park map, while reward-based fine-tuning with 20 target-region scenes provides substantially larger gains. On matched evaluation slices, joint replay, which mixes target-region and training scenes during fine-tuning, achieves a fleet-mean offset of 6.9 m, compared with 12.4 m for the static default. Comparisons with other fine-tuning methods show that target-region training drives the improvement, while replay primarily preserves performance on the original training ODDs.

We also examine the limits of these improvements. On nuPlan, fine-tuning across three training cities reduces open-loop lateral offset in each held-out city but degrades closed-loop performance. In addition, two test-time adaptation baselines produce low lateral offsets by collapsing toward nearly stationary or scene-independent trajectories. These observations distinguish improvements in open-loop trajectory metrics from improvements in driving behaviour, which remain to be established for the proposed adaptation methods.

Related Work

Diffusion planning and conformal prediction. Our planner builds on reward-based diffusion policy training [1, 2], using a shared adapter and per-ODD experts. Conformal prediction has been applied to trajectory uncertainty [4, 5] and semantic uncertainty in BEV planning [6]. Selective conformal risk control combines abstention with calibrated prediction [7]. We examine whether a conformal corridor can help select among the trajectories of existing experts when the deployment region differs from the calibration domains.

Geographic conditioning in driving. GeCo [8] uses geographic channel attention and contrastive imitation learning to train a policy across regions. Drive-Anywhere [9] instead uses multimodal foundation model representations to improve generalisation to unseen environments. Our setting differs from both: the planner and its domain-specific experts are already trained, and we examine whether geographic location can guide their selection or weight mixing without retraining the backbone.

Expert routing and weight merging. Related approaches include online expert selection for trajectory prediction [10], mixtures of denoising experts for robotic manipulation [11], and CLIP-based LoRA retrieval for open-vocabulary segmentation [12]. These methods differ in their tasks and available supervision. We evaluate both selecting among the trajectories generated by existing experts and combining their adapter weights. The latter is related to model soups and weight-space merging [13, 14], although our geographic mixing weights depend on the deployment location.

Multi-task learning and domain adaptation. The shared-plus-expert adapter structure is related to multi-task learning with shared representations [15, 16]. For adaptation, we study fine-tuning on geometrically perturbed training scenes, related to scene augmentation for OOD generalisation [17, 18] and generative simulation [19, 20]. We also fine-tune with a small set of target-region scenes, using replay of training scenes to limit forgetting [21, 22]. Separately, we evaluate test-time adaptation baselines [23, 24] and analyse their degenerate predictions in App. § 10 and App. § 11.

Method

Generator–Selector decomposition. We follow the Generator–Selector framework of the Autoware end-to-end reference architecture [3], as shown in Figure 1. The Generator consists of a diffusion planner [2] with a shared low-rank adapter (LoRA [25]) and four per-ODD expert adapters of comparable rank. For each scene, we activate the shared adapter together with each expert in turn, producing $K = 4$ candidate trajectories. The Selector ranks these candidates and returns a single trajectory.

We evaluate eight routing schemes that choose among or weight the existing candidates, alongside three mechanisms that modify the adapter weights before generation. The conformal routing scheme also uses geographic weight mixing as a fallback, as described in § 5.1. The adapter ranks and optimisation settings are inherited from the training of the adapter stack (App. § 21). The per-ODD structure supports independent updates and rollbacks for regions with different data volumes and maintenance schedules. Our experiments do not cover monolithic planners trained on pooled data.

Eight routing schemes. We evaluate eight schemes grouped by the information used to choose an expert.

Feature and geometry. (i) A two-hidden-layer MLP takes eight groups of scene features: lane count, mean curvature, mean lane length, lateral and longitudinal lane spread, neighbour speed, route-lane count, and ego state. (ii) Lane-following scores each candidate by its perpendicular distance to the nearest route-lane centreline.

Consistency and uncertainty. (iii) Self-consistency scores the agreement among five trajectories generated by each expert, using mean pairwise trajectory distance. (iv) A magnitude-normalised variant uses the same samples. (v) A split-conformal corridor uses a multi-noise nonconformity score calibrated on training scenes (App. § 23).

Loss and reward. (vi) Denoising-loss scoring ranks experts using their denoising losses [26]. (vii) A reward-supervised dynamic gate is trained directly on realised lateral offset (§ 4). (viii) Reward-as-scorer selects $\arg\max R(\tau_e)$ using the planner’s training reward.

We compare each scheme with the static default on the scenes where it is evaluated.

Three constructive mechanisms. We also investigate three ways to modify the planner’s adapters, shown in Figure 2. First, geographic weight mixing (the vMF mixture) combines the existing expert weights according to their distances from the deployment location (§ 5.1). Second, shared-adapter repair fine-tunes the shared module on training scenes augmented with lanelet rotations, centreline warps, and boundary removal (§ 5.2). Third, joint replay fine-tunes the full adapter stack using target-region scenes together with 200 training scenes (§ 5.3). The latter two methods update model parameters, whereas geographic mixing combines existing parameters without further optimisation.

Reward and safety gate. We use the trajectory-level reward inherited from the training of the adapter stack, with terms for forward progress, route alignment, comfort, and safety. The safety term draws on the Reachability-of-Safe-State requirement discussed in the Autoware reference architecture [3]. The full reward, its weights, and the braking-distance parameters are provided in App. § 21.

A Safety Gate downstream of the Selector rejects trajectories that violate hard limits on lateral offset, braking distance, or forward progress. All lateral-offset results in this paper are measured on the Selector’s output before the Safety Gate.

Terms and evaluation protocol. We evaluate planned trajectories over 8 s at 10 Hz. For a trajectory $\tau= \{(x_t, y_t)\}_{t=1}^{80}$ expressed in the ego frame aligned with the start lanelet, the lateral offset is the maximum absolute lateral coordinate. The fleet mean gives equal weight to the three held-out maps:

where $S_m$ is the evaluation scene set for map $m$. This metric measures lateral displacement relative to the initial lanelet axis, rather than distance to the route centreline or a recorded trajectory.

The static default always activates the expert of the geographically nearest training ODD. For all three held-out maps, this is ODD-Nagoya, which also has the lowest offset among the four fixed experts.

We define oracle headroom as the improvement obtained by selecting, for each scene, the lowest-offset trajectory among the four experts:

This measures the potential gain from selecting among the four existing candidate trajectories; it does not bound the performance of weight mixing or fine-tuning.

We use two evaluation pools. Pool A contains 24 scenes used for the routing experiments. Pool B is used for fine-tuning evaluation and consists, for each training seed, of scenes drawn from lanelets disjoint from that seed’s training scenes. Table 1 specifies the evaluation pool for each experiment. Results from different pools are reported separately.

Experiment	Model evaluated	Training	Evaluation
Routing schemes (§ 4)	adapter stack	selector only	Pool A (24)
Oracle headroom (§ 4)	per-scene oracle	none	Pool A; 104 scenes
vMF mixture (§ 5.1)	average of experts	closed-form weights	Pool A (24)
Shared-adapter repair (§ 5.2)	shared module	500 steps, perturbed scenes	Pool A (24)
Joint replay, baselines (§ 5.3)	adapter stack	500 steps, 20 target scenes	Pool B, 8 seeds
nuPlan cross-city (§ 6)	rank-4 shared LoRA	500 steps on 3 cities	nuPlan, open loop
Real vehicle, DPO (§ 6)	other adapters	reward or DPO	ODD-Kashiwa course

Limited Headroom for Expert Routing

We begin by measuring how much could be gained from selecting among the four existing experts. For each scene, an oracle chooses the expert trajectory with the lowest lateral offset. This gives an upper bound on the improvement available to any selector restricted to those four trajectories, though not to methods that combine expert weights or update the planner.

On Pool A, the oracle improves the mean offset over the static default by only 0.9 m. The gain remains small on a larger 104-scene pool with new start lanelets (1.3 m) and on the disjoint evaluation slices of Pool B (1.1 m). Thus, most of the offset cannot be reduced by choosing a different existing expert for each scene. For comparison, joint replay (§ 5.3) reduces the mean offset on Pool A by 9.1 m. Seven of these scenes are among joint replay’s training scenes; on the remaining 17 scenes, the improvement is 12.7 m ($p = 0.0008$).

We next evaluate eight routing schemes on Pool A, reported in Table 2 and Figure 3a. The static default uses the geographically nearest expert, ODD-Nagoya, which is also the best fixed expert on all three held-out maps. It achieves a fleet-mean offset of 13.74 m. The conformal corridor slightly improves on this baseline on Knowledge Hub and Ishiodai, but performs worse on Morikoro, leaving its fleet mean higher than the static default. None of the schemes evaluated across all three maps improves the fleet mean. Paired Wilcoxon tests find no significant improvement, while six schemes perform significantly worse ($p \le0.012$; all six remain significant after Holm correction). Morikoro contributes the largest offsets. Its open-park layout differs from the training ODDs, all of which contain paired opposing lanes (App. § 26).

Routing scheme	Knowledge Hub	Ishiodai	Morikoro	Fleet
Scene-conditioned MLP	4.5 ± 0.8	9.0 ± 4.2	63.3 ± 58.0	25.61
Self-consistency	14.3 ± 4.1	7.7 ± 4.6	46.3 ± 35.3	22.76
Self-consistency (normalised)	14.3 ± 4.1	7.7 ± 4.6	46.3 ± 35.3	22.76
Lane-following	6.0 ± 2.1	7.8 ± 4.0	41.1 ± 46.9	18.29
Denoising-loss	14.0 ± 4.0	8.1 ± 4.3	42.9 ± 33.7	21.67
Conformal corridor ($T=15$)	4.0 ± 0.1	4.6 ± 0.7	38.9 ± 37.1	15.86
Reward-supervised gate	n/a	n/a	32.3 ± 0.6	n/a
Reward-as-scorer	13.6 ± 3.6	9.2 ± 4.7	56.9 ± 51.8	26.57
Static default (ODD-Nagoya)	4.5 ± 0.8	4.8 ± 0.8	31.9 ± 32.1	13.74

The routing schemes encounter different problems on the held-out maps. The scene-conditioned MLP separates the training ODDs perfectly but assigns most held-out scenes to ODD-Hongo, resulting in large offsets. Self-consistency favours small-magnitude trajectories and effectively selects the shared module alone. The denoising loss has little correlation with realised offset, while the planner’s own reward frequently selects ODD-Shalun instead of the lowest-offset expert. The reward-supervised gate converges almost entirely to ODD-Nagoya, recovering approximately the static default. The conformal corridor abstains on every scene at $T = 5$ m; at $T = 15$ m, its output reduces to the geographic weight mixture of § 5.1. Further results are provided in App. § 22.

We also test whether scene features can predict which expert will have the lowest offset. Leave-one-out classifiers using either hand-crafted scene features or the planner’s encoder embeddings do not outperform the majority-class baseline on the 24- or 104-scene pools (permutation $p \ge0.29$). A richer 38-dimensional feature set separates the training ODDs perfectly but does not improve selection on the held-out maps (App. § 20). A sum of per-coordinate mutual-information estimates [27] between the encoder embedding and the oracle label is at most suggestive ($p=0.088$ with 24 scenes in 256 dimensions). The conformal predictor faces a separate problem: its training and held-out residuals fail an exchangeability test ($p = 0.0035$; App. § 23).

These results show that the tested representations and routing methods do not reliably identify better experts under cross-region shift. Together with the small oracle headroom, they suggest that more effective selection among the four existing experts would offer limited benefit on these maps.

Beyond Expert Selection: Weight Mixing and Adaptation

We next examine three alternatives to selecting among existing expert trajectories. Geographic weight mixing combines pretrained experts without further training; shared-adapter repair uses geometrically perturbed training scenes; and joint replay introduces a small number of target-region scenes. Only the last method requires target-region training data. Figure 3b compares their results.

Geographic Weight Mixing

We first test whether geographic proximity can guide the combination of existing experts. Let $d_{\mathrm{geo}}(\ell,\mu_d)$ denote the great-circle distance between deployment location $\ell$ and the centre $\mu_d$ of training ODD $d$. We compute a weighted average of the merged expert weights $W_d$:

The temperature $\tau$ controls the contribution of distant experts. We evaluate $\tau\in\{1, 10, 50, 200\}$ km; as $\tau$ approaches zero, the mixture approaches the nearest-expert static default (App. § 12).

At $\tau= 200$ km, the mixture slightly improves Knowledge Hub and Ishiodai but increases the Morikoro offset from 31.9 to 38.9 m. Its fleet mean is 15.86 m, compared with 13.74 m for the static default (Table 10). Learning the mixture coefficients directly from 20 target-region scenes performs worse (App. § 13). Neither approach improves the fleet mean over the static default.

$\tau$ (km)	Knowledge Hub	Ishiodai	Morikoro
1 / 10 / 50 (one-hot $\rightarrow$ static default)	4.51 $\pm$ 0.79	4.82 $\pm$ 0.84	31.9 $\pm$ 32.1
200 (soft mix)	4.02 $\pm$ 0.11	4.63 $\pm$ 0.68	38.9 $\pm$ 37.1
200 (top-2 mix)	4.13 $\pm$ 0.73	4.49 $\pm$ 0.80	40.7 $\pm$ 37.7

Shared-Adapter Repair with Geometric Perturbations

We next fine-tune the shared adapter without using target-region training scenes. For 500 steps, we train on scenes from the original ODDs with three geometric perturbations: per-lanelet $SE(2)$ rotations of up to $45^\circ$, cubic Bezier centreline warps of up to 3 m, and random removal of one lane boundary with probability 0.5. These perturbations introduce variations in lane orientation, curvature, and boundary structure that are relevant to the open-park map.

The repaired shared adapter more than halves Morikoro’s offset relative to the original shared adapter and also improves the other two maps. When combined with the ODD-Kashiwa expert, it achieves 11.1 m on Morikoro, compared with 31.9 m for the static default. Ablations across three seeds show that lanelet rotation contributes the largest improvement (App. § 14).

Joint Replay with Target-Region Scenes

We then fine-tune the full adapter stack $\theta$ using target-region scenes together with scenes from the original training ODDs. The training set contains 20 target-region scenes from Ishiodai ($D_{\mathrm{tgt}}$) and 200 training scenes ($D_{\mathrm{src}}$), with 50 from each training ODD. Replaying training scenes follows the rehearsal approach to continual learning [21, 22]. We optimise the trajectory-level reward for 500 steps:

Here $\tau_{\theta}(x)$ is the trajectory generated by a differentiable DPM-Solver++ rollout, and $R_{c(x)}$ uses the reward weights assigned to the scene’s ODD. Training scenes activate their respective experts, while target-region scenes use the shared adapter alone with ODD-Nagoya reward weights. The reward is computed from scene maps and routes, without requiring recorded driving trajectories.

On Pool B, joint replay achieves a fleet-mean offset of $6.91 \pm2.16$ m across eight seeds, compared with 12.4 m for the static default (Table 3).¹ Because all target-region training scenes come from Ishiodai, improvements on Knowledge Hub and Morikoro reflect transfer to the other two held-out maps. The sample-complexity results in Figure 4 also show reduced variation across seeds as the target training set grows to 20 scenes.

Method	Target [m] $\downarrow$	Forgetting [m] $\downarrow$
Shared module only	$20.0 \pm2.4$	0
Static default	$12.4 \pm3.0$	0
Fine-tune best fixed expert	$4.69 \pm1.90$	$+22.6 \pm2.9$
Target-only LoRA	$5.34 \pm4.46$	$+37.4 \pm11.9$
Target-only + $L_2$-SP	$4.04 \pm0.77$	$+37.8 \pm13.2$
Adapter from scratch	$6.03 \pm2.64$	$+17.3 \pm23.4$
EWC ($\lambda= 10^2$, 3 seeds)	$8.20 \pm0.83$	$+4.7 \pm1.3$
Prioritised replay	$6.78 \pm1.33$	$+1.7 \pm0.8$
Joint replay (ours)	$6.91 \pm2.16$	$+0.9 \pm1.4$

Target-region training and replay. To separate the effects of target-region training and replay, we compare methods using the same 20 target scenes, optimisation steps, LoRA ranks, and learning rate (Table 3). All methods trained on target-region scenes achieve offsets of approximately 4–8 m. Target-only fine-tuning with $L_2$-SP [28] gives the lowest target offset (4.04 m), although its 95th-percentile jerk is 27% higher than that of joint replay.

The main difference is performance retention on the training ODDs. Fine-tuning without replay or EWC increases their summed offset by 17–38 m, including when $L_2$-SP regularisation is used. EWC [29] reduces forgetting at the cost of higher target offsets. Joint replay limits the summed regression to $0.9 \pm1.4$ m while retaining a target offset of $6.91 \pm2.16$ m. Prioritised replay shows no clear advantage over uniform replay. These comparisons indicate that target-region training accounts for the offset reduction, whereas replay mainly preserves performance on the original training ODDs.

Additional trajectory diagnostics. The target-region scenes contain no neighbouring agents, so time-to-collision and collision rates cannot be evaluated. We instead report additional trajectory diagnostics in App. § 25. Jerk and lateral acceleration are calculated from unsmoothed finite differences of the raw 10 Hz trajectories, so only comparisons between models are meaningful.

Compared with the static default, joint replay reduces the 95th-percentile jerk by 26% and increases forward progress over 8 s from 164 to 187 m. Lateral acceleration changes little, and large lateral excursions relative to the initial lanelet remain. The from-scratch variant of joint replay reduces lateral acceleration and the frequency of excursions beyond the straight $\pm3$ m band, but substantially degrades performance on the training ODDs (App. § 16).

Variance-Collapse Diagnostics for Test-Time Adaptation

Low lateral offset alone does not establish that a trajectory is useful. We examine two test-time adaptation methods that achieve low offsets but produce degenerate trajectories: TENT [23], which updates normalisation parameters during inference, and a hypernetwork that predicts LayerNorm offsets from geographic location.

We use two diagnostics: the variance $\sigma_K^2$ across $K$ samples from the same scene and the mean pairwise $L_2$ distance between trajectories from different scenes. Starting from the static default, TENT achieves an offset of 3.37 m, but its cross-scene trajectory distance falls from over 100 m to approximately 10 m, consistent with similar predictions across different scenes. The hypernetwork reduces $\sigma_K^2$ by two orders of magnitude and produces only 12 m of forward progress over 8 s. These cases illustrate how low lateral offset can accompany a loss of trajectory diversity or forward motion (App. § 10, App. § 11).

Cross-City Evaluation and Real-Vehicle Runs

Cross-city evaluation on nuPlan. We evaluate cross-city transfer on nuPlan using four leave-one-city-out splits. For each split, we fine-tune a rank-4 shared LoRA on the other three cities using the planner’s diffusion training loss. Across three seeds and using the same lateral-offset metric as on the held-out maps, fine-tuning reduces the open-loop lateral offset on Singapore from 8.64 to $5.60 \pm0.78$ m, by 35%, despite the difference in traffic direction. Improvements over the base planner are also observed in the other held-out cities (App. § 19). Unlike the target-region experiments, this evaluation uses no data from the held-out city and measures transfer from fine-tuning on the training cities.

Real-vehicle runs of the base planner. The base diffusion planner has also been tested on a physical vehicle with two adapter configurations: a production DPO LoRA trained on human preferences and a reward-trained shared-plus-expert adapter. For the latter, we conducted two runs on the ODD-Kashiwa course with the ODD-Kashiwa expert active. The first completed the course, with a comfort-violation rate of 47.7% under our proxy, compared with 37.7% for a human driver. In the second run, the vehicle travelled 72 m at speeds no greater than 0.23 m/s before stopping. These runs document the behaviour of the base planner on a physical vehicle; the joint-replay adapters have not yet been tested on the vehicle. Additional results for the DPO adapter are given in App. § 24.

Discussion, Limitations, and Conclusion

Our experiments show that selecting among the four existing experts offers limited improvement on the held-out maps, even with per-scene oracle selection. Updating the planner with a small amount of target-region data produces much larger reductions in open-loop lateral offset. Under matched training conditions, replaying training scenes mainly helps retain performance on the original ODDs rather than accounting for the target-region gains.

Geographic proximity. On the three primary held-out maps, ODD-Nagoya is both the nearest training ODD and the best fixed expert. We examine two additional regions to separate these effects. In a suburban area adjacent to ODD-Kashiwa but outside its training footprint, the nearest expert performs 1.4 m worse than ODD-Nagoya ($p = 0.001$, $n = 30$). In a dense urban region nearest to ODD-Hongo, the ODD-Hongo expert performs worst among the four (App. § 27). Geographic proximity therefore does not consistently identify the best expert. The success of the static default on our primary maps appears to reflect the strength of ODD-Nagoya rather than its proximity alone.

Limitations. The main limitation is that all results on the held-out maps are open-loop. In nuPlan’s reactive closed-loop simulator, the fine-tuned models score below the unadapted planner in all four held-out cities, with significant differences in three. For Singapore, the simulator score decreases from 0.858 to 0.598, and drivable-area compliance from 0.97 to 0.76. The joint-replay adapters have not been evaluated on a physical vehicle.

The primary held-out evaluation is also limited in scale, covering 4–10 road lanelets per map. We extend the oracle and feature-classifier analyses to 104 scenes, but the full eight-method routing comparison remains on the smaller pool. Our findings therefore concern the tested experts, routing methods, and representations. Their applicability to monolithic planners trained on pooled data [2] remains unknown.

The maps are proprietary. We release the model weights, scene splits, evaluation pipeline, and per-scene results through the project repository.

Conclusion. Overall, the results favour updating the planner over selecting among its existing experts when the objective is to reduce open-loop lateral offset in unseen regions. Whether these gains translate into better closed-loop driving remains an open question.

Acknowledgments

This work was supported by JSPS KAKENHI Grant Number JP26KJ0799 and by TIER IV, Inc.

Overview of the Appendix

This appendix gives the details behind the main text. Table 4 lists each appendix section next to the main-text section it supports. Appendix § 24 reports the real-vehicle runs and a separate study of DPO adapters on the same base planner; it is context for § 6 and does not evaluate the adaptation methods proposed in this paper.

Test-Time Adaptation Details

TENT Recipes and Variance-Collapse Diagnostics

Table 5 reports TENT-style test-time adaptation under two recipes on the disjoint target-region evaluation pool of seed 7. The lightweight recipe, TENT-LN, updates only the affine parameters of the decoder LayerNorm layers. Its loss is the variance across $K=4$ sampled trajectories, which serves as the diffusion analogue of the prediction entropy used by TENT [23, 24]. TENT-LN runs 5 SGD steps at lr=$10^{-4}$, starting from a fresh model for each scene, and its trainable parameters make up $\sim0.01\%$ of the model. The full recipe, TENT-online, follows the defaults of Wang et al. (2021) where the architecture allows: Adam at lr=$10^{-3}$, $K=32$ samples, model state carried over from scene to scene, and 10 epochs over the stream of 24 target-region scenes. We update LayerNorm rather than BatchNorm affine parameters because the Diffusion-Planner base planner has no Batch-Norm layers; this is the standard substitution for transformer-based planners [24]. A SAR variant backpropagates, in each epoch, only on the 50% of scenes with the lowest variance.

Collapse diagnostics. The best TENT-online fleet mean, 4.11 m at epoch 1, comes from variance collapse rather than from learning the new region. Over ten epochs, the $K$-sample variance loss falls by four orders of magnitude (40.6 $\to$ 0.0095), while the fleet mean rises to 5.09 m. For a diffusion trajectory planner under cross-region shift, any non-trivial TTA fleet mean should be reported together with (i) the within-scene variance $\sigma_K^2$ across $K$ samples and (ii) the pairwise $L_2$ distance between the mean trajectories of different scenes [30, 17]. Healthy configurations have $\sigma_K^2 \sim10^{-11}$ and a cross-scene $L_2 \in[105,150]$ m. TENT started from the static default reaches 3.37 m, but its cross-scene $L_2$ collapses to 10.2 m. The hypernetwork-LN recipe (§B.1) reduces $\sigma_K^2$ to $4 \times10^{-13}$. Stacking TENT on the hypernetwork recipe gives a cross-scene $L_2$ of 1.2 m and 3.7 m of forward progress at 0.46 m/s.

Table 5: Test-time adaptation baselines on the disjoint target-region evaluation pool of seed 7. TENT updates only the affine parameters of the decoder LayerNorm layers, using a trajectory-variance loss over $K$ samples. TENT-LN: $K=4$, 5 SGD steps, fresh model for each scene. TENT-online: $K=32$, Adam with $\mathrm{lr}=10^{-3}$, 10 epochs, model state carried over between scenes.

Method	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
Shared module only (TTA slice)	$14.26 \pm4.13$	$7.43 \pm6.11$	$37.40 \pm29.68$	$19.70$
Shared module only (HyperLN slice)	—	—	—	$22.76$
TENT-LN ($K=4$, 5 steps)	$14.15 \pm4.18$	$7.47 \pm6.14$	$36.99 \pm29.45$	$19.54$
TENT-online ($K=32$, epoch 1)	—	—	—	4.11
TENT-online ($K=32$, epoch 10)	—	—	—	$5.09$
TENT-online SAR ($K=32$, epoch 4)	—	—	—	$4.56$
Static default (ODD-Nagoya)	$4.51$	$4.82$	$31.88$	$13.74$
Joint replay (single checkpoint)	2.24	2.77	7.78	4.26

Hypernetwork-Conditioned LayerNorm

Recipe, Results and Diagnostic Probe

This section describes a context-aware TTA recipe that trains a supervised mapping from the ECEF unit vector $\ell$ of the deployment location to offsets $(\Delta\gamma, \Delta\beta)$ of the 36,608 LayerNorm affine parameters in the decoder DiT. The recipe reaches a low lateral offset, but the diagnostic probe of Table 7 shows that this offset is an artefact of nearly stationary trajectories.

Configuration	lat (m)	progress (m, 8 s)	speed (m/s)	cross-scene $L_2$
Frozen shared module only	24.89	170.0	21.3	150.4
Static default (ODD-Nagoya)	16.04	166.7	20.8	105.0
vMF mixture $\tau=200$ km	19.64	172.2	21.5	124.2
Hypernet-LN (this work)	5.27	12.3	1.5	73.0
Hypernet-LN + TENT polish	1.21	3.7	0.46	1.2
Static default + TENT polish	3.40	174.8	21.9	10.2

Recipe. Let $\ell\in S^2$ be the ECEF unit vector of the deployment location (§ 5.1). The hypernetwork $h_\theta: S^2 \to\mathbb{R}^{36,608}$ is a three-layer MLP with hidden width 64 and SiLU activations; it has 4.73 M parameters in total, and its output layer is zero-initialised. During training, each scene from a training ODD is paired with the ECEF unit vector $\ell_d$ of that ODD. At every forward pass we compute $(\Delta\gamma, \Delta\beta) = h_\theta(\ell_d)$ and apply these offsets to the LayerNorm modules through a forward hook that computes $F.\operatorname{layer\_norm}(x, w+\Delta\gamma, b+\Delta\beta, \varepsilon)$. We then run the diffusion sampler and minimise the mean-squared error to the recorded ego trajectory $\tau_{\mathrm{gt}}$. Training runs for 500 optimiser steps at $\mathrm{lr}=5\cdot10^{-5}$ and $\mathrm{wd}=10^{-3}$ on a pool of 772 pairs from the four training ODDs, and takes 2.7 minutes of wall-clock time on one consumer GPU. At deployment, the trained hypernetwork is conditioned on the unit vector of the centroid of the target-region map, and its output is applied to the LayerNorm affine parameters.

Results before the probe. Table 6 reports a fleet mean of 5.74 m for the best single seed (6.27 $\pm$ 0.59 over three seeds). Reducing the hidden width (64 $\to$ 16) raises the fleet mean to 11.0 m, which rules out a trivial lookup.

Table 6: Lateral offset of hypernetwork-conditioned LayerNorm before the diagnostic probe of Table 7.

Recipe	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
Shared module only	$14.26$	$7.72$	$46.30$	$22.76$
Static default (ODD-Nagoya)	$4.51$	$4.82$	$31.88$	$13.74$
Joint replay (single checkpoint)	$2.24$	$2.77$	$7.78$	$4.26$
HyperLN, $h=64$, no jitter (best single seed)	$11.19$	$1.34$	$4.68$	$5.74$
HyperLN, $h=64$, no jitter, 3-seed mean	$12.17 \pm1.18$	$1.39 \pm0.20$	$5.26 \pm0.39$	$6.27 \pm0.59$
HyperLN, $h=16$, jitter $0.1^\circ$ (capacity ablation)	$15.42$	$1.95$	$15.71$	$11.02$

Diagnostic probe. The probe shows that the hypernetwork recipe produces nearly stationary trajectories. We measure forward progress $\lVert x(T)-x(0)\rVert$, mean speed $\lVert x(T)-x(0)\rVert/T$ at $T=8$ s, and the cross-scene pairwise $L_2$ between trajectories, each centred at its own starting frame. Table 7 shows that the hypernetwork recipe produces 12 m of forward progress at 1.5 m/s (walking speed).

Its low lateral offset is the trivial offset of a nearly stationary trajectory, so the apparent gains in Table 6 are artefacts.

Status of the hypernetwork recipe. We retract the hypernetwork-LN recipe as a constructive mechanism. The three constructive mechanisms reported in the main text are the vMF mixture (§ 5.1), shared-adapter repair (§ 5.2), and joint replay (§ 5.3). We include the hypernetwork-LN recipe as a documented failure mode, not as a deployable recipe, and it should not be cited as a constructive mechanism in later work.

Derivation and Weights of the vMF Mixture

Bayesian interpretation of the mixing weights. The mixing weights of the vMF mixture can be read as a Bayesian posterior over the training ODDs. Each weight is a softmax over the negative great-circle (Haversine) distance between the deployment location $\ell$ and the geographic centre $\mu_d$ of training ODD $d$:

where the temperature $\tau$ is in kilometres. Let $D \in\{1,\ldots,K\}$ be the unobserved index of the training ODD, with a uniform prior, and let the deployment location have the likelihood $p(\ell\mid D=d) \propto\exp(-d_{\mathrm{geo}}(\ell,\mu_d)/\tau)$ on the sphere, which decays exponentially with distance from $\mu_d$. The normalising constant of this likelihood is invariant under rotations of the sphere, so it does not depend on $d$, and Bayes’ rule gives $p(D=d \mid\ell)=\alpha_d(\ell)$ exactly. In the limit $\tau\to0$ the weights select the nearest ODD, which is the static default on our three maps; in the limit $\tau\to\infty$ they become uniform; intermediate values of $\tau$ lie between these two cases. We keep the name vMF mixture because each ODD contributes a kernel on the sphere centred at its location. A von Mises–Fisher likelihood $\exp(\kappa\mu_d^\mathsf{T}\ell)$, however, decays with the squared distance at small separations, so it defines a different weighting from the one we evaluate. Under quadratic loss, the Bayes-optimal trajectory given the scene and location $(x,\ell)$ is the posterior mean

where $f_d(x)$ is the expert of training ODD $d$. Our weight mixture $\widetilde{W}(\ell)=\sum_d\alpha_d(\ell)W_d$ averages the expert weights rather than their outputs, so it matches this rule only to first order in the differences between the expert weights. Table 8 lists the resulting weights.

$\tau$	$\alpha$ (Hongo, Kashiwa, Shalun, Nagoya)	Knowledge Hub	Ishiodai	Morikoro
$\rightarrow0$ (hard MAP = ODD-Nagoya)	(0, 0, 0, 1)	4.51	4.82	31.9
200 km (soft mix, headline)	(0.20, 0.18, 0.00, 0.62)	4.02	4.63	38.9
$\rightarrow\infty$ (uniform soup)	(0.25, 0.25, 0.25, 0.25)	—	—	—

Choice of distance metric. At our geographic scales, the mixing weights do not depend on the choice of distance metric. Table 9 reports the weights of the vMF mixture for Morikoro at $\tau=200$ km under four distance metrics: Haversine, the ECEF chord, an equirectangular flat-Earth approximation and a local tangent plane (UTM). The four weight vectors agree to four decimal places (largest $L_1$ deviation $7\times10^{-5}$).

Distance metric	$\alpha_{\mathrm{Hongo}}$	$\alpha_{\mathrm{Kashiwa}}$	$\alpha_{\mathrm{Shalun}}$	$\alpha_{\mathrm{Nagoya}}$
Haversine (great-circle)	0.1981	0.1774	0.0000	0.6245
ECEF chord on $S^2$	0.1982	0.1774	0.0000	0.6244
Equirectangular flat-Earth	0.1981	0.1774	0.0000	0.6245
Local-tangent-plane (UTM)	0.1981	0.1774	0.0000	0.6245

Table 10 reports the lateral offset of the vMF mixture, with the posterior weights derived above, at four temperatures.

Weight-Averaging Baselines: Learned Coefficients, Model Soups and TIES-Merging

Learned mixing coefficients. Learning the mixing coefficients on target-region scenes does not beat the static default either. We replace the vMF weights with a learnable 4-vector $\alpha$,

and train $\alpha$ for 200 Adam steps at lr=$10^{-2}$ on 20 target-region scenes under the 10-term reward (§ 3), with the base planner frozen. The learned weights concentrate on one expert that is not the geographically nearest ($\alpha=(0.06, 0.12, 0.70, 0.12)$, entropy 1.34 bits). On the seed-7 evaluation pool, the resulting fleet mean is 22.82 m (Knowledge Hub 8.74, Ishiodai 31.72, Morikoro 28.00), worse than the static default on the same pool (17.86 m, Table 11). No $\alpha$ that we tried within the convex hull of the four experts beats the static default; the larger gains in this paper come from shared-module repair (§ 5.2) and joint replay (§ 5.3).

Table 11: Greedy soup of the four per-ODD experts on the seed-7 disjoint target-region evaluation pool (CRC32 split, Appendix § 21). The experts are ranked by fleet mean (lowest first), the soup is initialised with the best one, and each subsequent expert is added only if the uniformly averaged soup improves on the evaluation pool. In the trial rows, A, B, C and D denote ODD-Hongo, ODD-Kashiwa, ODD-Shalun and ODD-Nagoya. Reference rows give the uniform soup over all four experts and the vMF mixture at $\tau=200$ km (GPS soft mix); the latter is copied from Table 10, was measured on Pool A, and is not comparable with the other rows.

Configuration	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
ODD-Hongo (ODD-Hongo) alone	5.99	39.06	55.59	33.55
ODD-Kashiwa (ODD-Kashiwa) alone	5.98	31.52	22.90	20.13
ODD-Shalun (ODD-Shalun) alone	13.6	31.53	30.63	25.25
ODD-Nagoya (ODD-Nagoya) alone	4.51	31.58	17.48	17.86
Soup {D, B} (trial)	4.62	31.80	19.93	18.78
Soup {D, C} (trial)	4.79	29.90	22.30	19.00
Soup {D, A} (trial)	3.79	34.12	31.09	23.00
Uniform soup over all four	4.93	32.91	27.60	21.81
Greedy soup final (single expert ODD-Nagoya)	4.51	31.58	17.48	17.86
GPS soft mix $\tau=200$ km (reference, Table 10)	4.02	4.63	38.9	—

Greedy soup. Greedy soup [13] over the four per-ODD experts ends with ODD-Nagoya alone (Table 11). We use the seed-7 disjoint target-region pool for validation. Starting from the best single expert, ODD-Nagoya, the procedure rejects every candidate addition. The uniform soup over all four experts (21.81 m) is worse than ODD-Nagoya alone (17.86 m).

Interpolation advantage of uniform soups. Uniform soups usually beat the average of their endpoints but not the best endpoint. We adapt the interpolation-advantage metric of Wortsman et al. [13] to errors, where lower is better:

$\Delta_{\mathrm{I}}$ is positive if and only if the soup beats the arithmetic mean of its endpoints, which indicates a bonus from linear mode connectivity [31]. For the soup to also beat the best endpoint (the strict soup effect of Wortsman et al.), $\Delta_{\mathrm{I}}$ must exceed the inter-task gap, defined as the mean endpoint error minus the best endpoint error. Equivalently, the gap to the best endpoint, $\Delta_{\mathrm{gap}}$, must be negative. $\Delta_{\mathrm{I}}$ is positive in nearly every cell of Table 12, but in fleet mean the inter-task gap is 1.4 to 5.4 times larger. The soup therefore loses to the best single expert except in two cells (visualised in Figure 5).

Table 12: Interpolation advantage $\Delta_{\mathrm{I}}$ (mean endpoint error minus soup error) for each two-expert and four-expert uniform soup on the seed-7 CRC32-disjoint target-region evaluation pool (Appendix § 21). Positive values indicate that the soup beats the arithmetic mean of its endpoints, a bonus from linear mode connectivity. Table 13 reports $\Delta_{\mathrm{gap}}$ for the same rows.

Soup	Knowledge Hub	Ishiodai	Morikoro	Fleet
{ODD-Nagoya, ODD-Kashiwa}	+0.63	−0.26	+0.26	+0.21
{ODD-Nagoya, ODD-Shalun}	+4.27	+1.66	+1.76	+2.56
{ODD-Nagoya, ODD-Hongo}	+1.46	+1.20	+5.45	+2.70
Uniform {D, B, C, A}	+2.60	+0.51	+4.06	+2.39

Soup	Knowledge Hub	Ishiodai	Morikoro	Fleet
{ODD-Nagoya, ODD-Kashiwa}	+0.10	+0.29	+2.45	+0.93
{ODD-Nagoya, ODD-Shalun}	+0.28	−1.63	+4.82	+1.14
{ODD-Nagoya, ODD-Hongo}	−0.72	+2.54	+13.61	+5.14
Uniform {D, B, C, A}	+0.41	+1.39	+10.11	+3.95

TIES-Merging. Sign-aware merging does not close the inter-task gap either (Table 14). TIES-Merging [14] reduces interference between task vectors in three steps: within each layer, each $\Delta_i$ is trimmed to its top-$k\%$ entries by magnitude; for each entry, the elected sign is that of the magnitude-weighted majority; and the merged $\Delta$ averages only the entries whose trimmed sign matches the elected sign. We use keep-densities of 20%, the standard setting of Yadav et al. (“canonical Yadav” in the table), and 50% as an ablation. Across all expert pairs and adapter layers, the mean absolute off-diagonal cosine similarity between task vectors is $\lvert\cos\rvert=0.065$. The task vectors are therefore nearly orthogonal, so TIES has few sign conflicts to resolve. TIES is statistically indistinguishable from the uniform soup (22.4–22.5 m versus 21.8–22.3 m, with $\sim0.5$ m of cuDNN re-evaluation noise) and loses to the best single expert (17.86 m).

Configuration	Knowledge Hub	Ishiodai	Morikoro	Fleet mean
Best single (ODD-Nagoya, Table 11)	4.51	31.58	17.48	17.86
Uniform soup all 4 (Table 11)	4.93	32.91	27.60	21.81
TIES-Merging, keep-density 20% (canonical Yadav)	5.83	35.56	26.14	22.51
TIES-Merging, keep-density 50% (ablation)	5.19	35.05	26.88	22.37
Uniform soup all 4 (TIES re-eval, cuDNN noise)	6.07	32.30	28.51	22.29
Joint-replay from-scratch (the rank-allocation sweep) – reference	1.94	6.00	6.81	4.92

Shared-Adapter Repair: Per-Expert Results and Perturbation Ablation

Configuration	Knowledge Hub	Ishiodai	Morikoro
Static default (ODD-Nagoya) (original shared)	$4.51 \pm0.79$	$4.82 \pm0.84$	$31.88 \pm32.05$
shared module only, original	$14.3 \pm4.1$	$7.7 \pm4.6$	$46.3 \pm35.3$
shared module only, repaired	$6.0 \pm2.2$	$6.1 \pm1.6$	$21.4 \pm26.0$
ODD-Hongo + repaired-shared	$24.5 \pm13.2$	$17.6 \pm6.4$	$50.3 \pm43.2$
ODD-Kashiwa + repaired-shared	$7.9 \pm0.5$	$7.8 \pm0.5$	$11.1 \pm10.5$
ODD-Shalun + repaired-shared	$6.0 \pm2.1$	$5.8 \pm1.5$	$18.3 \pm24.9$
ODD-Nagoya + repaired-shared	$11.0 \pm3.6$	$9.5 \pm2.6$	$12.2 \pm8.2$

Ablation of the perturbation components. The perturbation used for shared-module repair has three components: a per-lanelet SE(2) rotation drawn uniformly from $\pm45^\circ$, a cubic Bezier curvature warp with amplitude $\pm3$ m on each lane, and a random boundary drop that removes one of the two lane boundaries with probability 0.5. Table 16 disables each component in turn, repeats the 500-step fine-tune of the shared module under the same 10-term reward, and reports the resulting lateral offset, including per-seed values on Morikoro, the open-park map.

Configuration	Knowledge Hub (seeds)	Ishiodai (seeds)	Morikoro (seeds)	Morikoro per-seed
Baseline: rot + bezier + drop	$5.99 \pm2.23$	$6.05 \pm1.63$	$21.4 \pm26.0$	single seed
− SE(2) rotation	$6.05 \pm3.37$	$7.12 \pm3.61$	$33.13 \pm7.24$	[41.4, 28.0, 29.9]
− Bezier curvature warp	$7.01 \pm2.99$	$7.53 \pm2.69$	$26.28 \pm4.70$	[31.5, 22.4, 24.9]
− Boundary drop	$6.95 \pm2.50$	$7.56 \pm2.19$	$28.12 \pm13.96$	[44.1, 22.0, 18.3]

SE(2) rotation contributes the most; the Bezier warp and the boundary drop contribute less, and by similar amounts. An earlier single-seed run suggested that disabling the boundary drop costs nothing. We retract that claim: the seed-to-seed standard deviation of 13.96 m on Morikoro without the boundary drop shows that the finding was driven by noise.

Distilled Regional Adapter

Regional Adapter via Distillation

Table 17 reports the distilled regional adapter under the protocol of § 3. The student is a rank-4 LoRA on the frozen base planner, and the teacher is a soft mixture of the experts at $\tau=200$ km. The student is trained on 56 scenes from the seed-42 training pool and evaluated on the disjoint seed-7 lanelet pool.

The distilled student follows the coarse route geometry (forward progress of 138+ m) but beats the static default only on Ishiodai and is worse on Knowledge Hub and Morikoro (Table 17). The Lipschitz argument below explains this result at rank 4.

Map	Max lateral (m)	Forward progress (m)	Static default (m)	Change
Knowledge Hub	$18.63 \pm6.19$	$156.80 \pm2.34$	$4.51$	$+313\%$
Ishiodai	$19.32 \pm30.53$	$149.61 \pm25.40$	$31.58$	$-39\%$
Morikoro	$37.83 \pm20.69$	$151.00 \pm14.18$	$17.48$	$+116\%$

Lipschitz capacity of the student and its empirical limit. The disjoint-evaluation result follows from the function class of the student. A rank-$r$ LoRA student on a frozen base planner has a Lipschitz constant bounded by the product of per-layer operator norms plus a rank-dependent perturbation term. Let $f_T:\mathcal{X}\to\mathbb{R}^d$ denote the teacher (the $\alpha$-blended merged-expert dictionary) and $f_S$ the rank-$r$ student. Each LoRA layer perturbs the base linear map $W_0 \in\mathbb{R}^{d_{\mathrm{out}}\times d_{\mathrm{in}}}$ by $BA$, with $A \in\mathbb{R}^{r\times d_{\mathrm{in}}}$ and $B \in\mathbb{R}^{d_{\mathrm{out}}\times r}$. With the standard initialisation and the weight-decay-bounded training that we use, $\lVert BA\rVert_2 \le\beta\sqrt{r}$ for a layer-wise constant $\beta$, so the global Lipschitz upper bound across $L$ MLP layers is

The per-layer perturbation rank of the teacher is $K_{r_e}=32$ (four experts $\times$ rank 8). Its Lipschitz upper bound is the same product with $\sqrt{r}$ replaced by $\sqrt{32}$, which is roughly $\sqrt{8}$ larger at every layer. Structurally, the student is a low-pass version of the teacher.

The rank-128 Skyline of §I.1 (32× larger) still does not match the per-expert baseline, so the bottleneck is the supervision signal (trajectory MSE to the teacher) rather than $r$. Replacing this signal with the joint-replay recipe of § 5.3 (single checkpoint) gives 2.24/2.77/7.78 m on Knowledge Hub / Ishiodai / Morikoro with a budget of 20 target-region scenes, on the same evaluation pool.

Joint-Replay Recipe and Frontier

The Joint-Replay Frontier

The methods of § 5.1–§F.1 keep the experts frozen. They cause no forgetting by construction, but their target-region accuracy is limited to the disjoint-evaluation results of Table 17. Here we remove the freeze and measure what a small, targeted relaxation gains.

Recipe. Joint replay unfreezes the full adapter stack (parameter inventory in App. § 21) and trains it to maximise the original ODD-conditioned reward of § 3. The training pool combines 200 training-ODD scenes (50 from each of the four training ODDs) with a small target-region pool from the seed-42 disjoint training set, at a fixed ratio of 10:1 in favour of training-ODD scenes. We use AdamW with $\mathrm{lr}=5 \times10^{-5}$ and a gradient accumulation factor of 4, and stop after 500 optimiser steps ($\sim5$ minutes of wall-clock time on one consumer GPU). We call the resulting set of weights the joint-replay frontier, because a single setting, the target-region pool size $n_{\mathrm{target-region}}$, moves it between the frozen adapter stack and full retraining.

Trajectory metrics beyond lateral offset. Table 32 (App. § 25) reports lateral offset, 95th-percentile jerk magnitude, 95th-percentile lateral acceleration, the fraction of trajectories that leave the $\pm3$ m corridor, and forward progress over 8 seconds on Pool A, the 24-scene routing pool. These are open-loop proxies from a single rollout, not closed-loop safety measurements. The absolute jerk values (700–1300 m/s$^3$) are large because we report raw third-order finite differences, without the Savitzky–Golay smoothing that the V3 comfort proxy of §O applies before its ISO 2631 threshold check. Only relative comparisons between configurations are meaningful.

configuration	lateral offset (m)	jerk-p95	lat-acc-p95	exit-%	progress (m)
shared module only (no expert)	24.89	1323	44.31	95.8	164.3
static default (ODD-Nagoya)	16.04	970	54.40	100.0	163.7
joint-replay (inherit-shared)	6.95	719	52.25	100.0	186.9
joint-replay (from-scratch r=4)	4.35	848	23.47	50.0	178.1

Data budget and shared-module initialisation. The joint-replay frontier is a family with two settings, ($n_{\mathrm{target-region}}$, shared init). The pool size $n_{\mathrm{target-region}}$ trades data budget for held-out accuracy. The initialisation of the shared module, either inherited from the pretrained model or trained from scratch, trades forgetting on the training ODDs for target-region accuracy. The distilled regional adapter (§F.1) lies off this frontier, on the axis with no target data: it causes no forgetting by construction and reaches a fleet mean of 25.26 m. With the inherited shared module (inherit-shared), $n_{\mathrm{target-region}}=20$ gives 15.43 m with $\sum\Delta_{\mathrm{route-dev}}=0.04$ m. With the shared module trained from scratch, the same $n$ falls in the 5–9 m range but costs a +11–16 m regression on the training ODDs. These numbers come from the rank sweep and use the evaluation slice with 30 training scenes per map, which is harder than the per-seed slices of § 5.3. They can be compared with each other but not with the numbers in the main text (see the footnote in App. § 17).

Sample Complexity over Training Seeds

Joint-Replay Sample Complexity

Table 18 varies the target-region pool size $n_{\mathrm{target-region}} \in\{5, 10, 20, 40, 80\}$ for joint replay with the inherited shared module, with the training-ODD pool fixed at 200 scenes and training fixed at 500 optimiser steps. Target-region training scenes are drawn from the seed-42 disjoint training pool of 144 candidate scenes. The evaluation set is the corresponding seed-7 pool of 24 disjoint target-region scenes, built from the remaining lanelets.²

$n_{\mathrm{target-region}}$	fleet (seed-42, m)	fleet (3-seed mean$\pm$std, m)	Training-ODD $\sum\Delta_{\mathrm{route\ dev}}$ (m)	Training-ODD $\sum\Delta_{\mathrm{progress}}$ (m)	Train wall-clock
Pre (shared module only; $n_{\mathrm{train}}$=80 eval slice)	17.48	—	—	—	—
5	6.76	9.79 $\pm$ 5.14	+5.00	+25.86	4.5 min
10	7.54	10.14 $\pm$ 6.62	−0.33	+3.29	4.5 min
20	5.51	6.17 $\pm$ 1.23	+2.43	+21.37	4.5 min
40	5.10	5.67 $\pm$ 1.06	+0.54	+4.69	4.4 min
80†	4.44	— (†)	+0.23	−0.56	4.3 min

Seed variance at small $n$. At small $n$, the best result varies strongly across seeds. The three-seed std falls by 4.2$\times$ from $n$=5 (5.14 m) to $n$=20 (1.23 m) (Figure 4), and by a factor of five from $n$=10 (6.62 m) to $n$=20. Over the same sweep, summed training-ODD forgetting stays within a cross-seed std of 0.94–1.23 m at every $n$. We therefore give $n_{\mathrm{target-region}} \ge20$ as the budget at which results are stable in practice. The single-seed minimum at $n=5$ (seed-42; 6.76 m, −61%) is optimistic, since its three-seed mean is 9.79 m (−44%). At $n=40$ the mean (5.67 ± 1.06 m) is still above the single-seed $n=80$ reference (4.44 m).

Capacity Test with a High-Rank LoRA

Capacity under Reward Supervision

A LoRA with thirty-two times more parameters, trained by reward backpropagation, does not close the gap to the small adapter distilled with an MSE loss. This configuration, Skyline, attaches a rank-128 LoRA to every decoder MLP layer (≈ 2.5 M trainable parameters, ∼ 32× the distilled adapter), freezes the base planner, and overfits it to the held-out scenes by direct reward backpropagation for 2000 steps. Table 19 compares its lateral offset with that of the distilled adapter and the static default. The bottleneck is thus the supervision signal rather than capacity. Matching the teacher under an MSE loss is a low-curvature target that the Lipschitz-bounded student (§F.1) can track, whereas reward backpropagation admits reward maxima with large lateral offsets, which the high-capacity Skyline reaches first.

Configuration	Knowledge Hub	Ishiodai	Morikoro
Static default (no adaptation)	4.51	4.82	31.88
Distilled regional adapter (78 K params, 1.5 min)	6.10	4.05	18.88
Skyline rank-128 LoRA (2.5 M params, ≈ 15 min)	24.09 ± 0.02	24.28 ± 0.09	24.35 ± 0.12

nuPlan Leave-One-City-Out Evaluation

Cross-City Evaluation on a Public Benchmark

We repeat the cross-city evaluation on the public nuPlan dataset with a leave-one-city-out protocol over four cities: Boston, Pittsburgh and Las Vegas (right-hand traffic, ≈58 K scenes) and Singapore (sg-one-north, left-hand traffic, ≈9 K scenes). Singapore is the only left-hand-traffic city in nuPlan.

Planner variant and input/output changes. The nuPlan checkpoint is incompatible with our Autoware stack (740 missing keys under strict loading). We therefore use the nuPlan-compatible variant of the diffusion planner and reproduce our fine-tuning setup in it. A rank-4 shared LoRA is attached to every nn.Linear layer of the decoder outside multi-head attention (89,472 trainable parameters) and trained for 500 steps with the official diffusion training loss (marginal-probability noise schedule and score MSE) on the three training cities (Boston, Pittsburgh and Las Vegas when Singapore is held out). No data from the held-out city is used. We make two input/output changes. The agent-future tensor of each scene is stored as $(x,y,\theta)$ and is converted to $(x,y,\cos\theta,\sin\theta)$ before the loss, and the 32 neighbour-future tracks are truncated to predicted_neighbor_num=10. The training loss decreases monotonically from 10.37 to 3.38 on the three-city pool.

Three-seed 4×4 leave-one-city-out evaluation. For each held-out city, we fine-tune on the other three cities with three seeds {42, 43, 44} and evaluate on a fixed pool of 50 scenes per city. Table 20 reports the mean ± std over seeds; the std is below 1 m for every entry. Every held-out diagonal entry improves on the base planner in its column, and every entry for a training city also improves on the base, which shows that performance on the cities seen in training is preserved.

Configuration	Boston eval	Pittsburgh eval	Las Vegas eval	Singapore eval
Base (single seed)	2.17	4.51	1.86	8.64
Boston held-out (3 seeds)	1.63 $\pm$ 0.16	3.15 $\pm$ 0.24	1.25 $\pm$ 0.20	5.10 $\pm$ 0.30
Pittsburgh held-out (3 seeds)	1.71 $\pm$ 0.21	3.40 $\pm$ 0.37	1.37 $\pm$ 0.27	5.61 $\pm$ 0.66
Las Vegas held-out (3 seeds)	1.71 $\pm$ 0.18	3.27 $\pm$ 0.21	1.34 $\pm$ 0.18	5.44 $\pm$ 0.46
Singapore held-out (3 seeds, LHT)	1.71 $\pm$ 0.25	3.49 $\pm$ 0.44	1.42 $\pm$ 0.27	5.60 $\pm$ 0.78

Distance from the training cities. Singapore ($\approx1.3^\circ$ N, left-hand traffic) lies 5,000–15,000 km from the three training cities. The held-out maps of the target region lie 11–17 km from ODD-Nagoya, but for Singapore a static default has no nearby ODD to fall back on. Even so, the Singapore-held-out row of Table 20 reduces the lateral offset on Singapore from 8.64 to 5.60 $\pm$ 0.78 m ($-35\%$) without any Singapore data. Because no data from the held-out city is used, this experiment does not test joint replay; it shows that the fine-tuned planner transfers to a distant city in open loop.

Single-seed $4 \times4$ transfer matrix. To check whether the Singapore result is an artefact specific to that city, we also report the full $4 \times4$ transfer matrix for a single seed (Table 21). Held-out diagonal entries are within 80%–99% of the entries for cities seen during training. This is consistent with the fine-tuning transferring almost without loss across the three right-hand-traffic North American cities and partially to left-hand-traffic Singapore.

LoRA training set	Boston	Pittsburgh	Las Vegas	Singapore
None (base BC)	2.14 $\pm$ 6.68	4.58 $\pm$ 8.92	1.80 $\pm$ 3.95	8.55 $\pm$ 10.09
3-city, holdout Boston	[1.71 $\pm$ 4.55]	3.03 $\pm$ 5.94	1.36 $\pm$ 2.50	5.40 $\pm$ 6.53
3-city, holdout Pittsburgh	1.71 $\pm$ 4.24	[3.50 $\pm$ 6.42]	1.34 $\pm$ 2.21	5.41 $\pm$ 6.51
3-city, holdout Las Vegas	1.62 $\pm$ 4.28	3.36 $\pm$ 6.48	[1.25 $\pm$ 2.31]	5.30 $\pm$ 6.46
3-city, holdout Singapore	2.05 $\pm$ 4.42	3.69 $\pm$ 6.37	1.86 $\pm$ 2.77	[5.93 $\pm$ 6.68]

Routing Feature Ablations

This section reports the three routing and feature experiments referenced in § 4. (i) We extend the hand-crafted scene feature from 8 to 38 dimensions by adding histograms of traffic lights, line types and speed limits. The extended feature attains 1.000 validation accuracy on the four-ODD training pool, but oracle routing accuracy drops from 0.375 at 8 dimensions to 0.250 (chance) at 38 dimensions, and the resulting fleet mean rises from 31.0 to 36.9 m. (ii) We measure how much information a feature carries about the per-scene oracle expert with a summed mutual-information statistic: we sum per-coordinate KSG estimates [27] over the feature dimensions. The sum is not the joint mutual information, which cannot exceed $\log4 \approx1.39$ nats for a four-valued label, and it counts redundant information more than once. We therefore use it only as a test statistic against a permutation null. For the 256-d planner-encoder embedding, the statistic drops from 60.3 on the in-distribution training-ODD pool to 15.4 on the held-out pool, against a permutation-null mean of 9.5 ($p=0.088$). For the 3-d GPS position, it drops from 4.25 to 0.00 ($p=1.000$), because GPS coordinates vary little within the target region compared with the variation between training ODDs on which GPS was discriminative. (iii) The reward-as-scorer Selector picks $\arg\max_{\epsilon} R(\tau_{\epsilon})$ at inference time, using the planner’s own training reward. It picks ODD-Shalun on 20/24 held-out scenes, which gives a routing accuracy of 0.125 (half that of random choice) and an offset of 29.8 m (mean over scenes; 26.6 m when averaged over maps as in Table 2). The advantage of the static default comes from a constant marginal prior (always use the expert of the nearest training ODD), not from per-scene discrimination, regardless of whether the routing feature is based on perception or on geography.

Hyperparameters and Training Recipes

Table 22 lists all training recipes; each runs on a single consumer GPU. All recipes use AdamW (weight decay 0.01 unless noted otherwise), gradient-norm clipping at 1.0 and gradient accumulation of 4 (effective batch of 4 scenes), without mixed precision. The DPM-Solver++ sampler runs $N=10$ second-order denoising steps with logSNR-spaced timesteps. It is deterministic and differentiable end to end, which enables reward back-propagation [1, 2]. No hyperparameter is tuned on the held-out maps; all values are inherited from the base Diffusion-Planner recipe or set by in-distribution validation.

Table 22: Hyperparameters of the training recipes: optimisation budget. The budgets exclude the training of the underlying base planner, which is not part of this paper’s contribution. The loss and training data of each recipe are given in Table 23.

Recipe	Loss	Train data
Shared-module repair (§5.2)	ODD reward	$4 \times50$ training-ODD npz, perturbed in-place
Rank-8 shared replication (App. E)	ODD reward	same as above
Regional-adapter distillation (§F.1)	MSE to teacher trajectory	60 seed-42 target-region train scenes
Joint replay (§7)	ODD reward	200 prod npz + 20 target-region seed-42
Joint-replay sample-complexity (§H.1)	ODD reward	200 prod + {5, 10, 20, 40, 80} target-region
Skyline rank-128 (§I.1)	ODD reward	24 target-region eval scenes (overfit)
VD-GRPO (c=50) (variance-decoupled GRPO study)	VD-GRPO advantage · noise-MSE log-pi	200 prod + perturbations
nuPlan 3-city LoRA (§J.1, per LOO row)	diffusion noise-MSE	3000 npz per non-held-out city
nuPlan Singapore distillation	MSE to teacher trajectory	100 Singapore teacher rollouts

Table 23: Hyperparameters of the training recipes: loss and training data (companion to Table 22). In the training-data column, “npz” denotes scene files and “prod” denotes the training ODDs.

Recipe	Trainable params	LR	Steps	Wall-clock
Shared-module repair (§5.2)	78,368	$5 \times10^{-5}$	500	3.9 min
Rank-8 shared replication (App. E)	156,736	$5 \times10^{-5}$	500	4.0 min
Regional-adapter distillation (§F.1)	78,368	$1 \times10^{-4}$	300	1.5 min
Joint replay (§7)	862,048	$5 \times10^{-5}$	500	5.0 min
Joint-replay sample-complexity (§H.1)	862,048	$5 \times10^{-5}$	500	4.4–5.7 min each
Skyline rank-128 (§I.1)	$\sim2.5 \times10^{6}$	$5 \times10^{-5}$	2000	15 min
VD-GRPO (c=50) (variance-decoupled GRPO study)	78,368	$5 \times10^{-5}$	500	13 min
nuPlan 3-city LoRA (§J.1, per LOO row)	89,472	$5 \times10^{-5}$	500	1 min per row
nuPlan Singapore distillation	89,472	$1 \times10^{-4}$	200	1 min

Reward function (per-ODD weights). The ODD-conditioned reward is a linear combination of 10 terms that depend only on the trajectory, with separate weights for each ODD (§ 3). The per-ODD weights are taken from the underlying Diffusion-Planner training run and are not tuned in this paper. As an example, the default weights are progress 2.0, route deviation 2.0, curvature 3.0, comfort 0.5, heading error 1.0, stop bias 1.0, lateral acceleration 1.0, collision 4.0, RSS obstacle 1.5 and RSS route 0.5. The progress term is clamped at 200 m so that the reward does not diverge on long-horizon predictions. At convergence, the reward typically lies in the $O(300$–$500)$ range.

Disjoint training and evaluation split. The training pool (seed 42) and the evaluation pool (seed 7) of road lanelets are produced by the deterministic helper function disjoint_scene_split in our release. For each held-out map, the helper (i) extracts all road lanelets, (ii) shuffles them with seed 42 plus a per-map salt and takes the first $n_{\mathrm{train}}$ as training lanelets, and (iii) shuffles the remaining lanelets with seed 7 and takes the first $n_{\mathrm{eval}}$ as evaluation lanelets. Knowledge Hub has only four road lanelets, so all four are reserved for evaluation and the map contributes no training scenes. The helper is unit-tested to guarantee zero overlap between the two index sets.

Parameter-count breakdown of the base planner and adapter stack. Table 24 lists the parameters of the base planner, its DiT decoder and the adapter stack. LoRA wraps only the MLP nn.Linear layers of the DiT decoder, a subset of 4.05 M parameters. The remaining $\sim3.04$ M DiT parameters (self-attention, cross-attention, LayerNorm and adaLN modulation) are frozen without LoRA modulation. They are not wrapped because the forward pass of PyTorch’s nn.MultiheadAttention accesses out_proj.weight through a fused-attention fast path, which fails on a wrapped LoRALinear child (see § 3).

Component	Parameters	Role
Base Diffusion-Planner (vanilla, no LoRA)
encoder (frozen)	7,419,264	frozen
decoder (frozen)	7,083,929	frozen
of which DiT total	7,082,564	frozen
DiT.preproj (fc1 + fc2)	297,728	LoRA target
DiT.blocks (×3)	5,922,816	mixed
DiT.final layer (proj[1] + proj[4])	729,924	LoRA target
of which decoder wrapper/glue	1,365	frozen
Full model total	14,503,193	frozen
Per DiT block (×3, identical structure)
self-attention	263,168	frozen, no LoRA
cross-attention	263,168	frozen, no LoRA
mlp1 (fc1 + fc2)	525,568	LoRA target
mlp2 (fc1 + fc2)	525,568	LoRA target
adaLN_modulation	394,752	frozen, no LoRA
norm×4	2,048	frozen, no LoRA
LoRA-wrapped frozen subset (the ”modulated” base)
sum over LoRA-target nn.Linear layers	4,046,404	frozen base, modulated by LoRA
adapter trainable modules (joint-replay configuration, § 5.3)
shared LoRA (rank 4)	78,368	trainable
expert LoRA ×4 (rank 8 each)	626,944	trainable
adapter trainable total	705,312	trainable
Full model with adapter	15,208,505	95.4% frozen, 4.6% trainable

Details of the Routing Schemes

This section gives the per-scheme details summarised in § 4. Unless stated otherwise, all results are on Pool A.

Scene-conditioned MLP. The MLP reaches 1.000 validation accuracy on the four-ODD training pool. On the held-out maps, however, it routes nine of ten Ishiodai scenes and five of ten Morikoro scenes to ODD-Hongo rather than to the geographically nearest expert, ODD-Nagoya. This doubles the static default’s offset on Ishiodai and on Morikoro.

Self-consistency. Both variants, with and without magnitude normalisation, effectively select the shared module alone, because the consistency metric systematically favours small-magnitude outputs.

Denoising loss. The pooled Kendall-$\tau$ correlation between the denoising loss and the realised offset of each expert is 0.172, below the preregistered threshold of 0.2.

Conformal corridor. At $T=5$ m, the corridor abstains on every scene. At $T=15$ m, it reduces to the vMF mixture (§ 5.1) and adds no triage signal of its own.

Reward-supervised gate. The gate is trained directly on realised offset. Across 50 seeds, it converges to a solution that places 0.967 of its weight on ODD-Nagoya, and it matches the static default on Morikoro (32.26 $\pm$ 0.56 m).

Reward-as-scorer. Selecting $\operatorname{arg\,max}_{e} R(\tau_e)$ at inference time routes 20 of 24 scenes to ODD-Shalun. Its routing accuracy against the oracle is 0.125, below the 0.25 of random choice.

Oracle headroom and classifiers. The oracle improves the mean offset over the 24 scenes from 16.04 to 15.15 m ($p=0.012$). This is a mean over scenes; Table 2 instead reports fleet means (13.74 m for the same default). On a 104-scene pool built from the same maps with the same protocol but new start lanelets, the gain is 1.34 m (bootstrap CI [0.7, 2.2]), and on Pool B it is 1.1 $\pm$ 0.5 m. For comparison, joint replay improves the mean over the 24 scenes from 16.04 to 6.95 m ($p=0.0005$; 19 of 24 scenes improve). Leave-one-out classifiers (logistic regression, $k$-NN and SVM) using the 8 hand-crafted features or the 256-d encoder embedding reach exactly the majority-class accuracy: 0.667 on the 24 scenes and 0.625 on the 104 scenes.

Conformal Calibration Details

Table 25 reports the split-conformal calibration of each expert. For reproducibility, the last column also gives the in-sample residual quantile used in an earlier draft, which has no coverage interpretation.

Expert	$n_{\mathrm{train}}$	$n_{\mathrm{cal}}$	mean	std	split-conformal	in-sample
ODD-Hongo	108	12	20.5	20.0	67.9	83.5
ODD-Kashiwa	108	12	17.4	11.0	34.2	53.9
ODD-Shalun	108	12	11.4	4.6	17.1	15.5
ODD-Nagoya	108	12	32.6	20.4	61.4	33.4

Exchangeability permutation test. The calibration residuals on the training ODDs and the residuals on the target region fail a pooled exchangeability test. For each expert, we draw $B=10000$ permutations of the labels that mark each residual as a training-ODD calibration residual or a target-region residual, recompute the difference in means under each permutation, and report the two-sided $p$-value as the fraction of permutations whose absolute difference is at least the observed value. The pooled test, with 48 training-ODD and 96 target-region residuals, gives an observed difference of $+18.15$ m and $p=0.0035$. Per-expert tests at $\alpha=0.05$ reject for ODD-Hongo ($p=0.045$) and ODD-Shalun ($p=0.0001$), but not for ODD-Kashiwa ($p=0.70$) or ODD-Nagoya ($p=0.094$). The residuals, the permutation-test results and a summary of the null distribution are in results/routing-pool/conformal_exchangeability.json of the released repository.

Real-Vehicle Runs and a Separate DPO Adapter Study

This appendix reports a separate, deployment-oriented study on the same base planner and per-ODD experts. It is not part of the evaluation of joint replay or the other adaptation methods in the main text. The study fine-tunes a LoRA with a loss that combines Direct Preference Optimisation (DPO) [32] with an L2 imitation anchor, and trains it inside an outer loop of Sharpness-Aware Minimisation (SAM) [33]. Every output trajectory is scored with a three-layer proxy for the JAMA preventability framework, whose layers cover hard safety, careful-and-competent driving, and comfort; the tables call this proxy V3. The resulting configuration is compared with a production DPO LoRA that has been validated on the real vehicle in ODD-Kashiwa, and with the reward-back-prop family of reward-trained adapters, whose regression in comfort motivated the study.

JAMA-Inspired Preventability Proxy

The proxy is a per-trajectory scorer. It reports three layers separately and assigns each scenario to one of the buckets {cold_start, curve, straight, route_following, object_interaction}. It is not a full implementation of JAMA Ver. 4.0 §6, which requires a brake-delay simulator and a judge of Responder and Initiator roles; we build neither. A layer flags a trajectory if any of its criteria is triggered.

The strict_safety layer covers hard constraints with five criteria. These are a collision proxy ($0.5$ m; this threshold is our own, since JAMA does not specify an absolute distance), a minimum time-to-collision ($2.0$ s, taken from JAMA Ver. 4.0 §6.3.1 fig:108, which cites UNR ECE/TRANS/WP.29/1091), departure from the route corridor ($1.75$ m, derived from the $0.375$ m wobble allowance in JAMA fig:102 plus a half-lane buffer), extreme deceleration ($9.81$ m/s$^2$, the physical ceiling of $1$ G; the JAMA cap for a careful and competent driver is much tighter at $0.774$ G), and extreme lateral acceleration ($6.0$ m/s$^2$, roughly $0.6$ G). The c_and_c_driverlike layer covers behaviour that a careful and competent driver would not produce, with six criteria: a burst of acceleration from a cold start, driver-like limits on lateral acceleration, deceleration and acceleration, inconsistency between heading and velocity, and a check for a stuck planner. The comfort layer covers degraded ride quality rather than safety, with three criteria: jerk above $5$ m/s$^3$ (ISO 2631), lateral acceleration above $2$ m/s$^2$, and a speed-change rate above $3$ m/s$^2$.

Kinematics are computed from raw positions after a Savitzky–Golay filter (window 11, polynomial order 3, mode='interp'). The filter removes the finite-difference noise floor of $\sim250$ m/s$^3$ in raw 10 Hz position data. An earlier version of the proxy (v1) used mode='nearest' at the trajectory boundaries. This choice alone added a $32$ m/s$^3$ artefact on linear motion and made the jerk criterion over-trigger on the recorded human baseline. We therefore switched to mode='interp', which extrapolates the boundary samples with the fitted polynomial.

Scene-level split of training and validation data. Training and validation data are split at the level of scenes rather than preference pairs. This fixes a problem found by an audit of an earlier iteration of this study (v2): the in-loop evaluator drew from all ODD-Kashiwa scenes, whether or not a scene also appeared in a training preference pair. With seed 2026, the 3722 ODD-Kashiwa scenes are split into 2977 training and 745 validation scenes, and an assertion checks that the two pools are disjoint. Tables 26 and 28 report results on the validation pool only, so no scene used for evaluation appears in a preference pair seen during training.

Hybrid DPO + L2 Imitation Loss and SAM Outer Loop

Preference pairs are built from ODD-Kashiwa training scenes. The chosen trajectory is the recorded ego trajectory (the ego_agent_future field of the scene file). The rejected trajectory is sampled from a reward-back-prop LoRA. We use three samplers, Reward-back-prop (joint-replay), Reward-back-prop, and Reward-LoRA soup (12-variant), and generate $\sim3000$ candidates with each. A pair is accepted if and only if the chosen trajectory passes the c_and_c_driverlike layer of V3 and the rejected trajectory violates at least one criterion. This gives 9553 accepted pairs out of 11166 attempts (85.6%) on 3722 ODD-Kashiwa scenes. Pairs from the 745 validation scenes are not used for training (see the scene-level split above).

The hybrid loss interpolates between standard DPO and an imitation loss, the mean squared error to the chosen trajectory:

Setting $w_{\mathrm{imit}}=0$ recovers vanilla DPO, and we show below that this configuration collapses. Setting $w_{\mathrm{imit}}=1$ recovers behaviour cloning with the L2 loss only. The DPO trust-region parameter $\beta$ controls how far the policy may drift from the reference distribution; a lower $\beta$ trusts the reference less and produces better-calibrated generations. The SAM outer loop perturbs the weights by $\rho\nabla_{\theta}\mathcal{L}/\lVert\nabla_{\theta}\mathcal{L}\rVert$ and re-evaluates the gradient at the perturbed point. This encourages convergence to a flat minimum, at $\sim1.9\times$ the wall-clock cost.

Sweep results. We swept 29 configurations in the second stage of the study (Phase 2). SAM is the most effective single regulariser. Any non-zero anchor weight in $[0.3, 0.9]$ is stable, whereas pure DPO collapses (§O.5). LoRA ranks 4 and 8 work best; rank 2 collapses and ranks $\ge16$ degrade. For DPO, $\beta=0.01 > 0.1 > 1.0$. The source of the rejected trajectories affects the outcome substantially: Reward-back-prop alone gives a 3.3% violation rate, against 40% for Reward-back-prop (joint-replay). Across seeds, comfort varies by up to 30 pp.

Selected configuration. The best of all 29 trials, denoted DPO+L2+SAM, uses a shared module of rank 4 and an expert of rank 8 ($\alpha=32$), expert index 1 (ODD-Kashiwa), the hybrid loss with $w_{\mathrm{imit}}=0.5$ and $\beta_{\mathrm{DPO}}=0.1$, AdamW (lr $=3\cdot10^{-5}$, wd $=10^{-4}$) with SAM ($\rho=0.05$), a constant learning-rate schedule, 10 epochs with early stopping on the in-loop evaluation over the disjoint validation scenes, and 1500 pairs.

Final Comparison (Phase 4) on 500 Validation Scenes

The comfort column is the one that separates the models. The reward-back-prop family (Reward-back-prop, Reward-back-prop (joint-replay), Reward-LoRA soup (12-variant)) has comfort-violation rates of 79–88%, whereas DPO+L2+SAM, with the same LoRA architecture, reaches 0%. This isolates the fault to the fine-tuning method. As a further check, DPO+L2+SAM (block-restricted), with LoRA only on the block bodies and not on perproj or final_layer, also reaches 0%, which is consistent with the per-layer ablation in §O.4. The longer run of the third stage (Phase 3; 25 epochs, 3000 pairs) rises to 5.20%, which reflects overfitting rather than checkpoint noise.

Per-Layer Ablation and a Training-Free Fix

When a reward-back-prop LoRA is already deployed on a vehicle and full retraining is not affordable, a per-layer ablation offers a cheaper alternative. We zero each of the 16 LoRA-adapted DiT layers of Reward-back-prop in turn and measure comfort on a held-out pool. A single layer stands out: decoder.dit.preproj.fc1 accounts for a −74 pp swing on its own, while every other layer contributes 7 pp or less. preproj.fc1 is the first projection of the noisy input $x_t$ at the entry to the denoising chain. At this layer, the reward-back-prop gradient accumulates over all 80 sampling steps and pulls the weights off the diffusion manifold. Zeroing only the LoRA update of this layer at inference, which takes three lines of code, lowers the comfort-violation rate of Reward-back-prop from 81.4% to 7.4% on the $n=500$ validation pool. This recovers about 90% of the gap to the base model:

for name, module in model.named_modules():
    if isinstance(module, adapterLinear) and ’preproj.fc1’ in name:
        module.shared_scale = 0.0
        module.expert_scale = 0.0

The resulting design rule is to keep the input and output projections of the DiT out of the LoRA target set and to place the rank budget on the block bodies.

Bag	$n$	strict %	drv %	cmf %	Note
rep1 baseline	27154	0.1	2.1	37.7	human driver
rep1 (ODD-Kashiwa adapter)	14275	0.8	5.2	47.7	adapter, autonomous
rep2 (ODD-Kashiwa adapter)	15755	0.0	0.0	0.0	crept 72 m, then stopped

Collapse of DPO Without the L2 Anchor

Without the imitation anchor, DPO collapses. Setting $w_{\mathrm{imit}}=0$ reduces the hybrid loss to pure DPO. This configuration triggers 100% on every V3 layer in every scenario bucket on $n=500$. Its median sampled jerk is 3627 m/s$^3$, against 0.8 for the base planner, and its mean predicted speed is 46.6 m/s (167 km/h), against 4 m/s for the base planner. The collapse is not an artefact of the jerk computation: it appears under the Savitzky–Golay-filtered jerk of V3 on $n=500$ and reproduces across the seeds we tried. Any non-zero anchor weight prevents the collapse. With $w_{\mathrm{imit}}=0.1$ alone, the comfort-violation rate drops to 53.3%, which is still poor but no longer catastrophic. With $w_{\mathrm{imit}}\ge0.5$, it lies between 0% and 13%, depending on the rest of the configuration.

Greedy Weight Soup over the Sweep Variants

A greedy soup over the 12 variants from the sweep (Phase 2), with the strict-accept criterion of [13], reduces to DPO+L2+SAM alone. No other candidate strictly improves on its 0% comfort-violation rate, so the greedy-soup row (marked degenerate) in Table 26 is identical to DPO+L2+SAM. The metric is saturated at $n=500$.

Table 26: Final comparison (Phase 4) on $n=500$ ODD-Kashiwa validation scenes, disjoint from the training scenes, scored with the V3 proxy (§O.1). Each entry is the percentage of the 500 scenes in which at least one criterion of the layer is triggered (any-triggered). strict: hard-constraint layer; drv: careful-and-competent driver layer; cmf: comfort layer.

Rank	Model	strict %	drv %	cmf %
1	DPO+L2+SAM (this work, headline)	0.00	100.0	0.00
1	DPO+L2+SAM (block-restricted, LoRA on blocks.0..2 only)	0.00	99.8	0.00
1	greedy soup (degenerate; $\to$ sam alone)	0.00	100.0	0.00
4	Base (no LoRA, Plan-R1 base planner)	0.00	97.2	0.80
5	DPO+L2 ($w_{\mathrm{imit}}=0.9$)	0.00	100.0	3.80
6	DPO+L2 ($\beta_{\mathrm{DPO}}=0.01$)	0.00	100.0	5.00
7	DPO+L2+SAM (25 ep, final ckpt; 25 ep $\times$ 3000 pairs)	0.00	99.8	5.20
8	Reward-LoRA (surgical zero, decoder.dit.preproj.fc1)	0.00	98.2	7.40
9	DPO+L2+SAM (25 ep, best ckpt; early checkpoint)	0.00	98.8	10.60
10	DPO+L2 ($\alpha=64$)	0.00	100.0	28.80
11	Reward-back-prop (joint-replay)	0.00	99.2	79.80
12	Reward-back-prop (ODD-Kashiwa expert)	0.00	99.0	81.40
13	Reward-LoRA soup (12-variant Wortsman soup of reward-LoRAs)	0.00	99.2	88.00
14	DPO only ($w_{\mathrm{imit}}=0$; vanilla DPO, no anchor)	100.0	100.0	100.0

Test Vehicle

The real-vehicle runs in § 6 use a PIX Moving Pixkit 3.0, an electric drive-by-wire chassis with an Autoware-compatible CAN interface (Figure 9). On this vehicle, the base planner has been run with either a reward-trained shared-plus-expert adapter or the production DPO LoRA. The joint-replay weights have not been run on the vehicle.

Model	Origin	strict %	cmf %	Real vehicle
DPO+L2+SAM (proposed)	this work	0.00	0.00	simulation only
DPO+L2+SAM (block-restricted)	this work	0.00	0.00	simulation only
Production DPO (human labels)	production, 3 months	0.00	0.40	validated (April)
Base (no LoRA)	Plan-R1 base planner	0.00	0.80	simulation only
Reward-back-prop	reward-back-prop	0.00	81.40	failed (rep2)
Reward-LoRA (surgical zero, §O.4)	this work, training-free	0.00	7.40	not tested

Scoring Real-Vehicle Recordings with V3

Comfort in simulation and on the vehicle. On the same course and day, the human driver has a comfort-violation rate of 37.7% and the adapter-controlled run 47.7%. The deployed adapter is therefore 10 pp worse than the human driver it replaces. This matches the comfort regression of reward-back-prop training in simulation and motivated the switch to DPO+L2+SAM. In simulation, the planner’s trajectories score below the human baseline (DPO+L2+SAM 0%, Base (no LoRA) 0.8%), because the output of the diffusion planner is smoother than raw human positions recorded at 10 Hz.

Stalled second run (rep2). Row 3 reads 0.0% because the vehicle never exceeded 0.23 m/s (15755 frames in the cold_start bucket). We therefore add a progress check over the whole recording ($\bar{v} < 0.5$ m/s, $\ge95\%$ stationary frames, $n \ge300$). This check flags such a run as a deployment failure and complements V3. With the same adapter, on the same course and day, rep1 was reasonable (47.7%, 107 m driven), whereas in rep2 the vehicle crept 72 m and then stopped.

Comparison with the Production DPO LoRA

The proposed configuration matches the production DPO LoRA on hard safety (0%) and is slightly better on comfort (0.00% vs. 0.40%), without human preference labels, because its preference pairs are assembled automatically. Deployment requires a LoRA delta of about 78 K parameters. When a deployed adapter cannot be retrained, the training-free surgical fix v5_surgical (§O.4) can be used instead.

This comparison holds in simulation only. Two reference points from the real vehicle, the production DPO LoRA (0.40% in simulation) and the adapter-controlled rep1 run (47.7% vs. 37.7% for the human driver), place the comfort gap between simulation and vehicle on ODD-Kashiwa within 0–10 pp.

Adversarial Scenarios from AWSIM-Script

In the natural ODD-Kashiwa data, 400/400 sampled neighbor_agents_past tensors contain no active neighbours. We therefore synthesise dangerous interactions from the AWSIM-Script library [34], which provides 42 cut-in, 8 cut-out and 4 deceleration scripts. Each script is parameterised by $(V_e,V_o,V_y,d x_0)$: the ego speed, the NPC speed, the lateral speed of the NPC and the initial longitudinal gap. For each ODD-Kashiwa scene, we insert one synthetic NPC into slot 0 of neighbor_agents_past, with a three-second history at constant speed $V_o$ and a lane offset of $\pm3.5$ m for cut-in and cut-out, or $y=0$ for deceleration. We set the ego speed at $t=0$ to $V_e$ and score the planned trajectory against the analytically projected NPC future. The evaluation uses $n=200$ scenes per scenario and 4 models, for 43,200 inferences in total.

In the adversarial scenarios, the strict-safety layer (strict_safety) separates the models. On cut-in, aggregated over 42 scripts, Reward-back-prop has a collision rate of 39.8%, compared with 17.0% for the base planner (+22.8 pp). Reward-LoRA (surgical zero) reduces this to 27.4% without retraining, and DPO+L2+SAM stays close to the base planner at 18.5%. On deceleration, the collision rate is uniformly high for all models (48–67%). This reflects a lack of training data, since the ODD-Kashiwa pool contains no emergency-braking examples; §O.11 addresses this.

Time-to-collision heatmap. Figure 12 reports $TTC_{p25}$ over a 7×6 ($dx_0$, $V_o$) grid ($dx_0 \in[5,25]$ m, $V_o \in[10,60]$ km/h, $V_e=1.5V_o$, $V_y=1.6$ m/s, $n=15$ scenes per cell). The heatmap is markedly darker, that is, more dangerous, for Reward-back-prop than for DPO+L2+SAM, with Reward-LoRA (surgical zero) in between.

Limitations. The evaluation modifies one slot of the planner input and projects the NPC future analytically. It skips the perception and behaviour stages of AWSIM-Labs and the AW-Checker. Collisions are detected with a proxy based on a 0.5 m circular footprint. The values in Table 29 should therefore be read as relative comparisons, not as absolute rates.

Table 29: Collision rates in the AWSIM-Script adversarial scenarios, aggregated over the full 54-script library, with $n=200$ ODD-Kashiwa scenes per scenario. Cut-in aggregates 42 scripts spanning $V_e \in[20,50]$ km/h, $V_o \in[10,40]$ km/h, $V_y \in[0.6,1.6]$ m/s and $d x_0 \in[5,17]$ m; cut-out aggregates 8 scripts; deceleration aggregates 4 scripts, in which the NPC brakes at 1 G from $V_o \in\{20,30,40,50\}$ km/h. Entries are the mean collision % across the scripts of each family. Table 30 gives the results for the five canonical scripts.

Model	cutin (42)	cutout (8)	decel (4)
Base (no LoRA)	17.0	0.2	48.0
Reward-back-prop (reward-LoRA)	39.8	4.5	67.0
Reward-LoRA (surgical zero) (§O.4)	27.4	0.7	59.1
DPO+L2+SAM (ours)	18.5	1.0	53.5

Table 30: Per-script results on the five canonical scripts from the original AW-Runtime-Verification publication, with $n=200$ ODD-Kashiwa scenes per script, for comparison with the earlier pilot with $n=50$. The models are those of Table 29.

Model	ci30–10–6	ci40–20–3	ci20–10–1	co50–1	decel20
Base (no LoRA)	35.0	17.0	41.0	0.0	73.5
Reward-back-prop (reward-LoRA)	63.0	39.0	65.5	0.0	81.5
Reward-LoRA (surgical zero) (§O.4)	50.5	30.0	54.0	0.0	78.5
DPO+L2+SAM (ours)	40.0	17.5	42.5	0.0	82.0

Training with AWSIM-Script Adversarial Pairs

The deceleration failures in Table 29 (every model at 48–67%) reflect a lack of training data. ODD-Kashiwa contains no scenarios in which a leading vehicle stops, so no fine-tuned model has seen reactive braking. We therefore generate adversarial preference pairs from the AWSIM-Script library and add them to the natural-data pool.

The pairs use the same NPC insertion as §O.10. For each AWSIM-Script script, we take 12 ODD-Kashiwa training scenes, insert the NPC, and pair each modified scene with two trajectories. The rejected trajectory is sampled from DPO+L2+SAM itself. The pair is kept only if this sampled trajectory collides or has a TTC below 2 s, which removes scripts on which DPO+L2+SAM is already safe and keeps only the hard cases. The chosen trajectory is constructed analytically. For cut-in, the ego brakes from $V_e$ to $V_o$ at a comfort-capped 4 m/s$^2$. For deceleration, it brakes at the rate required to stop with a 5 m safety gap behind the NPC’s stopping position. For cut-out, it continues at $V_e$, because the NPC moves out of the ego’s path. The filter accepts 162 adversarial pairs out of 648 attempts across the 54 scripts. Together with 1500 natural ODD-Kashiwa pairs, they form a training pool of 1662 pairs ($\sim$10% adversarial).

Training uses the headline configuration of §O.2 (lr $= 3 \cdot10^{-5}$, $w_{\mathrm{imit}}=0.5$, weight decay $10^{-4}$, SAM, constant schedule, 8 epochs). It is initialised from the DPO+L2+SAM checkpoint rather than from the base planner, so that training starts from the existing 0% comfort-violation rate on natural data.

Comfort on natural data. Comfort on natural data is preserved at the end of training. During the eight training epochs, the in-loop comfort-violation rate on $n=30$ disjoint validation scenes is 23.3% at epoch 2, immediately after the adversarial pool enters the gradient. It falls to 0.0% at epoch 6 and stays at 0.0% through epoch 8, with a median jerk of 1.3 m/s$^3$. The final checkpoint, DPO+L2+SAM+Adv, therefore matches DPO+L2+SAM on natural-data comfort (both 0%, Table 26), while its LoRA delta also covers the adversarial pool.

Family (# scripts)	DPO+L2+SAM	+Adv (162 pairs)	+Adv (500 pairs)	$\Delta$ (500 vs. base)
cutin (42)	18.51%	19.57%	17.07%	−1.44 pp
cutout ( 8)	1.00%	0.06%	0.00%	−1.00 pp
decel ( 4)	53.50%	54.75%	51.12%	−2.38 pp
peak decel p95 (m/s$^2$)	1.20	2.20	4.04	+2.84
# scripts improved vs. base	—	13/54	31/54	—
natural-data comfort (n=500)	0.00%	0.00%	0.00%	$\pm$0.00

Effect of the adversarial pool. With 500 adversarial pairs (DPO+L2+SAM+Adv (scaled), $\sim$ 25% of the mixture), 31/54 scripts improve. Cut-in collisions fall to 17.07% from 18.51% for DPO+L2+SAM, cut-out collisions fall to 0%, and the peak ego deceleration rises to 4.04 m/s$^2$ (3.4$\times$ the natural-data baseline). The deceleration family remains at 51.12%, because the chosen trajectory brakes at no more than 4 m/s$^2$ for comfort, which is too weak for an NPC braking at 1 G. An ablation that instead generates the chosen trajectory with an IDM lookahead [35] ($a_{\max}=1.5$ m/s$^2$, $T_{\mathrm{hw}}=1.5$ s, $s_0=2$ m, 483 pairs) performs worse on every family (cut-in 22.02%, peak deceleration 2.87 m/s$^2$), which indicates that the generator of chosen trajectories is not the bottleneck.

Relation to the Main Text

The V3 study and the adaptation methods of the main text share the base planner (adapter stack with shared rank 4 and expert rank 8, $\alpha=32$) and the ODD-Kashiwa site, but they address different questions. The main-text methods (§ 4–§ 5.3) optimise an L2 loss on target-region lanelets for transfer to new regions. The V3 study optimises the hybrid DPO+L2 loss on ODD-Kashiwa to close the comfort regression.

Trajectory Diagnostics on the Target-Region Pool

The diagnostics in this section are proxies for comfort and corridor compliance, not closed-loop safety measurements. They are computed in open loop from a single deterministic DPM-Solver++ rollout per scene on the 24-scene pool. Time-to-collision and collision rates are undefined on these scenes, because they contain no neighbouring agents.

Held-Out Target-Region Topologies

Regions Where the Nearest Expert Is Not ODD-Nagoya

On the three held-out maps of the main study, the geographically nearest training ODD is ODD-Nagoya, which is also the best fixed expert, so proximity and expert quality cannot be separated there. Table 33 therefore reports two further regions in which the static default selects a different expert. In both regions, the nearest expert is not the best fixed expert. The first region is a suburban bus-route map adjacent to ODD-Kashiwa. We exclude scenes whose start lanelet falls inside the bounding box of the ODD-Kashiwa training map (398 lanelets), which leaves 30 scenes. Here the nearest expert (ODD-Kashiwa) is worse than ODD-Nagoya by 1.37 m (paired Wilcoxon $p=0.001$). The second region is a dense urban area nearest ODD-Hongo (10 scenes). Data from this area were used to train the shared module, because it is the ODD of a fifth expert that is not part of the four-expert adapter stack. This region therefore tests expert selection only, not adaptation to held-out data. Here the nearest expert (ODD-Hongo) is the weakest of the four and is 30.0 m worse than the best fixed expert (ODD-Kashiwa); with 10 scenes, this difference is not significant ($p=0.084$).

Region	$n$	Hongo	Kashiwa	Shalun	Nagoya	Shared only	Nearest	Best
Suburb near ODD-Kashiwa	30	19.70	12.70	15.90	11.33	15.59	Kashiwa	Nagoya
Urban area nearest ODD-Hongo†	10	38.62	8.61	13.97	8.65	14.60	Hongo	Kashiwa