Domain Arithmetic: One-Shot VLA Adaptation under Environmental Shifts¶

Conference: ECCV 2026
arXiv: 2607.00666
Code: https://github.com/snumprlab/dart
Area: Multimodal VLM / Robotics
Keywords: VLA adaptation, weight arithmetic, domain shift, one-shot learning, subspace alignment

TL;DR¶

DART proposes a one-shot domain adaptation method for VLA models based on weight-space analogy arithmetic. By fine-tuning separately with a single source-domain and target-domain demonstration, it extracts a pure domain vector via subtraction after subspace alignment filtering and adds it back to the base model. Under LIBERO multi-view, visual perturbations, cross-embodiment, and real robot scenarios, it significantly outperforms existing adaptation baselines using only a single demonstration.

Background & Motivation¶

VLA models (such as RT-2, OpenVLA, and the \(\pi\) series) exhibit strong multi-task capabilities after pre-training on large-scale robotics datasets. However, when deployed in new scenarios with domain shifts from the training environment (such as camera pose changes, lighting variations, different sensor calibrations, or even different robot arm models), their performance on the same task drops drastically. Existing adaptation methods either require collecting large numbers of demonstrations for every task in the target domain (making full fine-tuning extremely costly) or introduce architecture-specific modifications (such as tuning only the visual encoder or adding LoRAs), which limits their generalizability across different VLA backbones.

This presents a sharp contradiction: domain shifts are ubiquitous in real-world deployment, yet collecting demonstrations on a task-by-task basis is completely impractical in settings like households. Consequently, the authors push the goal to the limit—one-shot VLA adaptation: using only a single demonstration of one task in the target domain to restore the base model's execution capabilities for all learned tasks in that target domain.

The intuition is that although the parameter changes (update vectors) after one-shot fine-tuning are dominated by task-specific directions (leading to poor generalization on held-out tasks), these update vectors simultaneously contain a smaller but reusable domain-specific direction that encodes information about what the target domain looks like. Through subspace alignment analysis, the authors find that cross-domain update vectors for the same task are highly aligned, cross-task update vectors in the same domain also show higher-than-random alignment, and the task/domain directions approximately decompose additively in the weight space. This directly inspires the core insight of DART: using analogy arithmetic (target update minus source update) to eliminate the task direction while keeping only the domain direction, then injecting it into the base model—akin to a weight-space version of "queen = king + woman - man".

Method¶

Overall Architecture¶

The goal of DART is: given a multi-task VLA base model \(\theta_0\) trained on the source domain \(\epsilon_{src}\), and a single demonstration \(D_{m,tgt}\) of a single task \(T_m\) in the target domain \(\epsilon_{tgt}\), to output adapted parameters \(\theta^*\) such that \(\theta^*\) performs well on all tasks in the target domain. The overall workflow consists of three steps:

Separate One-Shot Fine-Tuning: Fine-tune \(\theta_0\) with behavior cloning (1,000 steps each) using the source-domain demonstration \(D_{m,src}\) and target-domain demonstration \(D_{m,tgt}\) of the same task \(T_m\) to obtain \(\theta_{m,src}\) and \(\theta_{m,tgt}\), and then compute two update vectors: \(\Delta_{m,src} = \theta_{m,src} - \theta_0\) and \(\Delta_{m,tgt} = \theta_{m,tgt} - \theta_0\).
Subspace-Enhanced Domain Vector Extraction: Conduct SVD decomposition on \(\Delta_{m,src}\) and \(\Delta_{m,tgt}\) for each layer, compute the subspace alignment score \(\gamma^{(l)}\), filter via overlap energy to keep only the source bases aligned with the target subspace (subspace filtering), and then scale down the domain vector layer-by-layer using \(\gamma^{(l)}\) (subspace scaling) to obtain the refined domain vector \(\tilde{\delta}_{tgt}\).
Domain Vector Injection: Add the domain vector back to the base model \(\theta^* = \theta_0 + \alpha \cdot \tilde{\delta}_{tgt}\) to obtain the target-domain adapted model, which is then used directly for inference on all tasks.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Base Model θ₀<br/>(Source domain multi-task)"] --> B["Source One-Shot Fine-Tuning<br/>θ_{m,src}"]
    A --> C["Target One-Shot Fine-Tuning<br/>θ_{m,tgt}"]
    B --> D["Δ_{m,src} = θ_{m,src} − θ₀"]
    C --> E["Δ_{m,tgt} = θ_{m,tgt} − θ₀"]
    D --> F["SVD + Subspace Filtering<br/>Keep only source bases aligned with target"]
    E --> F
    F --> G["Analogy Subtraction + Subspace Scaling<br/>δ̃_tgt = γ · (Δ_{m,tgt} − Δ̃_{m,src})"]
    G --> H["θ* = θ₀ + α·δ̃_tgt<br/>Adaptation done, target domain multi-task inference"]

Key Designs¶

1. Analogy Subtraction for Domain Vector Extraction: Eliminating Task Directions through Source-Target Update Vector Subtraction

In Section 4, the authors demonstrate that target-specific directions dominate the one-shot update vector \(\Delta_{m,tgt}\) (highly aligned with \(\gamma\) for the same task cross-domain), but a weak yet consistent domain direction also exists (where \(\gamma\) of same-domain cross-tasks is slightly higher than cross-domain cross-tasks). Furthermore, both directions are approximately linearly additive in the weight space (the synthesized direction of "task prototype + domain prototype - global prototype" has the highest \(\gamma\) with the actual update vector). Based on this, DART decouples them via a clever analogy operation: let the update vector of the same task \(T_m\) be \(\Delta_{m,src}\) in the source domain and \(\Delta_{m,tgt}\) in the target domain; the domain vector is then formulated as \(\delta_{tgt} = \Delta_{m,tgt} - \Delta_{m,src}\). Since both update vectors share the task-specific direction, the task component cancels out during subtraction, leaving only pure domain transfer information. The elegance of this design lies in its simplicity: it only requires fine-tuning once on the same task demonstration in the source and target domains respectively, without any multi-task data or extra annotation. In practice, one can first select \(T_m\) from the source training set, then collect the demonstration for the same task in the target domain to ensure task matching.

2. Subspace Filtering: Subtracting Only Source Base Vectors Aligned with the Target Subspace to Prevent Source Domain Noise from Corrupting the Domain Vector

Direct subtraction has a caveat: \(\Delta_{m,src}\) might contain source-specific artifacts (task-irrelevant fine-tuning noise), and blindly subtracting them would inject this noise into the domain vector. DART's solution is to filter only the source update vector, keeping the complete information of the target update vector (as the unique bases of the target update precisely encode target domain information). Specifically, for each layer’s weight matrix \(\Delta_{m,src}\) and \(\Delta_{m,tgt}\), SVD is performed to obtain the left singular vectors \(U_{src}\) and \(U_{tgt}\). Then, an interaction matrix \(C = U_{tgt}^\top U_{src}\) is constructed, where the overlap energy of the \(j\)-th source base is computed as \(e_j = \|C_{:,j}\|_2^2\) to measure the fraction of the base that lies within the target subspace. Using the subspace alignment score \(\gamma\) as a threshold, DART greedily selects a set of base indices \(J_l\) whose cumulative energy reaches \(\gamma \cdot \sum e_j\), constructing the filtered source update vector as \(\tilde{\Delta}_{m,src} = U_{src}[:,J_l] \cdot U_{src}[:,J_l]^\top \cdot \Delta_{m,src}\). This is opposite to subspace alignment in model merging—where the latter preserves unique components of each update vector to maximize capacity, whereas DART searches for shared task-related components to precisely eliminate them.

3. Subspace Scaling: Scaling Down Low-Alignment Layers to Suppress Low-SNR Domain Vectors

Even after filtering out unaligned bases, if the two update vectors are fundamentally weakly aligned (\(\gamma \to 0\)), the noise ratio in the domain vector generated by subtraction remains high. DART directly scales the domain vector layer-by-layer using the alignment score \(\gamma^{(l)}\): \(\tilde{\delta}_{tgt}^{(l)} = \gamma^{(l)} \cdot (\Delta_{m,tgt}^{(l)} - \tilde{\Delta}_{m,src}^{(l)})\). Intuitively, layers with high \(\gamma\) indicate that the source and target share substantial task structures, meaning that the subtraction works well and the domain vector is clean, thus preserving full strength. Conversely, layers with low \(\gamma\) suggest large domain differences or noisy updates, and downscaling them reduces their impact on the final model. Ablation studies show that the gain from subspace scaling primarily comes from highly misaligned layers (e.g., the MLP Up_proj layer in the LLM), where \(\gamma\) is close to 0 and whose domain vectors would otherwise harm multi-task performance if not downweighted.

Loss & Training¶

The one-shot fine-tuning stage uses the standard behavior cloning (BC) loss to minimize the negative log-likelihood on actions from the target domain demonstration \(D_{m,tgt}\). The optimizer used is AdamW with a learning rate of \(5 \times 10^{-5}\), no warmup, a fixed training duration of 1,000 steps, and a batch size of 64. The base models are pre-trained according to the official protocols of respective VLAs (e.g., \(\pi_{0.5}\) on LIBERO uses the checkpoint released by openpi, while \(\pi_0\text{-FAST}\) is trained from scratch for 30,000 steps). The domain vector extraction phase involves no extra training, performing only weight-space arithmetic. The scaling coefficient \(\alpha\) is determined via a small search with 10 rollouts on the LIBERO Long subset (\(\alpha=0.8\) for viewpoint transfer, \(\alpha=0.6\) for visual perturbations) and is reused across all other scenarios (including real robots). By utilizing randomized SVD (rank \(r=256\)), the SVD computation time can be reduced from 15 minutes and 35 seconds to 6 minutes and 33 seconds for full decomposition with negligible performance loss (79.1% vs 78.7%).

Key Experimental Results¶

Main Results¶

LIBERO new-viewpoint transfer results of DART on \(\pi_{0.5}\) (40 tasks, averaged over 3 random adaptation tasks, 50 rollouts each):

Method	Small	Medium	Large	Average
Zero-shot	88.3	63.9	11.3	54.5
One-shot FT	43.4	33.3	17.8	31.5
RETAIN (ICLR 2026)	87.4	72.4	48.9	69.6
FLA (CVPR 2026)	92.2	76.4	54.3	74.3
DART (Ours)	92.0	80.8	64.4	79.1

Real-world robot UR10e 5-task viewpoint transfer results (adapted using only a single Stack Cube demonstration, 12 rollouts per task):

Method	Eggplant	Lemon	Carrot	Stack Cube	Press Stapler	Average
Zero-shot	50.0	33.3	41.7	16.7	75.0	43.3
One-shot FT	58.3	58.3	41.7	33.3	66.7	51.7
RETAIN	58.3	41.7	41.7	16.7	83.3	48.3
FLA	58.3	50.0	50.0	16.7	100.0	55.0
DART	91.7	91.7	83.3	41.7	100.0	81.7

Other main experimental results: Cross-embodiment transfer (Panda \(\to\) UR5e, MimicGen), DART achieves an average success rate of 69.4% (vs. Zero-shot 62.0%); on the \(\pi_0\text{-FAST}\) architecture, DART averages 79.4% (vs. FLA 76.6%); under combined visual perturbations (View+Noise+Light), DART averages 75.0% (vs. FLA 71.5%).

Ablation Study¶

Ablation study on the average success rate of three viewpoints in LIBERO (\(\pi_{0.5}\)):

Subspace Filtering	Subspace Scaling	Average Success Rate (%)
✗	✗	78.1
✓	✗	78.8
✗	✓	78.5
✓	✓	79.1

Compared to 31.5% of One-shot FT, pure analogy subtraction (without subspace components) reaches 78.1% (+46.6pp), demonstrating that the analogy arithmetic itself can effectively isolate domain knowledge. Subspace filtering further improves performance to 78.8% (+0.7pp), and subspace scaling improves it to 78.5% (+0.4pp), with their combination reaching 79.1%, indicating that filtering and scaling contribute to suppressing source-domain noise and reducing interference from misaligned layers, respectively.

Key Findings¶

Analogy arithmetic is the most core contribution: Relying solely on \(\Delta_{m,tgt} - \Delta_{m,src}\) yields a +46.6pp gain on average across three viewpoints (relative to One-shot FT), validating the additive decomposition hypothesis of task/domain directions in the one-shot update vector.
Scaling coefficient \(\alpha\) is highly robust: Variations of \(\alpha\) from 0.2 to 1.4 under Medium and Large viewpoints only result in standard deviations of 0.8% and 2.1%, whereas DART w/o SA exhibits larger fluctuations, indicating that subspace filtering + scaling suppresses noise components that would otherwise be amplified by \(\alpha\).
Tolerance to fine-tuning steps: While One-shot FT degrades as fine-tuning steps increase due to catastrophic forgetting, DART rises steadily (as the task direction becomes more prominent with training, facilitating pure domain vector extraction) and achieves competitive performance in just 200 steps.
LLM layer adaptation is critical: Among the Vis/LLM/Action layers, Vis+LLM achieves performance close to full-layer adaptation, whereas adapting Action alone is almost ineffective. Furthermore, the domain vector magnitude of the MLP Up_proj layer in the LLM is the largest with the lowest subspace alignment—suggesting that domain knowledge is primarily encoded within the MLP layers of the LLM.
Domain vectors can be merged: Merging the domain vectors of Small/Medium/Large viewpoints into a single vector using TSV yields an average success rate of 75.7%, which can reduce the parameter storage overhead for multi-domain deployment.

Highlights & Insights¶

Formulating domain adaptation via "analogy" rather than "merging" targets the problem accurately: The goal of model merging (such as TIES and Iso-C) is to combine the capabilities of different models, whereas the goal of analogy is to eliminate commonalities and extract differences—which is exactly what domain adaptation requires. DART is the first work to systematically utilize analogy for domain transfer in VLAs, and experiments demonstrate that directly applying merging methods (e.g., TIES merging \([\Delta_{m,tgt}, -\Delta_{m,src}]\)) is inferior to DART (77.6% vs. 79.1%).
Subspace alignment score serves two purposes with one stone: \(\gamma\) is used both as the threshold for base selection (determining how much to filter) and as the scaling coefficient for the domain vector (determining how much to downweight low-SNR layers), introducing no additional hyperparameters. This design is simple and highly efficient, rooted in a deep understanding of the low-rank structure of update vectors and the geometric relationship between task and domain directions.
The assumption of acquiring source-domain demonstrations is practically feasible: The authors explicitly point out that one can first select the adaptation task from the source training set and then collect the same task's demonstration in the target domain. Rather than requiring the search for "the same task" as the source domain within a massive, unstructured target-domain dataset, it does the reverse. This engineering detail makes the assumption viable for real-world deployment.
Method is insensitive to VLA architectures: It is effective on both \(\pi_{0.5}\) (flow matching continuous regression) and \(\pi_0\text{-FAST}\) (autoregressive discrete token), indicating that the additive decomposition of task/domain in the weight space is a general structural property of VLA models, deeply rooted in their shared vision-language pre-trained backbones.

Limitations & Future Work¶

The authors acknowledge that under extreme viewpoint offsets (Large viewpoint), all one-shot methods have limited performance (DART 64.4% vs. full-data FT upper bound of 90.9%). Extreme domain shifts remain a challenge, and future research could explore stronger domain vector extraction mechanisms or better base model fine-tuning strategies.
Although the scaling coefficient \(\alpha\) is robust within a wide range, it still requires a minor search process (10 rollouts), which is not fully "plug-and-play" for deployment scenarios without search capabilities; layer-wise adaptive scaling could be a potential solution.
This method requires the adaptation task to be identical in both the source and target domains (\(T_m = T_m'\)). When exact matching is impossible (e.g., when the source dataset is massive with no clear task indices), using similar tasks (retrieved via cosine similarity) can partially alleviate the issue but still results in a notable performance drop (80.8% \(\to\) 69.0%), indicating that domain vector extraction is sensitive to task matching. Stronger cross-domain task retrieval is a valuable direction for improvement.
Current experiments focus on visual domain shifts and cross-embodiment transfer, leaving the effect of dynamics changes (such as physical parameter shifts like object mass, friction, or joint damping) unverified. Whether such offsets likewise form linearly separable domain directions in weight space remains an area worthy of exploration.

vs. Task Arithmetic (ICLR 2023): TA uses addition and analogy to compose multi-task capabilities, but its analogy relies solely on direct subtraction for cross-lingual and alignment transfer. DART introduces two enhancement mechanisms—subspace filtering and scaling—on top of TA's analogy and re-targets analogy as "domain information extraction" rather than "capability composition," yielding significant gains in VLA adaptation.
vs. RETAIN (ICLR 2026): RETAIN balances new and old task capabilities via module-level interpolation, which is essentially linear interpolation in the parameter space and does not explicitly model the domain shift direction. DART's analogy subtraction explicitly extracts domain vectors, achieving a higher success rate under the same one-shot data budget (79.1% vs. 69.6%), indicating that explicit modeling is superior to implicit trade-offs.
vs. FLA (CVPR 2026): FLA inserts LoRA only into the vision encoder for parameter-efficient adaptation, freezing the LLM and the action expert. DART adapts all modules simultaneously via weight arithmetic, performing better in extremely data-scarce settings (one-shot per scene vs. task-wise) without introducing any architectural modifications, making it plug-and-play for any VLA.
vs. SCALE (ICML 2026, test-time adaptation): SCALE adapts at test time but primarily targets limited shifts. DART's three-viewpoint average of 79.4% on \(\pi_0\text{-FAST}\) vs. SCALE's 73.0% highlights that under larger environmental shifts, test-time adaptation has limited effectiveness, demonstrating that explicit adaptation of VLA policy parameters remains necessary.

Rating¶

Novelty: ⭐⭐⭐⭐⭐ Systematically applies analogy arithmetic from weight arithmetic to VLA domain adaptation for the first time, combined with subspace-alignment enhancement. Both the problem formulation and method design are highly novel.
Experimental Thoroughness: ⭐⭐⭐⭐⭐ Covers two VLA architectures, simulation + real robots, visual shifts + cross-embodiment, ablations + hyperparameter analysis + layer selection + domain vector merging + source-domain forgetting checks, showing a comprehensive experimental design.
Writing Quality: ⭐⭐⭐⭐⭐ Tight logical chain and self-consistent motivation, moving smoothly from empirical analysis in Section 4 (why one-shot FT fails) to method design in Section 5 (proposing DART based on analytical findings).
Value: ⭐⭐⭐⭐⭐ One-shot VLA adaptation is a core pain point for robot deployment. DART features outstanding practical value given its high data efficiency (1 demo per environment), architecture-agnostic, and plug-and-play nature.