DART: Domain ARiThmetic Adaptation

• Domain ARiThmetic (DART) is an analogy-based method that adapts pretrained Vision-Language-Action policies to new environments using weight vector arithmetic.
• It employs one-shot fine-tuning with subspace alignment and filtering to isolate domain-specific shifts while maintaining multi-task capabilities.
• Empirical results demonstrate significant improvements under visual and embodiment shifts, with up to 81.7% success in real-world scenarios.

Searching arXiv for the DART paper and closely related VLA adaptation context. Domain ARiThmetic (DART) is an analogy-based method for adapting pretrained Vision-Language-Action (VLA) policies to environmental shifts through weight vector arithmetic with domain-specific information addition. It addresses the setting in which a strong base multi-task VLA, trained in a source environment, is deployed in a target environment that differs by camera pose, background, lighting, or robot embodiment. The central objective is one-shot, scene-wise adaptation: using one target-domain demonstration of a single task, together with one source-domain demonstration of the same task, DART constructs a domain vector in weight space and adds it to the base policy so that performance transfers across all tasks in the new environment (Kang et al., 1 Jul 2026).

1. Problem formulation and adaptation objective

VLA models are policies of the form

$$\pi_\theta(\mathbf{a}_t \mid \mathbf{o}_t, \mathcal{T}),$$

where $\mathbf{o}_t$ denotes visual observations, $\mathcal{T}$ a language task instruction, and $\mathbf{a}_t$ low-level robot actions. In the reported instantiations, the policy is realized by large VLA backbones such as $\pi_{0.5}$, a flow-matching VLA, and $\pi_{\text{fast}}$, an autoregressive token VLA (Kang et al., 1 Jul 2026).

The motivating setting is environmental shift. The source environment $\mathcal{E}_{\text{src}}$ and target environment $\mathcal{E}_{\text{tgt}}$ differ visually or physically while preserving task semantics. The shifts considered include different third-person camera poses, lighting changes, camera noise, different backgrounds, robot-arm transfer from Panda to UR5e, and combinations such as view plus noise plus light (Kang et al., 1 Jul 2026). The paper reports that standard VLA policies generalize poorly across such shifts, with success on LIBERO dropping from approximately 90% to near 10% under heavily changed camera pose. A conventional remedy is behavior-cloning fine-tuning on target-domain demonstrations, but this typically requires many demonstrations per task and may specialize to the adapted task at the expense of multi-task generality (Kang et al., 1 Jul 2026).

DART formalizes a more data-efficient objective. Given a base multi-task VLA with parameters $\theta_0$, and a task set

$$\bm{\mathcal{T}} = \{\mathcal{T}_1,\dots,\mathcal{T}_M\},$$

the method assumes access, for a new target environment, to one target-domain demonstration of one task $\mathbf{o}_t$0 and one source-domain demonstration of that same task. From only those two trajectories, DART seeks to transform $\mathbf{o}_t$1 into an adapted policy $\mathbf{o}_t$2 that performs well across all tasks $\mathbf{o}_t$3 in the shifted environment (Kang et al., 1 Jul 2026).

2. Weight-space analogy and domain vector construction

The method rests on the hypothesis that one-shot fine-tuning updates contain separable task and domain components. For each layer $\mathbf{o}_t$4, DART defines one-shot target and source update-vectors relative to the base model:

$\mathbf{o}_t$5

Here $\mathbf{o}_t$6 is obtained by fine-tuning $\mathbf{o}_t$7 on a single target-domain demonstration of task $\mathbf{o}_t$8, and $\mathbf{o}_t$9 by fine-tuning on a single source-domain demonstration of the same task (Kang et al., 1 Jul 2026).

The paper proposes the following approximate decomposition:

$\mathcal{T}$0

$\mathcal{T}$1

Under this view, the difference

$\mathcal{T}$2

cancels the shared task component and much of the common fine-tuning bias, leaving a vector that primarily encodes the target-domain shift (Kang et al., 1 Jul 2026).

This yields the central analogy of the method:

• source multi-task model: $\mathcal{T}$3
• source one-shot task model: $\mathcal{T}$4
• target one-shot task model: $\mathcal{T}$5

DART then constructs a domain vector $\mathcal{T}$6 and injects it into the base model:

$\mathcal{T}$7

where $\mathcal{T}$8 is a global scaling coefficient. The intended effect is task-agnostic transfer: once the domain vector has been extracted from one task pair, adding it to the base multi-task model adapts all tasks in the target environment (Kang et al., 1 Jul 2026).

A naive per-layer version of this domain vector is

$\mathcal{T}$9

but the paper argues that raw subtraction is brittle because one-shot fine-tuning induces noisy, low-rank updates and because source and target update subspaces can be misaligned (Kang et al., 1 Jul 2026).

3. Subspace alignment, filtering, and scaling

To isolate domain-specific information more accurately, DART performs subspace alignment between singular components of the source and target update-vectors. The method operates layer-wise on 2D weight matrices and relies on singular value decomposition (SVD) (Kang et al., 1 Jul 2026).

For two layer-wise updates $\mathbf{a}_t$0 and $\mathbf{a}_t$1, DART computes an SVD of $\mathbf{a}_t$2,

$\mathbf{a}_t$3

and defines the subspace alignment score

$\mathbf{a}_t$4

This score lies in $\mathbf{a}_t$5 and measures the fraction of the energy of $\mathbf{a}_t$6 lying in the column space of $\mathbf{a}_t$7. DART uses

$\mathbf{a}_t$8

as a layer-wise reliability signal (Kang et al., 1 Jul 2026).

The first alignment operation is subspace filtering. Let

$\mathbf{a}_t$9

DART forms the interaction matrix

$\pi_{0.5}$0

and, for each source basis vector $\pi_{0.5}$1, defines the overlap energy

$\pi_{0.5}$2

High $\pi_{0.5}$3 indicates that the corresponding source singular direction lies largely in the target subspace and is therefore likely to encode shared task semantics rather than target-specific noise (Kang et al., 1 Jul 2026).

The method sorts the overlap energies and chooses the smallest $\pi_{0.5}$4 such that

$\pi_{0.5}$5

It then keeps the corresponding source basis vectors, forming

$\pi_{0.5}$6

and projects the source update into this shared subspace:

$\pi_{0.5}$7

Only the source update is filtered; the target update is left intact so that target-domain information is preserved (Kang et al., 1 Jul 2026).

The second alignment operation is subspace scaling. The refined layer-wise domain vector is

$\pi_{0.5}$8

This attenuates contributions from layers whose source and target one-shot updates are weakly aligned. The final adapted model is then

$\pi_{0.5}$9

with $\pi_{\text{fast}}$0 (Kang et al., 1 Jul 2026).

Ablation results indicate that direct subtraction already captures a substantial fraction of the effect, but filtering and scaling improve robustness and stabilize performance with respect to $\pi_{\text{fast}}$1. This suggests that the subspace-alignment stage primarily serves to regularize the arithmetic rather than to define it from scratch (Kang et al., 1 Jul 2026).

4. Data regime, architectures, and implementation

DART is architecture-agnostic and is applied to the full weight space of the VLA, including the vision encoder, the LLM backbone, and the action head or action expert. In practice, the method operates layer-wise on all 2D weight matrices, while 1D biases and norms are handled trivially (Kang et al., 1 Jul 2026).

The one-shot fine-tuning stage uses standard behavior-cloning loss on a single demonstration, with 1000 gradient steps using AdamW. The paper attributes DART’s gains not to a modified fine-tuning loss but to how the resulting update-vectors are post-processed and recombined (Kang et al., 1 Jul 2026). The global scaling coefficient is chosen via a small sweep on one development setup, and $\pi_{\text{fast}}$2 is used for most experiments (Kang et al., 1 Jul 2026).

The principal backbones are summarized below.

Backbone	Type	Action modeling
$\pi_{\text{fast}}$3	flow-matching VLA	continuous 7D action vectors
$\pi_{\text{fast}}$4	autoregressive token VLA	discretized action tokens

The evaluation spans three settings. On LIBERO, DART is tested across 4 suites with 10 tasks each and 5 scenes, under Small, Medium, and Large camera-pose shifts, as well as combined visual perturbations such as View+Noise and View+Noise+Light (Kang et al., 1 Jul 2026). On MimicGen, it is evaluated on Stack and Stack Three under cross-embodiment transfer from Panda to UR5e (Kang et al., 1 Jul 2026). On a real-world UR10e platform with three RealSense D455 cameras, it is evaluated on pick-and-place and fine-grained manipulation tasks under target-viewpoint shift (Kang et al., 1 Jul 2026).

The one-shot data regime is stringent. For each new scene, the method uses one target-domain demonstration of one adaptation task and one matching source-domain demonstration of the same task. In the LIBERO experiments this is done scene-wise, with one demo per scene and repeated for three different choices of adaptation task. In the real-world experiments, adaptation uses a single Stack Cube demo in the target viewpoint together with its matching source-view demo, yet the resulting policy is evaluated across five tasks (Kang et al., 1 Jul 2026). This suggests that the extracted vector is intended to encode scene-level or embodiment-level shift rather than task-specific skill.

5. Empirical performance under visual and embodiment shifts

The reported results position DART as a one-shot adaptation method for VLA models under environmental shift. On LIBERO with the $\pi_{\text{fast}}$5 backbone, averaged across 40 tasks, DART achieves 79.1% success, compared with 54.5% for zero-shot transfer, 31.5% for one-shot fine-tuning, 69.6% for RETAIN, and 74.3% for FLA (Kang et al., 1 Jul 2026). The gains are most pronounced under larger viewpoint shifts: on the Large condition, DART reaches 64.4%, compared with 54.3% for FLA, 48.9% for RETAIN, and 11.3% for zero-shot transfer (Kang et al., 1 Jul 2026).

On combined visual perturbations in LIBERO, averaged over View, View+Noise, and View+Noise+Light, DART obtains 75.0%, compared with 60.5% for zero-shot transfer, 29.8% for one-shot fine-tuning, 68.7% for RETAIN, and 71.5% for FLA (Kang et al., 1 Jul 2026). On the alternative $\pi_{\text{fast}}$6 architecture, averaged over Small, Medium, and Large viewpoint shifts, DART reaches 79.4%, compared with 73.4% for zero-shot transfer, 62.1% for one-shot fine-tuning, 76.5% for RETAIN, and 76.6% for FLA (Kang et al., 1 Jul 2026). This supports the claim that the method is not tied to a single action-decoding paradigm.

The main benchmark summaries are concise.

Setting	DART result	Comparison point
LIBERO viewpoint shifts, $\pi_{\text{fast}}$7 average	79.1%	FLA 74.3%
LIBERO visual perturbations average	75.0%	FLA 71.5%
LIBERO viewpoint shifts, $\pi_{\text{fast}}$8 average	79.4%	FLA 76.6%
MimicGen Panda$\pi_{\text{fast}}$9UR5e average success	69.4%	zero-shot 62.0%
Real-world UR10e average success	81.7%	FLA 55.0%

On MimicGen cross-embodiment transfer from Panda to UR5e, DART reports average Progress Rate 84.3 and Success Rate 69.4, compared with 79.8 and 62.0 for zero-shot transfer and 74.4 and 56.4 for one-shot fine-tuning (Kang et al., 1 Jul 2026). On Stack Three in particular, success improves from 37.2% to 45.4% (Kang et al., 1 Jul 2026). This is notable because the domain shift is not merely visual but also kinematic and embodiment-specific.

On the real-world UR10e platform, DART attains 81.7% average success across five tasks under the target viewpoint, compared with 43.3% for zero-shot transfer, 51.7% for one-shot fine-tuning, 48.3% for RETAIN, and 55.0% for FLA (Kang et al., 1 Jul 2026). The paper emphasizes that this transfer is achieved despite adapting on only a single Stack Cube demonstration.

Ablation results further clarify the contribution of each component. Direct subtraction without subspace alignment already yields 78.1% average success on LIBERO viewpoint shifts, versus 31.5% for one-shot fine-tuning. Adding subspace filtering alone raises this to 78.8%, scaling alone to 78.5%, and full DART to 79.1% (Kang et al., 1 Jul 2026). The paper also reports that adapting all layers is best; adapting vision plus LLM layers is nearly as strong, while action-only adaptation yields comparatively little benefit (Kang et al., 1 Jul 2026). This aligns with the reported observation that the domain vector has larger magnitude in the LLM and vision layers.

6. Conceptual interpretation, scope, and limitations

The conceptual contribution of DART is the claim that environmental shift can be represented as a transferable direction in parameter space. The paper supports this with prototype analyses in which update-vectors are decomposed into task prototypes, domain prototypes, and a global prototype. The composed estimator

$\mathcal{E}_{\text{src}}$0

aligns more strongly with actual task-domain updates than any prototype alone, which the authors interpret as empirical evidence for additive task-plus-domain structure (Kang et al., 1 Jul 2026). Feature-level analysis further indicates that task prototypes shift language and task-relevant object tokens more strongly, whereas domain prototypes shift background tokens more, suggesting a partial disentanglement between task and domain information in weight space (Kang et al., 1 Jul 2026).

This perspective places DART near prior work on task arithmetic and linear composability of fine-tuning directions. The paper explicitly relates its findings to task-vector literature, disentangled weight subspaces, and NTK-based arguments that pretrained models may remain approximately linear with respect to moderate weight perturbations (Kang et al., 1 Jul 2026). A plausible implication is that DART is less a standalone adaptation heuristic than a concrete instance of a broader linearization phenomenon in overparameterized multimodal models.

The method has explicit limitations. Performance still degrades under severe shifts, particularly the Large viewpoint condition, relative to full-data fine-tuning upper bounds (Kang et al., 1 Jul 2026). A small search over $\mathcal{E}_{\text{src}}$1 is required, even though the paper reports broad empirical stability once subspace alignment is included (Kang et al., 1 Jul 2026). The method also assumes access to a source-domain demonstration for the same task as the target-domain demonstration, which is natural when the source dataset is available but may be non-trivial for weakly labeled corpora (Kang et al., 1 Jul 2026). Finally, the observed additivity and disentanglement are described as inherited from large pretrained VLM and LLM backbones; the paper notes that smaller or under-trained VLAs may exhibit weaker decomposition structure (Kang et al., 1 Jul 2026).

The acronym itself is potentially ambiguous in the broader arXiv literature. Other works use “DART” for substantially different concepts, including “Draft-Agreement Routing” in hybrid reasoning models (Lee et al., 22 Jun 2026), “Divergence Aware adveRsarial Training” for robust unsupervised domain adaptation (Wang et al., 2024), and “Difficulty-Aware Rejection Tuning” for mathematical problem solving (Tong et al., 2024). In the VLA setting, however, Domain ARiThmetic refers specifically to one-shot adaptation under environmental shifts through weight vector arithmetic with domain-specific information addition (Kang et al., 1 Jul 2026).