Bridge: Basis-Driven Causal Inference Marries VFMs for Domain Generalization¶

Conference: CVPR 2026
arXiv: 2604.26820
Code: https://mingbohong.github.io/Bridge/ (Project Page)
Area: Object Detection / Domain Generalization / Causal Inference
Keywords: Domain Generalized Object Detection (DGOD), Front-door Adjustment, Causal Inference, Basis Learning, Vision Foundation Models (VFMs)

TL;DR¶

Addressing the issue where detectors easily learn spurious correlations from confounders like "lighting/co-occurrence/style" under data scarcity in single-source domains, this paper proposes the plug-and-play Causal Basis Block (CBB). By implementing causal front-door adjustment via learnable low-rank bases to "estimate two expectations," CBB allows for end-to-end calibration on frozen VFMs (DINOv2/3, SAM, Stable Diffusion). It consistently sets new SOTAs across five DGOD benchmarks (up to +5.4 mAP).

Background & Motivation¶

Background: Domain Generalized Object Detection (DGOD) aim to train on one or few source domains and generalize to unseen target domains. Mainstream approaches include learning domain-invariant representations, expanding source distributions via augmentation, or leveraging strong priors from Vision Foundation Models (VFMs). Recently, using frozen DINOv2/SAM/Stable Diffusion as backbones with detection heads has become popular.

Limitations of Prior Work: Most methods ignore confounding effects occurring during single-source, small-data training. Confounders \(\mathcal{Z}\) (lighting, object co-occurrence patterns, style differences) affect both input features \(\mathcal{X}\) and labels \(\mathcal{Y}\), creating spurious correlations. A provided example shows that a detector using a frozen DINOv2 (pre-trained on 142M images) but fine-tuned on only 3,000 Cityscapes images misclassifies bicycles next to pedestrians as "rider" (57%) or "person" (20%)—it learns the shortcut "bicycles often co-occur with people" rather than the causal features of the bicycle. The representation power of strong backbones is wasted on such shortcuts.

Key Challenge: To eliminate confounding, back-door adjustment is a classic approach, but it requires explicit modeling and enumeration of confounders \(\mathcal{Z}\) (\(\mathcal{P}(\mathcal{Y}\mid\mathrm{do}(\mathcal{X}))=\sum_{\mathcal{Z}}\mathcal{P}(\mathcal{Y}\mid\mathcal{X},\mathcal{Z})\mathcal{P}(\mathcal{Z})\)). In reality, many confounders are unobservable or difficult to measure, making back-door adjustment infeasible. Existing causal detection works (e.g., for adverse weather) rely on external confounder dictionaries and cumbersome post-processing like clustering/momentum updates, lacking flexibility and scalability.

Goal: Block spurious correlations without explicitly specifying confounders or using external dictionaries, while creating a plug-and-play module that seamlessly integrates with any frozen VFM.

Key Insight: Use front-door adjustment to bypass "confounder enumeration"—by finding a mediator variable \(\mathcal{M}\) on the causal path \(\mathcal{X}\to\mathcal{Y}\), the causal effect of \(\mathcal{X}\) on \(\mathcal{Y}\) can be identified. Drawing from dictionary learning, the two difficult-to-calculate expectations in front-door adjustment are approximated using learnable low-rank bases.

Core Idea: Rewrite front-door adjustment as "estimating two expectations \(\mathbb{E}[\mathcal{X}']\) and \(\mathbb{E}[\mathcal{M}]\)," and calculate these end-to-end using a set of low-rank learnable bases and Sample Queries. This blocks confounding while concurrently filtering out redundant, task-irrelevant features.

Method¶

Overall Architecture¶

Bridge is a DGOD framework built upon frozen VFMs. An input image is first processed by the VFM to extract multi-scale feature maps; these features enter the core Causal Basis Block (CBB) for causal calibration. The calibrated features are then passed to the task head (Faster R-CNN) for prediction. The VFM backbone remains frozen; only the CBB and task head are trained, avoiding the high cost of full network fine-tuning.

CBB performs two tasks: ① Expectation Estimation—using Sample Queries to aggregate global/generalizable information from the training set to obtain spatial weight maps, then projecting weighted features onto a subspace spanned by learnable low-rank bases to obtain expectations \(\mathbb{E}[\mathcal{X}]\) and \(\mathbb{E}[\mathcal{M}]\); ② Feature Aggregation—summing the two expectations and the mediator feature \(\mathcal{M}\) to form the final output \(\mathcal{F}_{\text{out}}=\hat{\mathbb{E}}[\mathcal{X}]+\hat{\mathbb{E}}[\mathcal{M}]+\mathcal{M}\). The first two terms implement front-door adjustment to block confounding, while \(\mathcal{M}\) retains task-specific information. CBB is fully differentiable and trained with the downstream detection loss.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Input Image"] --> B["Frozen VFM<br/>Extract Multi-scale Features"]
    B --> C["Basis-driven Front-door Adjustment<br/>P(Y|do(X)) ≈ Estimating Two Expectations"]
    C --> D["Sample Queries<br/>Aggregate Generalizable Sample Expectations"]
    D --> E["Low-rank Basis Subspace Projection<br/>Filter Redundancy/Retain Principal Components"]
    E --> F["Feature Aggregation<br/>E[X] + E[M] + Mediator M"]
    F --> G["Task Head<br/>Detection Prediction"]

Key Designs¶

1. Basis-driven Front-door Adjustment: Converting Confounding Removal to "Estimating Two Expectations"

Since back-door adjustment cannot handle unobservable confounders \(\mathcal{Z}\), this work adopts front-door adjustment: by finding a mediator \(\mathcal{M}\), then \(\mathcal{P}(\mathcal{Y}\mid\mathrm{do}(\mathcal{X}))=\mathbb{E}_{\mathcal{M}\sim\mathcal{P}(\mathcal{M}\mid\mathcal{X})}\big[\mathbb{E}_{\mathcal{X}'\sim\mathcal{P}(\mathcal{X})}[\mathcal{P}(\mathcal{Y}\mid\mathcal{X}',\mathcal{M})]\big]\). Calculating this nested expectation is computationally expensive, so NWGM (Normalized Weighted Geometric Mean) is used to move the expectation inside the probability. Following prior literature that extends front-door adjustment from prediction layers to intermediate feature layers, this is simplified as \(\mathcal{P}(\mathcal{Y}\mid do(\mathcal{X}))\approx\mathcal{P}\big(\mathcal{Y}\mid\mathbb{E}_{\mathcal{X}'}[\mathcal{X}']+\mathbb{E}_{\mathcal{M}\mid\mathcal{X}}[\mathcal{M}]\big)\).

The value of this step is that implementing front-door adjustment is reduced to estimating just two expectations: \(\mathbb{E}_{\mathcal{M}\mid\mathcal{X}}[\mathcal{M}]\) and \(\mathbb{E}_{\mathcal{X}'}[\mathcal{X}']\). Since expectations lack closed-form solutions in complex representation spaces, the authors approximate them as linear combinations of learnable basis vectors \(\mathbb{E}[\mathcal{V}]\approx\frac{1}{S}\sum_{i=1}^{S}\sum_{k=1}^{K}c_{ik}b_k\) (\(b_k\) is a basis, \(c_{ik}\) is a coefficient). Unlike old causal methods relying on external dictionaries, this approach requires no external confounder definitions and the bases naturally induce low-rank structures, making it plug-and-play and scalable.

2. Sample Queries: Aggregating Generalizable Information Across Samples to Estimate \(\mathbb{E}[\mathcal{X}]\)

The expectation \(\mathbb{E}_{\mathcal{X}'\sim\mathcal{P}(\mathcal{X})}[\mathcal{X}']\) is over the input marginal distribution and cannot be computed from a single image. CBB introduces learnable Sample Queries \(\mathcal{Q}_s\in\mathbb{R}^{S\times C}\), similar to object queries in DETR. During training, they implicitly aggregate global representations of the entire training set, thereby guiding expectation estimation. Given input features \(\mathcal{X}_{in}\in\mathbb{R}^{B\times N\times C}\), query responses \(\mathcal{X}'_q=\mathcal{X}_{in}\mathcal{Q}_s^{\top}\) are calculated. Softmax over the sample dimension \(S\) yields \(p\), and a weighted sum produces a spatial weight map \(\mathcal{A}=\sum_{i=1}^{S}p_i\mathcal{X}'_{q,i}\in\mathbb{R}^{B\times N\times 1}\). This \(\mathcal{A}\) re-weights the input to obtain query-guided features \(\mathcal{X}_q=\mathcal{A}\odot\mathcal{X}_{in}\).

Essentially, \(\mathcal{A}\) acts as an attention map identifying which spatial locations carry generalizable information, highlighting parts of \(\mathcal{X}_{in}\) shared across source domains that do not depend on specific confounders.

3. Low-rank Basis Subspace Projection: Filtering Redundancy and Estimating Expectations

To filter remaining redundancy, CBB introduces learnable bases \(\mathcal{B}=[b_1,\dots,b_K]\in\mathbb{R}^{K\times C}\) where \(K<C\), forming a low-rank subspace. Query-guided features \(\mathcal{X}_q\) are projected onto this subspace with coefficients \(\mathcal{C}=\mathcal{X}_q\mathcal{B}^{\top}(\mathcal{B}\mathcal{B}^{\top})^{-1}\in\mathbb{R}^{B\times N\times K}\) (where \((\mathcal{B}\mathcal{B}^{\top})^{-1}\) is a normalization term). Reconstructing back to the original space provides the expectation estimate \(\mathbb{E}[\mathcal{X}_{in}]\approx\mathcal{C}\mathcal{B}\in\mathbb{R}^{B\times N\times C}\).

This path \(\mathbb{R}^{N\times C}\to\mathbb{R}^{N\times K}\to\mathbb{R}^{N\times C}\) compresses the features to \(K\) dimensions to discard redundancy. Since \(K<C\), reconstruction uses only the most representative principal components, aligning features with the core directions of the sample distribution. The smaller \(K\) is, the more generic the representation remains—experiments show DINOv3 performs best with 12.5% dimensions, while SAM/SD require 50%–70%. At inference, \(\mathcal{B}^{\top}(\mathcal{B}\mathcal{B}^{\top})^{-1}\mathcal{B}\) can be pre-calculated as a fixed \(C\times C\) matrix.

4. Feature Aggregation: Mediator Features for Task Information

The expectations are "de-confounded and generalized," which might lose details necessary for detection. CBB first creates mediator features \(\mathcal{M}=\mathrm{Conv}(\mathcal{X}_{in})\) using a simple convolution block, then estimates \(\hat{\mathbb{E}}[\mathcal{X}]\) and \(\hat{\mathbb{E}}[\mathcal{M}]\) to produce the final output \(\mathcal{F}_{\text{out}}=\hat{\mathbb{E}}[\mathcal{X}]+\hat{\mathbb{E}}[\mathcal{M}]+\mathcal{M}\).

This summation has a clear division of labor: the first two terms \(\hat{\mathbb{E}}[\mathcal{X}]+\hat{\mathbb{E}}[\mathcal{M}]\) correspond to the requirements of front-door adjustment for blocking spurious correlations; the final addition of \(\mathcal{M}\) ensures that task-specific information, which might be filtered by low-rank compression, is preserved.

Key Experimental Results¶

Main Results¶

On five DGOD benchmarks using AP50: Bridge can be applied to discriminative VFMs (DINOv2-L / DINOv3-L / SAM-Huge) and generative VFMs (Stable Diffusion v2.1 with CrossKD distillation to R101). Representative comparisons (mAP / %):

Benchmark (Train \(\to\) Test)	Configuration	Baseline	Bridge	Gain
Cross-Camera (Cityscapes \(\to\) BDD100K)	Diff. Detector(SD) vs Boost	49.3	53.1	+3.8
Cross-Camera	DINOv2 backbone	51.8	56.9	+5.1
Adverse Weather (City \(\to\) FoggyCity)	DINOv2 backbone	52.8	58.2	+5.4
Adverse Weather	DINOv3 backbone	57.7	61.6	+3.9
Real-to-Artistic (VOC \(\to\) 3 styles, avg)	DINOv2 backbone	65.4	69.4	+4.0
Diverse Weather Datasets (avg)	DINOv2 backbone	40.8	44.8	+4.0
DroneVehicle Extreme-Dark	DINOv3 backbone	33.7	34.0	+0.3

Compared to respective runners-up, Bridge improves by +3.8 / +2.9 / +2.4 / +0.4 / +1.5 mAP. Notable gains are seen in the Extreme-Dark scenario of Diverse Weather DroneVehicle: Faster R-CNN alone yields 8.1 mAP, while Bridge with Diff. Detector / DINOv2 / DINOv3 reaches 24.2 / 29.8 / 34.0, proving that low-rank bases can focus on causal representations in high-noise/low-light environments.

Ablation Study¶

Component ablation (Table 6, City \(\to\) FoggyCity, mAP):

Configuration	DINOv3	SAM	SD	Description
baseline	57.7	45.8	51.8	Frozen VFM with Head
+ Low-rank Basis (LRB)	60.9	49.2	53.1	Gain of +3.2/+3.4/+1.3
+ LRB + Sample Queries	61.6	49.9	53.6	Gain of +0.7/+0.7/+0.5

Comparison of Causal Modeling (Table 7, DINOv3): Re-implementing GOAT's front-door adjustment as FACL with cross-attention between multi-scale layers showed minimal gain or even drops (BDD 57.8 \(\to\) 58.5, DWD 48.6 \(\to\) 48.2, R2A 72.7 \(\to\) 71.6). Replacing it with CBB led to consistent improvements (58.9 / 61.6 / 50.8 / 48.4 / 73.3).

Key Findings¶

Low-rank Basis is the primary driver: LRB alone accounts for most gains, while Sample Queries provide complementary benefits.
Basis ratio correlates with backbone strength: DINOv3 performs best at a 12.5% ratio, suggesting strong representations require very compact basis spaces; SAM/SD require 50%–70% to maintain feature diversity.
Harder scenarios see larger gains: Most significant improvements occur in categories with high co-occurrence (rider/bike) and extreme environments (darkness), validating that CBB effectively blocks "co-occurrence/lighting" confounders.
Cross-detector universality: Beyond Faster R-CNN, CBB consistently improves Sparse R-CNN and TOOD (e.g., TOOD on DWD 47.3 \(\to\) 50.1).

Highlights & Insights¶

Converting abstract causal formulas into computable expectations via low-rank bases: CBB approximates difficult front-door expectations via sample queries and low-rank projection, achieving both de-confounding and feature purification.
Backbone-agnostic and plug-and-play: Works across DINOv2/3, SAM, and Stable Diffusion while keeping backbones frozen. The projection matrix can be pre-computed for efficient inference.
The "Low-rank ratio \(\propto\) Backbone weakness" observation: This links "required subspace size" to "representation quality," providing a heuristic for other tasks using low-rank/bottleneck structures for feature purification.
Benchmark contribution: Annotated weather conditions for DroneVehicle (Clear/Dark/Foggy/Extreme-Dark) address the lack of diverse weather evaluations in UAV remote sensing DGOD.

Limitations & Future Work¶

Approximation bounds: CBB uses low-rank bases to approximate expectations in front-door adjustment; there is no theoretical guarantee on the quality of this approximation in complex representation spaces.
Mediator \(\mathcal{M}\) validity: The assumption that \(\mathcal{M}=\mathrm{Conv}(\mathcal{X}_{in})\) lies on the causal path and satisfies front-door criteria is not rigorously verified, acting more as an empirical mediator.
Marginal gains on strong baselines: Improvements are smaller when the backbone is already exceptionally strong (e.g., DINOv3 on Extreme-Dark).
Future directions: Enhancing mediator selection with causal guarantees (e.g., independence constraints) or extending basis learning to non-linear manifolds.

Vs. Back-door methods: Prior methods require explicit confounder enumeration and external dictionaries. Bridge uses front-door adjustment with no explicit confounders, offering better scalability.
Vs. GOAT/FACL: Ablations show that CBB's low-rank projection outperforms cross-attention mapping, suggesting that how expectations are estimated is more critical than the use of front-door adjustment itself.
Vs. Frozen VFM-based DGOD (Boost, GDD): These methods rely on VFM priors but ignore spurious correlations. Bridge adds a causal calibration layer to recover representation power lost to confounding.

Rating¶

Novelty: ⭐⭐⭐⭐ Translates front-door adjustment into "two expectations" via low-rank bases, elegantly combining causal theory with engineering.
Experimental Thoroughness: ⭐⭐⭐⭐⭐ Comprehensive evaluation across 5 benchmarks, 4 VFMs, 3 detectors, and a self-built weather benchmark.
Writing Quality: ⭐⭐⭐⭐ Clear link between causal derivation and module implementation.
Value: ⭐⭐⭐⭐ Highly practical plug-and-play causal calibration for VFM-based DGOD.