3D Localisation Auxiliary Task

• 3D localisation auxiliary tasks are defined as supportive objectives that enhance spatial encoding by predicting displacement and directional cues in 3D data.
• They are integrated via specialized network heads in CNNs and transformer architectures, leading to improved accuracy, convergence speed, and robustness in tasks like detection and segmentation.
• Empirical results demonstrate measurable gains—with up to 8% higher accuracy—validating these tasks as effective regularizers for enhancing model generalisation in 3D perception.

A 3D localisation auxiliary task is an auxiliary learning objective designed to improve a model’s ability to encode, predict, or reason about spatial relationships or positions within three-dimensional (3D) data. Such tasks are used as auxiliary heads, loss terms, or pre-training objectives in deep neural networks tackling 3D perception, reasoning, or vision problems. They inject spatial structure or regularization into representations, usually in conjunction with a primary task such as segmentation, detection, or language-grounding. This auxiliary supervision has proven effective across modalities—including point clouds, volumetric imagery, monocular images, and multimodal paired representations—yielding measurable improvements in accuracy, robustness, convergence, and generalisability.

1. Taxonomy of 3D Localisation Auxiliary Tasks

3D localisation auxiliary tasks are highly domain- and architecture-dependent, but canonical instantiations include:

• Displacement regression: Predicting a continuous vector offset from an estimated 3D position to a ground-truth landmark, as performed by the regression head in Patch-based Iterative Networks (PIN) for 3D medical landmark localisation (Li et al., 2018).
• Direction classification: Classifying the most likely axis-aligned direction toward the true landmark as an auxiliary task, providing confidence signals to aid the main regression (Li et al., 2018).
• Pairwise spatial regression: Predicting normalised relative 3D offsets between sampled pairs of masked patch tokens in masked self-supervised learning on video clips, as in the 3D Localised Loss auxiliary task for ViT-based V-JEPA pre-training (Ellis et al., 24 Jul 2025).
• Multimodal spatial alignment: For MLLMs and vision-LLMs, learning to align 3D point-cloud features and relative spatial cues (e.g., target-to-anchor/distractor deltas) to the text embedding space as a preparatory auxiliary alignment stage (Chang et al., 9 Dec 2024).
• Contextual feature matching: Aligning model features to reference features derived from ground-truth label data, as in label-guided auxiliary heads for 3D object detection (Huang et al., 2022).

Some methods exploit theoretical motivation, such as the Cramér–Wold theorem (Liu et al., 2021), to justify the use of low-dimensional projections (e.g., 2D keypoints) as sufficient for learning high-dimensional 3D structure.

2. Architectural Design and Integration

3D localisation auxiliary tasks are typically integrated via dedicated network heads, side-branches, or cross-modal fusion modules. Representative architectures include:

• Multi-task CNNs: The PIN approach uses a single CNN backbone with distinct branches for continuous regression (offsets) and discrete classification (axis-direction), trained jointly with a weighted multi-task loss (Li et al., 2018). The two heads back-propagate gradients into shared convolutional layers, facilitating feature reuse and regularisation.
• Transformer-based SSL Models: For ViT-based self-supervised models (e.g., V-JEPA), a compact MLP head is appended to the feature predictor. This head, applied only at pre-training, takes pairs of token embeddings and predicts their relative position in (normalized) 3D space, providing a strong spatial locality prior (Ellis et al., 24 Jul 2025).
• Auxiliary Cross-modal Encoders: In multimodal setups, dedicated projection MLPs encode per-object 3D features and relative spatial vectors into a joint embedding space. These are supplied as tokens to LLMs, providing explicit positional context (Chang et al., 9 Dec 2024).
• Auxiliary Feature Alignment for Detectors: The label-guided framework for 3D object detection (Huang et al., 2022) fuses point-cloud and annotation-derived representations via cross-attention modules (Label-Knowledge-Mapper, Label-Annotation-Inducer), aligning learned features with task-specific guidance.

Auxiliary heads are typically dropped at inference, ensuring computational efficiency.

3. Mathematical Formulations and Loss Functions

The supervisory signals associated with 3D localisation auxiliary tasks span a range:

• Regression objectives: $$L_{\text{reg}} = \frac{1}{3N} \sum_{n=1}^N \| d^{GT}_n - d_n \|_2^2$$ for vector displacement (Li et al., 2018); MSE over normalised 3D offsets for patch pairs (Ellis et al., 24 Jul 2025).
• Classification objectives: Cross-entropy loss on axis-direction classes, $$L_{\text{cls}} = -\frac{1}{N} \sum_{n=1}^N \log P_{c_n^{GT}, n}$$, providing per-axis confidence (Li et al., 2018).
• Hybrid/weighting schemes: Multi-task losses combine primary and auxiliary objectives with a manually tuned hyperparameter, e.g. $$L = (1-\alpha) L_{\text{reg}} + \alpha L_{\text{cls}}$$ or $$L_{\text{combined}} = \lambda L_{\text{JEPA}} + (1-\lambda) L_{ll}$$ (Li et al., 2018, Ellis et al., 24 Jul 2025). Optimal weighting settings (e.g., $\lambda=0.25$) are established by ablation studies.
• Contrastive/cosine alignment: Weighted combinations of MSE and cosine-distance align 3D vision and language representations, as in $$\mathcal{L}_1 = \alpha \cdot \operatorname{MSE}(v^i, \hat{h}_i) + \beta \cdot (1 - \cos(v^i, \hat{h}_i))$$ (Chang et al., 9 Dec 2024).
• Feature alignment L2 loss: $\mathcal{L}_{aux} = \| F_{det}^* - G \|_2^2$ aligns the backbone’s internal features with label-guided representations in 3D detection (Huang et al., 2022).

Auxiliary loss terms may focus supervision on select token pairs, anchor-distractor relations, or mask-restricted subsets for improved generalization.

4. Empirical Impact and Benchmark Results

Quantitative studies consistently demonstrate that integrating a 3D localisation auxiliary task yields substantive performance improvements:

Method/Domain	Baseline Metric	+Auxiliary Task Metric	Papers
PIN, single landmark	6.45 mm error, 0.09 s	5.47 mm error, 0.09 s (joint loss)	(Li et al., 2018)
PIN, 10-landmarks	6.42 mm error	5.59 mm error (joint PCA)	(Li et al., 2018)
ViT V-JEPA on US videos	DSC 0.644 (10% labels)	DSC 0.692 (w/ 3D LL, +7.45%)	(Ellis et al., 24 Jul 2025)
LOCATE 3D (ScanNet++)	51.5% Acc@25	56.7% (w/ 3D-JEPA pretrain, +5.2 pp)	(Arnaud et al., 19 Apr 2025)
LG3D on VoteNet	59.1 [email protected]	61.7 (+2.6), 65.1 (+2.2 mAP)	(Huang et al., 2022)
MonoCon (KITTI/Car)	21.19 AP$_{BEV}$	22.10 AP$_{BEV}$ (+1 pt)	(Liu et al., 2021)
MLLM, 3DVG accuracy	31.5% (Vote2Cap++)	48.7% (aux alignment, +17 pt)	(Chang et al., 9 Dec 2024)

In these examples, models consistently achieve 2–8% higher accuracy, or order-of-magnitude speed gains, when auxiliary 3D localisation objectives are incorporated. Gains are especially pronounced in settings with limited annotated data or where inductive biases for 3D structure are weak.

5. Theoretical Rationale and Inductive Bias

Auxiliary 3D localisation objectives serve multiple theoretical and practical functions:

• Locality and regularisation: In ViT-based or self-supervised settings lacking inherent spatial bias, auxiliary regression/classification tasks encourage the network to encode distance relationships or directionality, promoting precise spatial coherence (Ellis et al., 24 Jul 2025).
• Geometry constraints: Predicting multiple 2D projections, as justified by the Cramér–Wold theorem, suffices to identify high-dimensional 3D structure by constraining the underlying distribution through its projections (Liu et al., 2021).
• Cross-modal grounding: By explicitly aligning 3D spatial and linguistic representations, models learn to verbalize or reason about objects with correct geometric context and disambiguate among perceptually similar distractors (Chang et al., 9 Dec 2024).
• Label supervision without inference cost: Auxiliary heads are discarded at test time, ensuring that these regularization or supervision signals do not add computational burden during deployment (Huang et al., 2022, Liu et al., 2021).

Auxiliary tasks further regularize shared feature extractors, reducing overfitting and improving generalization, especially when labeled data is scarce.

6. Application Domains and Extensions

3D localisation auxiliary tasks have been systematically employed in diverse application contexts:

• Medical image analysis: PIN facilitates fast, accurate 3D anatomical landmark localisation in volumetric ultrasound, with multi-tasking for increased speed and precision (Li et al., 2018).
• Self-supervised representation learning: Both 3D-JEPA (Arnaud et al., 19 Apr 2025) and 3D Localised Loss (Ellis et al., 24 Jul 2025) employ masked prediction and pairwise regression to inject spatial structure and locality into representations, showing measurable benefits in downstream segmentation and referential grounding.
• Monocular and multi-view 3D detection: Monocular contexts or label-guided features provide effective supervision for single-image 3D detection, surpassing methods that rely solely on geometric priors (Liu et al., 2021, Huang et al., 2022).
• Multimodal language understanding: Auxiliary tasks in large vision-LLMs enforce 3D spatial precision, directly improving visual grounding and contextual disambiguation in LLMs (Chang et al., 9 Dec 2024).
• Gauge theory and mathematical physics: In the context of non-supersymmetric gauge theory, introduction of purely auxiliary fields enables path integral localisation and exact computation of quantum partition functions (Arvanitakis et al., 22 Apr 2024).

The methodology is adaptable to a range of spatial representations (volumetric, point cloud, image, sequence), network backbones (CNN, ViT, PointNet, Transformer), and multimodal integration schemes.

7. Limitations and Open Directions

Despite their empirical effectiveness, 3D localisation auxiliary tasks exhibit several limitations:

• Task specificity: Gains are dependent on design choices (e.g., pairing, masking strategy, auxiliary head capacity) and may be marginal in already well-localized models.
• Orientation encoding: Certain encoders (e.g., PointNet++) are rotation-invariant and may fail to encode directional cues essential for relational language (e.g., "in front of") (Chang et al., 9 Dec 2024).
• Modality constraints: Masked-latent objectives may be less effective when input signal is extremely sparse or scene ambiguity is high, and current methods are less effective for non-rigid or articulated objects.
• Lack of action-oriented grounding: Auxiliaries focusing on static geometry cannot capture functional or temporal spatial relationships without additional predicate or action heads (Chang et al., 9 Dec 2024).

Future advancements may involve integrating per-point normals or camera-frame axes, extending auxiliary objectives to articulated objects or human-scene interactions, and exploring predicate-level spatial reasoning.

---

In sum, the 3D localisation auxiliary task is a versatile and impactful technique across computer vision, medical imaging, geometric deep learning, self-supervised representation learning, and multimodal language understanding. Rigorous ablation and empirical results affirm its value as a regularization mechanism, a spatial bias injector, and an enabler of robust generalization in high-dimensional 3D domains (Li et al., 2018, Ellis et al., 24 Jul 2025, Chang et al., 9 Dec 2024, Arnaud et al., 19 Apr 2025, Huang et al., 2022, Liu et al., 2021, Arvanitakis et al., 22 Apr 2024).