Quantized Depth Auxiliary Task

• Quantized depth auxiliary tasks reframe continuous depth prediction into discrete intervals, enhancing stability and robust geometric feature extraction.
• Techniques such as interval quantization and vector-quantized VAE integration enable multi-modal models to leverage classification losses for effective regularization.
• Empirical results show improved spatial reasoning and performance in robotic manipulation and autonomous vehicle depth estimation tasks.

A quantized depth auxiliary task refers to the incorporation of discrete depth prediction objectives within larger neural network frameworks, serving either as regularization or as an auxiliary supervision signal to improve geometric representation and task-level performance. Rather than regressing raw depth values, models employing quantized depth auxiliaries partition depth into discrete intervals or latent tokens, enabling the use of classification or token prediction losses and facilitating more stable, geometry-aware learning. This technique has found utility in vision-language-action models for robotic manipulation and in single-image depth estimation in autonomous vehicle perception.

1. Principles and Motivation for Depth Quantization

Quantized depth auxiliary tasks address inherent instability and slow convergence of continuous depth regression by re-encoding depth values into discrete categories or latent tokens. The main approaches are interval quantization—dividing depth ranges into bins—and latent tokenization—assigning depth features to discrete codebook entries via vector quantization.

In "QDepth-VLA: Quantized Depth Prediction as Auxiliary Supervision for Vision-Language-Action Models" (Li et al., 16 Oct 2025), raw depth maps $D \in \mathbb{R}^{H \times W}$ are projected into a latent space using a vector-quantized variational autoencoder (VQ-VAE), resulting in discretized representations $z_q \in \{1, \ldots, 256\}^{h' \times w'}$ by nearest-neighbor codebook lookup. In "MultiDepth: Single-Image Depth Estimation via Multi-Task Regression and Classification" (Liebel et al., 2019), depth values are mapped with a logarithmic transform and partitioned into $n_\text{cls}$ intervals (typically 32), optimizing a classification objective over these bins as the auxiliary task.

The rationale for quantization includes improved training stability via the cross-entropy loss, faster convergence, coarser yet robust geometric features at early training, and the ability to regularize continuous regression branches by shared representation learning.

2. Architectures and Integration Strategies

Architectural integration of quantized depth auxiliaries varies depending on the context. The QDepth-VLA framework attaches an 18-layer transformer ("Depth Expert") to a multimodal backbone (PaliGemma-3B, visual encoder, action head). The Depth Expert ingests visual tokens and outputs scores over codebook entries at each spatial location, optimized using cross-entropy against frozen VQ-VAE indices.

QDepth-VLA employs hierarchical attention masking: text and image tokens are grouped; depth tokens attend to both visual and textual modalities, enriching geometric awareness; action tokens attend to all prior modalities and proprioception. Training schedules involve joint pretraining of policy and depth modules (e.g., Fractal, LIBERO datasets), fined-tuned with AdamW and large batch sizes.

In MultiDepth, a shared ResNet-101 encoder feeds into two parallel decoders: a regression head producing continuous log-scaled depth maps via pyramid pooling and a classification head outputting per-pixel SoftMax logits over quantized intervals. Uncertainty-weighted multi-task objectives balance loss terms with trainable scalars $s_\text{reg}$, $s_\text{cls}$, regularizing the combined objective. Both approaches constrain depth prediction at the feature or token level, facilitating geometry-aware learning in vision-based models.

3. Auxiliary Loss Functions and Training Regimes

Auxiliary supervision is realized via classification objectives over quantized depth, which stabilizes the training dynamics of the continuous regression or action prediction branches. QDepth-VLA sets the Depth Expert’s output logits $\ell_{i, k}$ proportional to the negative squared Euclidean distance between predicted feature $h_i$ and codebook vector $c_k$, scaled by temperature $\tau$:

$\ell_{i,k} = -\frac{1}{\tau} \|h_i - c_k\|_2^2$

A cross-entropy loss aligns these logits with the frozen ground-truth indices $z_i^*$:

$$L_\text{depth} = - \frac{1}{BN} \sum_{i=1}^{BN} \log \frac{\exp(\ell_{i, z_i^*})}{\sum_{k=1}^K \exp(\ell_{i, k})}$$

The total loss is a linear combination of the action policy loss (Conditional Flow Matching) and the auxiliary depth loss, with a decaying weight $\lambda_t = \lambda_0 \cdot \gamma^t$.

In MultiDepth, the multi-task loss incorporates both mean-squared error regression and classification cross-entropy, balanced via uncertainty weights:

$$L_\text{mt} = \frac{1}{2}e^{-s_\text{reg}^2}L_\text{reg} + \frac{1}{2}s_\text{reg} + e^{-s_\text{cls}^2}L_\text{cls} + \frac{1}{2}s_\text{cls}$$

Training protocols leverage standard classification augmentations (random crops, flips), optimizer choices (Adam/AdamW), and adaptive learning rate schedules.

4. Empirical Impact and Ablation Results

Quantized depth auxiliaries consistently yield improvements in geometric reasoning and downstream task performance, as substantiated by benchmark experiments.

In QDepth-VLA, single-view LIBERO results improved markedly over baselines without quantized depth prediction: spatial perception (77.2→86.0), object reasoning (84.0→88.8), goal fulfillment (83.6→94.0), and long-horizon tasks (66.0→72.6). Robotic manipulation on Simpler raised average success from 60.0% to 68.5%, with block-stack jumping from 29.2% to 39.6%. Real-robot setups saw an increase from 32.5% to 42.5% (Li et al., 16 Oct 2025).

Ablation studies reveal that removing the auxiliary depth loss or the Depth Expert transformer significantly degrades performance. Replacing quantized prediction with per-pixel regression, or substituting hierarchical attention masking with standard masks, results in lower success rates. Codebook resolution experiments indicated that $16 \times 16$ spatial size suffices.

MultiDepth reports improved stability and accuracy in single-image depth estimation. Regression-only and classification-only baselines yield higher SILog error scores (25.96 and 17.22, respectively) compared with multi-task learning: final scores with learned weights and larger patches reach 12.27 in regression. Any $n_\text{cls} \geq 4$ stabilizes training, with optimal convergence at $n_\text{cls}=32$ (Liebel et al., 2019).

Method/Modification	Success Rate / Metric	Notes
QDepth-VLA w/ quantized auxiliary	Up to 68.5% (Simpler)	Hierarchical attention, Depth Expert
Depth loss removed (λₜ→0)	Drops to 65.6% (Simpler)	Ablation
Depth Expert removed	Drops to 60.0% (Simpler)	Ablation
Pixel regression for depth	Drops to 64.6% (Simpler)	Ablation
SILog (MultiDepth, regression)	12.27–16.05	Better than regression or classification alone

5. Mechanisms Underlying Improved Spatial Reasoning

The primary mechanism by which quantized depth auxiliary tasks improve learning arises from their robust gradients and feature-level regularization. Classification over depth intervals provides strong, coarse supervision early in learning, guiding encoders to differentiate salient geometric structures such as object and gripper boundaries, contact planes, and spatial relationships, without the distraction of high-frequency per-pixel noise.

Sharing encoders between continuous regression and discrete classification heads acts as a regularizer, preventing overfitting and steering feature extraction toward more generalizable geometric cues. In transformers, hierarchical attention schemes isolate noisy depth fluctuations, ensuring multi-modal information exchange while safeguarding semantic priors.

Empirical ablations and analysis indicate that these auxiliaries particularly aid tasks demanding spatial precision and reasoning (e.g., object placement, stacking). However, fine-grained contact tasks or environments exhibiting extreme depth noise (glossy surfaces) may expose limitations in codebook granularity or latent representation capacity.

6. Limitations and Future Directions

While quantized depth auxiliaries provide significant benefits in geometric representation learning, several constraints persist. Latent vector granularity (e.g., 160-dimensional, $16 \times 16$ grid) may be inadequate for tasks requiring precision at sub-object or contact level. Depth prediction under extreme noise conditions remains challenging. Future research directions include:

• Prediction of future depth tokens for look-ahead reasoning in sequential tasks.
• Exploration of more efficient vector-quantized convolutional architectures with smaller, perhaps adaptive, codebooks to reduce computation and improve representational efficiency.
• Investigating scale-adaptive quantization for tasks spanning diverse depth ranges.

A plausible implication is that the depth auxiliary task may become a standard regularization primitive for multi-modal models in robotics and perception, particularly when spatial inference is paramount (Li et al., 16 Oct 2025, Liebel et al., 2019).