Simple Depth Transformer (SDT)

• Simple Depth Transformer (SDT) is a family of parameter-efficient architectures designed for structured prediction and depth estimation tasks.
• It integrates adaptive-depth sequence decoders for NLP and simplified vision transformers using max-based attention and efficient upsampling.
• SDT reduces decoder parameters, FLOPs, and latency while delivering competitive performance on benchmarks like KITTI and NYUv2.

The Simple Depth Transformer (SDT) refers to a class of highly parameter-efficient transformer-based architectures and decoders that have been specifically designed for structured prediction and depth estimation tasks. Three principal streams of work have used the SDT name: (1) adaptive-depth sequence decoders for NLP (Elbayad et al., 2019), (2) simplified vision transformers for self-supervised monocular depth (Yang et al., 2022), and (3) compact upsampling decoders for zero-shot monocular depth estimation (notably in AnyDepth) (Ren et al., 6 Jan 2026). Across these lines, SDT exhibits a shared emphasis on minimizing architectural complexity and computational cost while preserving or even exceeding state-of-the-art (SOTA) accuracy on standard depth and structured prediction benchmarks.

1. Model Architectures and Design Principles

1.1 Adaptive-Depth Transformer Decoders

The SDT architecture within NLP leverages a stack of $N$ Transformer blocks in both the encoder and decoder, with the encoder mirroring Vaswani et al. (2017). The SDT differentiates itself by attaching an intermediate classifier to each decoder depth, enabling output predictions to be made at various layers: $p(y_{t+1}\mid h_t^n) = \mathrm{softmax}(W_n h_t^n)$ where $h_t^n$ is the hidden state at step $t$ and depth $n$. During inference, early exit is permitted from any layer $n \leq N$ by selecting an appropriate classifier (Elbayad et al., 2019).

1.2 Efficient Vision Encoders for Self-Supervised Depth

In self-supervised monocular depth estimation, SDT is embodied in architectures such as Depth-Net, composed of four progressive stages with overlapping patch embedding and simplified transformer layers. Each stage reduces spatial resolution, and feature fusion follows a top-down FPN scheme. The transformer blocks are simplified by:

• Using single-head, softmax-free max-based attention.
• No explicit positional encodings.
• Mix-FFN built exclusively from GPU-friendly operations: $1 \times 1$ conv, depthwise $3 \times 3$ conv, batch norm, and ReLU (Yang et al., 2022).

1.3 Single-Path Transformer Decoder for Zero-Shot Depth

Within the AnyDepth framework, SDT refers to a compact transformer-based decoder that follows the extraction of dense multi-scale ViT (DINOv3) features. SDT exclusively consists of:

• A single linear projection with GELU activation per scale.
• Four learnable scalar weights for cross-scale fusion.
• A spatial detail enhancer (SDE) block using $3 \times 3$ depthwise conv + BN.
• A 4$\times$ learnable DySample upsampler interleaved with small conv refiners.
• Absence of self- or cross-attention layers in the decoder: all attention is confined within the frozen backbone (Ren et al., 6 Jan 2026).

2. Feature Fusion, Upsampling, and Attention Mechanisms

2.1 Single-Path Fusion

Distinct from multi-branch designs (e.g., DPT), SDT fuses four projected multi-scale token sets $P_i$ using softmax-normalized scalar weights $w_i$: $$T_{\text{fused}} = \sum_{i=1}^4 w_i P_i, \quad w_i = \frac{\exp(\alpha_i)}{\sum_{j=1}^4 \exp(\alpha_j)}$$ This fusion occurs before spatial detail enhancement and upsampling (Ren et al., 6 Jan 2026).

2.2 Spatial Detail Enhancement and Learnable Upsampling

SDE applies depthwise $3 \times 3$ convolution with BN, followed by ReLU: $$F' = \text{ReLU}(F + \text{BN}(\text{DWConv}_{3\times3}(F)))$$ Progressive upsampling is implemented as: $U(X) = R\left(S(R(S(X)))\right)$ with $S(X)$ and $R(X)$ chains of DySample and convolution layers, designed to restore spatial details with low computation (Ren et al., 6 Jan 2026).

2.3 Simplified Attention

• Max-based, single-head attention:
  • No softmax, multi-head, or explicit positional encoding (DEST/SDT for vision (Yang et al., 2022)).
  • Value projection by average-pooling.
• Decoder-attention is absent in AnyDepth-SDT; all cross-token communication arises in the frozen DINOv3 encoder (Ren et al., 6 Jan 2026).

3. Training Objectives and Data-Centric Strategies

3.1 Depth-Adaptive Halting (NLP)

Objective is a joint loss: $$\mathcal{L}(x,y) = \mathcal{L}_{\text{dec}}(x,y) + \alpha \mathcal{L}_{\text{exit}}(x,y)$$ with intermediate supervision (aligned training) and explicit cross-entropy on the learned exit distribution $q_t$ compared to an oracle $q_t^*$ at sequence or token level (Elbayad et al., 2019).

3.2 Self-Supervised Depth (Vision)

Photometric reconstruction loss (following Monodepth2) and edge-aware smoothness regularization: $$L_{\text{photo}}(p) = \alpha \frac{1 - \mathrm{SSIM}}{2} + (1 - \alpha)\|I_t(p) - \hat I_t(p)\|_1$$

$$L_{\text{smooth}} = \sum_p \left( |\partial_x d(p)| e^{-|\partial_x I_t(p)|} + |\partial_y d(p)|e^{-|\partial_y I_t(p)|} \right)$$

Total loss: $$L = L_{\text{photo}} + \lambda_{\text{smooth}} L_{\text{smooth}}$$ (Yang et al., 2022).

3.3 Training Data Filtering

AnyDepth-SDT introduces automated data-centric filtering using:

• Depth distribution score ($S_{\text{dist}}$).
• Gradient continuity score ($S_{\text{grad}}$). Samples with low informativeness or poor statistics are pruned, reducing the train pool from 584 K to 369 K while increasing average accuracy (Ren et al., 6 Jan 2026).

4. Efficiency, Parameter Counts, and Complexity

4.1 Parameters & Computational Cost

Model/Decoder	Params (M)	% vs DPT	FLOPs (G)	Dec Latency (ms)
DPT (ViT-S/16)	50.83	100%	444.1	6.66
SDT (ViT-S/16)	5.51	10.8%	234.2	6.10
DPT (ViT-B/16)	76.05	100%
SDT (ViT-B/16)	9.45	12.4%

SDT achieves 85-89% reduction in decoder parameters and 47% fewer FLOPs, with ~30% lower latency and ~33% lower memory footprint on embedded platforms (Jetson Orin Nano) (Ren et al., 6 Jan 2026).

4.2 Design Choices for Speed

• Single-head, softmax-free attention.
• Removal of cross-scale feature reassembly and per-layer alignment modules.
• Convolutional upsampling and SDE for local feature recovery.
• Exclusive use of batch normalization (no LayerNorm).

5. Experimental Performance and Applications

5.1 Depth-Adaptive Translation (NLP)

• IWSLT De→En: Matching baseline BLEU (35.4) with only 24% of decoder blocks ($\mathrm{AE}=1.42$).
• WMT En→Fr: SDT matches 43.4 BLEU baseline at $\mathrm{AE}=2.4$ (40% of blocks).
• Early-exit tokens exhibit strong correlation with token certainty/structure (Elbayad et al., 2019).

5.2 Monocular Depth Estimation

• KITTI, NYUv2, ETH3D, ScanNet, DIODE: Across all, SDT head matches or improves over DPT in AbsRel and $\delta<1.25$ (often $>94\%$).
• DEST-B3: 19.7 M parameters, 19.8 GMACs, surpasses PackNet-SfM (128.3 M, 205.5 GMACs) and Monodepth2 (Yang et al., 2022).
• AnyDepth-B (ViT-B + SDT): AbsRel improves from 9.5 to 7.2 on NYUv2 with filtering and SDE+DySample (Ren et al., 6 Jan 2026).

5.3 Generalization to Dense Prediction

SDT backbone directly transfers to semantic segmentation, achieving higher mIoU at significantly reduced latency and resource usage compared to SegFormer (Yang et al., 2022). SDT decoder consistently delivers crisper boundaries and fine structure due to SDE and learnable upsampling.

6. Limitations and Discussion

• In NLP, output classifier overhead can become significant for large vocabularies, partially mitigated by design, but remains a factor (Elbayad et al., 2019).
• Reliance on oracle-style supervision for halting remains an open challenge; SDT does not provide end-to-end halting training.
• The Learnable upsampling and SDE in vision SDT produce sharper edges and details, but their effect in extremely low-data scenarios or under severe domain shift remains a subject of ongoing evaluation.
• The single-path fusion and absence of cross-attention in SDT decoders (AnyDepth) suggest excellent hardware suitability but may constrain some expressivity compared to full transformer decoders; however, empirical metrics indicate no practical trade-off in zero-shot monocular depth (Ren et al., 6 Jan 2026).

7. Summary and Significance

Simple Depth Transformer unifies a family of mechanisms and architectures aiming to maximize parameter efficiency, computational speed, and empirical performance across both natural language and dense vision tasks. By eliminating architecturally redundant modules and focusing on lightweight, hardware-friendly operations—single-head attention, linear fusion, depthwise convs, and progressive upsampling—SDT achieves or exceeds comparable SOTA models with orders of magnitude fewer parameters and computations. Its decoupling of attention (frozen backbone) from upsampling and fusion (decoder) in AnyDepth (Ren et al., 6 Jan 2026) and its adaptive-depth computation for language modeling (Elbayad et al., 2019) establish it as a highly reproducible, resource-efficient choice for structured prediction in both research and deployment contexts.