Dual-Decoder Transformer Models

• Dual-decoder Transformer is an architecture that integrates two decoders (left-to-right and right-to-left) to capture comprehensive contextual signals from both past and future tokens.
• It leverages dual-attention mechanisms and reinforcement learning fine-tuning to strengthen encoder training and achieve ensemble-like inference in tasks such as math problem solving and speech recognition.
• This approach improves multi-task performance and accuracy by providing richer learning signals, leading to measurable gains in BLEU scores, CER, and WER in diverse applications.

A dual-decoder Transformer is an architectural extension of the standard Transformer framework in which two separate decoders operate in parallel or in coordinated fashion, leveraging complementary generative directions, modalities, or tasks. This paradigm provides richer learning signals, improved contextual modeling, and ensemble-like performance advantages—the encoder’s representations are jointly shaped by multi-directional or multi-task decoding. Dual-decoder Transformers have been deployed in sequence generation (left-to-right and right-to-left decoding), multi-task learning (e.g., speech recognition and translation), and other domains requiring refined context integration or auxiliary supervision.

1. Architectural Concepts and Dual-Decoding Principles

The canonical dual-decoder Transformer as described in "Solving Math Word Problems with Double-Decoder Transformer" (Meng et al., 2019) consists of a shared encoder followed by two decoders with opposite generation directions:

• Left-to-right decoder (L-to-R): Generates the target sequence from the start token sequentially using past output as history.
• Right-to-left decoder (R-to-L): Generates the sequence reversed, starting at the end and conditioning on future tokens.

Mathematically, with input $X$ and target sequence $\mathbf{y}$, the combined cross-entropy loss is:

$$L_{\text{CE}} = -\sum_{t=1}^{T} \log P_\theta(y_t | y_0\!:\!t-1, X) -\sum_{t=0}^{T-1} \log P_\theta\left(y_t | y_{t+1}:T, X\right)$$

Each decoder propagates its gradients into the shared encoder, enforcing comprehensive context encoding. During inference, the model selects the final output by comparing the confidence scores (log-probabilities) from both decoders, thereby yielding an ensemble-like decision mechanism.

In broader dual-decoder paradigms, the two decoders may address distinct tasks (e.g., phoneme and grapheme recognition (N, 2021), ASR and translation (Le et al., 2020)), modalities (audio-derived vs. text-derived context (Hu et al., 2021)), or modalities fused via learned strategies (low- and high-dimensional audio features (Sun et al., 2023)), with dedicated attention pathways or dual-attention modules enabling cross-decoder interaction.

2. Mathematical Formulation and Optimization

The dual-decoder approach augments the standard maximum likelihood objective with either an additive or multi-task loss formulation. Especially in sequence generation tasks, the aggregate loss structurally encourages the encoder to resolve both past and future token dependencies. This structure is valuable for problems requiring strict syntactic and semantic fidelity, as in symbolic equation generation.

Reinforcement learning (RL) may be introduced, as in (Meng et al., 2019), to address exposure bias and metric misalignment. The RL objective is:

$$L_\theta = -\mathbb{E}_{\hat{y}_{1:T} \sim \pi_\theta}[\log \pi_\theta(\hat{y}_{1:T}) \cdot r(\hat{y}_{1:T})]$$

where the reward $r$ evaluates success on the downstream task (e.g., equation correctness). In practice, the expectation is approximated by sampling and using a baseline $r_b$ to reduce variance, leading to:

$$L_\theta \approx -\frac{1}{N} \sum_{n=1}^{N} \sum_{t=1}^{T} \log \pi_\theta(\hat{y}_t|\hat{y}_{t-1}) [r(\hat{y}_{1:T}) - r_b]$$

This RL fine-tuning further optimizes for correct substantive output rather than token-level accuracy.

3. Empirical Performance and Comparative Results

Empirical benchmarks support the effectiveness of dual-decoder architectures. Representative accuracy results for math word problem equation generation (Meng et al., 2019):

Model	Accuracy (%)
Single-decoder, MLE	~19.4
Dual-decoder, MLE (ensemble)	~21.7
Dual-decoder, RL (ensemble)	~22.1

This demonstrates measurable improvements attributable to ensemble voting and enhanced encoder training. Further, in speech recognition, bidirectional decoders yield notable reductions in CER (character error rate), exemplified by a 3.6% relative CER reduction in Mandarin ASR (Chen et al., 2020).

In multi-task regimes, dual-decoder Transformers outperform multitask and cascaded baselines on joint ASR and translation, achieving higher BLEU scores and lower WER (Le et al., 2020), particularly when using parallel dual-attention interaction. In low-resource multilingual speech recognition, the inclusion of phoneme and grapheme decoders produced over 41% relative WER reduction versus classical GMM-HMM (N, 2021).

4. Encoder Training Dynamics and Contextual Modeling

A defining benefit of dual-decoding lies in the refinement and generalization of the encoder's latent representations. The encoder receives complementary gradients—left-contextual and right-contextual—from the decoders. This is directly analogous to the bidirectional signal in masked LLMing (e.g., BERT) but extends it to generative contexts.

The result is richer context modeling, reducing propagation of copy/align errors and improving strict output sequence validity—a property essential for mathematical or code-mixed language tasks. Dual-decoder interaction, especially with explicit cross-attention (as in CMLFormer (Baral et al., 19 May 2025)), further enables joint structural modeling of complex tasks by "peeking" into the counterpart's latent states.

5. Practical Considerations and Applications

Dual-decoder Transformers have found use in domains requiring strong context sensitivity:

• Math word problem equation generation: Dual directionality reduces reasoning errors (Meng et al., 2019).
• Speech recognition/translation: Parallel decoders generate transcriptions and translations for simultaneous subtitling and interpretation (Le et al., 2020).
• Multilingual speech recognition: Decoders for phonemes, graphemes, and auxiliary language ID improve performance in low-resource environments (N, 2021).
• Audio captioning: Fusing high- and low-dimensional audio features with dual Transformer decoders enhances caption accuracy (Sun et al., 2023).
• Code-mixed LLMing: Specialized dual decoders and cross-attention modules model frequent language switching and transitions (Baral et al., 19 May 2025).

The dual-decoder strategy is further applicable in segmentation tasks (infection/lung region masks (Bougourzi et al., 2023)), video captioning (semantic/syntactic separation (Gao et al., 2022)), and dynamic system modeling where symbolic structure and derivatives are predicted jointly (Chang et al., 23 Jun 2025).

6. Limitations and Future Directions

While dual-decoder architectures achieve substantial gains in encoder expressiveness and final accuracy, limitations persist:

• Computational overhead: Two decoders entail increased training and inference resource demands.
• Design complexity: Cross-decoder interaction introduces additional hyperparameters (merging operators, coupling strength), requiring tuning for balancing task interactions.
• Scalability: For highly chaotic or high-dimensional systems, dual-decoder models may exhibit increased prediction inaccuracies (Chang et al., 23 Jun 2025).

Future work may focus on encoder-heavy architectures to absorb multi-task optimization loads, direct divergence integration in loss formulations, more extensive pre-training data, and advanced positional encoding strategies. Domains with explicit task interdependence or context fusion requirements remain a fertile ground for these models.

7. Summary Table: Dual-Decoder Advantages

Dual-Decoder Feature	Task Impact
Multi-directional decoding	Mitigates copy/align errors, ensemble effect
Dual-attention/cross-coupling	Joint context modeling for multi-target tasks
Encoder signal enhancement	Richer representations via bi-directional flow
Ensemble inference	Improved output selection via score voting
RL integration	Alignment with final task metric

Dual-decoder Transformers represent a significant architectural evolution for sequence modeling and multi-task learning, enabling superior context integration and performance across diverse modalities and tasks.