ODE-Based Transformer Decoders for Iterative Sign Language Translation

# ODE-Based Transformer Decoders for Iterative Sign Language Translation
Source: [https://arxiv.org/html/2608.11352](https://arxiv.org/html/2608.11352)
###### Abstract

Sign language translation has achieved strong results with Transformer architectures, yet recent improvements largely rely on scaling model capacity at the cost of increased computation\. We propose a parameter\-efficient alternative that improves expressiveness without increasing model size\. Rather than scaling capacity, we focus on enhancing the update dynamics of iterative refinement decoders, where each refinement step corresponds to one internal decoder iteration that progressively improves the latent representation before translation generation\. We reinterpret residual refinement updates from an Ordinary Differential Equation \(ODE\) perspective and replace them with higher\-order numerical integration schemes, namely Runge–Kutta methods \(RK\-2 and RK\-4\)\. These methods perform multiple function evaluations within each refinement step to produce more accurate and stable representation updates without adding decoder parameters\. To the best of our knowledge, this is the first application of ODE\-inspired update dynamics to sign language translation\. RK\-2 achieves 22\.96 BLEU\-4 on the PHOENIX\-14T test set and 19\.34 BLEU\-4 on the CSL\-Daily test set, outperforming the IPSLT baseline on both benchmarks, with fewer decoder layers and refinement iterations on CSL\-Daily\. These results suggest that stronger refinement dynamics can improve translation performance under parameter\-efficient decoder designs, providing a complementary alternative to conventional model scaling\.

###### Keywords:

Sign Language Translation Iterative Refinement Ordinary Differential Equations Runge–Kutta Methods

## 1Introduction

![Refer to caption](https://arxiv.org/html/2608.11352v1/ode2.png)Figure 1:Overview of the proposed architecture\. A frozen visual encoder extracts features, followed by stacked Transformer encoder layers\. At each stage, representations are decoded by ODE\-based Transformer decoders within an iterative refinement framework\.Sign language translation \(SLT\) aims to generate fluent spoken\-language text directly from continuous visual sign language input\. SLT can be formulated as a gloss\-based approach relying on intermediate gloss representations or as a gloss\-free approach that directly maps visual input to text, where the latter offers improved scalability by eliminating costly gloss annotations\. Gloss\-free SLT requires jointly modeling fine\-grained spatiotemporal cues, such as hand shape, motion, and facial expressions, and capturing long\-range dependencies, while the lack of explicit visual–textual alignment and the linguistic differences between sign and spoken languages further complicate the task\.

Recent progress in SLT has been largely driven by scaling model capacity and leveraging large pretrained components, such as powerful visual encoders and large language models\. While these strategies yield strong performance gains, they increase computational cost, and comparatively less attention has been given to how representations are updated across layers\.

Transformer\-based architectures form the foundation of most modern SLT systems, where representations are updated across layers through residual connections\. Such connections can be viewed as discretizations of an underlying Ordinary Differential Equation \(ODE\), where each layer performs a single first\-order Euler integration step\[[25](https://arxiv.org/html/2608.11352#bib.bib53),[58](https://arxiv.org/html/2608.11352#bib.bib57)\]\. This first\-order formulation may limit the accuracy and stability of representation evolution, suggesting that more advanced numerical integration methods could improve the quality of representation updates\. This viewpoint provides an alternative to scaling, where improvements arise from better update dynamics rather than larger models\.

In this work, we propose a parameter\-efficient approach that enhances model expressiveness by improving update dynamics instead of increasing model capacity\. To the best of our knowledge, this is the first work to introduce an ODE\-based perspective into SLT\. Building on an iterative refinement framework, we replace standard residual decoder updates with higher\-order Runge–Kutta methods \(RK\-2 and RK\-4\), which approximate the underlying dynamics using multiple function evaluations per step, resulting in more accurate and stable updates\.

We evaluate the proposed approach on PHOENIX\-14T and CSL\-Daily\. The results demonstrate that ODE\-guided update dynamics can improve test performance without adding decoder parameters\. These outcomes suggest that enhancing the quality of iterative representation updates is a promising parameter\-efficient direction for SLT, complementary to conventional model scaling\.

## 2Related Work

### 2\.1Sign Language Translation

Sign language translation \(SLT\) is a challenging task within the broader field of Sign Language Understanding \(SLU\), which aims to infer semantic meaning from visual sign language data\. Earlier work in SLU has largely focused on recognition: isolated sign recognition classifies individual signs from short clips\[[27](https://arxiv.org/html/2608.11352#bib.bib7),[43](https://arxiv.org/html/2608.11352#bib.bib8),[26](https://arxiv.org/html/2608.11352#bib.bib10),[61](https://arxiv.org/html/2608.11352#bib.bib11)\], while continuous sign recognition transcribes signing video into gloss sequences\[[19](https://arxiv.org/html/2608.11352#bib.bib12),[27](https://arxiv.org/html/2608.11352#bib.bib7),[20](https://arxiv.org/html/2608.11352#bib.bib13),[48](https://arxiv.org/html/2608.11352#bib.bib14)\], where glosses serve as intermediate representations approximating sign\-level annotations\.

SLT can be formulated either as an end\-to\-end gloss\-free task or as a gloss\-based framework that leverages gloss supervision, either explicitly or through auxiliary alignment objectives\[[8](https://arxiv.org/html/2608.11352#bib.bib15),[44](https://arxiv.org/html/2608.11352#bib.bib16)\]\. In explicit settings, gloss sequences are first predicted via continuous sign language recognition \(CSLR\) and subsequently mapped to spoken\-language text\[[56](https://arxiv.org/html/2608.11352#bib.bib20),[53](https://arxiv.org/html/2608.11352#bib.bib21),[11](https://arxiv.org/html/2608.11352#bib.bib22),[10](https://arxiv.org/html/2608.11352#bib.bib23),[7](https://arxiv.org/html/2608.11352#bib.bib1)\]\. While gloss supervision provides strong intermediate constraints due to its temporal alignment with sign language, it is labor\-intensive and requires domain expertise, limiting scalability\. Moreover, gloss annotations are typically unavailable in large\-scale open\-domain datasets such as YouTube\-SL25\[[45](https://arxiv.org/html/2608.11352#bib.bib17)\], OpenASL\[[42](https://arxiv.org/html/2608.11352#bib.bib18)\], YouTube\-ASL\[[47](https://arxiv.org/html/2608.11352#bib.bib19)\], and BOBSL\[[3](https://arxiv.org/html/2608.11352#bib.bib24)\], making gloss\-free approaches a more scalable alternative for end\-to\-end SLT\.

Due to the limited size of SLT datasets and the multimodal nature of the task, transfer learning and pretraining have become key strategies\. Most SLT frameworks decouple visual representation learning from language modeling, employing independently pretrained visual encoders and language decoders\[[10](https://arxiv.org/html/2608.11352#bib.bib23),[59](https://arxiv.org/html/2608.11352#bib.bib25),[49](https://arxiv.org/html/2608.11352#bib.bib26),[33](https://arxiv.org/html/2608.11352#bib.bib27)\]\. To mitigate the modality gap, recent approaches adopt visual–language pretraining with contrastive objectives and masked modeling\[[59](https://arxiv.org/html/2608.11352#bib.bib25)\], while gloss\-free settings introduce pseudo\-gloss pretraining\[[49](https://arxiv.org/html/2608.11352#bib.bib26)\]and gloss\-attention mechanisms\[[55](https://arxiv.org/html/2608.11352#bib.bib28)\]to approximate gloss supervision\.

Recent advances increasingly leverage large pretrained and foundation models\. On the language side, large language models such as GPT\[[49](https://arxiv.org/html/2608.11352#bib.bib26)\], LLaMA\[[23](https://arxiv.org/html/2608.11352#bib.bib32),[15](https://arxiv.org/html/2608.11352#bib.bib29)\], FlanT5\-XL\[[22](https://arxiv.org/html/2608.11352#bib.bib31)\], and mBART\[[12](https://arxiv.org/html/2608.11352#bib.bib30)\]are integrated as decoders or auxiliary supervisors\[[18](https://arxiv.org/html/2608.11352#bib.bib33)\], enhancing linguistic fluency and long\-range dependency modeling\. On the visual side, foundation models pretrained on large\-scale image or video corpora, including DINOv2\[[49](https://arxiv.org/html/2608.11352#bib.bib26),[17](https://arxiv.org/html/2608.11352#bib.bib34)\], CLIP\[[50](https://arxiv.org/html/2608.11352#bib.bib35),[22](https://arxiv.org/html/2608.11352#bib.bib31)\], and VideoMAE\[[22](https://arxiv.org/html/2608.11352#bib.bib31)\], provide strong spatiotemporal representations\. While these approaches achieve substantial gains, they typically rely on increased model capacity and large pretrained backbones, reflecting a broader trend of scaling\.

### 2\.2Transformers and Ordinary Differential Equation \(ODE\) Techniques

Transformer architectures have increasingly been interpreted from an ODE\-based perspective, where residual layers correspond to discrete integration steps of an underlying continuous transformation\. This view builds on earlier connections between Neural ODEs and equilibrium formulations of deep networks\[[9](https://arxiv.org/html/2608.11352#bib.bib55),[6](https://arxiv.org/html/2608.11352#bib.bib56)\], under which standard residual updates resemble first\-order numerical solvers, motivating more expressive update rules\.

Recent studies extend this perspective specifically to Transformers\. Zhong et al\.\[[58](https://arxiv.org/html/2608.11352#bib.bib57)\]analyze Transformer layers through a Neural ODE formulation, while Li et al\.\[[25](https://arxiv.org/html/2608.11352#bib.bib53)\]introduce Runge–Kutta\-inspired updates for sequence generation, replacing the first\-order residual step with higher\-order integration\. Tong et al\.\[[46](https://arxiv.org/html/2608.11352#bib.bib54)\]further explore continuous\-depth architectures, depth\-dependent parameterizations, and adaptive fine\-tuning to improve flexibility and stability\.

Prior work has primarily applied the ODE perspective to general sequence generation or conventional Transformer layer stacks\. In contrast, we study this formulation in the context of iterative SLT, where representations are repeatedly refined over multiple update steps\. Building on Li et al\.\[[25](https://arxiv.org/html/2608.11352#bib.bib53)\], we integrate Runge–Kutta updates into the refinement process\.

### 2\.3Iterative Refinement

Iterative refinement is a general strategy for improving predictions by repeatedly updating intermediate representations or outputs over multiple steps\. It appears across vision and language tasks in various forms, including progressive generative refinement\[[16](https://arxiv.org/html/2608.11352#bib.bib39),[1](https://arxiv.org/html/2608.11352#bib.bib37),[39](https://arxiv.org/html/2608.11352#bib.bib38),[2](https://arxiv.org/html/2608.11352#bib.bib48),[40](https://arxiv.org/html/2608.11352#bib.bib47)\], structural alignment optimization\[[29](https://arxiv.org/html/2608.11352#bib.bib41),[37](https://arxiv.org/html/2608.11352#bib.bib40),[30](https://arxiv.org/html/2608.11352#bib.bib42),[57](https://arxiv.org/html/2608.11352#bib.bib43)\], and self\-feedback mechanisms\[[32](https://arxiv.org/html/2608.11352#bib.bib44)\]\.

In Transformer architectures, refinement is commonly realized through recursive or weight\-shared designs, where the same block is applied multiple times and the effective depth is determined by the number of iterations\[[4](https://arxiv.org/html/2608.11352#bib.bib45),[51](https://arxiv.org/html/2608.11352#bib.bib46),[41](https://arxiv.org/html/2608.11352#bib.bib49)\]\. Related approaches, such as the Universal Transformer and depth\-adaptive variants, further explore iterative computation by reusing shared layers or dynamically adjusting computation depth\[[13](https://arxiv.org/html/2608.11352#bib.bib50),[14](https://arxiv.org/html/2608.11352#bib.bib51),[5](https://arxiv.org/html/2608.11352#bib.bib52)\]\.

In sign language translation, iterative refinement has been adopted to progressively improve decoding outputs across multiple steps\[[52](https://arxiv.org/html/2608.11352#bib.bib36)\]\. Similar strategies have also been explored in sign language production, where iterative updates refine generated sign sequences\[[24](https://arxiv.org/html/2608.11352#bib.bib61)\]\. These approaches improve what is refined or how many refinement steps are taken, while the update within each step remains a first\-order residual operation\. In contrast, we recast each refinement step as a higher\-order numerical integration of an underlying continuous transformation, producing a more accurate per\-step update without adding parameters or refinement steps, complementary to existing iterative refinement methods\.

## 3Methodology

We propose ODE\-guided decoders for sign language translation, building on the iterative refinement framework\[[52](https://arxiv.org/html/2608.11352#bib.bib36)\]and enhancing representation updates through higher\-order numerical integration schemes\. An overview of the proposed model architecture is illustrated in Fig\.[1](https://arxiv.org/html/2608.11352#S1.F1)\.

### 3\.1Visual Features

We extract 512\-dimensional frame\-level visual features using dataset\-specific ResNet\-18 backbones pretrained under the CSLR setting\. For PHOENIX\-14T, we use the ResNet\-18 backbone pretrained with the VAC framework\[[34](https://arxiv.org/html/2608.11352#bib.bib5)\]\. For CSL\-Daily, we use the ResNet\-18 backbone pretrained with the Self\-Emphasizing Network framework\[[21](https://arxiv.org/html/2608.11352#bib.bib58)\]\. To reduce training cost, the visual backbones are kept frozen during training\. The extracted visual embeddings are then processed by a stack of 1D temporal convolution and max\-pooling layers, which model local motion patterns and provide hierarchical temporal abstraction before the features are passed to the translation model\.

### 3\.2Initialization

In the initialization stage, an encoder–decoder pair generates an initial prediction from visual features\. The initial encoderE1E\_\{1\}processes the input features, and its representation is used to obtain the predictionY0Y\_\{0\}\. This representation is then passed to the iterative refinement module, where it serves as input to the subsequent encoding stage \(E2E\_\{2\}\)\. The initialization decoder is used only during training and is not involved in inference\.

### 3\.3Iterative Refinement

Building on the initial representation, we perform iterative refinement to progressively improve the model predictions\. The refinement stage is implemented using a dedicated encoder, denoted asE2E\_\{2\}, which is applied iteratively\. At each iterationkk, the model updates its representation by conditioning on both the visual featuresVVand the representation obtained from the previous iteration\. Specifically, given the previous representationHk−1H\_\{k\-1\}, the refinement encoderE2E\_\{2\}produces an updated representation

​Hk=E2​\(Hk−1,V\)\.\\mbox\{\}\\hfill H\_\{k\}=E\_\{2\}\(H\_\{k\-1\},V\)\.\\hfill\\mbox\{\}\(1\)
The updated representationHkH\_\{k\}in Eq\.[1](https://arxiv.org/html/2608.11352#S3.E1)is then passed to the decoder to generate the refined predictionYkY\_\{k\}\. This process is repeated forKKiterations, enabling progressive improvement of the model outputs\.

In both the initialization and iterative refinement stages, the encoder uses the attention module introduced in\[[55](https://arxiv.org/html/2608.11352#bib.bib28)\]in place of standard attention blocks\.

### 3\.4ODE\-Based Transformer Decoder

To improve the quality of representation updates, we reinterpret the Transformer decoder as a dynamical system and replace standard residual updates with higher\-order numerical integration schemes\.

In standard Transformers, each layer performs a residual update of the form:

​yt\+1=yt\+F⁡\(yt\)​\\mbox\{\}\\hfill y\_\{t\+1\}=y\_\{t\}\+F\(y\_\{t\}\)\\hfill\\mbox\{\}\(2\)which can be interpreted as a first\-order Euler discretization\. To obtain more accurate updates, we employ higher\-order Runge–Kutta methods, specifically second\-order \(RK\-2\) and fourth\-order \(RK\-4\) schemes\.

##### Post\-update LayerNorm\.

After computing the RK\-style update at steptt, we optionally apply Layer Normalization to the updated latent representation\. For notational simplicity, we write the RK update increment using the same form as Eq\.[2](https://arxiv.org/html/2608.11352#S3.E2), i\.e\.,F⁡\(yt\)F\(y\_\{t\}\), whereF⁡\(⋅\)F\(\\cdot\)denotes the effective update\.

​y~t\+1=yt\+F⁡\(yt\),yt\+1=LayerNorm⁡\(y~t\+1\)\.\\hskip 0\.0pt\\mbox\{\}\\hfill\\tilde\{y\}\_\{t\+1\}=y\_\{t\}\+F\(y\_\{t\}\),\\qquad y\_\{t\+1\}=\\mathrm\{LayerNorm\}\(\\tilde\{y\}\_\{t\+1\}\)\.\\hfill\\mbox\{\}This post\-update normalization can be used to stabilize the iterative refinement process and reduce scale variation across refinement steps\.

##### Direct RK\-2 Formulation \(Method 1\)

Following prior work\[[25](https://arxiv.org/html/2608.11352#bib.bib53)\], we adopt a direct RK\-2 formulation by treating the Transformer decoder layer as the transformation functionF⁡\(⋅\)F\(\\cdot\)\. The update is computed as:

​F1=F⁡\(yt\),F2=F⁡\(yt\+F1\),yt\+1=yt\+12​\(F1\+F2\)\.\\hskip 0\.0pt\\mbox\{\}\\hfill F\_\{1\}=F\(y\_\{t\}\),\\quad F\_\{2\}=F\(y\_\{t\}\+F\_\{1\}\),\\quad y\_\{t\+1\}=y\_\{t\}\+\\tfrac\{1\}\{2\}\\left\(F\_\{1\}\+F\_\{2\}\\right\)\.\\hfill\\mbox\{\}This formulation directly applies RK\-2 by evaluating the decoder layer multiple times, and remains compatible with standard Transformer decoder layers without architectural modifications\.

##### Residual\-Compatible RK\-2 Formulation \(Method 2\)

Since Transformer layers inherently follow a residual structure as shown in Eq\.[2](https://arxiv.org/html/2608.11352#S3.E2), they can be interpreted as implementing a first\-order \(Euler\) update, whereF⁡\(yt\)F\(y\_\{t\}\)corresponds to the residual transformation\. In practice, a Transformer decoder layerg⁡\(⋅\)g\(\\cdot\)produces an output of the formg⁡\(yt\)=yt\+F⁡\(yt\)g\(y\_\{t\}\)=y\_\{t\}\+F\(y\_\{t\}\), allowing the update function to be implicitly recovered as:

​F​\(yt\)=g⁡\(yt\)−yt\.\\hskip 0\.0pt\\mbox\{\}\\hfill F\(y\_\{t\}\)=g\(y\_\{t\}\)\-y\_\{t\}\.\\hfill\\mbox\{\}
Building on this observation, we derive the RK\-2 update increments directly from the residual behavior of the decoder layer, without explicitly definingF⁡\(⋅\)F\(\\cdot\)\. Specifically, letg⁡\(⋅\)g\(\\cdot\)denote a Transformer decoder layer with residual connections\. We compute:

y~1=g\(yt\),F1=y~1−yt,\\hskip 0\.0pt\\mbox\{\}\\hfill\\tilde\{y\}\_\{1\}=g\(y\_\{t\}\),\\quad F\_\{1\}=\\tilde\{y\}\_\{1\}\-y\_\{t\},\\hfill\\mbox\{\}y~2=g\(yt\+F1\),F2=y~2−\(yt\+F1\),\\hskip 0\.0pt\\mbox\{\}\\hfill\\tilde\{y\}\_\{2\}=g\(y\_\{t\}\+F\_\{1\}\),\\quad F\_\{2\}=\\tilde\{y\}\_\{2\}\-\(y\_\{t\}\+F\_\{1\}\),\\hfill\\mbox\{\}and update the representation as:

​yt\+1=yt\+12​\(F1\+F2\)\.\\hskip 0\.0pt\\mbox\{\}\\hfill y\_\{t\+1\}=y\_\{t\}\+\\tfrac\{1\}\{2\}\\left\(F\_\{1\}\+F\_\{2\}\\right\)\.\\hfill\\mbox\{\}
This formulation naturally aligns with the residual structure of Transformers, allowing RK\-2 dynamics to be integrated without modifying the architecture or introducing additional parameters\.

##### RK\-4 Extension

We further extend both formulations to the fourth\-order Runge–Kutta \(RK\-4\) scheme, which performs four intermediate evaluations within a single update step to obtain a more accurate estimate of the underlying transformation\.

For the direct formulation \(Method 1\), whereF⁡\(⋅\)F\(\\cdot\)denotes the decoder\-layer transformation, the update is computed as:

​F1=F⁡\(yt\),F2=F⁡\(yt\+12​F1\),F3=F⁡\(yt\+12​F2\),F4=F⁡\(yt\+F3\),yt\+1=yt\+16​\(F1\+2​F2\+2​F3\+F4\)\.​\\mbox\{\}\\hfill\\begin\{gathered\}F\_\{1\}=F\(y\_\{t\}\),\\\\ F\_\{2\}=F\\left\(y\_\{t\}\+\\tfrac\{1\}\{2\}F\_\{1\}\\right\),\\\\ F\_\{3\}=F\\left\(y\_\{t\}\+\\tfrac\{1\}\{2\}F\_\{2\}\\right\),\\\\ F\_\{4\}=F\\left\(y\_\{t\}\+F\_\{3\}\\right\),\\\\ y\_\{t\+1\}=y\_\{t\}\+\\tfrac\{1\}\{6\}\\left\(F\_\{1\}\+2F\_\{2\}\+2F\_\{3\}\+F\_\{4\}\\right\)\.\\end\{gathered\}\\hfill\\mbox\{\}\(3\)
For the residual\-compatible formulation \(Method 2\), we compute each intermediate increment from the residual behavior of the decoder layerg⁡\(⋅\)g\(\\cdot\)\. That is, for each intermediate inputy^i\\hat\{y\}\_\{i\}, the corresponding increment is obtained asFi=g⁡\(y^i\)−y^iF\_\{i\}=g\(\\hat\{y\}\_\{i\}\)\-\\hat\{y\}\_\{i\}, wherey^i\\hat\{y\}\_\{i\}follows the same RK\-4 intermediate states used above\. This allows the RK\-4 update to be applied without removing the residual structure already present in Transformer decoder layers\.

In our RK\-based decoder, all stage evaluations \(F1F\_\{1\},F2F\_\{2\}in RK\-2 andF1,…,F4F\_\{1\},\\ldots,F\_\{4\}in RK\-4\) are computed by repeated applications of the same decoder functionfθf\_\{\\theta\}\. Increasing the RK order therefore increases the number of decoder evaluations per refinement step without introducing additional decoder parameters\.

### 3\.5Training Objective

We train the model with supervised cross\-entropy and an iteration\-wise distillation objective, which we refer to as the iterative distillation loss \(IDL\)\. Cross\-entropy is applied to the initialization output \(E1E\_\{1\}\) and to the final refined prediction from the refinement stage \(E2E\_\{2\}\)\. During refinement, IDL is implemented as a Kullback–Leibler divergence from each intermediate refinement prediction to the final refinement prediction, where the last refinement step acts as the teacher distribution\. We sum the IDL terms across refinement steps to encourage consistent refinement trajectories and reduce oscillations\.

## 4Experiments

### 4\.1Implementation Details

Dataset\.We evaluate on PHOENIX\-14T\[[7](https://arxiv.org/html/2608.11352#bib.bib1)\], a German Sign Language benchmark derived from weather forecast broadcasts, and CSL\-Daily\[[60](https://arxiv.org/html/2608.11352#bib.bib2)\], a large\-scale Chinese Sign Language dataset covering daily\-life topics with a broader vocabulary\. For both datasets, models are trained on video–translation pairs and evaluated against reference translations without ground\-truth gloss supervision\.

Evaluation Protocols\.We evaluate translation quality using BLEU\[[35](https://arxiv.org/html/2608.11352#bib.bib3)\], computed with SacreBLEU\[[38](https://arxiv.org/html/2608.11352#bib.bib60)\], and ROUGE\[[28](https://arxiv.org/html/2608.11352#bib.bib4)\]\.

Training Settings\.The proposed model was implemented using the PyTorch\[[36](https://arxiv.org/html/2608.11352#bib.bib9)\]framework and trained with the AdamW\[[31](https://arxiv.org/html/2608.11352#bib.bib6)\]optimizer using a weight decay of1×10−41\\times 10^\{\-4\}\. Gradient clipping with a maximum norm of 1\.0 is applied to stabilize training\.

The learning rate follows a warm\-up and cosine scheduling strategy\. For PHOENIX\-14T, it is warmed up from1×10−61\\times 10^\{\-6\}to2×10−42\\times 10^\{\-4\}over the first 30 epochs, with a minimum learning rate of2×10−62\\times 10^\{\-6\}\. For CSL\-Daily, the learning rate is set to1×10−41\\times 10^\{\-4\}with a minimum learning rate of1×10−61\\times 10^\{\-6\}\. The batch size is set to 32, dropout is set to 0\.1, and label smoothing with a factor of 0\.2 is used during training\.

Both the encoder and decoder consist of 3 Transformer layers by default, and the feed\-forward network dimension is set to 2048\.

Inference\.During inference, we employ autoregressive decoding with beam search to generate target sequences, using only the final decoder for prediction\. For both datasets, the beam width is set to 4 and the length penalty is fixed to 1\.0\.

### 4\.2Experimental Results

#### Comparison with SOTA

Tables[1](https://arxiv.org/html/2608.11352#S4.T1)and[3](https://arxiv.org/html/2608.11352#S4.T3)compare our approach with recent SLT methods on PHOENIX\-14T and CSL\-Daily\. Since existing methods differ in pretraining, visual representations, and model capacity, we include both the broader SOTA comparison and results under the same training and inference setup\. Specifically, we report a non\-iterative baseline withK=0K=0and reproduce IPSLT\[[52](https://arxiv.org/html/2608.11352#bib.bib36)\]using the same visual backbone\. The best IPSLT setting usesK=3K=3with an IDL weight of0\.20\.2\.

For our ODE\-guided decoders, we report the best configuration of each update variant selected by DEV BLEU\-4, including RK2SLT\-M1, RK2SLT\-M2, RK4SLT\-M1, and RK4SLT\-M2\. For the reproduced models, the tables distinguish total stored parameters from active\-path training parameters \(T\-P\) and inference parameters \(I\-P\), and report the selected refinement countKK, final\-decoder depth, realized FLOPs, and batch\-32 inference latency\. On PHOENIX\-14T, RK2SLT\-M1 achieves the strongest BLEU\-4 among our variants and improves BLEU\-4 over the IPSLT baseline\. On CSL\-Daily, the best BLEU\-4 score is achieved by RK2SLT\-M2 using a single refinement iteration and a reduced decoder depth, and RK4SLT\-M2 remains close behind with an even more compact single\-layer decoder\. Compared with recent SLT systems that often rely on larger capacity, pretrained components, or stronger visual representations, our models remain competitive by modifying only the refinement dynamics, supporting our argument that better update rules provide a parameter\-efficient route to stronger translation\.

The test results show a dataset\-dependent effect\. On PHOENIX\-14T, where videos are low\-resolution and the domain is narrow, higher\-order refinement provides more conservative gains, with RK\-2 generalizing best among our variants\. On the larger and more diverse CSL\-Daily dataset, the benefit is clearer: RK2SLT\-M2 achieves the best TEST BLEU\-4, while RK4SLT\-M2 is only0\.090\.09BLEU\-4 lower \(19\.2519\.25vs\.19\.3419\.34\) despite using a single refinement iteration and a single decoder layer\. This indicates that RK\-4 can trade additional per\-step computation for reduced decoder depth and fewer refinement steps, yielding a favorable accuracy–efficiency balance\.

Tables[2](https://arxiv.org/html/2608.11352#S4.T2)and[4](https://arxiv.org/html/2608.11352#S4.T4)show that the BLEU\-4 gains are not obtained by increasing the active parameter count\. On PHOENIX\-14T, RK2SLT\-M2 improves BLEU\-4 over IPSLT by0\.640\.64while reducing T\-P, I\-P, FLOPs, and measured latency by10\.6%10\.6\\%,12\.6%12\.6\\%,14\.1%14\.1\\%, and11\.5%11\.5\\%, respectively\. RK2SLT\-M1 provides a complementary quality\-oriented configuration, improving BLEU\-4 by1\.141\.14at a higher computational cost\. On CSL\-Daily, RK2SLT\-M2 achieves the highest BLEU\-4 of19\.3419\.34with7\.4%7\.4\\%fewer inference\-path parameters than IPSLT, at modest overheads of9\.7%9\.7\\%in FLOPs and6\.3%6\.3\\%in measured latency\. RK4SLT\-M2 remains competitive at19\.2519\.25BLEU\-4 and provides the most compact inference path, using14\.9%14\.9\\%fewer inference\-path parameters than IPSLT\. These results demonstrate that the proposed RK updates provide distinct quality–efficiency operating points without relying on increased model capacity\.

Table 1:Comparison with state\-of\-the\-art methods on the PHOENIX\-14T TEST set\.†: reproduced with our training and inference setup;∼\\sim: approximate size; underlined values denote the best results among iterative methods\.MethodKKDec\. layersParams \(M\)TESTB\-1B\-2B\-3B\-4RGFSLT\-VLP\[[55](https://arxiv.org/html/2608.11352#bib.bib28)\]––∼\\sim60043\.7133\.1826\.1121\.4442\.49SignCL\[[54](https://arxiv.org/html/2608.11352#bib.bib59)\]––∼\\sim60049\.7636\.8529\.9722\.7449\.04Sign2GPT with PGP\[[49](https://arxiv.org/html/2608.11352#bib.bib26)\]––∼\\sim170049\.5435\.9628\.8322\.5248\.90FLa\-LLM\[[12](https://arxiv.org/html/2608.11352#bib.bib30)\]––∼\\sim68046\.2935\.3328\.0323\.0945\.27SignLLM\[[15](https://arxiv.org/html/2608.11352#bib.bib29)\]––∼\\sim700045\.2134\.7828\.0523\.4044\.49Baseline0393\.1643\.7933\.9227\.1222\.5445\.43IPSLT\[[52](https://arxiv.org/html/2608.11352#bib.bib36)\]†3393\.1644\.0933\.6326\.4821\.8246\.35RK2SLT\-M1 \(Ours\)3393\.1644\.3534\.2527\.5322\.9646\.93RK2SLT\-M2 \(Ours\)3184\.7544\.5534\.2127\.2222\.4646\.81RK4SLT\-M1 \(Ours\)3393\.1644\.1934\.1827\.4822\.9147\.39RK4SLT\-M2 \(Ours\)3288\.9544\.3034\.1927\.2022\.6246\.78

Table 2:Parameter counts and measured efficiency on the PHOENIX\-14T TEST set\.T\-P and I\-P denote parameters active during training and inference, respectively\. Parameter counts, FLOPs, and latency exclude the visual encoder\. I\-P additionally excludes the initialization decoder and other training\-only modules\. Per\-sample FP32 latency was measured on a single NVIDIA RTX 4000 Ada Generation GPU and averaged over full batches of 32 after two warm\-up batches\.†Results reproduced using our setup\.

Table 3:Comparison with state\-of\-the\-art methods on the CSL\-Daily TEST set\.†: reproduced with our training and inference setup;∼\\sim: approximate size; underlined values denote the best results among iterative methods\.MethodKKDec\. layersParams \(M\)TESTB\-1B\-2B\-3B\-4RGFSLT\-VLP\[[55](https://arxiv.org/html/2608.11352#bib.bib28)\]––∼\\sim60039\.3724\.9316\.2611\.0036\.44SignCL\[[54](https://arxiv.org/html/2608.11352#bib.bib59)\]––∼\\sim60047\.4732\.5322\.6216\.1648\.92Sign2GPT with PGP\[[49](https://arxiv.org/html/2608.11352#bib.bib26)\]––∼\\sim170041\.7528\.7320\.6015\.4042\.36FLa\-LLM\[[12](https://arxiv.org/html/2608.11352#bib.bib30)\]––∼\\sim68037\.1325\.1218\.3814\.2037\.25SignLLM\[[15](https://arxiv.org/html/2608.11352#bib.bib29)\]––∼\\sim700039\.5528\.1320\.0715\.7539\.91Baseline0382\.9343\.5330\.9422\.4916\.9144\.36IPSLT\[[52](https://arxiv.org/html/2608.11352#bib.bib36)\]†3382\.9346\.2233\.3724\.5218\.4847\.07RK2SLT\-M1 \(Ours\)2382\.9348\.3834\.8825\.4018\.9548\.21RK2SLT\-M2 \(Ours\)1278\.7348\.0234\.8025\.6019\.3448\.69RK4SLT\-M1 \(Ours\)3382\.9346\.6233\.6424\.6818\.5646\.91RK4SLT\-M2 \(Ours\)1174\.5348\.9435\.3325\.7919\.2549\.37

Table 4:Parameter counts and measured efficiency on the CSL\-Daily TEST set\.T\-P and I\-P denote parameters active during training and inference, respectively\. Parameter counts, FLOPs, and latency exclude the visual encoder\. I\-P additionally excludes the initialization decoder and other training\-only modules\. Per\-sample FP32 latency was measured on a single NVIDIA RTX 4000 Ada Generation GPU and averaged over full batches of 32 after two warm\-up batches\.†Results reproduced using our setup\.

#### Ablation Studies

We conduct structured sequential ablations on the DEV sets of PHOENIX\-14T and CSL\-Daily\. Each table isolates one design factor at a time, including coefficients, ODE\-decoder placement, post\-update LayerNorm, iterative distillation loss \(IDL\) weight, refinement iteration count, and decoder depth; after each block, the setting with the best BLEU\-4 is selected and fixed for the following blocks\. Following the IPSLT baseline setting, we report configurations with up to three refinement iterations and three decoder layers, avoiding larger configurations to preserve a controlled parameter\-efficient comparison\. We denote the RK\-2 variants as RK2SLT\-M1 and RK2SLT\-M2, and the RK\-4 variants as RK4SLT\-M1 and RK4SLT\-M2, where M1 and M2 refer to the corresponding update methods\.

##### PHOENIX\-14T\.

The PHOENIX\-14T ablations are shown in Tables[5](https://arxiv.org/html/2608.11352#S4.T5)–[6](https://arxiv.org/html/2608.11352#S4.T6)\. For RK\-2, we first ablate the coefficient formulation, while RK\-4 uses fixed fourth\-order coefficients and therefore starts from the placement and normalization block\.

##### RK2SLT\-M1\.

Table[5](https://arxiv.org/html/2608.11352#S4.T5)selects the learnable RK\-2 combinationα​F1\+\(1−α\)​F2\\alpha F\_\{1\}\+\(1\-\\alpha\)F\_\{2\}; the averaged update12​\(F1\+F2\)\\frac\{1\}\{2\}\(F\_\{1\}\+F\_\{2\}\)yields slightly higher ROUGE but lower BLEU\-4\. The best configuration applies the ODE update to all decoder layers without post\-update LayerNorm, uses IDL weight0\.30\.3, and retains three refinement iterations and three decoder layers, indicating that this variant benefits from full refinement capacity on PHOENIX\-14T\.

##### RK2SLT\-M2\.

Table[5](https://arxiv.org/html/2608.11352#S4.T5)favors the averaged update12​\(F1\+F2\)\\frac\{1\}\{2\}\(F\_\{1\}\+F\_\{2\}\), only marginally ahead of the learnable combination, suggesting Method 2 is less sensitive to coefficient weighting\. It selects refinement\-only placement without LayerNorm, IDL weight0\.30\.3, and three refinement iterations, while the depth ablation prefers a single decoder layer\.

Table 5:Structured sequential ablations for RK2SLT\-M1 and RK2SLT\-M2 on the PHOENIX\-14T DEV set\. BLEU\-4 is the selection criterion; within each block, the selected setting of each variant is marked with✓\\checkmarkand fixed for subsequent blocks\.RK2SLT\-M1RK2SLT\-M2ConfigurationBLEU\-4ROUGEBLEU\-4ROUGECoefficientsF1\+F2F\_\{1\}\+F\_\{2\}23\.1748\.2323\.0247\.6212​\(F1\+F2\)\\frac\{1\}\{2\}\(F\_\{1\}\+F\_\{2\}\)23\.9048\.96✓\\checkmark23\.5447\.93α​F1\+\(1−α\)​F2\\alpha F\_\{1\}\+\(1\-\\alpha\)F\_\{2\}✓\\checkmark24\.0648\.6123\.5247\.92PlacementRefinement layers23\.3047\.79✓\\checkmark23\.9248\.70Refinement layers \+ LN23\.7147\.9923\.8348\.31All layers✓\\checkmark24\.0648\.6123\.5447\.93All layers \+ LN23\.5648\.1823\.4748\.19IDL Weight0\.223\.5848\.4823\.6347\.960\.3✓\\checkmark24\.0648\.61✓\\checkmark23\.9248\.700\.423\.9648\.9823\.5048\.060\.523\.5847\.2723\.3648\.28Refinement IterationsKK123\.5648\.4023\.3348\.06223\.3947\.9322\.9147\.463✓\\checkmark24\.0648\.61✓\\checkmark23\.9248\.70Decoder Depth122\.9047\.22✓\\checkmark23\.9948\.37223\.5547\.6523\.7248\.443✓\\checkmark24\.0648\.6123\.9248\.70
##### RK4SLT\-M1\.

Table[6](https://arxiv.org/html/2608.11352#S4.T6)selects the RK\-4 update on all decoder layers without LayerNorm\. IDL weight0\.20\.2is chosen, and BLEU\-4 favors three refinement iterations and three decoder layers\.

##### RK4SLT\-M2\.

As shown in Table[6](https://arxiv.org/html/2608.11352#S4.T6), the strongest RK4SLT\-M2 configuration applies the RK\-4 update only within the refinement stage without the additional LayerNorm, in line with the broader trend that LayerNorm degrades BLEU\-4\. The best configuration uses IDL weight0\.30\.3and three refinement iterations, while a two\-layer decoder outperforms the three\-layer one\.

Table 6:Structured sequential ablations for RK4SLT\-M1 and RK4SLT\-M2 on the PHOENIX\-14T DEV set\. BLEU\-4 is the selection criterion; within each block, the selected setting of each variant is marked with✓\\checkmarkand fixed for subsequent blocks\. RK\-4 coefficients are fixed\.RK4SLT\-M1RK4SLT\-M2ConfigurationBLEU\-4ROUGEBLEU\-4ROUGEPlacementRefinement layers23\.5347\.67✓\\checkmark23\.7148\.29Refinement layers \+ LN23\.3747\.8823\.4347\.39All layers✓\\checkmark23\.7848\.1423\.6648\.02All layers \+ LN23\.7548\.6323\.4248\.11IDL Weight0\.123\.7448\.5723\.0247\.140\.2✓\\checkmark23\.9048\.0323\.5947\.530\.323\.7848\.14✓\\checkmark23\.7148\.290\.423\.5347\.6023\.1447\.42Refinement IterationsKK123\.8049\.1223\.1648\.54223\.8248\.6523\.2547\.443✓\\checkmark23\.9048\.03✓\\checkmark23\.7148\.29Decoder Depth123\.6248\.5222\.7347\.46223\.6448\.03✓\\checkmark23\.9248\.693✓\\checkmark23\.9048\.0323\.7148\.29
##### CSL\-Daily\.

The CSL\-Daily ablations are reported in Tables[7](https://arxiv.org/html/2608.11352#S4.T7)–[8](https://arxiv.org/html/2608.11352#S4.T8)\. Compared with PHOENIX\-14T, the selected settings more often favor fewer refinement iterations or shallower decoders, indicating that the most effective refinement dynamics are dataset\- and method\-dependent\.

##### RK2SLT\-M1\.

Table[7](https://arxiv.org/html/2608.11352#S4.T7)selects the averaged RK\-2 update, refinement\-only placement with LayerNorm, and a small IDL weight of0\.050\.05, consistent with CSL\-Daily favoring lighter intermediate supervision\. Two refinement iterations outperform one and three, and three decoder layers are selected, though the depth trade\-off is relatively flat\.

##### RK2SLT\-M2\.

Table[7](https://arxiv.org/html/2608.11352#S4.T7)selects the averaged RK\-2 update over the unscaled and learnable alternatives, refinement\-only placement without LayerNorm, IDL weight0\.10\.1, a single refinement iteration, and two decoder layers\. This compact configuration also gives the strongest TEST BLEU\-4 among our variants on CSL\-Daily\.

Table 7:Structured sequential ablations for RK2SLT\-M1 and RK2SLT\-M2 on the CSL\-Daily DEV set\. BLEU\-4 is the selection criterion; within each block, the selected setting of each variant is marked with✓\\checkmarkand fixed for subsequent blocks\.RK2SLT\-M1RK2SLT\-M2ConfigurationBLEU\-4ROUGEBLEU\-4ROUGECoefficientsF1\+F2F\_\{1\}\+F\_\{2\}18\.4747\.6117\.1444\.9412​\(F1\+F2\)\\frac\{1\}\{2\}\(F\_\{1\}\+F\_\{2\}\)✓\\checkmark18\.6747\.50✓\\checkmark18\.1946\.50α​F1\+\(1−α\)​F2\\alpha F\_\{1\}\+\(1\-\\alpha\)F\_\{2\}18\.5946\.9117\.6245\.94PlacementRefinement layers17\.9746\.46✓\\checkmark18\.1946\.50Refinement layers \+ LN✓\\checkmark18\.6747\.5017\.7646\.06All layers18\.1146\.9618\.1446\.33All layers \+ LN18\.6647\.2917\.7946\.01IDL Weight0\.05✓\\checkmark18\.8447\.8817\.8446\.080\.118\.6747\.29✓\\checkmark18\.1946\.500\.218\.6746\.9318\.0046\.140\.318\.6747\.2917\.8146\.33Refinement IterationsKK118\.8647\.84✓\\checkmark18\.4947\.582✓\\checkmark19\.1748\.1118\.0246\.73318\.8447\.8818\.1946\.50Decoder Depth118\.9048\.4318\.7247\.59219\.0748\.03✓\\checkmark18\.9647\.783✓\\checkmark19\.1748\.1118\.4947\.58
##### RK4SLT\-M1\.

Table[8](https://arxiv.org/html/2608.11352#S4.T8)selects the RK\-4 update in the refinement decoder layers with LayerNorm\. IDL weight0\.20\.2is chosen, and BLEU\-4 favors three refinement iterations and three decoder layers\. RK4SLT\-M1 improves longer n\-gram consistency through deeper refinement\.

##### RK4SLT\-M2\.

Table[8](https://arxiv.org/html/2608.11352#S4.T8)shows the strongest efficiency\-oriented trend: refinement\-only placement with LayerNorm is best, while all\-layer LayerNorm degrades performance sharply\. With IDL weight0\.30\.3, both the iteration and depth blocks select the single\-step, single\-layer setting, so RK4SLT\-M2 exploits the stronger RK\-4 update in a compact configuration\.

Table 8:Structured sequential ablations for RK4SLT\-M1 and RK4SLT\-M2 on the CSL\-Daily DEV set\. BLEU\-4 is the selection criterion; within each block, the selected setting of each variant is marked with✓\\checkmarkand fixed for subsequent blocks\. RK\-4 coefficients are fixed\.RK4SLT\-M1RK4SLT\-M2ConfigurationBLEU\-4ROUGEBLEU\-4ROUGEPlacementRefinement layers17\.7946\.3017\.9845\.87Refinement layers \+ LN✓\\checkmark18\.6846\.85✓\\checkmark18\.0346\.05All layers17\.9546\.1317\.9545\.95All layers \+ LN18\.2646\.7016\.7343\.83IDL Weight0\.118\.4847\.0317\.9146\.550\.2✓\\checkmark18\.6846\.8518\.0346\.050\.318\.3346\.69✓\\checkmark18\.0445\.910\.418\.0346\.3917\.6345\.99Refinement IterationsKK118\.5848\.10✓\\checkmark18\.5147\.34218\.3846\.3517\.9345\.973✓\\checkmark18\.6846\.8518\.0445\.91Decoder Depth118\.2147\.57✓\\checkmark18\.7648\.33218\.1846\.9418\.3448\.113✓\\checkmark18\.6846\.8518\.5147\.34
##### Overall observations\.

Across both datasets, the optimal ODE\-decoder design is method\- and dataset\-dependent\. For RK\-2, coefficient scaling matters, with averaged or learnable combinations outperforming the unscaled update\. ODE\-update placement and post\-update LayerNorm are not universally beneficial, and IDL requires moderate weighting, as stronger supervision can reduce final BLEU\-4\. Finally, PHOENIX\-14T generally favors more refinement iterations, whereas CSL\-Daily admits compact configurations with fewer iterations and shallower decoders, supporting the accuracy–efficiency trade\-off of ODE\-guided refinement\.

## 5Conclusion

In this work, we introduced ODE\-guided Transformer decoders for iterative sign language translation, replacing standard residual updates with Runge–Kutta\-inspired formulations that improve decoder update dynamics without adding model parameters\. Experiments on PHOENIX\-14T and CSL\-Daily show that the proposed updates improve TEST BLEU\-4 over the matched IPSLT baseline, while the ablation studies identify dataset\-specific choices for coefficient weighting, placement, normalization, IDL weighting, and refinement depth\. On CSL\-Daily, the fourth\-order RK4SLT\-M2 is especially notable: it stays within0\.090\.09TEST BLEU\-4 of the best variant while using a single refinement iteration and a single decoder layer, so its extra per\-step function evaluations effectively substitute for decoder depth and repeated refinement\. Since RK\-2 and RK\-4 involve multiple function evaluations, we distinguish parameter efficiency from computational efficiency and report iteration counts and decoder depth to clarify the accuracy–efficiency trade\-off\. These results suggest that refining how representations are updated is a promising direction, complementary to scaling pretrained models for SLT\.

## Acknowledgments

This work is supported by the Scientific and Technological Research Council of Türkiye \(TÜBİTAK\) under the 1001 Scientific and Technological Research Projects Funding Program \(Project No\. 124E618\)\. We acknowledge the EuroHPC Joint Undertaking for awarding us access to Vega at IZUM, Slovenia, through Development Access allocation 2025D08\-090\.

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