Predictor-Corrector Enhanced Transformers with Exponential Moving Average Coefficient Learning (2411.03042v1)

Abstract: Residual networks, as discrete approximations of Ordinary Differential Equations (ODEs), have inspired significant advancements in neural network design, including multistep methods, high-order methods, and multi-particle dynamical systems. The precision of the solution to ODEs significantly affects parameter optimization, thereby impacting model performance. In this work, we present a series of advanced explorations of Transformer architecture design to minimize the error compared to the true ``solution.'' First, we introduce a predictor-corrector learning framework to minimize truncation errors, which consists of a high-order predictor and a multistep corrector. Second, we propose an exponential moving average-based coefficient learning method to strengthen our higher-order predictor. Extensive experiments on large-scale machine translation, abstractive summarization, LLMing, and natural language understanding benchmarks demonstrate the superiority of our approach. On the WMT'14 English-German and English-French tasks, our model achieved BLEU scores of 30.95 and 44.27, respectively. Furthermore, on the OPUS multilingual machine translation task, our model surpasses a robust 3.8B DeepNet by an average of 2.9 SacreBLEU, using only 1/3 parameters. Notably, it also beats LLama models by 5.7 accuracy points on the LM Harness Evaluation.

• The paper proposes a novel predictor-corrector framework integrating EMA-based coefficient learning to minimize truncation errors in Transformer models.
• It leverages ODE discretization techniques to refine intermediate approximations, enhancing accuracy and efficiency over traditional high-order methods.
• Empirical evaluations demonstrate significant gains with BLEU scores of 30.95 and 44.27 on machine translation benchmarks, outperforming larger models.

Overview: Predictor-Corrector Enhanced Transformers with Exponential Moving Average Coefficient Learning

The paper introduces innovative advancements in the design of Transformer architectures, specifically enhancing parameter learning through a numerical analysis perspective. By leveraging insights from Ordinary Differential Equations (ODEs), the researchers present a novel predictor-corrector framework designed to improve the precision of solutions generated by neural networks. This approach addresses inefficiencies found in previous methods, such as high-order and linear multistep methods, particularly in scaling to larger datasets or model sizes.

Theoretical Contributions

The research exploits the analogy between residual networks and the discretization of ODEs to propose a more precise numerical solution framework by minimizing truncation errors. The core contribution is the integration of a predictor-corrector paradigm, inspired by the classical predictor-corrector methods in numerical analysis, into the Transformer architecture. This paradigm features a high-order predictor and a multistep corrector to refine intermediate approximations. Unlike prior attempts using fixed coefficients, this paper implements an Exponential Moving Average (EMA) based coefficient learning strategy, enhancing the predictor's performance through dynamic adjustment of coefficients.

Empirical Results

Empirical evaluations across multiple benchmarks—including machine translation, abstractive summarization, LLMing, and language understanding—demonstrate significant performance advancements. Notably, the PCformer models achieve BLEU scores of 30.95 on WMT’14 English-German and 44.27 on WMT’14 English-French, setting new performance standards compared to existing methods. Furthermore, the proposed model outperforms a robust 3.8 billion parameter DeepNet on the OPUS multilingual machine translation task by an average of 2.9 SacreBLEU, utilizing only a third of the parameters.

Impact and Implications

The introduction of the predictor-corrector framework in the Transformer architecture offers both practical and theoretical advancements in the design of more efficient neural networks. Practically, the method reduces computational resources while achieving higher accuracy, indicating significant cost reductions in large-scale deployments. Theoretically, the paper underscores the efficacy of integrating numerical methods directly into neural architecture designs, suggesting a promising direction for future research to adopt and adapt mathematical principles for enhanced learning efficiency.

Future Prospects

The results suggest promising exploration avenues for further enhancing AI systems by applying similar principles across different neural network designs and applications. Future research could explore adopting this framework in various deep learning models and across additional domains, potentially extending its scalable benefits and computational efficiencies. Moreover, improving inference speed for large-scale models while maintaining the accuracy boost remains an essential next step for practical deployment in real-world settings.

The authors successfully offer an innovative approach that potentially reshapes the Transformer architecture paradigm, providing insights and strategies that resonate across the computational intelligence community. The integration of mathematical disciplines reflects a broader trend and opens discussions on leveraging diverse knowledge areas to enhance the robustness and capability of AI systems.