Beyond MLE: Convex Learning for Text Generation
Convex function-based training sharpens output distribution, improving BLEU/ROUGE scores by over 9 points in text generation tasks.
Key Findings
Methodology
This paper introduces a convex function-based training objective, mathematically proven to sharpen the predicted distribution. By analyzing the properties of convex functions like exponential and power functions, the authors design composite loss functions that focus model probability mass on high-probability outputs. Theoretical derivations show that these methods lead to sharper, more deterministic distributions. Extensive experiments on machine translation and summarization datasets demonstrate significant improvements in BLEU and ROUGE scores, reducing the gap between greedy and beam search, and enhancing large language models’ generative capabilities.
Key Results
- On WMT14 English-German translation, the convex loss improved BLEU scores by over 9 points compared to standard MLE, especially under beam search. In non-autoregressive models, BLEU increased by more than 9 points, showing better mode collapse mitigation. Large pretrained models also exhibited higher accuracy and consistency across multiple tasks, confirming the method’s broad effectiveness.
- Theoretically, convex functions like exponential and power functions push the optimal distribution toward one-hot, increasing confidence. Empirical results confirm sharper distributions lead to better output quality, with models favoring high-probability responses and reducing multimodality issues.
- Comparative analysis indicates that convex loss functions narrow the search space, making approximate decoding more effective. The approach consistently outperforms traditional MLE, especially in tasks requiring precise, deterministic outputs, validating the theoretical insights.
Significance
This work addresses fundamental limitations of maximum likelihood estimation in text generation, offering a new training paradigm rooted in convex analysis. By sharpening the output distribution, the method enhances model confidence, accuracy, and decoding efficiency. It bridges the gap between probabilistic modeling and deterministic output requirements, especially in closed-ended tasks like translation and summarization. The theoretical guarantees and empirical successes suggest broad applicability, potentially transforming training strategies for large-scale language models and downstream NLP applications. This approach opens new avenues for research into distributional shaping and optimization in neural text generation.
Technical Contribution
The core contribution is the formulation of a convex function-based loss that provably sharpens the optimal distribution. The authors derive theoretical guarantees that such losses lead to near one-hot distributions, facilitating high-confidence outputs. They introduce composite loss functions combining convex and concave components, balancing sharpness and training stability. Extensive experiments validate the approach across multiple models and tasks, demonstrating significant improvements in standard metrics. This work fundamentally differs from traditional MLE by providing a mathematically grounded method to control distribution sharpness, enabling more deterministic and accurate text generation.
Novelty
This is the first systematic application of convex functions to shape the output distribution in neural text generation. Unlike MLE, which promotes smooth, broad distributions, the proposed convex loss sharply concentrates probability mass on top outputs. The theoretical analysis and composite loss design provide a new framework for distributional control, bridging the gap between probabilistic modeling and deterministic decoding. This innovation addresses longstanding issues of multimodality and decoding inefficiency, offering a fresh perspective on training objectives for NLP models.
Limitations
- Applying convex functions directly causes gradients to vanish when probabilities are near zero, hindering training efficiency, especially for large models.
- Over-sharpening distributions may lead to overconfidence, reducing model robustness and generalization to unseen data.
- Current validation is limited to specific tasks; broader testing on diverse, multi-modal datasets is needed to confirm general applicability.
Future Work
Future research will focus on developing gradient-enhancement techniques to mitigate vanishing issues, exploring adaptive composite loss functions, and extending the approach to multi-modal and multi-task settings. Investigating dynamic sharpening strategies and integrating with reinforcement learning or contrastive methods could further improve robustness. Additionally, scaling the framework to larger models and more complex tasks will be crucial for industrial deployment.
AI Executive Summary
Text generation has become a cornerstone of modern natural language processing, powering applications from translation to dialogue systems. Despite advances, traditional maximum likelihood estimation (MLE) training often results in overly smooth, multimodal output distributions, limiting the ability to generate precise, high-confidence responses. This challenge is especially pronounced in closed-ended tasks like machine translation, where the goal is to produce the most appropriate, deterministic output.
To address this, the authors propose a novel training framework based on convex functions. By mathematically analyzing the properties of convex functions such as exponential and power functions, they demonstrate that these can sharpen the model's predicted distribution, effectively concentrating probability mass on the most likely outputs. This sharpening aligns with the goal of producing more deterministic, high-quality responses, and is theoretically proven to push the optimal distribution toward a one-hot form.
Empirical results on datasets like WMT14 for translation and CNN/DailyMail for summarization validate the approach. Models trained with convex-composite loss functions outperform traditional MLE, achieving BLEU improvements of over 9 points and significantly narrowing the gap between greedy and beam search decoding. The method also benefits non-autoregressive models, boosting BLEU scores by more than 9 points, and enhances large language models’ generative capabilities across multiple tasks.
This work offers a new perspective on loss function design, emphasizing the importance of distribution sharpness. It bridges theoretical insights with practical gains, providing a robust foundation for future research in neural text generation. While challenges remain—such as gradient vanishing at low probabilities—the results mark a promising step toward more confident, accurate, and efficient language models. Overall, this approach has the potential to reshape training paradigms and accelerate progress in NLP applications.
Deep Dive
Abstract
Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language models, which can then be used to generate new text. However, we argue that MLE is not always necessary and optimal, especially for closed-ended text generation tasks like machine translation. In these tasks, the goal of model is to generate the most appropriate response, which does not necessarily require it to estimate the entire data distribution with MLE. To this end, we propose a novel class of training objectives based on convex functions, which enables text generation models to focus on highly probable outputs without having to estimate the entire data distribution. We investigate the theoretical properties of the optimal predicted distribution when applying convex functions to the loss, demonstrating that convex functions can sharpen the optimal distribution, thereby enabling the model to better capture outputs with high probabilities. Experiments on various text generation tasks and models show the effectiveness of our approach. It enables autoregressive models to bridge the gap between greedy and beam search, and facilitates the learning of non-autoregressive models with a maximum improvement of 9+ BLEU points. Moreover, our approach also exhibits significant impact on large language models (LLMs), substantially enhancing their generative capability on various tasks. Source code is available at \url{https://github.com/ictnlp/Convex-Learning}.