Permutation Randomization on Nonsmooth Nonconvex Optimization: A Theoretical and Experimental Study

While gradient-based optimizers that incorporate randomization often showcase superior performance on complex optimization, the theoretical foundations underlying this superiority remain insufficiently understood. A particularly pressing question has emerged: What is the role of randomization in dimension-free nonsmooth nonconvex optimization? To address this gap, we investigate the theoretical and empirical impact of permutation randomization within gradient-based optimization frameworks, using it as a representative case to explore broader implications. From a theoretical perspective, our analyses reveal that permutation randomization disrupts the shrinkage behavior of gradient-based optimizers, facilitating continuous convergence toward the global optimum given a sufficiently large number of iterations. Additionally, we prove that permutation randomization can preserve the convergence rate of the underlying optimizer. On the empirical side, we conduct extensive numerical experiments comparing permutation-randomized optimizer against three baseline methods. These experiments span tasks such as training deep neural networks with stacked architectures and optimizing noisy objective functions. The results not only corroborate our theoretical insights but also highlight the practical benefits of permutation randomization. In summary, this work delivers both rigorous theoretical justification and compelling empirical evidence for the effectiveness of permutation randomization. Our findings and evidence lay a foundation for extending analytics to encompass a wide array of randomization.

HOME-3: High-Order Momentum Estimator with Third-Power Gradient for Convex and Smooth Nonconvex Optimization

Momentum-based gradients are essential for optimizing advanced machine learning models, as they not only accelerate convergence but also advance optimizers to escape stationary points. While most state-of-the-art momentum techniques utilize lower-order gradients, such as the squared first-order gradient, there has been limited exploration of higher-order gradients, particularly those raised to powers greater than two. In this work, we introduce the concept of high-order momentum, where momentum is constructed using higher-power gradients, with a focus on the third-power of the first-order gradient as a representative case. Our research offers both theoretical and empirical support for this approach. Theoretically, we demonstrate that incorporating third-power gradients can improve the convergence bounds of gradient-based optimizers for both convex and smooth nonconvex problems. Empirically, we validate these findings through extensive experiments across convex, smooth nonconvex, and nonsmooth nonconvex optimization tasks. Across all cases, high-order momentum consistently outperforms conventional low-order momentum methods, showcasing superior performance in various optimization problems.

Trans-Zero: Self-Play Incentivizes Large Language Models for Multilingual Translation Without Parallel Data

The rise of Large Language Models (LLMs) has reshaped machine translation (MT), but multilingual MT still relies heavily on parallel data for supervised fine-tuning (SFT), facing challenges like data scarcity for low-resource languages and catastrophic forgetting. To address these issues, we propose TRANS-ZERO, a self-play framework that leverages only monolingual data and the intrinsic multilingual knowledge of LLM. TRANS-ZERO combines Genetic Monte-Carlo Tree Search (G-MCTS) with preference optimization, achieving strong translation performance that rivals supervised methods. Experiments demonstrate that this approach not only matches the performance of models trained on large-scale parallel data but also excels in non-English translation directions. Further analysis reveals that G-MCTS itself significantly enhances translation quality by exploring semantically consistent candidates through iterative translations, providing a robust foundation for the framework's succuss.

Unveiling the Mathematical Reasoning in DeepSeek Models: A Comparative Study of Large Language Models

With the rapid evolution of Artificial Intelligence (AI), Large Language Models (LLMs) have reshaped the frontiers of various fields, spanning healthcare, public health, engineering, science, agriculture, education, arts, humanities, and mathematical reasoning. Among these advancements, DeepSeek models have emerged as noteworthy contenders, demonstrating promising capabilities that set them apart from their peers. While previous studies have conducted comparative analyses of LLMs, few have delivered a comprehensive evaluation of mathematical reasoning across a broad spectrum of LLMs. In this work, we aim to bridge this gap by conducting an in-depth comparative study, focusing on the strengths and limitations of DeepSeek models in relation to their leading counterparts. In particular, our study systematically evaluates the mathematical reasoning performance of two DeepSeek models alongside five prominent LLMs across three independent benchmark datasets. The findings reveal several key insights: 1). DeepSeek-R1 consistently achieved the highest accuracy on two of the three datasets, demonstrating strong mathematical reasoning capabilities. 2). The distilled variant of LLMs significantly underperformed compared to its peers, highlighting potential drawbacks in using distillation techniques. 3). In terms of response time, Gemini 2.0 Flash demonstrated the fastest processing speed, outperforming other models in efficiency, which is a crucial factor for real-time applications. Beyond these quantitative assessments, we delve into how architecture, training, and optimization impact LLMs' mathematical reasoning. Moreover, our study goes beyond mere performance comparison by identifying key areas for future advancements in LLM-driven mathematical reasoning. This research enhances our understanding of LLMs' mathematical reasoning and lays the groundwork for future advancements

Evaluation of OpenAI o1: Opportunities and Challenges of AGI

This comprehensive study evaluates the performance of OpenAI's o1-preview large language model across a diverse array of complex reasoning tasks, spanning multiple domains, including computer science, mathematics, natural sciences, medicine, linguistics, and social sciences. Through rigorous testing, o1-preview demonstrated remarkable capabilities, often achieving human-level or superior performance in areas ranging from coding challenges to scientific reasoning and from language processing to creative problem-solving. Key findings include: -83.3% success rate in solving complex competitive programming problems, surpassing many human experts. -Superior ability in generating coherent and accurate radiology reports, outperforming other evaluated models. -100% accuracy in high school-level mathematical reasoning tasks, providing detailed step-by-step solutions. -Advanced natural language inference capabilities across general and specialized domains like medicine. -Impressive performance in chip design tasks, outperforming specialized models in areas such as EDA script generation and bug analysis. -Remarkable proficiency in anthropology and geology, demonstrating deep understanding and reasoning in these specialized fields. -Strong capabilities in quantitative investing. O1 has comprehensive financial knowledge and statistical modeling skills. -Effective performance in social media analysis, including sentiment analysis and emotion recognition. The model excelled particularly in tasks requiring intricate reasoning and knowledge integration across various fields. While some limitations were observed, including occasional errors on simpler problems and challenges with certain highly specialized concepts, the overall results indicate significant progress towards artificial general intelligence.

An Adaptive Gradient Regularization Method

Optimizer plays an important role in neural network training with high efficiency and performance. Weight update based on its gradient is the central part of the optimizer. It has been shown that normalization and standardization operation on weight and gradient can accelerate the training process and improve performance such as Weight Standardization (WS), weight normalization (WN) and gradient normalization (GN); there is also gradient centralization (GC). In this work, we introduce a new optimization technique based on the gradient magnitude in a gradient vector named adaptive gradient regularization (AGR), which normalizes the gradient vector in all dimensions as a coefficient vector and subtracts the product of the gradient and its coefficient vector by the vanilla gradient. It can be viewed as an adaptive gradient clipping method. We show that the AGR can improve the loss function Lipschitzness with a more stable training process and better generalization performance. AGR is very simple to be embedded into vanilla optimizers such as Adan and AdamW with only three lines of code. Our experiments are conducted in image generation, image classification and language representation, which shows that our AGR improves the training result.

Decomposed Direct Preference Optimization for Structure-Based Drug Design

Diffusion models have achieved promising results for Structure-Based Drug Design (SBDD). Nevertheless, high-quality protein subpocket and ligand data are relatively scarce, which hinders the models' generation capabilities. Recently, Direct Preference Optimization (DPO) has emerged as a pivotal tool for the alignment of generative models such as large language models and diffusion models, providing greater flexibility and accuracy by directly aligning model outputs with human preferences. Building on this advancement, we introduce DPO to SBDD in this paper. We tailor diffusion models to pharmaceutical needs by aligning them with elaborately designed chemical score functions. We propose a new structure-based molecular optimization method called DecompDPO, which decomposes the molecule into arms and scaffolds and performs preference optimization at both local substructure and global molecule levels, allowing for more precise control with fine-grained preferences. Notably, DecompDPO can be effectively used for two main purposes: (1) fine-tuning pretrained diffusion models for molecule generation across various protein families, and (2) molecular optimization given a specific protein subpocket after generation. Extensive experiments on the CrossDocked2020 benchmark show that DecompDPO significantly improves model performance in both molecule generation and optimization, with up to 100% Median High Affinity and a 54.9% Success Rate.

EDT: Improving Large Language Models' Generation by Entropy-based Dynamic Temperature Sampling

Recently, Large Language Models (LLMs) have demonstrated outstanding performance across a wide range of downstream language tasks. Temperature sampling is a commonly used decoding strategy for LLMs' generation process. However, a fixed temperature parameter is used in most cases, which may not always be an optimal choice for balancing generation quality and diversity. In this paper, we propose an effective Entropy-based Dynamic Temperature (EDT) Sampling method, to achieve a more balanced performance in terms of both generation quality and diversity by dynamically selecting the temperature parameter. Additionally, we also show model performance and comprehensive analyses for 4 different generation benchmarks. Our experiments show that EDT significantly outperforms the existing strategies across different tasks.

Diffusion Language Models Can Perform Many Tasks with Scaling and Instruction-Finetuning

The recent surge of generative AI has been fueled by the generative power of diffusion probabilistic models and the scalable capabilities of large language models. Despite their potential, it remains elusive whether diffusion language models can solve general language tasks comparable to their autoregressive counterparts. This paper demonstrates that scaling diffusion models w.r.t. data, sizes, and tasks can effectively make them strong language learners. We build competent diffusion language models at scale by first acquiring knowledge from massive data via masked language modeling pretraining thanks to their intrinsic connections. We then reprogram pretrained masked language models into diffusion language models via diffusive adaptation, wherein task-specific finetuning and instruction finetuning are explored to unlock their versatility in solving general language tasks. Experiments show that scaling diffusion language models consistently improves performance across downstream language tasks. We further discover that instruction finetuning can elicit zero-shot and few-shot in-context learning abilities that help tackle many unseen tasks by following natural language instructions, and show promise in advanced and challenging abilities such as reasoning.

Selective Knowledge Distillation for Non-Autoregressive Neural Machine Translation

Benefiting from the sequence-level knowledge distillation, the Non-Autoregressive Transformer (NAT) achieves great success in neural machine translation tasks. However, existing knowledge distillation has side effects, such as propagating errors from the teacher to NAT students, which may limit further improvements of NAT models and are rarely discussed in existing research. In this paper, we introduce selective knowledge distillation by introducing an NAT evaluator to select NAT-friendly targets that are of high quality and easy to learn. In addition, we introduce a simple yet effective progressive distillation method to boost NAT performance. Experiment results on multiple WMT language directions and several representative NAT models show that our approach can realize a flexible trade-off between the quality and complexity of training data for NAT models, achieving strong performances. Further analysis shows that distilling only 5% of the raw translations can help an NAT outperform its counterpart trained on raw data by about 2.4 BLEU.