Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimization

Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard adversarial training which focuses on pointwise adversarial perturbations. However, WDRO still suffers fundamentally from the robust overfitting problem, as it does not consider statistical error. We address this gap by proposing a novel robust optimization framework under a new uncertainty set for adversarial noise via Wasserstein distance and statistical error via Kullback-Leibler divergence, called the Statistically Robust WDRO. We establish a robust generalization bound for the new optimization framework, implying that out-of-distribution adversarial performance is at least as good as the statistically robust training loss with high probability. Furthermore, we derive conditions under which Stackelberg and Nash equilibria exist between the learner and the adversary, giving an optimal robust model in certain sense. Finally, through extensive experiments, we demonstrate that our method significantly mitigates robust overfitting and enhances robustness within the framework of WDRO.

Generalizability of Neural Networks Minimizing Empirical Risk Based on Expressive Ability

The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep learning exhibit nice generalizability. On the other hand, algorithm-dependent generalization bounds, like stability bounds, often rely on strict assumptions. To establish generalizability under less stringent assumptions, this paper investigates the generalizability of neural networks that minimize or approximately minimize empirical risk. We establish a lower bound for population accuracy based on the expressiveness of these networks, which indicates that with an adequate large number of training samples and network sizes, these networks, including over-parameterized ones, can generalize effectively. Additionally, we provide a necessary condition for generalization, demonstrating that, for certain data distributions, the quantity of training data required to ensure generalization exceeds the network size needed to represent the corresponding data distribution. Finally, we provide theoretical insights into several phenomena in deep learning, including robust generalization, importance of over-parameterization, and effect of loss function on generalization.

Multi-Agent Collaboration for Multilingual Code Instruction Tuning

Recent advancement in code understanding and generation demonstrates that code LLMs fine-tuned on a high-quality instruction dataset can gain powerful capabilities to address wide-ranging code-related tasks. However, most previous existing methods mainly view each programming language in isolation and ignore the knowledge transfer among different programming languages. To bridge the gap among different programming languages, we introduce a novel multi-agent collaboration framework to enhance multilingual instruction tuning for code LLMs, where multiple language-specific intelligent agent components with generation memory work together to transfer knowledge from one language to another efficiently and effectively. Specifically, we first generate the language-specific instruction data from the code snippets and then provide the generated data as the seed data for language-specific agents. Multiple language-specific agents discuss and collaborate to formulate a new instruction and its corresponding solution (A new programming language or existing programming language), To further encourage the cross-lingual transfer, each agent stores its generation history as memory and then summarizes its merits and faults. Finally, the high-quality multilingual instruction data is used to encourage knowledge transfer among different programming languages to train Qwen2.5-xCoder. Experimental results on multilingual programming benchmarks demonstrate the superior performance of Qwen2.5-xCoder in sharing common knowledge, highlighting its potential to reduce the cross-lingual gap.

CodeElo: Benchmarking Competition-level Code Generation of LLMs with Human-comparable Elo Ratings

With the increasing code reasoning capabilities of existing large language models (LLMs) and breakthroughs in reasoning models like OpenAI o1 and o3, there is a growing need to develop more challenging and comprehensive benchmarks that effectively test their sophisticated competition-level coding abilities. Existing benchmarks, like LiveCodeBench and USACO, fall short due to the unavailability of private test cases, lack of support for special judges, and misaligned execution environments. To bridge this gap, we introduce CodeElo, a standardized competition-level code generation benchmark that effectively addresses all these challenges for the first time. CodeElo benchmark is mainly based on the official CodeForces platform and tries to align with the platform as much as possible. We compile the recent six months of contest problems on CodeForces with detailed information such as contest divisions, problem difficulty ratings, and problem algorithm tags. We introduce a unique judging method in which problems are submitted directly to the platform and develop a reliable Elo rating calculation system that aligns with the platform and is comparable with human participants but has lower variance. By testing on our CodeElo, we provide the Elo ratings of 30 existing popular open-source and 3 proprietary LLMs for the first time. The results show that o1-mini and QwQ-32B-Preview stand out significantly, achieving Elo ratings of 1578 and 1261, respectively, while other models struggle even with the easiest problems, placing in the lowest 25 percent among all human participants. Detailed analysis experiments are also conducted to provide insights into performance across algorithms and comparisons between using C++ and Python, which can suggest directions for future studies.

PowerMLP: An Efficient Version of KAN

The Kolmogorov-Arnold Network (KAN) is a new network architecture known for its high accuracy in several tasks such as function fitting and PDE solving. The superior expressive capability of KAN arises from the Kolmogorov-Arnold representation theorem and learnable spline functions. However, the computation of spline functions involves multiple iterations, which renders KAN significantly slower than MLP, thereby increasing the cost associated with model training and deployment. The authors of KAN have also noted that ``the biggest bottleneck of KANs lies in its slow training. KANs are usually 10x slower than MLPs, given the same number of parameters.'' To address this issue, we propose a novel MLP-type neural network PowerMLP that employs simpler non-iterative spline function representation, offering approximately the same training time as MLP while theoretically demonstrating stronger expressive power than KAN. Furthermore, we compare the FLOPs of KAN and PowerMLP, quantifying the faster computation speed of PowerMLP. Our comprehensive experiments demonstrate that PowerMLP generally achieves higher accuracy and a training speed about 40 times faster than KAN in various tasks.

ExecRepoBench: Multi-level Executable Code Completion Evaluation

Code completion has become an essential tool for daily software development. Existing evaluation benchmarks often employ static methods that do not fully capture the dynamic nature of real-world coding environments and face significant challenges, including limited context length, reliance on superficial evaluation metrics, and potential overfitting to training datasets. In this work, we introduce a novel framework for enhancing code completion in software development through the creation of a repository-level benchmark ExecRepoBench and the instruction corpora Repo-Instruct, aim at improving the functionality of open-source large language models (LLMs) in real-world coding scenarios that involve complex interdependencies across multiple files. ExecRepoBench includes 1.2K samples from active Python repositories. Plus, we present a multi-level grammar-based completion methodology conditioned on the abstract syntax tree to mask code fragments at various logical units (e.g. statements, expressions, and functions). Then, we fine-tune the open-source LLM with 7B parameters on Repo-Instruct to produce a strong code completion baseline model Qwen2.5-Coder-Instruct-C based on the open-source model. Qwen2.5-Coder-Instruct-C is rigorously evaluated against existing benchmarks, including MultiPL-E and ExecRepoBench, which consistently outperforms prior baselines across all programming languages. The deployment of \ourmethod{} can be used as a high-performance, local service for programming development\footnote{\url{https://execrepobench.github.io/}}.

Evaluating and Aligning CodeLLMs on Human Preference

Code large language models (codeLLMs) have made significant strides in code generation. Most previous code-related benchmarks, which consist of various programming exercises along with the corresponding test cases, are used as a common measure to evaluate the performance and capabilities of code LLMs. However, the current code LLMs focus on synthesizing the correct code snippet, ignoring the alignment with human preferences, where the query should be sampled from the practical application scenarios and the model-generated responses should satisfy the human preference. To bridge the gap between the model-generated response and human preference, we present a rigorous human-curated benchmark CodeArena to emulate the complexity and diversity of real-world coding tasks, where 397 high-quality samples spanning 40 categories and 44 programming languages, carefully curated from user queries. Further, we propose a diverse synthetic instruction corpus SynCode-Instruct (nearly 20B tokens) by scaling instructions from the website to verify the effectiveness of the large-scale synthetic instruction fine-tuning, where Qwen2.5-SynCoder totally trained on synthetic instruction data can achieve top-tier performance of open-source code LLMs. The results find performance differences between execution-based benchmarks and CodeArena. Our systematic experiments of CodeArena on 40+ LLMs reveal a notable performance gap between open SOTA code LLMs (e.g. Qwen2.5-Coder) and proprietary LLMs (e.g., OpenAI o1), underscoring the importance of the human preference alignment.\footnote{\url{https://codearenaeval.github.io/ }}

Generalizability of Memorization Neural Networks

The neural network memorization problem is to study the expressive power of neural networks to interpolate a finite dataset. Although memorization is widely believed to have a close relationship with the strong generalizability of deep learning when using over-parameterized models, to the best of our knowledge, there exists no theoretical study on the generalizability of memorization neural networks. In this paper, we give the first theoretical analysis of this topic. Since using i.i.d. training data is a necessary condition for a learning algorithm to be generalizable, memorization and its generalization theory for i.i.d. datasets are developed under mild conditions on the data distribution. First, algorithms are given to construct memorization networks for an i.i.d. dataset, which have the smallest number of parameters and even a constant number of parameters. Second, we show that, in order for the memorization networks to be generalizable, the width of the network must be at least equal to the dimension of the data, which implies that the existing memorization networks with an optimal number of parameters are not generalizable. Third, a lower bound for the sample complexity of general memorization algorithms and the exact sample complexity for memorization algorithms with constant number of parameters are given. It is also shown that there exist data distributions such that, to be generalizable for them, the memorization network must have an exponential number of parameters in the data dimension. Finally, an efficient and generalizable memorization algorithm is given when the number of training samples is greater than the efficient memorization sample complexity of the data distribution.

Aligning CodeLLMs with Direct Preference Optimization

The last year has witnessed the rapid progress of large language models (LLMs) across diverse domains. Among them, CodeLLMs have garnered particular attention because they can not only assist in completing various programming tasks but also represent the decision-making and logical reasoning capabilities of LLMs. However, current CodeLLMs mainly focus on pre-training and supervised fine-tuning scenarios, leaving the alignment stage, which is important for post-training LLMs, under-explored. This work first identifies that the commonly used PPO algorithm may be suboptimal for the alignment of CodeLLM because the involved reward rules are routinely coarse-grained and potentially flawed. We then advocate addressing this using the DPO algorithm. Based on only preference data pairs, DPO can render the model rank data automatically, giving rise to a fine-grained rewarding pattern more robust than human intervention. We also contribute a pipeline for collecting preference pairs for DPO on CodeLLMs. Studies show that our method significantly improves the performance of existing CodeLLMs on benchmarks such as MBPP and HumanEval.

Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models

Recent advancements in large language models (LLMs) have led to significant breakthroughs in mathematical reasoning capabilities. However, existing benchmarks like GSM8K or MATH are now being solved with high accuracy (e.g., OpenAI o1 achieves 94.8% on MATH dataset), indicating their inadequacy for truly challenging these models. To bridge this gap, we propose a comprehensive and challenging benchmark specifically designed to assess LLMs' mathematical reasoning at the Olympiad level. Unlike existing Olympiad-related benchmarks, our dataset focuses exclusively on mathematics and comprises a vast collection of 4428 competition-level problems with rigorous human annotation. These problems are meticulously categorized into over 33 sub-domains and span more than 10 distinct difficulty levels, enabling a holistic assessment of model performance in Olympiad-mathematical reasoning. Furthermore, we conducted an in-depth analysis based on this benchmark. Our experimental results show that even the most advanced models, OpenAI o1-mini and OpenAI o1-preview, struggle with highly challenging Olympiad-level problems, with 60.54% and 52.55% accuracy, highlighting significant challenges in Olympiad-level mathematical reasoning.