Periodicity, as one of the most important basic characteristics, lays the foundation for facilitating structured knowledge acquisition and systematic cognitive processes within human learning paradigms. However, the potential flaws of periodicity modeling in Transformer affect the learning efficiency and establishment of underlying principles from data for large language models (LLMs) built upon it. In this paper, we demonstrate that integrating effective periodicity modeling can improve the learning efficiency and performance of LLMs. We introduce FANformer, which integrates Fourier Analysis Network (FAN) into attention mechanism to achieve efficient periodicity modeling, by modifying the feature projection process of attention mechanism. Extensive experimental results on language modeling show that FANformer consistently outperforms Transformer when scaling up model size and training tokens, underscoring its superior learning efficiency. To further validate the effectiveness of FANformer, we pretrain a FANformer-1B on 1 trillion tokens. FANformer-1B exhibits marked improvements on downstream tasks compared to open-source LLMs with similar model parameters or training tokens. The results position FANformer as an effective and promising architecture for advancing LLMs.

Large language models (LLMs) have shown significant advancements in code generation, but still face challenges on tasks beyond their basic capabilities. Recently, the notion of self-debugging has been proposed to boost the performance of code generation by leveraging execution feedback from tests. Despite its promise, the availability of high-quality tests in real-world scenarios is limited. In this context, self-debugging with self-generated tests is a promising solution but lacks a full exploration of its limitations and practical potential. Therefore, we investigate its efficacy on diverse programming problems. To deepen our understanding, we propose two distinct paradigms for the process: post-execution and in-execution self-debugging. Within the scope of self-contained Python programming tasks, we find that post-execution self-debugging struggles on basic problems but shows potential for improvement on competitive ones, due to the bias introduced by self-generated tests. On the other hand, in-execution self-debugging enables LLMs to mitigate the bias by solely leveraging intermediate states during execution, thereby enhancing code generation.

Despite the remarkable success achieved by neural networks, particularly those represented by MLP and Transformer, we reveal that they exhibit potential flaws in the modeling and reasoning of periodicity, i.e., they tend to memorize the periodic data rather than genuinely understanding the underlying principles of periodicity. However, periodicity is a crucial trait in various forms of reasoning and generalization, underpinning predictability across natural and engineered systems through recurring patterns in observations. In this paper, we propose FAN, a novel network architecture based on Fourier Analysis, which empowers the ability to efficiently model and reason about periodic phenomena. By introducing Fourier Series, the periodicity is naturally integrated into the structure and computational processes of the neural network, thus achieving a more accurate expression and prediction of periodic patterns. As a promising substitute to multi-layer perceptron (MLP), FAN can seamlessly replace MLP in various models with fewer parameters and FLOPs. Through extensive experiments, we demonstrate the effectiveness of FAN in modeling and reasoning about periodic functions, and the superiority and generalizability of FAN across a range of real-world tasks, including symbolic formula representation, time series forecasting, and language modeling.

Large Language Models (LLMs) have been widely used in code completion, and researchers are focusing on scaling up LLMs to improve their accuracy. However, larger LLMs will increase the response time of code completion and decrease the developers' productivity. In this paper, we propose a lightweight and effective LLM for code completion named aiXcoder-7B. Compared to existing LLMs, aiXcoder-7B achieves higher code completion accuracy while having smaller scales (i.e., 7 billion parameters). We attribute the superiority of aiXcoder-7B to three key factors: (1) Multi-objective training. We employ three training objectives, one of which is our proposed Structured Fill-In-the-Middle (SFIM). SFIM considers the syntax structures in code and effectively improves the performance of LLMs for code. (2) Diverse data sampling strategies. They consider inter-file relationships and enhance the capability of LLMs in understanding cross-file contexts. (3) Extensive high-quality data. We establish a rigorous data collection pipeline and consume a total of 1.2 trillion unique tokens for training aiXcoder-7B. This vast volume of data enables aiXcoder-7B to learn a broad distribution of code. We evaluate aiXcoder-7B in five popular code completion benchmarks and a new benchmark collected by this paper. The results show that aiXcoder-7B outperforms the latest six LLMs with similar sizes and even surpasses four larger LLMs (e.g., StarCoder2-15B and CodeLlama-34B), positioning aiXcoder-7B as a lightweight and effective LLM for academia and industry. Finally, we summarize three valuable insights for helping practitioners train the next generations of LLMs for code. aiXcoder-7B has been open-souced and gained significant attention. As of the submission date, aiXcoder-7B has received 2,193 GitHub Stars.

Large language models (LLMs) have demonstrated an impressive ability to generate codes on competitive programming tasks. However, with limited sample numbers, LLMs still suffer from poor accuracy. Inspired by the process of human programming, we propose a generate-and-edit approach named Self-Edit that utilizes execution results of the generated code from LLMs to improve the code quality on the competitive programming task. We execute the generated code on the example test case provided in the question and wrap execution results into a supplementary comment. Utilizing this comment as guidance, our fault-aware code editor is employed to correct errors in the generated code. We perform extensive evaluations across two competitive programming datasets with nine different LLMs. Compared to directly generating from LLMs, our approach can improve the average of pass@1 by 89\% on APPS-dev, 31\% on APPS-test, and 48\% on HumanEval over nine popular code generation LLMs with parameter sizes ranging from 110M to 175B. Compared to other post-processing methods, our method demonstrates superior accuracy and efficiency.

Developers often perform repetitive code editing activities for various reasons (e.g., code refactoring) during software development. Pre-trained code editing models have achieved the state-of-the-art (SOTA) results. Pre-trained models are first pre-trained with pre-training tasks and fine-tuned with the code editing task. Existing pre-training tasks mainly are code infilling tasks (e.g., masked language modeling), which are derived from the natural language processing field and are not designed for automatic code editing. This paper proposes a novel pre-training task specialized in code editing and presents an effective pre-trained code editing model named CodeEditor. Our pre-training task further improves the performance and generalization ability of code editing models. Specifically, we collect lots of real-world code snippets as the ground truth and use a powerful generator to rewrite them into mutated versions. Then, we pre-train our CodeEditor to edit mutated versions into the corresponding ground truth, to learn edit patterns. We conduct experiments on four code editing datasets and evaluate the pre-trained CodeEditor in three settings. (1) In the fine-tuning setting, we train the pre-trained CodeEditor with four datasets and evaluate it on the test data. CodeEditor outperforms the SOTA baselines by 15%, 25.5%, and 9.4% and 26.6% on four datasets. (2) In the few-shot setting, we train the pre-trained CodeEditor with limited data and evaluate it on the test data. CodeEditor substantially performs better than all baselines. (3) In the zero-shot setting, CodeEditor correctly edits 1,113 programs while the SOTA baselines can not work.

Source code representation with deep learning techniques is an important research field. There have been many studies that learn sequential or structural information for code representation. But sequence-based models and non-sequence-models both have their limitations. Researchers attempt to incorporate structural information to sequence-based models, but they only mine part of token-level hierarchical structure information. In this paper, we analyze how the complete hierarchical structure influences the tokens in code sequences and abstract this influence as a property of code tokens called hierarchical embedding. The hierarchical embedding is further divided into statement-level global hierarchy and token-level local hierarchy. Furthermore, we propose the Hierarchy Transformer (HiT), a simple but effective sequence model to incorporate the complete hierarchical embeddings of source code into a Transformer model. We demonstrate the effectiveness of hierarchical embedding on learning code structure with an experiment on variable scope detection task. Further evaluation shows that HiT outperforms SOTA baseline models and show stable training efficiency on three source code-related tasks involving classification and generation tasks across 8 different datasets.

Learning vector representations for programs is a critical step in applying deep learning techniques for program understanding tasks. Various neural network models are proposed to learn from tree-structured program representations, e.g., abstract syntax tree (AST) and concrete syntax tree (CST). However, most neural architectures either fail to capture long-range dependencies which are ubiquitous in programs, or cannot learn effective representations for syntax tree nodes, making them incapable of performing the node-level prediction tasks, e.g., bug localization. In this paper, we propose Tree-Transformer, a novel recursive tree-structured neural network to learn the vector representations for source codes. We propose a multi-head attention mechanism to model the dependency between siblings and parent-children node pairs. Moreover, we propose a bi-directional propagation strategy to allow node information passing in two directions, bottom-up and top-down along trees. In this way, Tree-Transformer can learn the information of the node features as well as the global contextual information. The extensive experimental results show that our Tree-Transformer significantly outperforms the existing tree-based and graph-based program representation learning approaches in both the tree-level and node-level prediction tasks.