Conversely,ifsuch xandy donot exist,wesayT doesnotcontainunarychains. Then we present Algorithm 1 for computing oracle actions. Given a constituency treeT without unary chains, it recursively finds and undoes the last action untilT becomes empty_tree. Let T be a constituency tree for a sentence of length n. And this sequence of actions can be computed via Algorithm1. When n > 0, it is sufficient to proveT0 is a valid constituency tree without unary chains for a sentence oflengthn 1. Weproceed byenumerating allpossible execution traces inlast_action.

Conditional acceptability refers to how plausible a conditional statement is perceived to be. It plays an important role in communication and reasoning, as it influences how individuals interpret implications, assess arguments, and make decisions based on hypothetical scenarios. When humans evaluate how acceptable a conditional "If A, then B" is, their judgments are influenced by two main factors: the $\textit{conditional probability}$ of $B$ given $A$, and the $\textit{semantic relevance}$ of the antecedent $A$ given the consequent $B$ (i.e., whether $A$ meaningfully supports $B$). While prior work has examined how large language models (LLMs) draw inferences about conditional statements, it remains unclear how these models judge the $\textit{acceptability}$ of such statements. To address this gap, we present a comprehensive study of LLMs' conditional acceptability judgments across different model families, sizes, and prompting strategies. Using linear mixed-effects models and ANOVA tests, we find that models are sensitive to both conditional probability and semantic relevance-though to varying degrees depending on architecture and prompting style. A comparison with human data reveals that while LLMs incorporate probabilistic and semantic cues, they do so less consistently than humans. Notably, larger models do not necessarily align more closely with human judgments.

The root node must be an internal node. Now we are ready to state and prove Theorem 1 and Theorem 2 in the main paper. We prove the correctness of Algorithm 1 by induction on the sentence length n . " to denote the execution trace taking the Case 1-1-- last_leaf has siblings, and last_subtree is the root node. We have last_subtree = last_leaf (the first conditional statement).

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing. Feedforward neural networks using the ReLU activation function represent continuous and piecewise linear functions and can approximate many others. The study of their expressivity addresses the question: which ones? Contributing to the available answers, we take the perspective of a neural network as an algorithm. In this analogy, a neural network is programmed constructively, rather than trained from data. An interesting example is a sorting algorithm: we explicitly construct a neural network that sorts its inputs exactly, not approximately, and that, in a sense, has optimal computational complexity if the input dimension is large. Such constructed networks may have several billion parameters. We construct and analyze several other examples, both existing and new. We find that, in these examples, neural networks as algorithms are typically recursive and parallel. Compared to conventional algorithms, ReLU networks are restricted by having to be continuous. Moreover, the depth of recursion is limited by the depth of the network, with deep networks having superior properties over shallow ones.

Compilers are complex, and significant effort has been expended on testing them. Techniques such as random program generation and differential testing have proved highly effective and have uncovered thousands of bugs in production compilers. The majority of effort has been expended on validating that a compiler produces correct code for a given input, while less attention has been paid to ensuring that the compiler produces performant code. In this work we adapt differential testing to the task of identifying missed optimization opportunities in compilers. We develop a novel testing approach which combines large language models (LLMs) with a series of differential testing strategies and use them to find missing code size optimizations in C / C++ compilers. The advantage of our approach is its simplicity. We offload the complex task of generating random code to an off-the-shelf LLM, and use heuristics and analyses to identify anomalous compiler behavior. Our approach requires fewer than 150 lines of code to implement. This simplicity makes it extensible. By simply changing the target compiler and initial LLM prompt we port the approach from C / C++ to Rust and Swift, finding bugs in both. To date we have reported 24 confirmed bugs in production compilers, and conclude that LLM-assisted testing is a promising avenue for detecting optimization bugs in real world compilers.

LLMs trained in the understanding of programming syntax are now providing effective assistance to developers and are being used in programming education such as in generation of coding problem examples or providing code explanations. A key aspect of programming education is understanding and dealing with error message. However, 'logical errors' in which the program operates against the programmer's intentions do not receive error messages from the compiler. In this study, building on existing research on programming errors, we first define the types of logical errors that can occur in programming in general. Based on the definition, we propose an effective approach for detecting logical errors with LLMs that makes use of relations among error types in the Chain-of-Thought and Tree-of-Thought prompts. The experimental results indicate that when such logical error descriptions in the prompt are used, the average classification performance is about 21% higher than the ones without them. We also conducted an experiment for exploiting the relations among errors in generating a new logical error dataset using LLMs. As there is very limited dataset for logical errors such benchmark dataset can be very useful for various programming related applications. We expect that our work can assist novice programmers in identifying the causes of code errors and correct them more effectively.

The advancement of large language models (LLMs) has significantly propelled the field of code generation. Previous work integrated reinforcement learning (RL) with compiler feedback for exploring the output space of LLMs to enhance code generation quality. However, the lengthy code generated by LLMs in response to complex human requirements makes RL exploration a challenge. Also, since the unit tests may not cover the complicated code, optimizing LLMs by using these unexecuted code snippets is ineffective. To tackle these challenges, we introduce StepCoder, a novel RL framework for code generation, consisting of two main components: CCCS addresses the exploration challenge by breaking the long sequences code generation task into a Curriculum of Code Completion Subtasks, while FGO only optimizes the model by masking the unexecuted code segments to provide Fine-Grained Optimization. In addition, we furthermore construct the APPS+ dataset for RL training, which is manually verified to ensure the correctness of unit tests. Experimental results show that our method improves the ability to explore the output space and outperforms state-of-the-art approaches in corresponding benchmarks. Our dataset APPS+ and StepCoder are available online.

DL compiler's primary function is to translate DNN programs written in high-level DL frameworks such as PyTorch and TensorFlow into portable executables. These executables can then be flexibly executed by the deployed host programs. However, existing DL compilers rely on a tracing mechanism, which involves feeding a runtime input to a neural network program and tracing the program execution paths to generate the computational graph necessary for compilation. Unfortunately, this mechanism falls short when dealing with modern dynamic neural networks (DyNNs) that possess varying computational graphs depending on the inputs. Consequently, conventional DL compilers struggle to accurately compile DyNNs into executable code. To address this limitation, we propose \tool, a general approach that enables any existing DL compiler to successfully compile DyNNs. \tool tackles the dynamic nature of DyNNs by introducing a compilation mechanism that redistributes the control and data flow of the original DNN programs during the compilation process. Specifically, \tool develops program analysis and program transformation techniques to convert a dynamic neural network into multiple sub-neural networks. Each sub-neural network is devoid of conditional statements and is compiled independently. Furthermore, \tool synthesizes a host module that models the control flow of the DyNNs and facilitates the invocation of the sub-neural networks. Our evaluation demonstrates the effectiveness of \tool, achieving a 100\% success rate in compiling all dynamic neural networks. Moreover, the compiled executables generated by \tool exhibit significantly improved performance, running between $1.12\times$ and $20.21\times$ faster than the original DyNNs executed on general-purpose DL frameworks.

With the research advancement of Artificial Intelligence in the last years, there are new opportunities to mitigate real-world problems and advance technologically. Image recognition models in particular, are assigned with perception tasks to mitigate complex real-world challenges and lead to new solutions. Furthermore, the computational complexity and demand for resources of such models has also increased. To mitigate this, model optimization and hardware acceleration has come into play, but effectively integrating such concepts is a challenging and error-prone process. In order to allow developers and researchers to explore the robustness of deep learning image recognition models deployed on different hardware acceleration devices, we propose MutateNN, a tool that provides mutation testing and analysis capabilities for that purpose. To showcase its capabilities, we utilized 21 mutations for 7 widely-known pre-trained deep neural network models. We deployed our mutants on 4 different devices of varying computational capabilities and observed discrepancies in mutants related to conditional operations, as well as some unstable behaviour with those related to arithmetic types.

Pre-trained language models are effective in a variety of natural language tasks, but it has been argued their capabilities fall short of fully learning meaning or understanding language. To understand the extent to which language models can learn some form of meaning, we investigate their ability to capture semantics of code beyond superficial frequency and co-occurrence. In contrast to previous research on probing models for linguistic features, we study pre-trained models in a setting that allows for objective and straightforward evaluation of a model's ability to learn semantics. In this paper, we examine whether such models capture the semantics of code, which is precisely and formally defined. Through experiments involving the manipulation of code fragments, we show that code pre-trained models of code learn a robust representation of the computational semantics of code that goes beyond superficial features of form alone