Charles Sutton

Aakanksha Chowdhery, Sharan Narang, Jacob Devlin et al. · deepmind, stanford

Large language models have been shown to achieve remarkable performance across a variety of natural language tasks using few-shot learning, which drastically reduces the number of task-specific training examples needed to adapt the model to a particular application. To further our understanding of the impact of scale on few-shot learning, we trained a 540-billion parameter, densely activated, Transformer language model, which we call Pathways Language Model PaLM. We trained PaLM on 6144 TPU v4 chips using Pathways, a new ML system which enables highly efficient training across multiple TPU Pods. We demonstrate continued benefits of scaling by achieving state-of-the-art few-shot learning results on hundreds of language understanding and generation benchmarks. On a number of these tasks, PaLM 540B achieves breakthrough performance, outperforming the finetuned state-of-the-art on a suite of multi-step reasoning tasks, and outperforming average human performance on the recently released BIG-bench benchmark. A significant number of BIG-bench tasks showed discontinuous improvements from model scale, meaning that performance steeply increased as we scaled to our largest model. PaLM also has strong capabilities in multilingual tasks and source code generation, which we demonstrate on a wide array of benchmarks. We additionally provide a comprehensive analysis on bias and toxicity, and study the extent of training data memorization with respect to model scale. Finally, we discuss the ethical considerations related to large language models and discuss potential mitigation strategies.

David Bieber, Kensen Shi, Petros Maniatis et al. · deepmind

Graph representations of programs are commonly a central element of machine learning for code research. We introduce an open source Python library python_graphs that applies static analysis to construct graph representations of Python programs suitable for training machine learning models. Our library admits the construction of control-flow graphs, data-flow graphs, and composite ``program graphs'' that combine control-flow, data-flow, syntactic, and lexical information about a program. We present the capabilities and limitations of the library, perform a case study applying the library to millions of competitive programming submissions, and showcase the library's utility for machine learning research.

David Dohan, Winnie Xu, Aitor Lewkowycz et al. · anthropic, deepmind

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are probabilistic models, and may be expressed in the language of graphical models with random variables whose values are complex data types such as strings. Cases with control flow and dynamic structure require techniques from probabilistic programming, which allow implementing disparate model structures and inference strategies in a unified language. We formalize several existing techniques from this perspective, including scratchpads / chain of thought, verifiers, STaR, selection-inference, and tool use. We refer to the resulting programs as language model cascades.

Pengcheng Yin, Wen-Ding Li, Kefan Xiao et al. · stanford

Computational notebooks, such as Jupyter notebooks, are interactive computing environments that are ubiquitous among data scientists to perform data wrangling and analytic tasks. To measure the performance of AI pair programmers that automatically synthesize programs for those tasks given natural language (NL) intents from users, we build ARCADE, a benchmark of 1082 code generation problems using the pandas data analysis framework in data science notebooks. ARCADE features multiple rounds of NL-to-code problems from the same notebook. It requires a model to understand rich multi-modal contexts, such as existing notebook cells and their execution states as well as previous turns of interaction. To establish a strong baseline on this challenging task, we develop PaChiNCo, a 62B code language model (LM) for Python computational notebooks, which significantly outperforms public code LMs. Finally, we explore few-shot prompting strategies to elicit better code with step-by-step decomposition and NL explanation, showing the potential to improve the diversity and explainability of model predictions.

Xinyun Chen, Renat Aksitov, Uri Alon et al. · deepmind

Self-consistency with chain-of-thought prompting (CoT) has demonstrated remarkable performance gains on various challenging tasks, by utilizing multiple reasoning paths sampled from large language models (LLMs). However, self-consistency relies on the answer extraction process to aggregate multiple solutions, which is not applicable to free-form answers. In this work, we propose Universal Self-Consistency (USC), which leverages LLMs themselves to select the most consistent answer among multiple candidates. We evaluate USC on a variety of benchmarks, including mathematical reasoning, code generation, long-context summarization, and open-ended question answering. On open-ended generation tasks where the original self-consistency method is not applicable, USC effectively utilizes multiple samples and improves the performance. For mathematical reasoning, USC matches the standard self-consistency performance without requiring the answer formats to be similar. Finally, without access to execution results, USC also matches the execution-based voting performance on code generation.

Du Phan, Matthew D. Hoffman, David Dohan et al. · deepmind

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the \emph{marginal} log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT.

Kensen Shi, Hanjun Dai, Kevin Ellis et al.

Many approaches to program synthesis perform a search within an enormous space of programs to find one that satisfies a given specification. Prior works have used neural models to guide combinatorial search algorithms, but such approaches still explore a huge portion of the search space and quickly become intractable as the size of the desired program increases. To tame the search space blowup, we propose training a neural model to learn a hands-on search policy for bottom-up synthesis, instead of relying on a combinatorial search algorithm. Our approach, called CrossBeam, uses the neural model to choose how to combine previously-explored programs into new programs, taking into account the search history and partial program executions. Motivated by work in structured prediction on learning to search, CrossBeam is trained on-policy using data extracted from its own bottom-up searches on training tasks. We evaluate CrossBeam in two very different domains, string manipulation and logic programming. We observe that CrossBeam learns to search efficiently, exploring much smaller portions of the program space compared to the state-of-the-art.

Kensen Shi, Joey Hong, Yinlin Deng et al.

When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, we can measure whether they compositionally generalize, that is, whether a model that has been trained on the simpler subtasks is subsequently able to solve more complex tasks. In this paper, we characterize several different forms of compositional generalization that are desirable in program synthesis, forming a meta-benchmark which we use to create generalization tasks for two popular datasets, RobustFill and DeepCoder. We then propose ExeDec, a novel decomposition-based synthesis strategy that predicts execution subgoals to solve problems step-by-step informed by program execution at each step. When used with Transformer models trained from scratch, ExeDec has better synthesis performance and greatly improved compositional generalization ability compared to baselines. Finally, we use our benchmarks to demonstrate that LLMs struggle to compositionally generalize when asked to do programming-by-example in a few-shot setting, but an ExeDec-style prompting approach can improve the generalization ability and overall performance.

Kensen Shi, Deniz Altınbüken, Saswat Anand et al.

We propose using natural language outlines as a novel modality and interaction surface for providing AI assistance to developers throughout the software development process. An NL outline for a code function comprises multiple statements written in concise prose, which partition the code and summarize its main ideas in the style of literate programming. Crucially, we find that modern LLMs can generate accurate and high-quality NL outlines in practice. Moreover, NL outlines enable a bidirectional sync between code and NL, where a developer can change either code or NL and have the LLM automatically update the other. We discuss many use cases for NL outlines: they can accelerate understanding and navigation of code and diffs, simplify code maintenance, augment code search, steer code generation, and more. We then propose and compare multiple LLM prompting techniques for generating outlines and ask professional developers to judge outline quality. Finally, we present two case studies applying NL outlines toward code review and malware detection.

Kensen Shi, Joey Hong, Manzil Zaheer et al.

When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, what we can measure is whether they compositionally generalize, that is, whether a model that has been trained on the simpler subtasks is subsequently able to solve more complex tasks. In this paper, we focus on measuring the ability of learned program synthesizers to compositionally generalize. We first characterize several different axes along which program synthesis methods would be desired to generalize, e.g., length generalization, or the ability to combine known subroutines in new ways that do not occur in the training data. Based on this characterization, we introduce a benchmark suite of tasks to assess these abilities based on two popular existing datasets, SCAN and RobustFill. Finally, we make first attempts to improve the compositional generalization ability of Transformer models along these axes through novel attention mechanisms that draw inspiration from a human-like decomposition strategy. Empirically, we find our modified Transformer models generally perform better than natural baselines, but the tasks remain challenging.

Kensen Shi, Hanjun Dai, Wen-Ding Li et al.

Search is an important technique in program synthesis that allows for adaptive strategies such as focusing on particular search directions based on execution results. Several prior works have demonstrated that neural models are effective at guiding program synthesis searches. However, a common drawback of those approaches is the inability to handle iterative loops, higher-order functions, or lambda functions, thus limiting prior neural searches from synthesizing longer and more general programs. We address this gap by designing a search algorithm called LambdaBeam that can construct arbitrary lambda functions that compose operations within a given DSL. We create semantic vector representations of the execution behavior of the lambda functions and train a neural policy network to choose which lambdas to construct during search, and pass them as arguments to higher-order functions to perform looping computations. Our experiments show that LambdaBeam outperforms neural, symbolic, and LLM-based techniques in an integer list manipulation domain.

Lazar Valkov, Akash Srivastava, Swarat Chaudhuri et al.

Modular approaches that use a different composition of modules for each problem are a promising direction in continual learning (CL). However, searching through the large, discrete space of module compositions is challenging, especially because evaluating a composition's performance requires a round of neural network training. We address this challenge through a modular CL framework, PICLE, that uses a probabilistic model to cheaply compute the fitness of each composition, allowing PICLE to achieve both perceptual, few-shot and latent transfer. The model combines prior knowledge about good module compositions with dataset-specific information. We evaluate PICLE using two benchmark suites designed to assess different desiderata of CL techniques. Comparing to a wide range of approaches, we show that PICLE is the first modular CL algorithm to achieve perceptual, few-shot and latent transfer while scaling well to large search spaces, outperforming previous state-of-the-art modular CL approaches on long problem sequences.

Simao Eduardo, Kai Xu, Alfredo Nazabal et al.

Data cleaning often comprises outlier detection and data repair. Systematic errors result from nearly deterministic transformations that occur repeatedly in the data, e.g. specific image pixels being set to default values or watermarks. Consequently, models with enough capacity easily overfit to these errors, making detection and repair difficult. Seeing as a systematic outlier is a combination of patterns of a clean instance and systematic error patterns, our main insight is that inliers can be modelled by a smaller representation (subspace) in a model than outliers. By exploiting this, we propose Clean Subspace Variational Autoencoder (CLSVAE), a novel semi-supervised model for detection and automated repair of systematic errors. The main idea is to partition the latent space and model inlier and outlier patterns separately. CLSVAE is effective with much less labelled data compared to previous related models, often with less than 2% of the data. We provide experiments using three image datasets in scenarios with different levels of corruption and labelled set sizes, comparing to relevant baselines. CLSVAE provides superior repairs without human intervention, e.g. with just 0.25% of labelled data we see a relative error decrease of 58% compared to the closest baseline.

Gheorghe Comanici, Eric Bieber, Mike Schaekermann et al. · amazon-science, baidu

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Rafael-Michael Karampatsis, Charles Sutton

Program repair is an important but difficult software engineering problem. One way to achieve acceptable performance is to focus on classes of simple bugs, such as bugs with single statement fixes, or that match a small set of bug templates. However, it is very difficult to estimate the recall of repair techniques for simple bugs, as there are no datasets about how often the associated bugs occur in code. To fill this gap, we provide a dataset of 153,652 single statement bug-fix changes mined from 1,000 popular open-source Java projects, annotated by whether they match any of a set of 16 bug templates, inspired by state-of-the-art program repair techniques. In an initial analysis, we find that about 33% of the simple bug fixes match the templates, indicating that a remarkable number of single-statement bugs can be repaired with a relatively small set of templates. Further, we find that template fitting bugs appear with a frequency of about one bug per 1,600-2,500 lines of code (as measured by the size of the project's latest version). We hope that the dataset will prove a resource for both future work in program repair and studies in empirical software engineering.

Miltiadis Allamanis, Charles Sutton

We present the first method for automatically mining code idioms from a corpus of previously written, idiomatic software projects. We take the view that a code idiom is a syntactic fragment that recurs across projects and has a single semantic role. Idioms may have metavariables, such as the body of a for loop. Modern IDEs commonly provide facilities for manually defining idioms and inserting them on demand, but this does not help programmers to write idiomatic code in languages or using libraries with which they are unfamiliar. We present HAGGIS, a system for mining code idioms that builds on recent advanced techniques from statistical natural language processing, namely, nonparametric Bayesian probabilistic tree substitution grammars. We apply HAGGIS to several of the most popular open source projects from GitHub. We present a wide range of evidence that the resulting idioms are semantically meaningful, demonstrating that they do indeed recur across software projects and that they occur more frequently in illustrative code examples collected from a Q&A site. Manual examination of the most common idioms indicate that they describe important program concepts, including object creation, exception handling, and resource management.

Jaroslav Fowkes, Pankajan Chanthirasegaran, Razvan Ranca et al.

Developers spend much of their time reading and browsing source code, raising new opportunities for summarization methods. Indeed, modern code editors provide code folding, which allows one to selectively hide blocks of code. However this is impractical to use as folding decisions must be made manually or based on simple rules. We introduce the autofolding problem, which is to automatically create a code summary by folding less informative code regions. We present a novel solution by formulating the problem as a sequence of AST folding decisions, leveraging a scoped topic model for code tokens. On an annotated set of popular open source projects, we show that our summarizer outperforms simpler baselines, yielding a 28% error reduction. Furthermore, we find through a case study that our summarizer is strongly preferred by experienced developers. More broadly, we hope this work will aid program comprehension by turning code folding into a usable and valuable tool.

Miltiadis Allamanis, Earl T. Barr, Christian Bird et al.

Every programmer has a characteristic style, ranging from preferences about identifier naming to preferences about object relationships and design patterns. Coding conventions define a consistent syntactic style, fostering readability and hence maintainability. When collaborating, programmers strive to obey a project's coding conventions. However, one third of reviews of changes contain feedback about coding conventions, indicating that programmers do not always follow them and that project members care deeply about adherence. Unfortunately, programmers are often unaware of coding conventions because inferring them requires a global view, one that aggregates the many local decisions programmers make and identifies emergent consensus on style. We present NATURALIZE, a framework that learns the style of a codebase, and suggests revisions to improve stylistic consistency. NATURALIZE builds on recent work in applying statistical natural language processing to source code. We apply NATURALIZE to suggest natural identifier names and formatting conventions. We present four tools focused on ensuring natural code during development and release management, including code review. NATURALIZE achieves 94% accuracy in its top suggestions for identifier names and can even transfer knowledge about conventions across projects, leveraging a corpus of 10,968 open source projects. We used NATURALIZE to generate 18 patches for 5 open source projects: 14 were accepted.

Ansong Ni, Miltiadis Allamanis, Arman Cohan et al. · cambridge, microsoft-research

A fundamental skill among human developers is the ability to understand and reason about program execution. As an example, a programmer can mentally simulate code execution in natural language to debug and repair code (aka. rubber duck debugging). However, large language models (LLMs) of code are typically trained on the surface textual form of programs, thus may lack a semantic understanding of how programs execute at run-time. To address this issue, we propose NExT, a method to teach LLMs to inspect the execution traces of programs (variable states of executed lines) and reason about their run-time behavior through chain-of-thought (CoT) rationales. Specifically, NExT uses self-training to bootstrap a synthetic training set of execution-aware rationales that lead to correct task solutions (e.g., fixed programs) without laborious manual annotation. Experiments on program repair tasks based on MBPP and HumanEval demonstrate that NExT improves the fix rate of a PaLM 2 model, by 26.1% and 14.3% absolute, respectively, with significantly improved rationale quality as verified by automated metrics and human raters. Our model can also generalize to scenarios where program traces are absent at test-time.

Hanjun Dai, Bethany Yixin Wang, Xingchen Wan et al.

Analytics on structured data is a mature field with many successful methods. However, most real world data exists in unstructured form, such as images and conversations. We investigate the potential of Large Language Models (LLMs) to enable unstructured data analytics. In particular, we propose a new Universal Query Engine (UQE) that directly interrogates and draws insights from unstructured data collections. This engine accepts queries in a Universal Query Language (UQL), a dialect of SQL that provides full natural language flexibility in specifying conditions and operators. The new engine leverages the ability of LLMs to conduct analysis of unstructured data, while also allowing us to exploit advances in sampling and optimization techniques to achieve efficient and accurate query execution. In addition, we borrow techniques from classical compiler theory to better orchestrate the workflow between sampling methods and foundation model calls. We demonstrate the efficiency of UQE on data analytics across different modalities, including images, dialogs and reviews, across a range of useful query types, including conditional aggregation, semantic retrieval and abstraction aggregation.

Gemini Team, Rohan Anil, Sebastian Borgeaud et al.

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

Maxwell Nye, Anders Johan Andreassen, Guy Gur-Ari et al.

Large pre-trained language models perform remarkably well on tasks that can be done "in one pass", such as generating realistic text or synthesizing computer programs. However, they struggle with tasks that require unbounded multi-step computation, such as adding integers or executing programs. Surprisingly, we find that these same models are able to perform complex multi-step computations -- even in the few-shot regime -- when asked to perform the operation "step by step", showing the results of intermediate computations. In particular, we train transformers to perform multi-step computations by asking them to emit intermediate computation steps into a "scratchpad". On a series of increasingly complex tasks ranging from long addition to the execution of arbitrary programs, we show that scratchpads dramatically improve the ability of language models to perform multi-step computations.

Jacob Austin, Augustus Odena, Maxwell Nye et al.

This paper explores the limits of the current generation of large language models for program synthesis in general purpose programming languages. We evaluate a collection of such models (with between 244M and 137B parameters) on two new benchmarks, MBPP and MathQA-Python, in both the few-shot and fine-tuning regimes. Our benchmarks are designed to measure the ability of these models to synthesize short Python programs from natural language descriptions. The Mostly Basic Programming Problems (MBPP) dataset contains 974 programming tasks, designed to be solvable by entry-level programmers. The MathQA-Python dataset, a Python version of the MathQA benchmark, contains 23914 problems that evaluate the ability of the models to synthesize code from more complex text. On both datasets, we find that synthesis performance scales log-linearly with model size. Our largest models, even without finetuning on a code dataset, can synthesize solutions to 59.6 percent of the problems from MBPP using few-shot learning with a well-designed prompt. Fine-tuning on a held-out portion of the dataset improves performance by about 10 percentage points across most model sizes. On the MathQA-Python dataset, the largest fine-tuned model achieves 83.8 percent accuracy. Going further, we study the model's ability to engage in dialog about code, incorporating human feedback to improve its solutions. We find that natural language feedback from a human halves the error rate compared to the model's initial prediction. Additionally, we conduct an error analysis to shed light on where these models fall short and what types of programs are most difficult to generate. Finally, we explore the semantic grounding of these models by fine-tuning them to predict the results of program execution. We find that even our best models are generally unable to predict the output of a program given a specific input.

Xinyun Chen, Petros Maniatis, Rishabh Singh et al.

Spreadsheet formula prediction has been an important program synthesis problem with many real-world applications. Previous works typically utilize input-output examples as the specification for spreadsheet formula synthesis, where each input-output pair simulates a separate row in the spreadsheet. However, this formulation does not fully capture the rich context in real-world spreadsheets. First, spreadsheet data entries are organized as tables, thus rows and columns are not necessarily independent from each other. In addition, many spreadsheet tables include headers, which provide high-level descriptions of the cell data. However, previous synthesis approaches do not consider headers as part of the specification. In this work, we present the first approach for synthesizing spreadsheet formulas from tabular context, which includes both headers and semi-structured tabular data. In particular, we propose SpreadsheetCoder, a BERT-based model architecture to represent the tabular context in both row-based and column-based formats. We train our model on a large dataset of spreadsheets, and demonstrate that SpreadsheetCoder achieves top-1 prediction accuracy of 42.51%, which is a considerable improvement over baselines that do not employ rich tabular context. Compared to the rule-based system, SpreadsheetCoder assists 82% more users in composing formulas on Google Sheets.

Joey Hong, David Dohan, Rishabh Singh et al.

In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically meant for search: rich enough to specify the desired output but compact enough to make search more efficient. Discrete latent codes are appealing for this purpose, as they naturally allow sophisticated combinatorial search strategies. The latent codes are learned using a self-supervised learning principle, in which first a discrete autoencoder is trained on the output sequences, and then the resulting latent codes are used as intermediate targets for the end-to-end sequence prediction task. Based on these insights, we introduce the \emph{Latent Programmer}, a program synthesis method that first predicts a discrete latent code from input/output examples, and then generates the program in the target language. We evaluate the Latent Programmer on two domains: synthesis of string transformation programs, and generation of programs from natural language descriptions. We demonstrate that the discrete latent representation significantly improves synthesis accuracy.

Hanjun Dai, Rishabh Singh, Bo Dai et al.

Discrete structures play an important role in applications like program language modeling and software engineering. Current approaches to predicting complex structures typically consider autoregressive models for their tractability, with some sacrifice in flexibility. Energy-based models (EBMs) on the other hand offer a more flexible and thus more powerful approach to modeling such distributions, but require partition function estimation. In this paper we propose ALOE, a new algorithm for learning conditional and unconditional EBMs for discrete structured data, where parameter gradients are estimated using a learned sampler that mimics local search. We show that the energy function and sampler can be trained efficiently via a new variational form of power iteration, achieving a better trade-off between flexibility and tractability. Experimentally, we show that learning local search leads to significant improvements in challenging application domains. Most notably, we present an energy model guided fuzzer for software testing that achieves comparable performance to well engineered fuzzing engines like libfuzzer.

David Bieber, Charles Sutton, Hugo Larochelle et al.

Graph neural networks (GNNs) have emerged as a powerful tool for learning software engineering tasks including code completion, bug finding, and program repair. They benefit from leveraging program structure like control flow graphs, but they are not well-suited to tasks like program execution that require far more sequential reasoning steps than number of GNN propagation steps. Recurrent neural networks (RNNs), on the other hand, are well-suited to long sequential chains of reasoning, but they do not naturally incorporate program structure and generally perform worse on the above tasks. Our aim is to achieve the best of both worlds, and we do so by introducing a novel GNN architecture, the Instruction Pointer Attention Graph Neural Networks (IPA-GNN), which achieves improved systematic generalization on the task of learning to execute programs using control flow graphs. The model arises by considering RNNs operating on program traces with branch decisions as latent variables. The IPA-GNN can be seen either as a continuous relaxation of the RNN model or as a GNN variant more tailored to execution. To test the models, we propose evaluating systematic generalization on learning to execute using control flow graphs, which tests sequential reasoning and use of program structure. More practically, we evaluate these models on the task of learning to execute partial programs, as might arise if using the model as a heuristic function in program synthesis. Results show that the IPA-GNN outperforms a variety of RNN and GNN baselines on both tasks.

Maria I. Gorinova, Andrew D. Gordon, Charles Sutton et al.

A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models in order to improve efficiency of inference or meet restrictions imposed by the PPL. Conditional independence (CI) relationships among parameters are a crucial aspect of probabilistic models that capture a qualitative summary of the specified model and can facilitate more efficient inference. We present an information flow type system for probabilistic programming that captures conditional independence (CI) relationships, and show that, for a well-typed program in our system, the distribution it implements is guaranteed to have certain CI-relationships. Further, by using type inference, we can statically deduce which CI-properties are present in a specified model. As a practical application, we consider the problem of how to perform inference on models with mixed discrete and continuous parameters. Inference on such models is challenging in many existing PPLs, but can be improved through a workaround, where the discrete parameters are used implicitly, at the expense of manual model re-writing. We present a source-to-source semantics-preserving transformation, which uses our CI-type system to automate this workaround by eliminating the discrete parameters from a probabilistic program. The resulting program can be seen as a hybrid inference algorithm on the original program, where continuous parameters can be drawn using efficient gradient-based inference methods, while the discrete parameters are inferred using variable elimination. We implement our CI-type system and its example application in SlicStan: a compositional variant of Stan.

Augustus Odena, Kensen Shi, David Bieber et al.

Program synthesis is challenging largely because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analyzing their intermediate results to compose them in appropriate ways. Motivated by this intuition, we present a new synthesis approach that leverages learning to guide a bottom-up search over programs. In particular, we train a model to prioritize compositions of intermediate values during search conditioned on a given set of input-output examples. This is a powerful combination because of several emergent properties. First, in bottom-up search, intermediate programs can be executed, providing semantic information to the neural network. Second, given the concrete values from those executions, we can exploit rich features based on recent work on property signatures. Finally, bottom-up search allows the system substantial flexibility in what order to generate the solution, allowing the synthesizer to build up a program from multiple smaller sub-programs. Overall, our empirical evaluation finds that the combination of learning and bottom-up search is remarkably effective, even with simple supervised learning approaches. We demonstrate the effectiveness of our technique on two datasets, one from the SyGuS competition and one of our own creation.

Matej Balog, Rishabh Singh, Petros Maniatis et al.

We present a new program synthesis approach that combines an encoder-decoder based synthesis architecture with a differentiable program fixer. Our approach is inspired from the fact that human developers seldom get their program correct on the first attempt, and perform iterative testing-based program fixing to get to the desired program functionality. Similarly, our approach first learns a distribution over programs conditioned on an encoding of a set of input-output examples, and then iteratively performs fix operations using the differentiable fixer. The fixer takes as input the original examples and the current program's outputs on example inputs, and generates a new distribution over the programs with the goal of reducing the discrepancies between the current program outputs and the desired example outputs. We train our architecture end-to-end on the RobustFill domain, and show that the addition of the fixer module leads to a significant improvement on synthesis accuracy compared to using beam search.

Rafael - Michael Karampatsis, Charles Sutton

Continuous embeddings of tokens in computer programs have been used to support a variety of software development tools, including readability, code search, and program repair. Contextual embeddings are common in natural language processing but have not been previously applied in software engineering. We introduce a new set of deep contextualized word representations for computer programs based on language models. We train a set of embeddings using the ELMo (embeddings from language models) framework of Peters et al (2018). We investigate whether these embeddings are effective when fine-tuned for the downstream task of bug detection. We show that even a low-dimensional embedding trained on a relatively small corpus of programs can improve a state-of-the-art machine learning system for bug detection.

Irene Vlassi Pandi, Earl T. Barr, Andrew D. Gordon et al.

We present a new approach to the type inference problem for dynamic languages. Our goal is to combine \emph{logical} constraints, that is, deterministic information from a type system, with \emph{natural} constraints, that is, uncertain statistical information about types learnt from sources like identifier names. To this end, we introduce a framework for probabilistic type inference that combines logic and learning: logical constraints on the types are extracted from the program, and deep learning is applied to predict types from surface-level code properties that are statistically associated. The foremost insight of our method is to constrain the predictions from the learning procedure to respect the logical constraints, which we achieve by relaxing the logical inference problem of type prediction into a continuous optimisation problem. We build a tool called OptTyper to predict missing types for TypeScript files. OptTyper combines a continuous interpretation of logical constraints derived by classical static analysis of TypeScript code, with natural constraints obtained from a deep learning model, which learns naming conventions for types from a large codebase. By evaluating OptTyper, we show that the combination of logical and natural constraints yields a large improvement in performance over either kind of information individually and achieves a 4% improvement over the state-of-the-art.

Rafael-Michael Karampatsis, Hlib Babii, Romain Robbes et al.

Statistical language modeling techniques have successfully been applied to large source code corpora, yielding a variety of new software development tools, such as tools for code suggestion, improving readability, and API migration. A major issue with these techniques is that code introduces new vocabulary at a far higher rate than natural language, as new identifier names proliferate. Both large vocabularies and out-of-vocabulary issues severely affect Neural Language Models (NLMs) of source code, degrading their performance and rendering them unable to scale. In this paper, we address this issue by: 1) studying how various modelling choices impact the resulting vocabulary on a large-scale corpus of 13,362 projects; 2) presenting an open vocabulary source code NLM that can scale to such a corpus, 100 times larger than in previous work; and 3) showing that such models outperform the state of the art on three distinct code corpora (Java, C, Python). To our knowledge, these are the largest NLMs for code that have been reported. All datasets, code, and trained models used in this work are publicly available.

Daniel A. Abolafia, Rishabh Singh, Manzil Zaheer et al.

We present a modular neural network architecture Main that learns algorithms given a set of input-output examples. Main consists of a neural controller that interacts with a variable-length input tape and learns to compose modules together with their corresponding argument choices. Unlike previous approaches, Main uses a general domain-agnostic mechanism for selection of modules and their arguments. It uses a general input tape layout together with a parallel history tape to indicate most recently used locations. Finally, it uses a memoryless controller with a length-invariant self-attention based input tape encoding to allow for random access to tape locations. The Main architecture is trained end-to-end using reinforcement learning from a set of input-output examples. We evaluate Main on five algorithmic tasks and show that it can learn policies that generalizes perfectly to inputs of much longer lengths than the ones used for training.

Kensen Shi, David Bieber, Charles Sutton

Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present an elegant procedure for sampling without replacement from a broad class of randomized programs, including generative neural models that construct outputs sequentially. Our procedure is efficient even for exponentially-large output spaces. Unlike prior work, our approach is incremental, i.e., samples can be drawn one at a time, allowing for increased flexibility. We also present a new estimator for computing expectations from samples drawn without replacement. We show that incremental sampling without replacement is applicable to many domains, e.g., program synthesis and combinatorial optimization.

Augustus Odena, Charles Sutton

We introduce the notion of property signatures, a representation for programs and program specifications meant for consumption by machine learning algorithms. Given a function with input type $τ_{in}$ and output type $τ_{out}$, a property is a function of type: $(τ_{in}, τ_{out}) \rightarrow \texttt{Bool}$ that (informally) describes some simple property of the function under consideration. For instance, if $τ_{in}$ and $τ_{out}$ are both lists of the same type, one property might ask `is the input list the same length as the output list?'. If we have a list of such properties, we can evaluate them all for our function to get a list of outputs that we will call the property signature. Crucially, we can `guess' the property signature for a function given only a set of input/output pairs meant to specify that function. We discuss several potential applications of property signatures and show experimentally that they can be used to improve over a baseline synthesizer so that it emits twice as many programs in less than one-tenth of the time.

Daniel Tarlow, Subhodeep Moitra, Andrew Rice et al.

Professional software developers spend a significant amount of time fixing builds, but this has received little attention as a problem in automatic program repair. We present a new deep learning architecture, called Graph2Diff, for automatically localizing and fixing build errors. We represent source code, build configuration files, and compiler diagnostic messages as a graph, and then use a Graph Neural Network model to predict a diff. A diff specifies how to modify the code's abstract syntax tree, represented in the neural network as a sequence of tokens and of pointers to code locations. Our network is an instance of a more general abstraction that we call Graph2Tocopo, which is potentially useful in any development tool for predicting source code changes. We evaluate the model on a dataset of over 500k real build errors and their resolutions from professional developers. Compared to the approach of DeepDelta (Mesbah et al., 2019), our approach tackles the harder task of predicting a more precise diff but still achieves over double the accuracy.

Simão Eduardo, Alfredo Nazábal, Christopher K. I. Williams et al.

We focus on the problem of unsupervised cell outlier detection and repair in mixed-type tabular data. Traditional methods are concerned only with detecting which rows in the dataset are outliers. However, identifying which cells are corrupted in a specific row is an important problem in practice, and the very first step towards repairing them. We introduce the Robust Variational Autoencoder (RVAE), a deep generative model that learns the joint distribution of the clean data while identifying the outlier cells, allowing their imputation (repair). RVAE explicitly learns the probability of each cell being an outlier, balancing different likelihood models in the row outlier score, making the method suitable for outlier detection in mixed-type datasets. We show experimentally that not only RVAE performs better than several state-of-the-art methods in cell outlier detection and repair for tabular data, but also that is robust against the initial hyper-parameter selection.

Jiaoyan Chen, Ernesto Jimenez-Ruiz, Ian Horrocks et al.

The usefulness of tabular data such as web tables critically depends on understanding their semantics. This study focuses on column type prediction for tables without any meta data. Unlike traditional lexical matching-based methods, we propose a deep prediction model that can fully exploit a table's contextual semantics, including table locality features learned by a Hybrid Neural Network (HNN), and inter-column semantics features learned by a knowledge base (KB) lookup and query answering algorithm.It exhibits good performance not only on individual table sets, but also when transferring from one table set to another.

Rafael-Michael Karampatsis, Charles Sutton

Statistical language modeling techniques have successfully been applied to source code, yielding a variety of new software development tools, such as tools for code suggestion and improving readability. A major issue with these techniques is that code introduces new vocabulary at a far higher rate than natural language, as new identifier names proliferate. But traditional language models limit the vocabulary to a fixed set of common words. For code, this strong assumption has been shown to have a significant negative effect on predictive performance. But the open vocabulary version of the neural network language models for code have not been introduced in the literature. We present a new open-vocabulary neural language model for code that is not limited to a fixed vocabulary of identifier names. We employ a segmentation into subword units, subsequences of tokens chosen based on a compression criterion, following previous work in machine translation. Our network achieves best in class performance, outperforming even the state-of-the-art methods of Hellendoorn and Devanbu that are designed specifically to model code. Furthermore, we present a simple method for dynamically adapting the model to a new test project, resulting in increased performance. We showcase our methodology on code corpora in three different languages of over a billion tokens each, hundreds of times larger than in previous work. To our knowledge, this is the largest neural language model for code that has been reported.

Jiaoyan Chen, Ernesto Jimenez-Ruiz, Ian Horrocks et al.

Automatically annotating column types with knowledge base (KB) concepts is a critical task to gain a basic understanding of web tables. Current methods rely on either table metadata like column name or entity correspondences of cells in the KB, and may fail to deal with growing web tables with incomplete meta information. In this paper we propose a neural network based column type annotation framework named ColNet which is able to integrate KB reasoning and lookup with machine learning and can automatically train Convolutional Neural Networks for prediction. The prediction model not only considers the contextual semantics within a cell using word representation, but also embeds the semantics of a column by learning locality features from multiple cells. The method is evaluated with DBPedia and two different web table datasets, T2Dv2 from the general Web and Limaye from Wikipedia pages, and achieves higher performance than the state-of-the-art approaches.

Maria I. Gorinova, Andrew D. Gordon, Charles Sutton

Stan is a probabilistic programming language that has been increasingly used for real-world scalable projects. However, to make practical inference possible, the language sacrifices some of its usability by adopting a block syntax, which lacks compositionality and flexible user-defined functions. Moreover, the semantics of the language has been mainly given in terms of intuition about implementation, and has not been formalised. This paper provides a formal treatment of the Stan language, and introduces the probabilistic programming language SlicStan --- a compositional, self-optimising version of Stan. Our main contributions are: (1) the formalisation of a core subset of Stan through an operational density-based semantics; (2) the design and semantics of the Stan-like language SlicStan, which facilities better code reuse and abstraction through its compositional syntax, more flexible functions, and information-flow type system; and (3) a formal, semantic-preserving procedure for translating SlicStan to Stan.

Annie Louis, Santanu Kumar Dash, Earl T. Barr et al.

Comments in software are critical for maintenance and reuse. But apart from prescriptive advice, there is little practical support or quantitative understanding of what makes a comment useful. In this paper, we introduce the task of identifying comments which are uninformative about the code they are meant to document. To address this problem, we introduce the notion of comment entailment from code, high entailment indicating that a comment's natural language semantics can be inferred directly from the code. Although not all entailed comments are low quality, comments that are too easily inferred, for example, comments that restate the code, are widely discouraged by authorities on software style. Based on this, we develop a tool called CRAIC which scores method-level comments for redundancy. Highly redundant comments can then be expanded or alternately removed by the developer. CRAIC uses deep language models to exploit large software corpora without requiring expensive manual annotations of entailment. We show that CRAIC can perform the comment entailment task with good agreement with human judgements. Our findings also have implications for documentation tools. For example, we find that common tags in Javadoc are at least two times more predictable from code than non-Javadoc sentences, suggesting that Javadoc tags are less informative than more free-form comments

Akash Srivastava, Kai Xu, Michael U. Gutmann et al.

Deep generative models can learn to generate realistic-looking images, but many of the most effective methods are adversarial and involve a saddlepoint optimization, which requires a careful balancing of training between a generator network and a critic network. Maximum mean discrepancy networks (MMD-nets) avoid this issue by using kernel as a fixed adversary, but unfortunately, they have not on their own been able to match the generative quality of adversarial training. In this work, we take their insight of using kernels as fixed adversaries further and present a novel method for training deep generative models that does not involve saddlepoint optimization. We call our method generative ratio matching or GRAM for short. In GRAM, the generator and the critic networks do not play a zero-sum game against each other, instead, they do so against a fixed kernel. Thus GRAM networks are not only stable to train like MMD-nets but they also match and beat the generative quality of adversarially trained generative networks.

Akash Srivastava, Charles Sutton

The Pachinko Allocation Machine (PAM) is a deep topic model that allows representing rich correlation structures among topics by a directed acyclic graph over topics. Because of the flexibility of the model, however, approximate inference is very difficult. Perhaps for this reason, only a small number of potential PAM architectures have been explored in the literature. In this paper we present an efficient and flexible amortized variational inference method for PAM, using a deep inference network to parameterize the approximate posterior distribution in a manner similar to the variational autoencoder. Our inference method produces more coherent topics than state-of-art inference methods for PAM while being an order of magnitude faster, which allows exploration of a wider range of PAM architectures than have previously been studied.

Lazar Valkov, Dipak Chaudhari, Akash Srivastava et al.

We present a neurosymbolic framework for the lifelong learning of algorithmic tasks that mix perception and procedural reasoning. Reusing high-level concepts across domains and learning complex procedures are key challenges in lifelong learning. We show that a program synthesis approach that combines gradient descent with combinatorial search over programs can be a more effective response to these challenges than purely neural methods. Our framework, called HOUDINI, represents neural networks as strongly typed, differentiable functional programs that use symbolic higher-order combinators to compose a library of neural functions. Our learning algorithm consists of: (1) a symbolic program synthesizer that performs a type-directed search over parameterized programs, and decides on the library functions to reuse, and the architectures to combine them, while learning a sequence of tasks; and (2) a neural module that trains these programs using stochastic gradient descent. We evaluate HOUDINI on three benchmarks that combine perception with the algorithmic tasks of counting, summing, and shortest-path computation. Our experiments show that HOUDINI transfers high-level concepts more effectively than traditional transfer learning and progressive neural networks, and that the typed representation of networks significantly accelerates the search.

Kai Xu, Dae Hoon Park, Chang Yi et al.

Interpreting black box classifiers, such as deep networks, allows an analyst to validate a classifier before it is deployed in a high-stakes setting. A natural idea is to visualize the deep network's representations, so as to "see what the network sees". In this paper, we demonstrate that standard dimension reduction methods in this setting can yield uninformative or even misleading visualizations. Instead, we present DarkSight, which visually summarizes the predictions of a classifier in a way inspired by notion of dark knowledge. DarkSight embeds the data points into a low-dimensional space such that it is easy to compress the deep classifier into a simpler one, essentially combining model compression and dimension reduction. We compare DarkSight against t-SNE both qualitatively and quantitatively, demonstrating that DarkSight visualizations are more informative. Our method additionally yields a new confidence measure based on dark knowledge by quantifying how unusual a given vector of predictions is.

Miltiadis Allamanis, Earl T. Barr, Premkumar Devanbu et al.

Research at the intersection of machine learning, programming languages, and software engineering has recently taken important steps in proposing learnable probabilistic models of source code that exploit code's abundance of patterns. In this article, we survey this work. We contrast programming languages against natural languages and discuss how these similarities and differences drive the design of probabilistic models. We present a taxonomy based on the underlying design principles of each model and use it to navigate the literature. Then, we review how researchers have adapted these models to application areas and discuss cross-cutting and application-specific challenges and opportunities.

Akash Srivastava, Lazar Valkov, Chris Russell et al.

Deep generative models provide powerful tools for distributions over complicated manifolds, such as those of natural images. But many of these methods, including generative adversarial networks (GANs), can be difficult to train, in part because they are prone to mode collapse, which means that they characterize only a few modes of the true distribution. To address this, we introduce VEEGAN, which features a reconstructor network, reversing the action of the generator by mapping from data to noise. Our training objective retains the original asymptotic consistency guarantee of GANs, and can be interpreted as a novel autoencoder loss over the noise. In sharp contrast to a traditional autoencoder over data points, VEEGAN does not require specifying a loss function over the data, but rather only over the representations, which are standard normal by assumption. On an extensive set of synthetic and real world image datasets, VEEGAN indeed resists mode collapsing to a far greater extent than other recent GAN variants, and produces more realistic samples.

Akash Srivastava, Charles Sutton

Topic models are one of the most popular methods for learning representations of text, but a major challenge is that any change to the topic model requires mathematically deriving a new inference algorithm. A promising approach to address this problem is autoencoding variational Bayes (AEVB), but it has proven diffi- cult to apply to topic models in practice. We present what is to our knowledge the first effective AEVB based inference method for latent Dirichlet allocation (LDA), which we call Autoencoded Variational Inference For Topic Model (AVITM). This model tackles the problems caused for AEVB by the Dirichlet prior and by component collapsing. We find that AVITM matches traditional methods in accuracy with much better inference time. Indeed, because of the inference network, we find that it is unnecessary to pay the computational cost of running variational optimization on test data. Because AVITM is black box, it is readily applied to new topic models. As a dramatic illustration of this, we present a new topic model called ProdLDA, that replaces the mixture model in LDA with a product of experts. By changing only one line of code from LDA, we find that ProdLDA yields much more interpretable topics, even if LDA is trained via collapsed Gibbs sampling.