A core challenge in program synthesis is online library learning: the incremental acquisition of reusable abstractions under uncertainty about future task demands. Existing algorithms treat library learning as retrospective compression over a static task distribution, where the learned library is determined by the corpus of past tasks. However, real-world learning domains are often non-stationary, with tasks arising from a generative process that evolves over time. We propose and test the hypothesis that in non-stationary domains human library learning selects abstractions prospectively: targeting compression of future tasks. We study this question using the Pattern Builder Task, a visual program synthesis paradigm in which participants construct increasingly complex geometric patterns from a small set of primitives, transformations, and custom helpers that carry forward across trials. Using this task, we conduct two experiments with complementary latent curricula, designed to dissociate between behaviors consistent with prospective compression, and alternative library learning accounts. Using six computational models spanning online library learning strategies, we show that human abstraction behavior reflects sensitivity to latent, non-stationary structure in the task-generating process. This behavior is consistent with prospective compression, and cannot be captured by existing retrospective compression-based algorithms, or inductive biases modeled by LLM-based program synthesis.

Vision-Language Models (VLMs) have made great strides in everyday visual tasks, such as captioning a natural image, or answering commonsense questions about such images. But humans possess the puzzling ability to deploy their visual reasoning abilities in radically new situations, a skill rigorously tested by the classic set of visual reasoning challenges known as the Bongard problems. We present a neurosymbolic approach to solving these problems: given a hypothesized solution rule for a Bongard problem, we leverage LLMs to generate parameterized programmatic representations for the rule and perform parameter fitting using Bayesian optimization. We evaluate our method on classifying Bongard problem images given the ground truth rule, as well as on solving the problems from scratch.

Large Language Models (LLMs) have been widely adopted as task planners for AI agents in sequential decision-making problems, leveraging their extensive world knowledge. However, the gap between their general knowledge and environment-specific requirements often leads to inaccurate plans. To address this, existing approaches rely on frequent LLM queries to iteratively refine plans based on immediate environmental feedback, which incurs substantial query costs. However, this refinement is typically guided by short-term environmental feedback, limiting LLMs from developing plans aligned with long-term rewards. We propose **Co**de Driven **P**lanning w**i**th Domain-Adaptive Sele**C**tor (CoPiC). Instead of relying on frequent queries, CoPiC employs LLMs to generate a diverse set of high-level planning programs, which iteratively produce and refine candidate plans. A trained domain-adaptive selector then evaluates these candidates and selects the one most aligned with long-term rewards for execution. Using high-level planning programs as planner and domain-adaptive selector as estimator, CoPiC improves planning while significantly reducing query costs. Results in ALFWorld, NetHack, and StarCraft II Unit Building show that CoPiC outperforms advanced LLM-based baselines, achieving an average (1) 19.14\% improvement in success rate and (2) 79.39\% reduction in token costs.

LLM prompting is widely used for naturally stated tasks, yet it is unreliable it may succeed on a few test cases but fail at deployment time. We study performance prediction: given a program, either symbolic (e.g. Python) or a prompt executed on an LLM, and a few in-domain examples, predict its performance on unseen tasks from the same domain. We use a simple coin-flip model, treating each pass/fail program execution as a Bernoulli random variable, whose success probability is the programs unknown performance. In this model, performance depends entirely on: 1) the observed execution outcomes on test cases, and 2) a prior over performances. We compile empirical performance priors from a corpus of diverse programs and tasks, and find that performance for symbolic programs (e.g., Python) are all or nothing, while prompt programs have a diffuse prior with many nearly-correct programs. This difference explains why a few passing tests can certify symbolic programs but not prompt programs. Building on this insight, we develop RAP (Retrieved Approximate Prior), which retrieves similar tasks and prompt programs from an existing corpus to construct a proxy prior, which is then used to predict performance. We show RAP achieves solid performances.

Recent advancements in open-source code large language models (LLMs) have been driven by fine-tuning on the data generated from powerful closed-source LLMs, which are expensive to obtain. This paper explores whether it is possible to use a fine-tuned open-source model to generate additional data to augment its instruction-tuning dataset. We make two observations: (1) A code snippet can serve as the response to different instructions. (2) Instruction-tuned code LLMs perform better at translating code into instructions than the reverse. Based on these observations, we propose Inverse-Instruct, a data augmentation technique that uses a fine-tuned LLM to generate additional instructions of code responses from its own training dataset. The additional instruction-response pairs are added to the original dataset, and a stronger code LLM can be obtained by fine-tuning on the augmented dataset. We empirically validate Inverse-Instruct on a range of open-source code models (e.g. CodeLlama-Python and DeepSeek-Coder) and benchmarks (e.g., HumanEval(+), MBPP(+), DS-1000 and MultiPL-E), showing it consistently improves the base models.

In collaborative creation tasks, people steer artifacts towards specific goals by _refining_ them with _multimodal_ communication over multiple rounds of interaction. In contrast, generative AI excels at creating artifacts in a single turn but can struggle to make precise refinements that match our design intent. To close this gap, we present mrCAD, a dataset of multi-turn interactions in which pairs of humans iteratively created and refined computer-aided designs (CADs). In each game, a _Designer sent instructions to a _Maker_, explaining how to create and subsequently refine a CAD to match a target design that only the _Designer_ could see. mrCAD consists of 6,082 communication games, 15,163 instruction-execution rounds, played between 1,092 pairs of human players. Crucially, _Designers_ had access to two communication modalities – text and drawing. Analysis finds that players relied more on text in refinement than in initial generation instructions, and used different linguistic elements for refinement than for generation. We also find that state-of-the-art VLMs are better at following generation instructions than refinement instructions. These results lay the foundation for modeling multi-turn, multimodal communication not captured in prior datasets.

A key feature of human collaboration is the ability to iteratively refine the concepts we have communicated. In contrast, while generative AI excels at the generation of content, it often struggles to make specific language-guided modifications of its prior outputs. To bridge the gap between how humans and machines perform edits, we present mrCAD, a dataset of multimodal instructions in a communication game. In each game, players created computer aided designs (CADs) and refined them over several rounds to match specific target designs. Only one player, the Designer, could see the target, and they must instruct the other player, the Maker, using text, drawing, or a combination of modalities. mrCAD consists of 6,082 communication games, 15,163 instruction-execution rounds, played between 1,092 pairs of human players. We analyze the dataset and find that generation and refinement instructions differ in their composition of drawing and text. Using the mrCAD task as a benchmark, we find that state-of-the-art VLMs are better at following generation instructions than refinement instructions. These results lay a foundation for analyzing and modeling a multimodal language of refinement that is not represented in previous datasets.

Enhancing LLMs with the ability to actively search external knowledge is crucial for complex and real-world tasks. Current approaches either rely on prompting to elicit the model's innate agent capabilities, or suffer from performance ceilings and collapse when applying RL to complex interactive tasks, leaving their true agentic potential untapped. To address this, we introduce Dynamic-filter Sequence-level Policy Optimization (DSPO), an improved RL algorithm designed for robust agent training through sequence-level optimization and dynamic sample filtering. We train our model purely through RL to interleave multi-turn search and reasoning, obviating the need for supervised demonstration data. Across multiple QA benchmarks, our DSPO-trained 7B model improves over a comparable previous work by 34.1%, and even outperforms the 14B model from previous work in complex multihop QA such as HotpotQA by nearly 9% relative, maintaining exceptional training stability.

When learning an input-output mapping from very few examples, is it better to first infer a latent function that explains the examples, or is it better to directly predict new test outputs, e.g. using a neural network? We study this question on ARC by training neural models for \emph{induction} (inferring latent functions) and \emph{transduction} (directly predicting the test output for a given test input). We train on synthetically generated variations of Python programs that solve ARC training tasks. We find inductive and transductive models solve different kinds of test problems, despite having the same training problems and sharing the same neural architecture: Inductive program synthesis excels at precise computations, and at composing multiple concepts, while transduction succeeds on fuzzier perceptual concepts. Ensembling them approaches human-level performance on ARC.

Editing 2D icon images can require significant manual effort from designers. It involves manipulating multiple geometries while maintaining the logical or physical coherence of the objects depicted in the image. Previous language driven image editing methods can change the texture and geometry of objects in the image but fail at producing spatial variations, i.e. modifying spatial relations between objects while maintaining their identities. We present a language driven editing method that can produce spatial variations of icon images. Our method takes in an icon image along with a user's editing request text prompt and outputs an edited icon image reflecting the user's editing request. Our method is designed based on two key observations: (1) A user's editing requests can be translated by a large language model (LLM), with help from a domain specific language (DSL) library, into to a set of geometrical constraints defining the relationships between segments in an icon image. (2) Optimizing the affine transformations of the segments with respect to these geometrical constraints can produce icon images that fulfill the editing request and preserve overall physical and logical coherence. Quantitative and qualitative results show that our system outperforms multiple baselines, enabling natural editing of icon images.

Realizing a designer's intent in software currently requires tedious manipulation of geometric primitives, such as points and curves. By contrast, designers routinely communicate more abstract design goals to one another using an efficient combination of natural language and drawings. What would it take to develop artificial systems that understand how humans naturally convey design intent, and thereby enable more seamless interactions between humans and machines throughout the design process? First, it is vital to establish benchmarks that showcase the full range of strategies that humans use to successfully communicate about design intent. Here we take initial steps towards that goal by conducting an online study in which pairs of human participants - a "Designer" and "Maker" - collaborated over multiple turns to recreate target designs. In each turn, Designers sent messages containing language, drawings, or both to the Maker, describing how to modify an existing design toward the target. We found a preference for communicating using drawings in early turns and observed several multimodal strategies for conveying design intent. By comparing how human Makers and GPT-4V carried out instructions, we identify a gap in human and machine understanding of multimodal instructions and suggest a path for bridging this gap.

Inductive reasoning is a core problem-solving capacity: humans can identify underlying principles from a few examples, which can then be robustly generalized to novel scenarios. Recent work has evaluated large language models (LLMs) on inductive reasoning tasks by directly prompting them yielding "in context learning." This can work well for straightforward inductive tasks, but performs very poorly on more complex tasks such as the Abstraction and Reasoning Corpus (ARC). In this work, we propose to improve the inductive reasoning ability of LLMs by generating explicit hypotheses at multiple levels of abstraction: we prompt the LLM to propose multiple abstract hypotheses about the problem, in natural language, then implement the natural language hypotheses as concrete Python programs. These programs can be directly verified by running on the observed examples and generalized to novel inputs. To reduce the hypothesis search space, we explore steps to filter the set of hypotheses to be implemented as programs: we either ask the LLM to summarize them into a smaller set of hypotheses, or ask human annotators to select a subset. We verify our pipeline's effectiveness on the ARC visual inductive reasoning benchmark, its variant 1D-ARC, and string transformation dataset SyGuS. On a random 40-problem subset of ARC, our automated pipeline using LLM summaries achieves 27.5% accuracy, significantly outperforming the direct prompting baseline (accuracy of 12.5%). With the minimal human input of selecting from LLM-generated candidates, the performance is boosted to 37.5%. Our ablation studies show that abstract hypothesis generation and concrete program representations are both beneficial for LLMs to perform inductive reasoning tasks.

Programming-by-example is the task of synthesizing a program that is consistent with a set of user-provided input-output examples. As examples are often an under-specification of one's intent, a good synthesizer must choose the intended program from the many that are consistent with the given set of examples. Prior work frames program synthesis as a cooperative game between a listener (that synthesizes programs) and a speaker (a user choosing examples), and shows that models of computational pragmatic inference are effective in choosing the user intended programs. However, these models require counterfactual reasoning over a large set of programs and examples, which is infeasible in realistic program spaces. In this paper, we propose PraX, a novel way to amortize this search with neural networks. We sample pairs of programs and examples via self-play between listener and speaker models, and use pragmatic inference to choose informative training examples from this sample. We then use the informative dataset to train models to improve the synthesizer's ability to disambiguate user-provided examples _without human supervision_. We validate PraX on the challenging task of synthesizing regular expressions from example strings, and find that our method (1) outperforms models trained without choosing pragmatic examples by 23% (a 51% relative increase) (2) matches the performance of supervised learning on a dataset of pragmatic examples provided by humans, despite using no human data in training.

The usage of Rational Speech Acts (RSA) framework has been successful in building \emph{pragmatic} program synthesizers that return programs which, in addition to being logically consistent with user-generated examples, account for the fact that a user chooses their examples informatively. We present a general method of amortizing the slow, exact RSA synthesizer. Our method first query the exact RSA synthesizer to compile a communication dataset. The dataset contains a number of example-dependent rankings of subsets of programs. It then distills a \textit{single} global ranking of all programs as an approximation to every ranking in the dataset. This global ranking is then used at inference time to rank multiple logically consistent candidate programs generated from a fast, non-pragmatic synthesizer. Experiments on two program synthesis domains using our ranking method resulted in orders of magnitudes of speed ups compared to the exact RSA synthesizer, while being more accurate than a non-pragmatic synthesizer when communicating with humans. Finally, we prove that in the special case of synthesis from a single example, this approximation is exact.

Parametric Computer-Aided Design (CAD) is central to contemporary mechanical design. However, it encounters challenges in achieving precise parametric sketch modeling and lacks practical evaluation metrics suitable for mechanical design. We harness the capabilities of pre-trained foundation models, renowned for their successes in natural language processing and computer vision, to develop generative models specifically for CAD. These models are adept at understanding complex geometries and design reasoning, a crucial advancement in CAD technology. In this paper, we propose CadVLM, an end-to-end vision language model for CAD generation. Our approach involves adapting pre-trained foundation models to manipulate engineering sketches effectively, integrating both sketch primitive sequences and sketch images. Extensive experiments demonstrate superior performance on multiple CAD sketch generation tasks such as CAD autocompletion, CAD autoconstraint, and image conditional generation. To our knowledge, this is the first instance of a multimodal Large Language Model (LLM) being successfully applied to parametric CAD generation, representing a pioneering step in the field of computer-aided mechanical design.

A typical way in which a machine acquires knowledge from humans is by programming. Compared to learning from demonstrations or experiences, programmatic learning allows the machine to acquire a novel skill as soon as the program is written, and, by building a library of programs, a machine can quickly learn how to perform complex tasks. However, as programs often take their execution contexts for granted, they are brittle when the contexts change, making it difficult to adapt complex programs to new contexts. We present natural programming, a library learning system that combines programmatic learning with a hierarchical planner. Natural programming maintains a library of decompositions, consisting of a goal, a linguistic description of how this goal decompose into sub-goals, and a concrete instance of its decomposition into sub-goals. A user teaches the system via curriculum building, by identifying a challenging yet not impossible goal along with linguistic hints on how this goal may be decomposed into sub-goals. The system solves for the goal via hierarchical planning, using the linguistic hints to guide its probability distribution in proposing the right plans. The system learns from this interaction by adding newly found decompositions in the successful search into its library. Simulated studies and a human experiment (n=360) on a controlled environment demonstrate that natural programming can robustly compose programs learned from different users and contexts, adapting faster and solving more complex tasks when compared to programmatic baselines.

Programming-by-example (PBE) systems aim to alleviate the burden of programming. However, user-specified examples are often ambiguous, leaving multiple programs to satisfy the specification. Consequently, in most prior work, users have had to provide additional examples, particularly negative ones, to further constrain the search over compatible programs. Recent work resolves additional ambiguity by modeling program synthesis tasks as pragmatic communication, showing promising results on a graphics domain using a rudimentary user-study. We adapt pragmatic reasoning to a sub-domain of regular expressions and rigorously study its usability as a means of communication both with and without the ability to provide negative examples. Our user study (N=30) demonstrates that, with a pragmatic synthesizer, end-users can more successfully communicate a target regex using positive examples alone (95%) compared to using a non-pragmatic synthesizer (51%). Further, users can communicate more efficiently (57% fewer examples) with a pragmatic synthesizer compared to a non-pragmatic one.

Combining gradient-based trajectory optimization with differentiable physics simulation is an efficient technique for solving soft-body manipulation problems. Using a well-crafted optimization objective, the solver can quickly converge onto a valid trajectory. However, writing the appropriate objective functions requires expert knowledge, making it difficult to collect a large set of naturalistic problems from non-expert users. We introduce DiffVL, a method that enables non-expert users to communicate soft-body manipulation tasks -- a combination of vision and natural language, given in multiple stages -- that can be readily leveraged by a differential physics solver. We have developed GUI tools that enable non-expert users to specify 100 tasks inspired by real-life soft-body manipulations from online videos, which we'll make public. We leverage large language models to translate task descriptions into machine-interpretable optimization objectives. The optimization objectives can help differentiable physics solvers to solve these long-horizon multistage tasks that are challenging for previous baselines.

Though LLMs are capable of generating plausible programs, it’s challenging to interact with the LLMs further to revise the program, especially if the user’s specific requirements are different from the initial proposal. In this paper, we introduce ANPL, an interactive programming system that ensures users can always refine the generated code towards their specific programmatic intents via structured decompositions. Borrowing the paradigm of sketching from program synthesis, an ANPL program consists of a set of input-outputs that it must satisfy, a “sketch” — control/data flow expressed in precise code (e.g. Python), and “holes” — sub-modules to be implemented by the LLM specified with natural language. The user revises an ANPL program by either modifying the sketch, changing the language used to describe the holes, or providing additional input-outputs to a particular hole, turning it into a sub-ANPL program that can be solved recursively. This workflow allows the users to offload programming burdens to the LLM as much as possible while retaining the ability to pinpoint and resolve bugs locally, without exposing the rest of the program to the LLM. We deploy ANPL on the Abstraction and Reasoning Corpus (ARC), a set of unique tasks that are challenging for state-of-the-art AI systems, showing it outperforms baseline programming systems that (a) without the ability to decompose tasks interactively and (b) without the guarantee that the modules can be correctly composed together. Additional evaluations on APPS, HumanEval, and real-world programming tasks have validated that the ANPL framework is applicable to multiple programming domains. We release the ANPL solutions to the ARC tasks as a dataset, providing insights into how humans decompose novel tasks programmatically.

The Abstraction and Reasoning Corpus (ARC) is a set of procedural tasks that tests an agent's ability to flexibly solve novel problems. While most ARC tasks are easy for humans, they are challenging for state-of-the-art AI. What makes building intelligent systems that can generalize to novel situations such as ARC difficult? We posit that the answer might be found by studying the difference of \emph{language}: While humans readily generate and interpret instructions in a general language, computer systems are shackled to a narrow domain-specific language that they can precisely execute. We present LARC, the \textit{Language-complete ARC}: a collection of natural language descriptions by a group of human participants who instruct each other on how to solve ARC tasks using language alone, which contains successful instructions for 88\% of the ARC tasks. We analyze the collected instructions as `natural programs', finding that while they resemble computer programs, they are distinct in two ways: First, they contain a wide range of primitives; Second, they frequently leverage communicative strategies beyond directly executable codes. We demonstrate that these two distinctions prevent current program synthesis techniques from leveraging LARC to its full potential, and give concrete suggestions on how to build the next-generation program synthesizers.