Is Programming by Example Solved by LLMs?

Thank you for the thoughtful review. Please see below for a new experimental results that you suggested we run, together with our responses to your questions.

In the experiments, there are no LLM competitors in the graphics domain. Any reasons?

Thank you for your suggestion! We added the GPT-4o and GPT-4o-mini multimodal model results with image input. We summarize the results on the graphics domain as below:

(We updated our LOGO results because we found a small code issue post-submission; fixing that issue significantly improved our system, hence why our system's numbers above are better from the original submission, but the qualitative conclusions are the same.)

The examples used in the experiments are relatively weak and do not closely resemble real-world programming tasks.

We disagree for the following reasons:

1. Text editing PBE is used millions of times every week [1]

2. PBE is not about e.g. repo-level edits, but is instead about creating individual subroutines, including for users that can't even program. Accordingly the datasets we use cover real-world situations where an individual subroutine is desired. For example, the Shi et al. List dataset comprises 100 programming tasks manually designed to be interesting and useful in practice, while PROSE/SyGuS test common spreadsheet operations.

3. Our benchmarks are typical ones for PBE on neural/symbolic systems, allowing comparisons of LLMs against the recent neurosymbolic literature, done as follows:

[1] https://blog.sigplan.org/2021/09/14/the-story-of-the-flash-fill-feature-in-excel/

Why are only FlashFill and LambdaBeam compared in the experiments of Figure 6?

For lists, LambdaBeam is the primary comparison because it was designed specifically to solve the list benchmark Fig 6 evaluates on (and it does well on that benchmark).

For strings, FlashFill is the primary comparison because we are evaluating on holdout test inputs, and FlashFill++ does not report numbers for holdout tests (and FlashFill++ is not publicly available so we can't run it ourselves).

The adaptation method used to improve out-of-distribution performance exposes the model to the test set content beforehand. Especially in string tasks, directly selecting the adaptation seed program from all test cases may be unfair.

Motivated by your comment we ran the OOD-adapted model on a random sample of never-before-seen PROSE problems (unseen during adaptation). We see that the domain gap is approximately halved:

If the adaptation's seed program is not provided, even after fine-tuning, the out-of-distribution generalization ability of LLMs still appear to be quite weak.

Yes! Without (unlabeled) adaptation data, out-of-distribution generalization is quite weak. We hope to paint a nuanced picture of LLM abilities rather than claim LLMs are universally better along every dimension.

Would the key factors that lead to the success or failure of LLMs differ across problems in three different domains?

Primarily if the problems are in-distribution, which is why we focus on OOD adaptation methods.

Thank you for your input and please let us know if you have any further questions.

Thank you for the thoughtful review. We really believe that our responses and new experiment can address your concerns, and hope that you will agree. Please see below.

empirical results was not surprising or unusual

Papers in the past year find negative results for LLMs on PBE [1-3], and none try unusual PBE domains like our visual graphics programs. For example, our system beats the neurosymbolic LambdaBeam [3], and in LambdaBeam, they also compare to a strong LLM baseline - a Python fine-tuned LLM internal to Google - which was found to not do well on PBE. Our system also beats systems like DreamCoder [4] on unusual domains such as LOGO, where DreamCoder-like approaches are thought to excel. Our results should surprise the cited authors, and are unusual in that sense.

[1] Shi et al. ‘24 ICLR [2] Rule et al. 2024 Nature Comms. [3] Shi et al. ‘23 NeurIPS [4] Ellis et al. ‘21 PLDI

does not introduce any new approach or technique

A core part of the paper is a wake-sleep inspired algorithm for OOD generalization. Would you mind pointing us to a citation that we can refer to which previously introduced our specific approach/technique for adaptation?

The OOD claim is a bit weak... "assuming we have access to problems drawn from the testing distribution" (without their labels, but these labels can be sampled and validated).

Deployed PBE systems are presented with a stream of "testing problems" generated by end users. In the wild, the requisite data is available for our adaptation technique.

What does "solve" mean?

We’ll revise to make explicit our different definitions of solve:

1. Beating SOTA on mainstream benchmarks, including those used for deployed real world PBE systems [we solve in that sense]
2. Beating SOTA on unusual benchmarks very different from pretraining data [we solve in that sense: LOGO]
3. Achieving 100% success rate [we don’t solve in that sense, no free lunch]
4. Being practical for deployment [we don’t solve in that sense]
5. Generalizing out of distribution [partly: see our response above to "The OOD claim is a bit weak"]

“absolute performance in LOGO remains poor" - 16% accuracy is not "poor" when you do not compare it to anything

We compare against 3 baselines (Fig 3)

Can the authors evaluate the baseline where the "program" is the LLM itself?

Thanks for the suggestion. Please see below for the result of your proposed baseline, which does well on strings but not on lists.

• Strings

• Lists

Another trivial claim: in Section 4.2, the authors find that "posterior description length is more predictive than program size and prior description length"... basically says: the perplexity of the desired output sequence is predictive of its accuracy on downstream tasks

Thank you for catching an error in the writing: By posterior we meant the marginal probability of solving the task under $q$ (marginalizing over sampled programs we found that pass), not evaluating perplexity of a single gold-truth target sequence. While it’s unsurprising this marginal is at least as predictive as the prior, it is noteworthy that it is more predictive than the prior, showing the LLM does not engage in blind guess-and-check, and did not merely learn to sample from the self-instruct distribution.

the reason that LLMs are better than classic symbolic methods is not the use Turing-complete languages... The reason is that LLMs were trained on trillions of Python tokens

LLMs benefit from both massive data and expressive Turing-complete programming languages. As a thought experiment, consider an LLM trained on trillions of programs in the FlashFill++ DSL: It would still be utterly unable to solve the problems in Fig 4.

In L96 the authors write: "we use samples from a generative model to train an inference network, but we do not further train the generative model itself" - what does this exactly mean?

We sample from the generative model $\mathcal{G}$, defined by prompting an LLM with seed problems (see L86). The inference network $q$ is our fine-tuned model (see L91). The prior $\mathcal{G}$ is a function of the seeds, so by holding the seeds fixed, we don’t update/train the generative model further, deferring such updates to Eq 5 (Adaptation).

What exactly does the "Search Budget (Num Samples)" mean in the experimental section?... [Do you] sample different outputs, and consider the output as correct if any of these outputs is correct?

Thanks for inviting this clarification. We model PBE in-the-wild where we commit to a single program and must run it on new unseen test inputs. This means we sample $k$ programs (the search budget), filter by the training input-outputs, pick a program randomly if more than one passes that filter, and finally report success only if that program correctly predicts all test input-outputs (following Eq 1). We will revise to clarify.

What temperature was used… Since evaluation depends on sampling of up to 200 outputs, the temperature might have a drastic effect on the success of each model

The first sentence of the appendix gives the temperature ($T=1$). We used this somewhat high temperature (by the standards of code generation) because we wanted more diversity in the outputs, and did not tune this parameter because of the high cost of our experiments.

Please let us know if you have further questions.

Thank you for your response.

Papers in the past year find negative results for LLMs on PBE [1-3] and in LambdaBeam, they also compare to a strong LLM baseline - a Python fine-tuned LLM internal to Google - which was found to not do well on PBE Our system also beats systems like DreamCoder [4]

• LambdaBeam compared to PaLM 62B - PaLM is also ~2 years old, and as far as publicly known, pre-RLHF. I am not surprised that the most recent GPT-4 performs significantly better.
• DreamCoder (2020), while being algorithmically clever, was also in the pre-LLM era.
• I'm not sure what is the "Shi et al. ‘24 ICLR" - can you please give a link? I don't think it is cited in your paper.
• I also cannot find a public link to "[2] Rule et al. 2024 Nature Comm" (although it is cited, I can't find a PDF).

A core part of the paper is a wake-sleep inspired algorithm for OOD generalization. Would you mind pointing us to a citation that we can refer to which previously introduced our specific approach/technique for adaptation?

As I understand from the paper, the wake-sleep inspired algorithm is explained under standard "finetuning", and "adaptation" starts only later (in page 4). Is the wake-sleep inspired algorithm for finetuning or adaptation? Further, regarding the novelty of the wake-sleep algorithm, as mentioned in the paper:

This method is closely related to self-instruct [29] and wake-sleep [30]. Like self-instruct, we use prompting to bootstrap a large dataset from a small manually-constructed one. Our method differs by using the LLM to generate a hidden latent variable (the program) while a different generative process produces an observed variable (the program outputs).

So, what is the difference between this paper and [29,30]? That a different model generates the program outputs, instead of being the same model?

Deployed PBE systems are presented with a stream of "testing problems" generated by end users. In the wild, the requisite data is available for our adaptation technique. It's a similar setting for a variety of machine-learning-based systems (e.g., Google Translate, Siri, etc.). If a system depends on "a stream of testing problems generated by end users", how does it respond to the first end-user queries? The authors's argument is almost like saying: "in a real system, we will wait for a few (hundreds? thousands?) queries to be sent, and only then we will be able to respond".

In contrast, a machine learning system that "truly" generalizes OOD, should ideally generalize starting from the first OOD example.

I know that it's OOD generalization starting from the first OOD example is not trivial and is still one of the open problems in machine learning - I just said that the OOD argument is a bit weak.

Beating SOTA on mainstream benchmarks, including those used for deployed real world PBE systems [we solve in that sense]

I would still argue that beating SOTA does not mean that the problem is "solved".

“absolute performance in LOGO remains poor" - 16% accuracy is not "poor" when you do not compare it to anything

We compare against 3 baselines (Fig 3)

I don't understand this response - LOGO is "graphics", right? Which means Fig 3(c)? Isn't "Ours" better than the baselines there? So why is performance considered "poor"?

Please see below for the result of your proposed baseline, which does well on strings but not on lists. Thank you for these additional results.

LLMs benefit from both massive data and expressive Turing-complete programming languages. As a thought experiment, consider an LLM trained on trillions of programs in the FlashFill++ DSL: It would still be utterly unable to solve the problems in Fig 4.

But would it change the downstream results if we improved any DSL to be Turing complete?

. We used this somewhat high temperature (by the standards of code generation) because we wanted more diversity in the outputs, and did not tune this parameter because of the high cost of our experiments.

Tuning the best temperature for each model separately can significantly affect the results and the order between the models. This tuning is only needed at test time.

We thank Reviewer e1ch for the thoughtful review. Please see the global response PDF for the requested LOGO graphics details, and below for other new experiments and responses to your specific questions.

CoT and other simple prompting methods are not evaluated

Thanks for the suggestion. We evaluated chain-of-thought and summarized the results below.

• String Domain

• List Domain

We'll update the manuscript to include these results.

the ASCII grid [for LOGO], etc. With this design, it does not make sense for a non-fine-tuned LLM to solve the task. But technically you could still fine-tune GPT-3.5 with these inputs, but I guess it is okay to not include this experiment.

Motivated by your observation we ran a new experiment using the multimodal GPT-4o and GPT-4o-mini with a few-shot prompt as a baseline for LOGO. This baseline was prompted with example programs and images and then given a new test image to write a program for. Please see below:

The LOGO visual examples are converted to an ASCII grid of characters (Fig. 8b). This might not be the most intuitive representation. Details about the transformation is not shown, such as how each number (0-9) is derived, the resolution of the ASCII grid, etc.

Please see the attached PDF, which shows an example of the ASCII transformation with a detailed conversion process in the caption. Interestingly, because the transformation down-samples the image, it is able to somewhat generalize to hand drawings, which we also show in the attached PDF, and would include in a revision.

Outcome is relatively predictable

Papers in the past year find negative results for LLMs on PBE [1-3], and none try unusual PBE domains like our visual graphics programs. For example, our system beats the neurosymbolic LambdaBeam [3], and in LambdaBeam, they also compare to a strong LLM baseline - a Python fine-tuned LLM internal to Google - finding that the LLM is a poor PBE solver, counter to our findings. Our system also beats systems like DreamCoder [4] on unusual domains such as LOGO, where DreamCoder-like approaches are thought to excel. Our results are not predictable given the state of the recent literature.

[1] Shi et al. ‘24 ICLR [2] Rule et al. ‘24 Nature Comms. [3] Shi et al. ‘23 NeurIPS [4] Ellis et al. ‘21 PLDI

Typos and grammar mistakes

Fixed! Thank you for pointing them out.

I see in the prompt the authors wrote “You are a CS professor”. As far as I know this might not be the perfect prompt for code generation (this is just a joke).

We will consider adding to the prompt “You are reviewer #2, please improve the code like how you would improve a paper” (this is just a joke).

Thanks again for the review and please let us know if we can answer any further questions.

Thank you for the detailed review, and for your support. Please see the global review for a PDF with new results (including a fun new LOGO experiment). We address your specific questions below.

Regarding Contamination

We avoided contamination as follows:

1. String dataset: The datasets contain only input/output examples, and thus the program could not be in pretraining data.
2. List dataset: The dataset from Rule et al. does not include program solutions, and furthermore, the dataset is in BigBench, which is conventionally excluded from LLM pretraining data.
3. LOGO dataset: The python program LOGO dataset (from Regal) was released within 1 week of the beginning of training of deepseek (the model that we fine tune), so is almost certainly not in pretraining. Just in case, we further tried prompting the model to confirm that it cannot complete a partial ground truth python LOGO program.

We also tried running our system on new problems that we created by hand, illustrated in Figure 4, and also illustrated in the attached main-response PDF, where we ran the LOGO synthesizer on a hand drawing we made. The system was surprisingly able to handle all of these new problems that could not possibly have been in the pretraining data.

How much does a turing-complete language help in solving PBE, excluding the fact that LLMs have seen lots of python code? Is the expressiveness of a turing-complete language itself helpful?

We believe the expressiveness itself is helpful due to the fact that a handcrafted restricted programming language may not be able to capture the space of all user-desired programs, even within a single domain. For example, in Fig 4 (top), we can see that a simple example—numbering the lines of a paragraph—can easily be solved by our model but cannot be solved by FlashFill++. We believe this is a general problem with handcrafted domain-specific programming languages: Although they make the search space smaller and therefore more tractable, they inevitably exclude important computations.

In other words, LLMs benefit from both massive data and expressive Turing-complete programming languages. As a thought experiment, consider an LLM trained on trillions of programs in the FlashFill++ DSL: It would still be utterly unable to solve the problems in Fig 4.

How far can the adaption go? Right now the adaption discussed is still within the same category of problems (such as lists), I imagine a more general PBE system might be able to adapt to problems that are more different

Adaptation hinges on solving at least some problems in the OOD target, and we have observed that after fine-tuning for domain A, the model can still solve some problems in domain B. We believe this is because LoRA finetuning does not cause too much catastrophic forgetting about domain B.

We’ll update to include experiments of cross domain adaptation (lists task adapt to string task, string task adapt to list task), which could be very interesting as progress toward truly general purpose program synthesis. Thanks for the suggestion!