Searching Latent Program Spaces (2411.08706v1)

Abstract: Program synthesis methods aim to automatically generate programs restricted to a language that can explain a given specification of input-output pairs. While purely symbolic approaches suffer from a combinatorial search space, recent methods leverage neural networks to learn distributions over program structures to narrow this search space significantly, enabling more efficient search. However, for challenging problems, it remains difficult to train models to perform program synthesis in one shot, making test-time search essential. Most neural methods lack structured search mechanisms during inference, relying instead on stochastic sampling or gradient updates, which can be inefficient. In this work, we propose the Latent Program Network (LPN), a general algorithm for program induction that learns a distribution over latent programs in a continuous space, enabling efficient search and test-time adaptation. We explore how to train these networks to optimize for test-time computation and demonstrate the use of gradient-based search both during training and at test time. We evaluate LPN on ARC-AGI, a program synthesis benchmark that evaluates performance by generalizing programs to new inputs rather than explaining the underlying specification. We show that LPN can generalize beyond its training distribution and adapt to unseen tasks by utilizing test-time computation, outperforming algorithms without test-time adaptation mechanisms.

Searching Latent Program Spaces: An Expert Overview

The paper, "Searching Latent Program Spaces," presents an innovative approach to program synthesis by leveraging latent representation techniques for effective search and adaptation of programs during inference. Traditionally, program synthesis aims to generate programs that meet specific criteria, often based on input-output examples. While symbolic methods have been successful in constrained environments, they falter under the expansive search spaces characterizing modern computational problems like those presented by the Abstraction and Reasoning Corpus (ARC).

Core Proposition

The authors introduce the Latent Program Network (LPN), a framework designed to explore latent spaces of program representations, allowing efficient search and adaptation at test-time without parameter updates. This approach diverges from conventional methodologies by integrating test-time adaptability into the neural architecture itself. The core elements of LPN include:

1. Encoder-Decoder Architecture: The encoder maps input-output pairs to a continuous latent space, and the decoder executes the program on specific inputs. The decoder generates outputs directly, circumventing the constraints of domain-specific languages (DSLs).
2. Latent Optimization: Test-time adaptation is conducted using gradient ascent in the continuous latent space. By structuring latent spaces amenable to gradient-based search, the LPN effectively refines its programmatic representations to maximize log-likelihoods of observed data.
3. Training Strategy: The network is trained from scratch, focusing on crafting a structured latent space that supports test-time search functionalities. This is achieved without leveraging large-scale pre-trained LLMs or synthetic datasets, conferring scalability across domains.

Methodological Insights

LPN's strength lies in its elegant integration of learning and searching within a latent space. The gradient ascent mechanism facilitates efficiently navigating the high-dimensional program spaces, substantially improving test-time performance. Training incorporates meta-learning aspects by conditioning the network on gradient updates, ensuring that the latent space learns to facilitate effective search processes.

The research showcases that constructive generalization — the ability to extend learned concepts to novel, potentially non-distributive tasks — is enhanced when models are capable of efficient test-time search. Empirical evaluations on benchmarks like ARC-AGI highlight LPN's capacity to maintain a balance between learning efficiency and generalization prowess.

Empirical Evaluation

The LPN was systematically evaluated against the ARC-AGI benchmark, a challenging program synthesis problem designed to test out-of-distribution generalization and reasoning capability over abstract tasks. The model displayed competitive performance, generalizing beyond the constraints of its training distribution. Notably, the model's performance improved significantly with increased test-time computation allotted for latent space navigation.

Implications and Future Directions

The paper offers significant theoretical and pragmatic implications for neural program synthesis:

• Latent Search Efficacy: The demonstrated efficiencies in latent space optimization mark a pivotal shift towards structured search in neural program synthesis.
• Rejection of Overfitting Risks: By avoiding reliance on synthetic data generation, LPN highlights a trajectory that embraces adaptive methodologies over purely data-intensive strategies.
• Scaling Potential: Although the paper illustrates initial successes, the authors acknowledge the need for further exploration with more extensive computational resources to fully extrapolate the potential of LPN.

The integration of test-time computation into learning models exemplifies a paradigm shift, showcasing the move towards architectures that not only learn but adapt dynamically. Nevertheless, challenges such as the exploration of local optima during search warrant additional investigation, potentially through hybrid optimization approaches.

In conclusion, "Searching Latent Program Spaces" underscores the value of latent spaces in enhancing the adaptability and efficiency of program synthesis models. It advocates for a structured intersection of learning and search, setting a promising trajectory for future work in efficient program induction and synthesis.