End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking (2202.05826v3)

Abstract: Machine learning systems perform well on pattern matching tasks, but their ability to perform algorithmic or logical reasoning is not well understood. One important reasoning capability is algorithmic extrapolation, in which models trained only on small/simple reasoning problems can synthesize complex strategies for large/complex problems at test time. Algorithmic extrapolation can be achieved through recurrent systems, which can be iterated many times to solve difficult reasoning problems. We observe that this approach fails to scale to highly complex problems because behavior degenerates when many iterations are applied -- an issue we refer to as "overthinking." We propose a recall architecture that keeps an explicit copy of the problem instance in memory so that it cannot be forgotten. We also employ a progressive training routine that prevents the model from learning behaviors that are specific to iteration number and instead pushes it to learn behaviors that can be repeated indefinitely. These innovations prevent the overthinking problem, and enable recurrent systems to solve extremely hard extrapolation tasks.

End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking

The paper addresses a pivotal challenge in machine learning: the application of neural networks to complex reasoning and algorithmic problems, particularly in terms of algorithmic extrapolation. Extrapolation involves extending the capability of models trained on simple instances to solve substantially more complex problems. While successful in many areas, neural networks struggle with the logical reasoning that this problem entails.

Problem Statement

The research identifies a limitation in existing recurrent systems: the phenomenon of "overthinking." As models perform extended iterations beyond their training limits, their output degenerates, jeopardizing the effectiveness of the reasoning task. This paper suggests combating this through the innovation of a recall architecture and a novel training procedure.

Methodology

The recall architecture is designed to retain an explicit memory of the problem instance, preventing it from being lost or obscured in the network's features, which might become noisy or distorted over many iterations. Additionally, a progressive training regimen is introduced to ensure that the network learns iteration-agnostic procedures. In this approach, the setup encourages models to perform incremental improvements and continue enhancing feature representation with each pass, effectively avoiding iteration-specific behavior learning.

Key Contributions

1. Recurrent Architecture Enhancement: By concatenating problem inputs directly to selected layers within the recurrent unit, the architecture ensures that essential inputs remain intact throughout extended computations.
2. Progressive Training Routine: This incrementally discourages iteration-dependent learning, enabling networks to refine solutions consistently across multiple iterations.
3. Analysis and Mitigation of Overthinking: The paper examines the detrimental effects of overthinking and shows that the proposed architecture and training modifications substantially mitigate these issues.

Experiments and Results

Tests were conducted across benchmark tasks including prefix sums, maze solving, and chess puzzles. The enhanced recurrent architectures demonstrated significant improvements, both in accuracy and capability to handle larger, more challenging extrapolation tasks. Specifically, models trained on 9x9 mazes were able to solve 59x59 mazes, with some extending their accuracy to 201x201 mazes.

• Prefix Sums: The models achieved 97% accuracy on 512-bit strings, a clear testament to the method's efficacy.
• Maze Solving: The approach drastically improved performance on large mazes, maintaining high accuracy with models demonstrating capability on puzzles far beyond training size.
• Chess Puzzles: The method sustained accuracy across a range of increasingly complex chess puzzles, a challenging domain for logical extrapolation.

Implications and Future Work

The work presented contributes theoretical and practical advancements in designing neural networks capable of complex problem-solving without succumbing to overthinking. The results affirm that neural networks can be configured not only for incremental reasoning but for robust algorithmic development.

This research opens multiple avenues for exploration, such as expanding these techniques to other domains like automated theorem proving or more generalized planning tasks. Future work may investigate the scalability and adaptability of these architectures to larger real-world datasets or integrate them with other emerging AI strategies to further enhance logical reasoning capabilities in neural networks.