Transformer-Based Models Are Not Yet Perfect At Learning to Emulate Structural Recursion (2401.12947v1)

Abstract: This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general \textit{syntax} of structural recursion, coupled with two different frameworks for understanding their \textit{semantics} -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art LLMs to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

• The paper introduces a dual-framework combining syntactic encoding and dual semantic perspectives to analyze recursion in transformers.
• The paper demonstrates that transformers often rely on shortcut algorithms that fail in under-represented edge cases.
• The paper provides empirical findings from tasks such as binary successor functions and tree traversals, highlighting challenges in recursive learning.

Overview of the Framework

The paper introduces a framework that conceptualizes how transformer-based models deal with structural recursion, an essential concept straddling the programming language and machine learning domains. Structural recursion involves computationally defining a function or a data structure in terms of itself, which is a ubiquitous technique in formal theorem proving and programming tasks. The framework comprises two angles: a syntactic view for sequential encoding that converts recursive structures to linear sequences, and a dual semantic perspective—including a stepwise reduction semantics and an Abstract State Machine (ASM) semantics—to bridge the syntax to behavioral understanding in transformer models.

Discoveries and Issues

Analyzing model behavior within this dual-framework reveals that transformers struggle with learning structural recursion. They appear to compensate by fitting shortcut algorithms, which break in edge cases, especially those that are less represented in the training data. The state-of-the-art LLMs, moreover, have demonstrated difficulties in mining recursive rules in-context, indicating a gap in their learning capabilities.

Empirical Insights

The research provides empirical results from analyzing transformer models trained from scratch on these aspects of structural recursion. Several experiments are conducted, testing transformer behavior on tasks like learning the binary successor function and tree traversal tasks. The models' ability to emulate recursive computation is dissected to understand the extent of its capabilities and shortcomings. These experiments outline the mechanics behind the models' learned algorithms and explored the conditions under which they fail. Furthermore, experiments are extended to pre-trained LLMs, revealing how tokenization and pre-training data influence their performance on recursion tasks.

Implications for Transformer Models

This paper's findings have essential implications for the development and training of transformer models, particularly in tasks requiring structural recursion. While transformers exhibit remarkable pattern recognition abilities, they do not inherently understand or execute the sophisticated concept of structural recursion. The research points out possibilities to improve this by adjusting models' learning agendas to handle under-represented cases better and by aligning model architecture more closely with the tasks' structural nature. Understanding these limitations and behaviors is crucial for future advancements in applying AI to areas like formal mathematics and programming, where recursion plays a fundamental role.