Faith and Fate: Limits of Transformers on Compositionality
Introduction
The capacity of transformer-based LLMs to perform intricate multi-step reasoning tasks has drawn notable attention within the AI research community. However, despite their impressive performance on complex tasks, these models exhibit notable deficiencies on apparently trivial problems. This paper aims to investigate whether these failures are isolated incidents or indicative of intrinsic limitations within transformer LLMs. Specifically, the paper examines the models' performance across three representative compositional tasks: multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks necessitate decomposing problems into sub-steps and integrating these into a final holistic solution.
Key Hypotheses
The authors propose two main hypotheses:
- Transformers handle compositional tasks by simplifying multi-step compositional reasoning into linearized subgraph matching, rather than developing systematic problem-solving skills.
- Transformers have inherent limitations in solving high-complexity compositional tasks due to error propagation, where initial errors accumulate, amplifying inaccuracies in subsequent steps.
Methodological Framework
To scrutinize these hypotheses, the paper introduces a methodological framework for evaluating compositional tasks as computation graphs. This framework involves:
- Computation Graphs: Representing problem-solving tasks as directed acyclic graphs (DAGs), where nodes signify variable values and edges denote function operations.
- Complexity Metrics: Utilizing graph metrics such as reasoning depth, reasoning width, and average parallelism to quantify task complexity.
- Information Gain: Applying relative information gain to predict the surface patterns that models are likely to recognize without engaging in complete multi-step reasoning.
Experimentation and Findings
The empirical investigation involves evaluating multiple LLMs (GPT3, ChatGPT, and GPT4) using zero-shot, few-shot, and fine-tuning techniques. The LLMs' performances are compared across different complexities and configurations of the tasks.
Zero-shot and Few-shot Settings
The paper reveals that the performance of LLMs degrades significantly with increasing task complexity. Both zero-shot and few-shot evaluations yield high accuracy on simple tasks but fall to near-zero accuracy as complexity increases. This suggests that pre-training lacks sufficient task-specific data to equip models for complex compositional reasoning.
Fine-tuning with Question-Answer and Scratchpad Pairs
Exhaustive fine-tuning on question-answer pairs yields mixed results. Models achieve near-perfect accuracy on in-domain examples but fail dramatically on out-of-domain (OOD) examples. Fine-tuning on question-scratchpad pairs, designed to explicitly teach computational operations, results in high in-domain accuracy but does not improve OOD generalization. These outcomes underscore the challenges posed by the transformers' autoregressive nature, which inherently limits their global understanding of tasks.
Empirical Insights into Error Propagation
The paper systematically categorizes errors into local, propagation, and restoration errors, revealing that models frequently fail to accurately compose multiple reasoning steps. This supports the hypothesis that models primarily rely on pattern matching rather than true compositional reasoning.
Theoretical Limits
Theoretical arguments complement the empirical findings by demonstrating that transformers' performance on abstract multi-step reasoning problems degrades exponentially with increasing task complexity. Under reasonable assumptions, the likelihood of inaccurate predictions converges to almost certainty as problem size increases. These insights are generalizable to any high-performing estimator of reasoning tasks.
Implications and Future Directions
The paper's findings indicate fundamental limitations in transformers' ability to perform compositional reasoning robustly. This has broader implications for the deployment of transformers in tasks requiring stepwise reasoning and could guide future research. Some potential directions include:
- Employing transformers for tasks involving fewer reasoning steps or approximate solutions.
- Integrating transformers with planning modules and refinement methods to enhance systematic problem-solving capabilities.
Conclusion
As transformers continue to advance, it remains critical to critically assess their limitations, particularly in handling compositional tasks. This paper provides a comprehensive examination of these limits, leveraging both empirical and theoretical approaches. The insights gleaned highlight the necessity for future innovations to overcome or complement these limitations, advancing the robustness and systematic reasoning capabilities of AI systems.
References
The paper references numerous foundational and recent works in the AI and machine learning domain, supporting its theoretical and empirical analysis. The code and data are available at GitHub Repository.
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@article{dziri2023faith,
title={Faith and Fate: Limits of Transformers on Compositionality},
author={Dziri, Nouha and Lu, Ximing and Sclar, Melanie and Li, Xiang Lorraine and Jiang, Liwei and Lin, Bill Yuchen and West, Peter and Bhagavatula, Chandra and Le Bras, Ronan and Hwang, Jena D and others},
journal={arXiv preprint 2305.09854},
year={2023}
} |