On the Design and Analysis of LLM-Based Algorithms (2407.14788v2)

Abstract: We initiate a formal investigation into the design and analysis of LLM-based algorithms, i.e. algorithms that contain one or multiple calls of LLMs as sub-routines and critically rely on the capabilities of LLMs. While LLM-based algorithms, ranging from basic LLM calls with prompt engineering to complicated LLM-powered agent systems and compound AI systems, have achieved remarkable empirical success, the design and optimization of them have mostly relied on heuristics and trial-and-errors, which is largely due to a lack of formal and analytical study for these algorithms. To fill this gap, we start by identifying the computational-graph representation of LLM-based algorithms, the design principle of task decomposition, and some key abstractions, which then facilitate our formal analysis for the accuracy and efficiency of LLM-based algorithms, despite the black-box nature of LLMs. Through extensive analytical and empirical investigation in a series of case studies, we demonstrate that the proposed framework is broadly applicable to a wide range of scenarios and diverse patterns of LLM-based algorithms, such as parallel, hierarchical and recursive task decomposition. Our proposed framework holds promise for advancing LLM-based algorithms, by revealing the reasons behind curious empirical phenomena, guiding the choices of hyperparameters, predicting the empirical performance of algorithms, and inspiring new algorithm design. To promote further study of LLM-based algorithms, we release our source code at https://github.com/modelscope/agentscope/tree/main/examples/paper_LLM_based_algorithm.

On the Design and Analysis of LLM-Based Algorithms

Authors: Yanxi Chen, Yaliang Li, Bolin Ding, Jingren Zhou

As the integration of pre-trained LLMs into diverse computational tasks continues to expand, it becomes imperative to formally understand and analyze the underpinnings of such integrations, beyond empirical heuristics. The paper "On the Design and Analysis of LLM-Based Algorithms" embarks on this challenge by introducing a structured framework to paper and optimize LLM-based algorithms systematically.

Key Contributions

This scholarly work makes several significant contributions to the burgeoning field of LLM-based algorithms:

1. Formulation of LLM-Based Algorithms as Computational Graphs:
   • The authors propose modeling LLM-based algorithms using computational graphs. Here, nodes represent LLM or non-LLM operations, capturing how sub-routines interconnect to form a holistic solution. This approach aids in the analytical treatment of these algorithms, despite LLMs being black-box solvers.
2. Principle of Task Decomposition:
   • A primary design principle emphasized in this work is task decomposition. The computational graph framework supports breaking down a primary task into smaller, manageable sub-tasks that LLMs or symbolic algorithms can process more efficiently. This decomposition is crucial given LLMs' limitations, such as finite context windows and potential degradation in reasoning for complex tasks.
3. Analytical Case Study on Parallel Decomposition:
   • The authors conduct an in-depth paper on parallel decomposition as a foundational pattern for LLM-based algorithms. Through four diverse tasks—counting, sorting, retrieval, and retrieval-augmented generation—they provide formal analysis complemented by empirical validation. This dual approach ensures the theoretical findings are practically relevant.

Formal Analyses and Insights

Accuracy and Efficiency:

• Error Metrics: The accuracy of a given LLM-based algorithm is framed in terms of error metrics that are task-specific. By employing computational graphs, the paper links individual node errors to the overall algorithm's error, providing a clear pathway for predicting performance. For instance, tasks such as sorting involve error metrics that capture monotonicity, length mismatch, and fuzzy grades, applicable even when individual LLM calls may not yield perfectly sorted outputs.
• Cost Metrics: Efficiency is quantified through cost metrics such as token counts (prefilling and decoding lengths), LLM call counts, and end-to-end latency. Various configurations (e.g., extent of parallelism in LLM calls) influence these metrics, providing a framework for optimizing resource usage in algorithm implementations.

Implications of Hyperparameters:

• The authors highlight the influence of the sub-task size parameter $m$ on both error and cost metrics. For instance, smaller $m$ values typically enhance accuracy owing to manageable sub-task sizes within LLMs’ context windows. Conversely, greater $m$ values can optimize for latency in highly parallel settings, balancing the algorithm's demands.

Experimental Validation

The empirical studies conducted using various LLMs, including Llama-3-8B, Llama-3-70B, and GPT-4-Turbo, substantiate the theoretical analyses:

• Counting Task: Smaller sub-task sizes ($m$) improve accuracy by reducing per-instance complexity, evidenced by lowered absolute counting errors as $m$ decreases.
• Sorting Task: The complexity of tasks like sorting elucidates that while LLMs might produce outputs close to sorted lists, further error reduction is accomplished via computational graphs involving multi-level merging.
• Retrieval and Retrieval-Augmented Generation: These tasks illustrate that task decomposition helps mitigate LLMs’ sensitivity to context length and the irrelevant information in retrieval settings.

Future Directions

The paper identifies several promising avenues for future research:

1. Stateful LLM Nodes:
   • Extending the framework to LLM nodes with state (e.g., agent systems with memory) and exploring how this statefulness impacts performance.
2. Diverse Patterns of Task Decomposition:
   • Investigating deeper sequential decompositions and recursive divide-and-conquer strategies to uncover new algorithmic insights.
3. Multi-Objective Optimization:
   • Emphasizing other configurable aspects like LLM model selection, prompting techniques, and decoding methods, which could offer multi-dimensional optimization for error and cost metrics.
4. Optimization Algorithms:
   • Introduction of systematic methodologies for hyperparameter tuning and trade-offs in LLM-based algorithms, potentially inspiring novel optimizers tailored to these computational frameworks.

By providing a foundational framework and actionable insights, this work establishes a structured baseline for formal studies on LLM-based algorithms, inviting further contributions from the AI research community to enrich this rapidly evolving field.