Quantifying Generalization Complexity for Large Language Models

Abstract: While LLMs have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

• The paper introduces Scylla, a novel framework to quantify how Large Language Models balance generalization and memorization across varying task complexities, revealing a "generalization valley" indicating where memorization peaks.
• Scylla uses ID and OOD data across five complexity levels, showing larger models can handle more complex tasks before over-relying on memorization.
• Benchmarking 28 LLMs, the study found closed-source models generally outperform open-source ones, introducing a Generalization Score metric to evaluate robustness and penalize reliance on in-distribution data.

Quantifying Generalization Complexity for LLMs

The paper entitled "Quantifying Generalization Complexity for LLMs" proposes a novel evaluation framework, Scylla, specifically designed to assess how LLMs negotiate the dichotomy between generalization and memorization. As LLMs continue to advance, their ability to understand and generalize from complex queries becomes increasingly pertinent. This study identifies a critical need to disentangle genuine generalization capabilities from memorization effects in order to fully understand these models' potential and limitations.

Scylla Framework and Methodological Insights

Scylla is introduced as a dynamic evaluation tool that quantitatively measures the generalization capacities of LLM models by testing them on both in-distribution (ID) and out-of-distribution (OOD) data. The framework categorizes tasks across five levels of complexity to elucidate how task difficulty influences LLM performance. Through this structured assessment, the authors reveal a non-linear correlation—termed the "generalization valley"—between task complexity and performance gap (the difference in accuracy between ID and OOD tasks). This relationship identifies a point of "critical complexity" where reliance on memorization peaks, suggesting a boundary to LLMs' generalization abilities. Intriguingly, as model size increases, this critical complexity threshold shifts towards more complex tasks, implying that larger models manage complex tasks with more adeptness before over-relying on memorized data.

The framework offers four essential criteria for evaluating LLM generalization: scalability in task complexity, dynamic problem generation, low reliance on external knowledge, and an awareness of memorization. By failing existing evaluation methods against these dimensions, Scylla emerges as a more robust and nuanced tool for fine-tuning our understanding of LLM reasoning capabilities. It not only generates ID and OOD datasets for a given task but restricts the task complexity range and removes overlap with training data, thereby offering a precise analysis of a model's reasoning ability.

Experimental Findings and Generalization Score

The authors benchmarked 28 LLMs using Scylla, including both open-source and proprietary models. Results indicate that closed-source models outperform their open-source counterparts, with notable performance from GPT-4o-mini and o1-mini, which handle a broad spectrum of tasks showing lower dependencies on memorization. The introduction of a new metric, the Generalization Score, further refines model evaluations by rewarding robustness in OOD environments while penalizing a heavy reliance on ID data. This score highlights an ideal LLM reasoner, achieving high OOD accuracy with minimal performance disparities between conditions.

Implications for AI Development

The insights derived from the Scylla framework have significant implications for theoretical understanding and real-world applications. On the theoretical plane, the study provokes discussion about the intrinsic limits of generalization in AI models, potentially guiding future architectural designs and training methodologies. Practically, these findings can inform the development of more capable AI systems in fields like natural language processing, autonomous systems, and decision-making applications, where the ability to generalize from limited data without overfitting is crucial.

Future evolutions in AI development may see enhanced focus on balancing the size and complexity of models against ethical and computational cost considerations. As AI technologies continue to scale, tools like Scylla could prove indispensable in optimizing model training, ensuring more ethical and efficient AI applications are developed, minimizing the risk of over-reliance on vast and potentially biased datasets.

In conclusion, this paper contributes substantially to the discourse on LLM capabilities, presenting Scylla as a comprehensive evaluation framework that addresses key limitations in existing models. It fosters a deeper understanding of the trade-offs between generalization and memorization, setting the stage for future advancements in the field.