Enterprise AI Analysis
TRAPPED IN THE PAST? Disentangling Fluid and Crystallized Intelligence of Large Language Models Using Chess
This research investigates the fundamental question of whether Large Language Models (LLMs) rely on sophisticated recall (crystallized intelligence) or genuine reasoning ability (fluid intelligence). By leveraging the structured domain of chess, the study systematically evaluates multiple GPT generations across a spectrum of training corpus proximity, from common, memorizable states to novel positions requiring first-principles reasoning.
The findings reveal a consistent degradation in performance as fluid intelligence demands increase, with performance collapsing to random levels in out-of-distribution tasks. While newer models show improvement, progress significantly slows for tasks outside the training distribution. Reasoning-augmented inference offers benefits, but its marginal utility diminishes with decreased distributional proximity. These results underscore current architectures' limitations in systematic generalization, highlighting the critical need for advancements beyond mere scale to achieve robust fluid intelligence.
Authored by Leonard S. Pleiss, Maximilian Schiffer, and Robert K. von Weizsäcker.
Executive Impact Summary
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AI Performance Uplift (GPT-3.5 to GPT-5)
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Higher ACPL in OOD vs. WD Positions
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ACPL Reduction with Chain-of-Thought Reasoning
Deep Analysis & Enterprise Applications
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Introduction & Problem
Methodology
Key Results
Discussion & Implications
The Intelligence Debate: Crystallized vs. Fluid
Large Language Models (LLMs) have demonstrated impressive capabilities, yet it remains debated whether these stem from enhanced memorization (crystallized intelligence) or true problem-solving and reasoning (fluid intelligence). This distinction is vital for understanding LLMs' ability to generalize to novel problems.
Current benchmarks often conflate retrieval and reasoning, making it challenging to precisely quantify distributional proximity. This study addresses this gap by using chess as a controlled, verifiable environment to systematically analyze LLM performance across tasks requiring varying degrees of these two forms of intelligence.
Structured Testbed: Chess as a Controlled Environment
We employed chess as a controlled testbed to disentangle fluid and crystallized intelligence. Its clear rules, deep combinatorial structure, and computationally verifiable metrics via chess engines provide a robust framework. We categorized chess positions into Within-Distribution (WD), Near-Distribution (ND), and Out-of-Distribution (OOD) based on their likelihood of appearing in training data.
Enterprise Process Flow
Formalize Intelligence & Generalization
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Instantiate Framework in Chess
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Generate WD, ND, OOD Datasets
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Define Performance Metrics
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Detail Experimental Protocol
Performance was quantified using Centipawn Loss (CPL) to measure decision regret, and illegal move rates for syntactic reasoning. Evaluations were conducted across GPT-3.5, GPT-4, and GPT-5, including GPT-5 with varying reasoning efforts, to observe developmental trajectories.
Performance Gradient: Decreasing Accuracy with Novelty
Our analysis revealed a consistent performance gradient: model accuracy declines significantly as the demand for fluid intelligence increases. In OOD positions, performance often collapses to levels comparable to random play, suggesting severe limitations in generalizing beyond memorized patterns.
7.79x
Higher ACPL in OOD vs. WD Positions
While newer GPT generations show continuous improvement in overall performance, the rate of progress slows significantly for tasks further from the training distribution. This suggests that simply scaling current architectures may not be sufficient for robust fluid intelligence.
66.2%
Legal Moves from GPT-5 (Still 33.8% Illegal Overall)
Reasoning-augmented inference, such as chain-of-thought, notably improves performance across all conditions. However, the marginal benefit of reasoning per token decreases as distributional proximity diminishes, indicating that reasoning primarily amplifies existing knowledge rather than generating novel insights.
| Condition | GPT-5 ACPL | GPT-5 Legal Moves (%) | GPT-5 w/ Reasoning ACPL | GPT-5 w/ Reasoning Legal Moves (%) |
|---|---|---|---|---|
| Within-Distribution (WD) | ~50 | ~95 | ~10 | ~99.5 |
| Near-Distribution (ND) | ~400 | ~85 | ~70 | ~97 |
| Out-of-Distribution (OOD) | ~450 | ~65 | ~300 | ~90 |
Architectural Bottlenecks & Future Trajectory
The consistent performance gradient and diminishing returns for fluid intelligence gains suggest fundamental architectural limitations in current LLMs. They excel in crystallized intelligence (recall) but struggle with novel syntax and first-principles reasoning in OOD contexts.
The Chess Challenge: Beyond Memorization
Our findings from the chess testbed reveal that LLMs, despite their scale and reasoning capabilities, still face significant challenges in genuine fluid intelligence. This suggests implications for their deployment in safety-critical formal systems.
- Brittle Generalization: Current models rely on surface-level heuristics learned from training data, becoming brittle when structural patterns of standard play are removed in novel situations.
- Diminishing Returns: Scaling alone increasingly yields smaller gains in fluid intelligence, implying an architectural bottleneck that limits extrapolation to novel state spaces.
- Reasoning as an Amplifier: Chain-of-thought mostly amplifies existing crystallized knowledge rather than inducing new conceptual representations or enabling true fluid discovery.
- Caution for Formal Systems: Without advances in capturing latent causal and relational structure, deploying LLMs in domains like mathematics or software synthesis requires caution due to potential brittleness in novel scenarios.
Overcoming these limitations will require innovations beyond mere architectural scale or explicit reasoning. New forms of representation and inference capable of truly capturing and composing latent causal and relational structure are essential for achieving robust fluid intelligence and generalization.
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