Cross-Entropy Games for Language Models: From Implicit Knowledge to General Capability Measures (2506.06832v2)

Abstract: LLMs define probability measures on text. By considering the implicit knowledge question of what it means for an LLM to know such a measure and what it entails algorithmically, we are naturally led to formulate a series of tasks that go beyond generative sampling, involving forms of summarization, counterfactual thinking, anomaly detection, originality search, reverse prompting, debating, creative solving, etc. These tasks can be formulated as games based on LLM measures, which we call Cross-Entropy (Xent) Games. Xent Games can be single-player or multi-player. They involve cross-entropy scores and cross-entropy constraints, and can be expressed as simple computational graphs and programs. We show the Xent Game space is large enough to contain a wealth of interesting examples, while being constructible from basic game-theoretic consistency axioms. We then discuss how the Xent Game space can be used to measure the abilities of LLMs. This leads to the construction of Xent Game measures: finite families of Xent Games that can be used as capability benchmarks, built from a given scope, by extracting a covering measure. To address the unbounded scope problem associated with the challenge of measuring general abilities, we propose to explore the space of Xent Games in a coherent fashion, using ideas inspired by evolutionary dynamics.

• The paper presents Xent Games, a novel framework that quantifies language models' implicit knowledge using cross-entropy loss metrics.
• It employs game-theoretic axioms to develop scalable benchmarks for assessing diverse capabilities such as creative problem-solving and anomaly detection.
• The approach highlights the benefits of transfer learning, evolutionary dynamics, and synthetic data generation in advancing LLM general performance.

Cross-Entropy Games for LLMs: Overview and Implications

The academic paper, titled "Cross-Entropy Games for LLMs: From Implicit Knowledge to General Capability Measures," presents a comprehensive framework for assessing and advancing the capabilities of LLMs through a novel approach based on cross-entropy evaluations termed "Cross-Entropy (Xent) Games." This framework provides a structured method to explore implicit knowledge within LLMs, extend their practical applications, and develop capability benchmarks.

Implicit Knowledge Exploration

The paper starts with an assertion distinguishing explicit knowledge—commonly assessed through direct question-answering or interactions in chatbot-like settings—from implicit knowledge, which encompasses all algorithmic computations feasible from the learned model measures. Implicit knowledge tasks include those requiring counterfactual reasoning, originality detection, creative problem-solving, and anomaly identification, among others.

The authors argue that implicit knowledge is vast and encompasses a variety of applications and reasoning tasks that LLMs might undertake. They contend this exploratory dimension unlocks opportunities for understanding and leveraging LLMs beyond their explicit-task strengths.

Cross-Entropy Games Framework

The introduction of Xent Games creates a paradigm where LLMs are examined through competitive and cooperative game formats. This paper formulates Xent Games as structured tasks involving measures of xent (cross-entropy) loss, affording an avenue to quantify LLM capabilities beyond traditional metrics. This framework not only establishes a way to simulate strategic thinking in LLMs but also suggests a method of evaluating capabilities across a broader spectrum, including creative, deductive, and comprehensively synthetic tasks.

The Xent Game construction relies on several game-theoretic axioms ensuring consistency, combinatorial flexibility, and adaptability. These axioms create a scalable environment where custom tasks can be generated, thus forming a versatile benchmarking structure based on implicit knowledge tasks.

Practical and Theoretical Implications

Benchmarking LLM Capabilities: A major implication of the Xent Games framework is its potential to offer more nuanced benchmarks for LLM capabilities than existing challenges based largely around direct answer retrieval. The authors propose utilizing measures derived from gameplay scenarios to establish a histogram of scores, which could reflect the LLM's proficiency across various complex tasks.

Evolutionary Dynamics: To address the theoretical challenge associated with infinite scope in benchmarking general capabilities, the paper introduces evolution-inspired dynamics. This enables the expansion of task scopes realistically yet comprehensively by mimicking competitive pressures found in evolutionary environments. Through an evolution-based exploration algorithm, it identifies relevant tasks for measuring general capabilities while avoiding oversampling or niche specialization.

Transfer Learning: The proposed framework suggests using transfer values—i.e., how much playing one Xent Game improves performance on another—as a basis for evaluating the utility of game-specific skills. This approach hinges on increasing versatility and adaptability among LLMs, fostering the continuous advancement of general capabilities.

Development of Synthetic Data for Training: The paper also presents potential prospects where synthetic game-derived data could enhance LLM pre-training phases by introducing complex, long-context interactions that better simulate real-world complexity and information dynamics.

Future Directions

Several promising future avenues arise from this research framework:

1. Implementation of Xent Games at Scale: Establishing a robust testing and benchmarking ecosystem using Xent Games could afford a standardized yet flexible platform for ongoing LLM evaluation.
2. Curriculum and Meta-Reinforcement Learning: The exploration of curriculum-learning algorithms drawing upon insights from Xent Games could further advance AI self-improvement capabilities, especially for adaptive tasks.
3. Self-Improvement Loops: Leveraging LLMs for multiple roles—judging, NPC interaction, map generation, and game sampling—could drive self-improvement loops, where LLMs progressively refine their capabilities autonomously via optimized exposure to diverse tasks.

Overall, this paper significantly advances the conception and application of LLM benchmarks, promoting a shift from static, narrowly defined evaluations toward dynamic, interaction-rich frameworks that capture broad, implicit competencies. This approach holds substantial promise in contributing to the development of more intelligent and versatile AI systems by grounding them in task flexibility and evolutionary adaptability.