The Consensus Game: Language Model Generation via Equilibrium Search (2310.09139v1)

Abstract: When applied to question answering and other text generation tasks, LLMs (LMs) may be queried generatively (by sampling answers from their output distribution) or discriminatively (by using them to score or rank a set of candidate outputs). These procedures sometimes yield very different predictions. How do we reconcile mutually incompatible scoring procedures to obtain coherent LM predictions? We introduce a new, a training-free, game-theoretic procedure for LLM decoding. Our approach casts LLM decoding as a regularized imperfect-information sequential signaling game - which we term the CONSENSUS GAME - in which a GENERATOR seeks to communicate an abstract correctness parameter using natural language sentences to a DISCRIMINATOR. We develop computational procedures for finding approximate equilibria of this game, resulting in a decoding algorithm we call EQUILIBRIUM-RANKING. Applied to a large number of tasks (including reading comprehension, commonsense reasoning, mathematical problem-solving, and dialog), EQUILIBRIUM-RANKING consistently, and sometimes substantially, improves performance over existing LM decoding procedures - on multiple benchmarks, we observe that applying EQUILIBRIUM-RANKING to LLaMA-7B outperforms the much larger LLaMA-65B and PaLM-540B models. These results highlight the promise of game-theoretic tools for addressing fundamental challenges of truthfulness and consistency in LMs.

Analyzing "The Consensus Game: LLM Generation via Equilibrium Search"

The paper "The Consensus Game: LLM Generation via Equilibrium Search" introduces a noteworthy approach to LLM (LM) decoding by utilizing a game-theoretic framework. This technique innovatively aims to reconcile discrepancies between generative and discriminative LLM predictions, which can sometimes diverge significantly. Notably, the authors propose a novel, training-free game-theoretic method that envisions LM decoding as a regularized imperfect-information sequential signaling game, termed the "Consensus Game."

Overview of the Methodology

The proposed Consensus Game reformulates LLM decoding as a game involving two key agents: the Generator (G) and the Discriminator (D). These agents operate within a signaling framework with the Generator tasked with communicating an unknown value to the Discriminator using natural language outputs drawn from a LLM. The primary objective is for both agents to achieve consensus on the correctness of generated statements through cooperative play aligned with a game-theoretical equilibrium.

The decomposition of the game into two primary components allows the method to integrate no-regret learning algorithms, thus effectively facilitating the computation of an approximate equilibrium. The consensus-derived equilibrium decodes outputs, yielding the equilibrium-ranking algorithm, which aims to enhance the consistency and truthfulness of LLMs' outputs.

Empirical Evaluation

This approach is validated through extensive benchmarking across multiple tasks including reading comprehension, commonsense reasoning, mathematical problem-solving, and dialogue. Noteworthy is the application of equilibrium-ranking to various benchmarks, demonstrating that models such as LLaMA-7B, while smaller in scale, outperform significantly larger models like LLaMA-65B and PaLM-540B when utilizing this method.

Key Outcomes and Implications

The paper presents strong numerical results indicating that equilibrium-ranking can improve model performance consistently across tasks, highlighting its potential effectiveness in enhancing the truthfulness and consistency of LLMs. These results underscore the potential of game-theoretic approaches to bridge discrepancies inherent in LM outputs, suggesting a promising direction for future research to tackle challenges of scale-induced inconsistencies in LMs.

Potential for Future Work

The intersection of game theory and LLMs, as proposed through the Consensus Game, opens avenues for further exploration, particularly in the optimization of decoding strategies in diverse LM applications. Given the complexity of LLM operations, the integration of signaling games and equilibrium computation could extend beyond question answering tasks to more complex domains of language understanding and generation.

By proposing an innovative game-theoretic approach to LM decoding, this work provides a solid foundation upon which future models can build, potentially leading to more reliable and consistent LLMs capable of trustworthy and factual textual generation. The methodology sheds light on the broader implications of utilizing game-theoretic principles in AI and serves as a benchmark for further empirical and theoretical advancements in the field of computational linguistics.