Can generative and discriminative models reach agreement?

Language models offer two fundamentally different ways to answer questions. Generatively: sample the most probable answer. Discriminatively: score candidate answers and pick the best. These two procedures often disagree — generative decoding fails when probability mass spreads across contradicting answers; discriminative decoding fails due to miscalibration or sensitivity to question wording. Both are noisy, and their noise is not correlated.

The Consensus Game formalizes this as a regularized imperfect-information sequential signaling game. A Generator agent must communicate an abstract correct/incorrect value to a Discriminator agent, but can only do so using natural language strings from a candidate set. An effective joint policy is one where both agents agree on which strings map to "correct." The resulting decoding algorithm — Equilibrium-Ranking — finds approximate equilibria of this game.

The results are striking: LLaMA-7B with Equilibrium-Ranking outperforms LLaMA-65B and PaLM-540B on multiple benchmarks spanning reading comprehension, commonsense reasoning, mathematical problem-solving, and dialogue. A 7B model matching a 540B model is a ~77x parameter efficiency gain.

The insight is that generative and discriminative procedures contain complementary information. Neither alone captures the model's "best guess at the truth." The game-theoretic framework extracts a consensus signal that is more reliable than either procedure individually — analogous to how ensemble methods combine weak learners, but operating within a single model's two modes of operation.

This is a training-free method — no fine-tuning required. The computational overhead comes from finding the equilibrium at inference time, making it a form of test-time compute scaling. Since Can inference compute replace scaling up model size?, Equilibrium-Ranking provides a concrete mechanism: the test-time compute goes into reconciling the model's own internal disagreements rather than generating longer reasoning chains.

The connection to multi-agent debate is suggestive. Since Why do multi-agent LLM systems converge without genuine deliberation?, the Consensus Game forces genuine deliberation between two perspectives (generative and discriminative) within a single model — the equilibrium constraint prevents premature convergence because both agents must independently arrive at consistent signals. And since When does debate actually improve reasoning accuracy?, the Consensus Game sidesteps the evidence-verification problem that plagues inter-model debate: both "agents" operate within the same model's knowledge, so there is no risk of one agent persuading the other with rhetorically superior but factually wrong arguments -- the equilibrium constraint forces agreement on what the model actually knows rather than what it can argue most convincingly.