Nash Equilibrium Text: A Game-Theoretic Decoding Framework for Text Generation

We introduce Gacha Decoding, an inference-time method for eliciting diverse language model generations that scales with model capability. Across open-ended domains (in-the-wild chat, creative writing, planning for image generation, and protein design), Gacha Decoding significantly outperforms existing generation diversity approaches at equal quality (up to 2.4x Vendi over the next-best prior approach), reaching the same number of high-quality modes with over an order of magnitude fewer samples (11.0x) and discovering novel modes that no other approach surfaces. Our key insight is to treat diversity as an instruction-following problem: rather than relying on the LM's token entropy, we combine its instruction-following capability with randomness from an external RNG tool to scalably identify and realize distinct modes of the response space. This approach of "planning with dice" enables Gacha to invert the long-observed tension between diversity and model capability. As the underlying LM becomes a better instruction follower, diversity under Gacha Decoding consistently improves--even as its token entropy and diversity under prior approaches decline. Together, our results highlight that instruction following, rather than token entropy alone, can drive generation diversity.

Language models are increasingly taught from synthetic question--answer (QA) supervision: a model generates questions about a document, answers them from the same text, and the resulting pairs are used to fine-tune, distill, or compress knowledge into another model. We show that this generation step is not neutral preprocessing. It is an implicit policy that both selects which evidence becomes training signal and decides how that evidence is answered, and it is fragile at both stages. When choosing what to ask, generators do not scan a document uniformly. Coverage saturates early and concentrates on salient spans, diverse prompts converge on the same regions, and what looks question-worthy is driven by local presentation. As a result, salient artifacts such as poorly cleaned markup can hijack question generation across model families and scales. When answering, the model that produces the supervision tends to obey instruction-like passages embedded in the text. This compliance depends on the intent and surface form of the passage rather than its strictness, and is worst under task conflict, where larger models comply more often. These failure modes arise from choices made during QA generation, so they can be reduced without changing the training loop. Tying each question to a fixed target reduces biased selection, and filtering instruction-like spans before answering lowers mean injection compliance from $88\%$ to $13\%$ in our evaluation while retaining nearly all clean text.

Autoregressive pretraining increasingly draws on heterogeneous data, making it important to understand how a model learns from an individual token. The next-token prediction objective naturally identifies a token's contribution with its own loss. However, each token is not only a prediction target but also context for what follows. Using controlled corruption, we decouple these two roles and find a reversal: making a noisy token easier to predict reduces its damage as a target but increases it as context. The same decoupling helps explain text generated by language models: generation selects each token by its fit to the prefix, while its role as context is never tested against an independently determined continuation, because that continuation is generated to fit it. At known corrupted positions, acting through the context can reduce damage that removing the token's own loss does not. Understanding and controlling what a model learns from a token therefore requires decoupling its roles.