Training LLMs Beyond Next Token Prediction - Filling the Mutual Information Gap

Generative modeling of discrete data has two popular paradigms: autoregressive models such as GPT, which factorize a sequence in a left-to-right (L2R) order, and masked diffusion models, which are essentially any-order autoregressive modeling. Rather than competing methods, these are the two extreme points of a single axis -- the generation order. For structured discrete domains without a natural traversal, both extremes may be suboptimal, yet the intermediate choice -- a single well-adapted order -- remains largely unexplored. We introduce OrderGPT, which builds on Any-Order GPT to learn a task-level generation order without canonical-order supervision. Our key observation is that predicting variables from randomly sampled reveal prefixes produces recurring attention patterns in the backbone that provide a model-dependent signal of predictive dependencies. We aggregate this signal into a reciprocal dependency graph and use a spectral teacher to derive continuous generation priorities. A lightweight OrderMLP integrated into the GPT backbone learns to predict these priorities from attention, incorporating order learning into the architecture within a single training run. Training gradually shifts toward the learned order, which is then frozen for subsequent autoregressive training and generation. The same mechanism adapts across modalities: adaptively it recovers near-L2R dependency structure in language, learns anatomically organized factorizations on human pose, and discovers a factorization on tabular data that places statistically and semantically related fields nearby, while improving downstream modeling metrics across all domains. The code is available at https://github.com/Chenhe-yang/OrderGPT/.

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.

Masked diffusion language models decode by iteratively unmasking tokens, where the unmasking order defines an "order of thought" that strongly influences generation quality yet is typically chosen heuristically. We derive a tractable upper bound on the sequential decoding mismatch, measured by the Kullback-Leibler divergence and expressed in terms of the model's pathwise log-likelihood, with tightness under sufficient model expressivity. This bound induces a dense self-aware reward over ordered trajectories, casting order selection as a principled policy optimization problem with a frozen denoiser. We instantiate this idea as Self-Aware Scheduling (SAS), which learns a lightweight order policy using Group Relative Policy Optimization and applies seamlessly to both any-order and semi-autoregressive decoding. On Sudoku with 1B MDM, SAS improves puzzle accuracy from 82.0% (best heuristic schedule) to 91.8%, and reaches 97.5% with second-stage fine-tuning along learned trajectories. On mathematical reasoning with LLaDA-8B, SAS improves pass@1 on GSM8K from 64% to 76% and on MBPP from 39.5% to 41%, consistently matching or exceeding heuristic schedules across generation lengths and block sizes. Project page: https://jimmyxu123.github.io/SAS