Causal Transformers model sequences through an autoregressive factorization of the joint distribution, which enables efficient left-to-right decoding and conditional likelihood computation. However, they cannot tractably sample from or evaluate arbitrary conditionals -- e.g., a block of text conditioned on past and future tokens. Recent work aims to solve this problem through novel architectures, but they often lead to sub-optimal modeling of such conditionals and degraded generations. We propose Arbitrary Conditionals GPT (AC-GPT) which introduces a simple modification to standard causal Transformers to enable evaluating and sampling from arbitrary conditionals -- including past, future, and mixed contexts -- within a single forward pass. Unlike prior approaches, our method preserves the standard left-to-right ordering and next-token prediction objective essential for both strong performance and efficient training on natural language. Crucially, this compatibility allows existing LLMs to be fine-tuned for arbitrary conditioning. Our empirical results indicate that our method outperforms baselines on modeling arbitrary conditionals, without degrading standard left-to-right performance.
Generative models are often trained with a next-token prediction objective, yet many downstream applications require the ability to estimate or control sequence-level properties. Next-token prediction can lead to overfitting of local patterns during training, underfitting of global structure, and requires significant downstream modifications or expensive sampling to guide or predict the global attributes of generated samples at inference time. Here, we introduce Conditional Attribute Transformers, a novel method for jointly estimating the next-token probability and the value of an attribute conditional on each potential next token selection. This framework enables three critical capabilities within a single forward pass, without modification of the input sequence: (1) per-token credit assignment across an entire sequence, by identifying how each token in a sequence is associated with an attribute's value; (2) counterfactual analysis, by quantifying attribute differences conditional on alternative next token choices; (3) steerable generation, by decoding sequences based on a combination of next-token and attribute likelihoods. Our approach achieves state of the art performance on sparse reward tasks, improves next-token prediction at sufficient model sizes, estimates attribute probabilities orders of magnitude faster than sampling, and can guide decoding of autoregressive sequence models on a range of language tasks.
Large Language Models remain plagued by hallucinations. Recent work has sought to tame their prevalence using statistical techniques based on conformal prediction, with both theoretical and empirical success. However, these methods operate in a post-hoc fashion, treating the sampling procedure itself as atomic and then surgically altering samples to remove hallucinated claims. This disconnect between filtering and generation can result in samples that are incoherent, inconsistent, or simply unlikely under the model itself. Moreover, post-hoc surgery is unable to shift probability mass towards more useful and helpful responses. To address these issues, we propose to instead sample from approximations to an LLM posterior, where the conditioning event corresponds to a calibrated, high-scoring region. We develop a calibration procedure tailored to the setting of conditional sequential generation that effectively identifies this region and achieves target risk control. Empirically, we apply our method to case studies focused on open-ended biography generation and mathematical problem solving; compared to prior work, we obtain the same statistical guarantees, with higher downstream utility.
Nicolas Emmenegger, Theo X. Olausson, Armando Solar-Lezama +1
Language models trained on observed sequences are often described as learning the conditional distribution of the next token given previous tokens. This description is only conditionally correct. A model trained on realized token trajectories does not observe full conditional laws; it receives sampled continuations. Moreover, real language generation is conditioned not only on previous words but also on non-textual circumstances: facts, events, intentions, goals, beliefs, social context, and task-specific constraints. This paper distinguishes three objects that are often conflated: the full conditional language process conditioned on latent circumstances, the marginal text-only process obtained by integrating those circumstances out, and the model-induced distribution learned from finite observed corpora. The paper argues that interpreting model training as estimating the marginal text-only law requires strong assumptions of stationarity, representativeness, and ergodicity, assumptions that are standard in statistical estimation but problematic when applied to heterogeneous language corpora. Even if these assumptions hold, the marginal text-only law is useful only when the observed prefix is an approximately sufficient statistic for the latent circumstances relevant to continuation. In information-theoretic terms, usefulness requires that the residual conditional mutual information between the next token and the omitted circumstances, given the observed text, be small. The paper then extends this argument to heterogeneous training corpora. Finally, the paper interprets Retrieval Augmented Generation (RAG) and tool use as conditional sufficiency devices.