Trace as State: Reasoning Traces as Conditional States for Long-Context Transformers

Transformers process information causally, but long-context reasoning may depend on task state discovered only later. We formalize this mismatch through conditional state update tasks. For causal state update processors, providing the condition first can require exponentially less memory in the worst case than providing it last. Motivated by this principle, we introduce Trace as State. We use collected reasoning traces as a textual proxy for task state and place it before the long-context block on a fresh pass, allowing information derived previously to guide rereading. We conduct extensive experiments on Trace as State and Trace Append, a matched control that uses the same task state proxy but put it after the context. Across three models and three long-context datasets, Trace as State outperforms Trace Append in 26 of 27 reported combinations of model, task, and metric. On GraphWalks Parents, exact match lifts DeepSeek V4 Pro Preview from 29.2% on the initial pass and 43.0% with Trace Appendto 81.8% with Trace as State, and from 66.4% and 83.2% to 100.0% for GLM-5.2. These results show that placing traces before the context can improve long-context reasoning while retaining the causal transformer structure.

Simplifying the Modeling of Arbitrary Conditionals in Natural Language

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.