In the LLM era, many symbolic and structured problems are presented to models through 1D text serialization. Yet some such problems are natively two-dimensional: their relevant relations, such as row–column correspondence or spatial adjacency, are defined by position in a 2D layout rather than by sequential order. This raises a representational question: does preserving the same symbolic entries in a 1D sequence also preserve the relational structure needed for computation? We study this issue through the lens of serialization friction: the representational mismatch in which the same underlying task instances and entries are still present, but relations that depend on layout become implicit under 1D serialization. The study uses a controlled synthetic testbed of three tasks: matrix transpose, Conway’s Game of Life, and LU decomposition. In each task, the same instances are presented either as 1D text serialization or as their native 2D layout rendered as an image. Across this testbed, 1D serialization degrades more sharply as task size grows, and errors under serialization exhibit spatially structured patterns, suggesting that this presentation choice is consequential within our testbed. To assess whether the gap is merely due to routing inputs through a visual pathway, we add a within-visual probe that renders the 1D serialized content as an image; this layout-disrupted rendering performs worse than native 2D rendering. These findings suggest that, for layout-defined tasks, reducing inputs to 1D serialization is not a neutral choice of representation.

Large language models (LLMs) exhibit strong reasoning capabilities but typically require expensive post-training to reach high performance. Recent test-time alignment methods offer a lightweight alternative, but have been explored mainly for preference alignment rather than reasoning. To bridge this gap, we propose Token-level Adaptive Routing (TARo), which steers frozen LLMs toward structured reasoning entirely at inference time. Specifically, we first train reward models on step-wise mathematical traces to capture fine-grained logical consistency signals, then introduce a learnable token-level router that automatically controls the guidance of the reward model to the base model. Extensive experiments show that TARo significantly improves reasoning performance by up to +22.4% over base model and +8.4% over existing token-level test-time alignment methods, while also boosting out-of-distribution clinical reasoning (MedXpertQA) and instruction following (AlpacaEval). Furthermore, TARo also generalizes from small to large backbones without retraining, extending test-time alignment from preference optimization to robust, cross-domain reasoning.

Previous studies on Natural Language Generation (NLG) from structured data have primarily focused on surface-level descriptions of record sequences. However, for complex structured data, e.g., multi-row tables, it is often desirable for an NLG system to describe interesting facts from logical inferences across records. If only provided with the table, it is hard for existing models to produce controllable and high-fidelity logical generations. In this work, we formulate high-fidelity NLG as generation from logical forms in order to obtain controllable and faithful generations. We present a new large-scale dataset, Logic2Text, with 10,753 descriptions involving common logic types paired with the underlying logical forms. The logical forms show diversified graph structure of free schema, which pose great challenges on the model’s ability to understand the semantics. We experiment on (1) Fully-supervised training with the full datasets, and (2) Few-shot setting, provided with hundreds of paired examples; We compare several popular generation models and analyze their performances. We hope our dataset can encourage research towards building an advanced NLG system capable of natural, faithful, and human-like generation. The dataset and code is available at https://github.com/czyssrs/Logic2Text.