The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning

Current Large Reasoning Models (LRMs) exhibit remarkable general capabilities but significantly underperform in spatial reasoning tasks. Existing approaches treat this gap as a knowledge deficit, relying on supervised fine-tuning (SFT) to ingest labeled spatial data from external vision sources or synthetic engines. In contrast, we argue that for many tasks, spatial reasoning capabilities are already present in pre-trained LRMs but require alignment through logical coherence under geometric 2D and 3D constraints. In this work, we propose a self-supervised reinforcement learning (RL) framework that targets the internal reasoning process without requiring ground-truth annotations. By formalizing the notion of consistency verifiers -- reward functions that check for geometric and semantic consistency under transformations -- we demonstrate that models can improve their spatial reasoning abilities. We use both image transformations, like flipping, and textual transformations, like swapping the order of objects in the question, and propose a new optimal transport-based RL strategy, OT-GRPO, which is a minimal-matching variant of group relative policy optimization tailored to pairwise verifiers. We show that this label-free consistency training approaches the accuracy of models trained with ground-truth supervision and achieves similar generalization across diverse tasks and data domains.

Consistency Training Along the Transformer Stack

Consistency training encourages models to behave similarly across different contexts, and has shown promise for reducing misalignment. We broaden the scope of consistency training in two ways. First, we introduce two new internal consistency targets: MLP Consistency Training (MLPCT), which matches post-activation MLP states, and Attention Consistency Training (AttCT), which matches per-head attention distributions. Second, we apply consistency training to four additional safety threats: persona in-context learning attacks, adversarial frustration, prefill attacks, and conditional misalignment. Across several models and threat settings, we find that consistency training reduces misalignment well beyond the sycophancy and jailbreak settings studied in prior work. We also find cases of cross-threat generalization, where training against one failure mode improves robustness to another, and identify a shared residual-stream mechanism underlying ACT, MLPCT, and AttCT, while distinguishing BCT as mechanistically distinct. Our results suggest that consistency training is a flexible and extensible framework for alignment, capable of unifying defenses against a broader class of model pathologies.

Consistency Training while Mitigating Obfuscation via Rate Matching

Large language models are often influenced by extraneous input features, such as cues revealing a user's preferred answer. Consistency training reduces this influence by training models to behave similarly across inputs with and without the extraneous feature. However, existing methods train for consistency over entire responses or internal activations, which also constrains whether the model verbalises said extraneous features. We show this leads to obfuscation, where the model learns not to mention a cue while remaining influenced by it, which may undermine monitorability. To address this, we introduce Rate Matching Consistency Training (RMCT), which trains for consistency over selected behavioural properties without constraining how this behaviour is expressed. RMCT matches the rate at which the model exhibits a target behaviour (e.g., following a bias cue) across input perturbations, rather than requiring paired inputs with and without the extraneous feature, extending consistency training to settings where the extraneous features cannot be removed. We evaluate RMCT on sycophancy reduction in two open-weight language models, achieving reductions in bias-following comparable to a standard consistency-training baseline on held-out bias types, while largely preserving the model's tendency to verbalise the bias cue. Further, we find that RMCT is more data-efficient at the expense of being less compute-efficient in our experiments. Overall, RMCT shows that consistency training can improve behavioural robustness without directly trading off against monitorability.

Reducing Political Manipulation with Consistency Training

Large language models (LLMs) exhibit systematic political bias across a variety of sensitive contexts. We find that LLMs handle counterpart topics from opposing political sides asymmetrically. We refer to this phenomenon as covert political bias and identify 7 categories of techniques through which it operates. We propose two metrics for covert bias: Sentiment Consistency measures symmetry in rhetoric and framing across paired political prompts; Helpfulness Consistency measures symmetric depth and engagement. To reduce both types of covert bias, we introduce Political Consistency Training (PCT), an RL training method with two complementary paradigms: Sentiment Consistency Training and Helpfulness Consistency Training. We show that PCT preserves overall helpfulness, substantially reduces covert political bias, and generalizes to held-out benchmarks. We release our work at https://political-manipulation.ai