The Verifiability Gap in table reasoning arises when multimodal LLMs produce correct answers while grounding intermediate steps in unsupported visual evidence. Intermediate visual claims are often not exposed in a symbolically addressable form, making standard RL with verifiable rewards unable to reliably inspect whether a reasoning step is actually supported by the image. We mitigate this gap for table reasoning with Anchored Reasoning, which turns each reasoning step into a checkable (coordinate, value, structural role) claim over the table grid. We instantiate this paradigm as V-tableR1: a policy VLM generates anchor-laden visual chains-of-thought, while a learned critic VLM estimates anchor fidelity against the source image. The policy is trained with PGPO, a GRPO-based process-guided formulation that integrates critic-gated trajectory rewards with stabilization mechanisms for long anchor-laden rollouts. V-tableR1 (4B) achieves the best open-source average accuracy across seven tabular reasoning benchmarks, obtains state-of-the-art results on several individual datasets, surpasses open-source models up to 18× its size in aggregate, and improves over its SFT baseline by up to 10.66% absolute accuracy.

Large vision–language models (LVLMs) excel at multimodal reasoning but still suffer from object-existence hallucinations when multi-step deliberation decouples from visual evidence. Think-with-Images (TwI) attempts to counter this by generating auxiliary observations (e.g., zoomed crops or highlighted views), yet it is not reliably beneficial. We identify two coupled failure modes: (1) a granularity–context trade-off of common operators, where zoom-in improves local detail but breaks global relations, while highlighting preserves topology but lacks fine evidence; and (2) an over-trust issue in tool-guided region proposals, where mislocalized evidence can dominate reasoning and even underperform standard prompting. We propose Active-Look, a training-free, plug-and-play TwI framework that allocates visual computation by uncertainty. Active-Look runs two heterogeneous grounding experts in parallel and uses their disagreement as a proxy for uncertainty, spending the budget only to verify disputed regions. It further mitigates the operator trade-off with conflict-aware hybrid rendering: highlighting retains global context, while selective zoom-in performs local verification. Experiments on hallucination-focused and general benchmarks (POPE, MME, and CHAIR) across multiple LVLM backbones show consistent gains.