Large language models (LLMs) have demonstrated strong performance on structured reasoning tasks, but what they encode and whether it informs model behavior remain unclear. We investigate this question through geometric reasoning, using parametric CAD constraints as a controlled testbed for separating local pairwise relations from sketch-level constraint status. By probing the hidden states of six frozen decoder-only LLMs, we examine four properties: linear decodability, forced-choice generation, activation-level influence, and behavioral steerability. Pretraining substantially improves the decoding of local geometric relations, and this advantage persists after accounting for positional cues with shuffled-order controls. In contrast, sketch-level DOF status is already highly decodable from randomly initialized representations and improves only modestly with pretraining, indicating that much of its probe performance is available without learned weights. Further analyses show that decodable information is not always actionable. Generation often fails to express this information, and on the two intervention-tested backbones, activation-restoration effects at the patched entity position vanish while decodability persists across depth. Mean-difference steering also does not reliably control outputs. These results show that decodability, generation, activation-level influence, and steerability can diverge in the tested setting. The audit provides a controlled way to distinguish failures to encode geometric structure from failures to express or control encoded information.
When visual evidence is occluded or chaotic, models should abstain. In this paper, we show that Vision-Language Models (VLMs) can internally distinguish when abstention is required, but fail to express it anyway. We introduce TRAPSBench, a procedurally generated video benchmark of 1,404 matched physics pairs in which a single targeted change renders the outcome undeterminable from the visual evidence. Furthermore, we introduce Penalized Epistemic Calibration Score (PECS), a new robust metric that requires models to both answer correctly when the outcome is knowable, and abstain when the outcome is not. Across 16 VLMs spanning five families, spontaneous restraint is poor: the best PECS is 0.292. The bottleneck is expression, not perception: linear probes decode answerability from hidden states at up to 0.91 AUROC across physics domains; steering a single-layer void direction causally induces or suppresses abstention. Our results replicate across three open-weight families (Qwen, Gemma, LLaVA). The failure is also more pronounced in visual than textual uncertainty: models detect textual impossibility about 4x more readily than missing visual evidence. Closing this representation--output gap likely requires output-stage interventions.
This work test whether action maps fitted without a source reach its natural post-action activation and compose and validate the geometric branch on a known affine S_5 carrier: all held-source folds pass one-step, composition, inverse, decoding, and commutativity gates.
Chain-of-Thought (CoT) improves the reasoning ability of Large Language Models (LLMs) but incurs substantial computation and context costs. Existing methods either lose intermediate information through hard pruning or lack a principled criterion for continuous compression. We present A*-Thought-V2, a geometric dynamics of LLM guided framework that models CoT as a hidden-state trajectory and replaces hard deletion with an explicit-implicit interleaved latent architecture. After projecting question, step, and solution representations into a 3D PCA space, it measures alignment between each local transition and global question-to-solution direction. Aligned steps remain explicit text, whereas deviating steps are compressed into continuous latent tokens. Directional angles capture both local semantics and reasoning dynamics: small angles indicate direct execution and answer formation, while large angles more frequently involve checking, correction, and branch exploration; their temporal variation reveals exploration, convergence, and refinement stages. To train this architecture, we introduce stepwise embedding forcing, which pools each redundant step into a single latent embedding, and label forcing, which supervises that latent token with a soft multi-modal vocabulary distribution instead of a hard one-hot label. Experiments on Qwen3.5-9B and Qwen3.6-27B across six in-domain and out-of-domain benchmarks show that A*-Thought-V2 improves average accuracy by up to 2.6% while reducing response length by up to half, increasing Accuracy per Computation Unit by 2.29$\times$, and reducing preprocessing and training time by 94.6% and up to 80.3%, respectively. Representation analyses suggest that latent states form a compact region distinct from textual states, while higher entropy at latent-token positions reflects broader soft targets that encourage richer step-level feature learning.
Xiaoang Xu, Siyuan Liu, Shuo Wang et al.· 0 citations
The results suggest that VLAs have rich, linearly readable internal representations of semantic quantities like task progress, and that learning to read these signals offers a lightweight, interpretable path toward monitoring deployed visuomotor policies.
Atiksh Bhardwaj, E. W. Duan, Prithwish Dan et al.· 0 citations
Multimodal large reasoning models often rely on long Chain-of-Thought (CoT) traces in which a substantial fraction of tokens, such as repeated visual descriptions, self-reflection, and other visually-disengaged filler, inflate inference cost without contributing to the answer. Existing CoT compression methods optimize output length but never measure whether a reasoning token is actually grounded in the image. We propose \textbf{VIG} (Visual Information Gain), an information-theoretic GRPO reward that scores each reasoning token by how much the image reduces its predictive uncertainty. VIG is computed online from two forward passes of the same policy, one with and one without the image, so no reference chains, external annotations, or auxiliary reward models are needed. Across six main multimodal reasoning benchmarks and three Qwen3-VL-Thinking model sizes (2B/4B/8B), plus an additional R1-Onevision-Bench evaluation on 8B, VIG consistently improves the accuracy--efficiency trade-off, supporting our central claim: \emph{efficient multimodal reasoning emerges from raising visual information density, where every reasoning token earns its place by anchoring to the image, rather than from imposing a length budget.} Our source code is available at https://github.com/chaser682/vig.
Wen Luo, Xiaohan Yi, Xiaotao Huang et al.· 0 citations
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