ProSR: Process-Shaped Spatial Reasoning for Reliable Chain-of-Thought in VLMs

Abstract: Reliable spatial reasoning remains a core bottleneck for vision-LLMs (VLMs). Existing mainstream training paradigms for spatial reasoning largely rely on outcome alignment or process imitation, lacking explicit constraints on the reasoning process, and therefore struggle to ensure genuine visual dependence and stable reasoning trajectories. In this paper, we construct a high-quality CoT dataset covering diverse spatial phenomena and diagnose the model's reasoning process, revealing two typical types of process degradation during reinforcement learning optimization: Spurious Grounding, which bypasses visual evidence, and Tail Instability, where uncertainty abnormally rises in the later stage of reasoning. To address these issues, we propose ProSR, a process-shaping optimization framework for spatial reasoning. Through a Counterfactual Invariance Penalty and a Tail Drift Penalty, ProSR extends the optimization objective from single answer correctness to two process-level dimensions: visual dependence and trajectory stability. Experiments on multiple complex and out-of-distribution spatial reasoning benchmarks show that ProSR improves answer accuracy while generating reasoning trajectories that are more stable and more dependent on visual evidence.

• The paper introduces ProSR, a diagnosis-driven GRPO framework that adds counterfactual invariance and tail-drift penalties to make spatial chain-of-thought more visually grounded and stable.
• Vanilla GRPO increased blank-image accuracy from 0.3688 to 0.5354 and late entropy re-rise from 0.0042 to 0.1792, while ProSR reduced these metrics to 0.3214 and 0.0017, respectively.
• ProSR achieved a 69.3 average across five spatial benchmarks, outperforming GeoThinker by 3.7 points and delivering its strongest gains on examples affected by spurious grounding or tail instability.

Motivation and problem statement

Spatial reasoning remains a persistent weakness of vision-LLMs (VLMs): answering correctly requires understanding relative positions, viewpoints, occlusion, and multi-step compositional relations, not just object recognition. The authors of ProSR argue that existing training paradigms—outcome alignment (rewarding final-answer correctness) and process imitation (supervised CoT distillation)—leave the reasoning process itself unconstrained. A model can therefore produce plausible chain-of-thought (CoT) traces that are not genuinely grounded in visual evidence, or whose uncertainty dynamics are unstable near answer generation. The paper's central claim is that final-answer correctness is an insufficient optimization signal for reliable spatial CoT reasoning, and that process-level defects can be diagnosed and converted into reward terms.

Diagnosing process degradation under vanilla GRPO

The paper first constructs a spatial CoT dataset by prompting Gemini-3.1-Pro-Preview to produce short, visually grounded rationales for questions drawn from MindCube, SenseNova-800K, and SPAR-7M. Rule-based filtering (answer correctness, length bounds of 40–400 tokens, a reconsideration-marker count limit, a repeated-sentence limit, and a spatial-anchor ratio threshold $\rho_{\mathrm{anchor}} \ge 0.04$) retains roughly 39–51% of raw traces per source, yielding 22,135 SFT samples and a 44,500-sample GRPO pool.

After supervised fine-tuning on Qwen3-VL-8B-Thinking, the authors run vanilla GRPO with only answer-correctness and format rewards, then perform paired rollout analysis on a balanced 480-example diagnostic set: each question is rolled out both with the original image and with size-matched blank images. Token-level entropy trajectories within the thinking span yield four diagnostic metrics:

Metric	What it measures
Blank-image Accuracy ($A_{\mathrm{blank}}$)	Task success without visual evidence
Same-Answer Rate (SAR)	Answer-level counterfactual invariance
Normalized Trajectory Similarity (NTS)	Shape similarity of entropy trajectories across image conditions
Late-Rise Rate (LRR@$\tau$)	Frequency of late-stage entropy re-rise

This analysis reveals two failure modes induced by outcome-only RL. Spurious Grounding: after GRPO, $A_{\mathrm{blank}}$ rises from 0.3688 to 0.5354 and SAR from 0.3854 to 0.5792 relative to the SFT checkpoint—i.e., RL makes the model more able to answer correctly without images, indicating increased reliance on language priors and dataset shortcuts. Tail Instability: [email protected] jumps from 0.0042 to 0.1792, meaning late-stage entropy frequently rises again rather than converging as the answer approaches. The implication is direct: vanilla GRPO actively degrades both visual dependence and trajectory stability even while improving benchmark accuracy.

The ProSR framework

ProSR converts these two diagnoses into bounded negative reward terms added to the standard GRPO objective:

$$R = R_{\mathrm{acc}} + \lambda_{\mathrm{fmt}}R_{\mathrm{fmt}} + \lambda_{\mathrm{cf}}R_{\mathrm{cf}} + \lambda_{\mathrm{drift}}R_{\mathrm{drift}}$$

Counterfactual Invariance Penalty: during rollouts, an additional blank-image rollout is sampled per prompt; entropy trajectories from both conditions are resampled to fixed length and $\ell_1$-normalized, and their similarity $s_{\mathrm{cf}}$ penalized via a clipped term activated only when original and blank rollouts produce the same answer. This suppresses overly invariant trajectory shapes while leaving genuine answer changes unconstrained.

Tail Drift Penalty: the thinking span is partitioned into early/middle/late segments (ratio 3:4:3), and positive exceedance of the late-segment mean entropy over the middle segment—beyond a margin $m = 0.1$—is penalized. Notably, this does not enforce globally monotonic entropy decay; it targets only unproductive tail-end search.

Both penalties use weight $\lambda = 0.1$, $\tau_{\mathrm{cf}} = 0.4$, and act as bounded diagnostic constraints complementing, not replacing, the answer reward. The extra blank-image rollout adds approximately 12.5% rollout cost at $A_{\mathrm{blank}}$0 samples per prompt.

Benchmark results

Evaluated on five benchmarks (3DSRBench, MindCube-Tiny, ViewSpatial, EmbSpatial, SPAR-Bench), ProSR reaches an average score of 69.3, exceeding the strongest prior baseline GeoThinker (65.6) by 3.7 points and surpassing proprietary systems including Gemini 3 Pro (64.6) and GPT-5.2 (60.5). Relative to its own ablations, ProSR improves the average from 60.8 (SFT-only) to 69.3, and from 64.0 (vanilla GRPO) to 69.3. It achieves 88.6 on MindCube-Tiny—the best score reported—and leads all evaluated models on ViewSpatial (51.4), while ranking second overall behind Gemini 3 Pro on 3DSRBench (62.4).

The diagnostic metrics confirm that accuracy gains coincide with process repair: ProSR reduces $A_{\mathrm{blank}}$1 to 0.3214, SAR to 0.3379, NTS to 0.2916, and [email protected] to 0.0017—all below even the SFT initialization. A failure-aware breakdown shows gains concentrated where degradation is worst: +17.5 points on tail-instability-only cases and +10.9 on cases exhibiting both failures, versus only +0.8 on clean samples. This indicates the method primarily repairs degraded trajectories rather than uniformly shifting behavior.

Ablations and robustness

Ablations isolate complementary roles: the Counterfactual Invariance Penalty alone mainly reduces SAR and NTS (average 67.1), while the Tail Drift Penalty alone mainly reduces [email protected] (average 66.4); combining them yields the best average (69.3) and best diagnostics. An additional ablation shows that filtered spatial CoT supervision matters independently of the RL stage: unconstrained CoT SFT reaches 59.4 average versus 61.7 for filtered data, so part of the benefit stems from grounded data construction rather than reward shaping alone. Sensitivity analyses show stable performance across moderate ranges of both reward weights ($A_{\mathrm{blank}}$2) and diagnostic thresholds ($A_{\mathrm{blank}}$3, $A_{\mathrm{blank}}$4), suggesting the results are not artifacts of narrow hyperparameter choices.

Limitations and open questions

The authors state several limitations explicitly. First, all experiments use a single base model (Qwen3-VL-8B-Thinking); generalization to other VLM architectures is untested. Second, the diagnostics rely on entropy trajectories and blank-image counterfactual probing, which are practical proxies rather than causal measurements: similar entropy trajectories do not necessarily imply identical internal reasoning mechanisms, and blank-image sensitivity estimated from a single matched probe is noisy. Third, a boundary-case analysis on 3DSRBench shows that ProSR can still invert left/right relations during egocentric viewpoint remapping even when object identification and self-rechecking are correct—process shaping improves grounding and stability but does not solve precise coordinate transformation under complex layouts. Whether entropy-based shaping transfers beyond spatial domains, and whether stronger geometric representations could close the remapping gap, remain open.

Conclusion

ProSR demonstrates that two concretely diagnosable process failures of outcome-only reinforcement learning—Spurious Grounding and Tail Instability—can be converted into bounded reward penalties that improve both benchmark accuracy (69.3 average, +3.7 over the strongest baseline) and process-level reliability (all four diagnostic metrics reduced below the SFT baseline). The work's main contribution is methodological: a diagnosis-driven loop in which paired counterfactual rollouts and entropy-trajectory analysis motivate reward design, offering a template for constraining reasoning processes rather than merely imitating or rewarding them.