Open-world 3D affordance grounding requires localizing functional object parts in 3D given free-form language queries. Existing methods typically assume pre-built object-centric 3D geometry and closed affordance ontologies, limiting deployment from raw RGB observations. We present AffordAny, an end-to-end framework that uses one monocular RGB image to construct large-scale text-conditioned 3D part supervision, ground affordances with a frozen vision-language model (VLM) guided decoder, and improve open-world generalization through pseudo-label self-training. Our automated pipeline produces a benchmark of 5,334 objects and 10,633 part-level samples spanning 473 categories, an order-of-magnitude increase in categorical diversity over prior work. The decoder progressively fuses frozen Cosmos-2B features with 3D geometry through spatial projection, instruction-conditioned semantic compression, and bidirectional geometry-semantics interaction. Minimal-perturbation pseudo-label self-training further adds new objects without human annotation. Under a systematic generalization protocol evaluating unseen objects, unseen categories, and unseen instruction paraphrases, our approach achieves 0.428 IoU on unseen objects and 0.315 IoU on unseen categories after self-training, with unseen-category mIoU improving by 6.3% relative (p<0.01) and an instruction sensitivity gap of only 0.105, demonstrating effectiveness and robustness of our method.
A model's agreement across perturbed inputs is used both as a label-free reliability signal and as a self-training target, on the premise that agreement tracks correctness. That coupling is rarely measured directly: natural-image perturbations preserve meaning only by assumption, and no exact answer key localizes errors. Scientific figures remove both obstacles, a figure is drawn from data by a program, so redrawing it yields images that are semantically equivalent by construction and share a programmatically exact answer. We build RENDEQ, a generator of such render-equivalence sets, and measure the coupling on three open-weight VLMs, checking every finding across three independent instantiations. Re-rendering beats resampling on both accuracy and reliability. Agreement beats an evidence-carrying baseline, mean token log-probability, on two of three models and ties on the third, reversing an intermediate, buggy replication traced to a rendering-pipeline failure. The dispersion behind this is concentrated in one style factor, the plotting library, more than double the next-largest factor and an order of magnitude above the noise floor. Fine-tuning on the model's own cross-render consensus inverts: accuracy falls in every one of five replication runs, the opposite sign to published results on natural images. Agreement certifies correctness only above a threshold set by how diffuse a model's errors are, and an objective that rewards agreement destroys exactly that diffuseness.
Achieving human-like reasoning in Vision-Language Models (VLMs) remains a long-standing challenge. Recent approaches leverage Chain-of-Thought (CoT) rationales generated by human annotators or proprietary models, which are costly and difficult to scale. Self-training offers a promising alternative but often suffers from visual hallucinations and language shortcuts because rationales are filtered only by answer correctness without verifying visual perception. We propose a perception-verified self-training framework that enforces visually grounded reasoning. Our method employs a CoT template (caption-reasoning-conclusion) that disentangles perception from reasoning, enabling independent verification of visual understanding. To compensate for the absence of ground-truth captions, we introduce PerceptEval, an unsupervised method that evaluates caption quality based on its alignment with visual and textual elements in the image. Using caption verification together with answer correctness, we partition the data into easy, medium, and hard subsets and design a two-stage curriculum learning strategy. Stage 1 trains on easy samples, while Stage 2 enhances medium samples by regenerating reasoning conditioned on verified captions and retaining only those with correct conclusions. This ensures training is performed exclusively on perceptually grounded reasoning, reducing hallucinations and language shortcuts. Extensive experiments across diverse domains and models demonstrate improvements of up to 16% over standard self-training baselines, showing that our framework provides a scalable and cost-effective solution for advancing multimodal reasoning without manually annotated CoT rationales.