Autoregressive large models have recently advanced Text-to-SVG generation from simple icons to complex, long-context graphics, yet standard autoregressive decoding often fails to maintain global consistency across geometry, layout, occlusion, and composition. We introduce CANVAS (Consistency-Aware Navigation via Visual Adaptive Sampling), a training-free, render-aware inference framework that combines power-sharpened trajectory likelihood with visual feedback from rendered futures and derives a stroke-wise navigation rule. It effectively estimates each candidate stroke's future value under a limited generation and rendering budget and adaptively allocates samples according to candidate uncertainty, decision influence, and rollout cost. Experiments across multiple autoregressive SVG backbones and complementary benchmarks demonstrate improvements in global consistency, which includes sound geometric relationships, spatial layouts, occlusion ordering, and overall composition, without additional training, demonstrating the effectiveness and generalization ability of our framework.
In image and surface-based learning tasks, convolutional features are typically extracted using receptive fields that are sampled uniformly across the entire domain. However, informative structures are rarely distributed uniformly in practice and are often concentrated in localized regions. Such phenomena are particularly common in medical imaging, where pathological changes are spatially confined. Consequently, uniform convolution allocates equal computational effort to both informative and uninformative regions, resulting in inefficient feature extraction and suboptimal utilization of model capacity. To address this issue, we propose a framework for task-adaptive sampling that dynamically redistributes computational attention according to the spatial importance of the data. Specifically, we introduce the Density-Equalizing Convolutional Neural Network (DECNN), which employs density-equalizing mappings to guide convolution through a learned density function. The density function encodes the relative importance of different regions and induces a transformation that enlarges informative areas while compressing less relevant ones. As a result, convolutional receptive fields are redistributed non-uniformly over the domain, enabling denser sampling in task-relevant regions. By coupling this importance-driven transformation with convolution, DECNN performs adaptive feature extraction that focuses computational resources on informative structures. This leads to more efficient use of model capacity, yielding a lightweight yet expressive architecture while simultaneously producing an interpretable saliency map. Experiments on image classification and craniofacial surface analysis demonstrate that DECNN achieves competitive or superior performance with fewer parameters, accurately identifies task-relevant regions, and remains robust under complex geometric variations.