Log Polar Visual Tokenization for Compute Bounded Human Aware Perception in Low Cost Social Robots: A Five Seed Matched Token Study

Low-cost social robots must perceive people and nearby obstacles under tight compute and sensing budgets. Reducing the number of visual tokens is a plausible way to cut transformer attention cost, but comparisons between spatial tokenizers are easily confounded when they use different token counts. This preprint evaluates a log-polar visual representation against both a 64-token Cartesian baseline and a matched 48-token Cartesian control in a PyBullet/Gymnasium human-aware mobile-robot simulation. The study uses five independent training seeds and episode-separated train, validation, test, and out-of-distribution (OOD) partitions. It covers six human-intention labels, eight sensor-condition classes, and a recorded bank of simulated robot-human scenes (48 task-condition snapshots from third-person and robot cameras, plus nine simulated recordings). Key findings: OOD intention accuracy was 94.90% for Cartesian-64, 94.37% for Cartesian-48, and 94.72% for log-polar-48. The paired log-polar-48 versus Cartesian-48 difference was +0.35 percentage points (95% seed-bootstrap interval [−0.32, +0.93], descriptive p = 0.394), so the experiment does not establish a geometry-specific accuracy advantage. Moving from 64 to 48 visual tokens reduces the theoretical attention-pair count per layer from 5,041 to 3,025 (about 40%). Median forward-pass latency on a Colab Tesla T4 fell from 0.02980 to 0.02323 ms/sample (about 22%) versus Cartesian-64. The comparison against the matched Cartesian-48 control was not statistically significant. Log-polar-48 had higher expert-action MAE than Cartesian-48 (0.0594 versus 0.0480), a reminder that intention accuracy and continuous action imitation are not interchangeable. The findings support a promising token-efficiency and perception trade-off, not universal log-polar superiority, real-robot deployment, or safe control. All observations and human agents are simulated, the teacher is a privileged simulation expert (not a pretrained VLA), and latency was measured on a T4 only, not on Raspberry Pi 5 or other edge hardware. This is one of two companion reports from the same experimental campaign. The companion study examines reliability-biased multimodal attention (MDTA) and reliability-aware adaptive feedback learning (RA-AFL) and reports a negative result.