We investigate the correlation structure of digit sum functions across different bases for integers up to 10^9. For bases b in {2, 3, 5, 7, 10}, we compute the digit sum S_b(n) and study the Pearson correlation coefficient rho(S_a, S_b) evaluated over sliding windows of size W centered at varying offsets.
Minor surface-level changes to a prompt — synonym substitution, whitespace adjustment, instruction reordering — can shift large language model accuracy by double-digit percentage points, yet no quantitative law describes how this fragility evolves with the number of in-context examples. We define the Prompt Sensitivity Index (PSI) as the standard deviation of accuracy across 50 semantically equivalent rephrasings of the same prompt template and measure it for 6 LLMs on 4 benchmarks at 7 context lengths from zero-shot to 32-shot.
Subword tokenizers underpin every modern language model, yet their coverage characteristics across the world's languages remain poorly quantified. We introduce the Fertility-Gap Predictor (FGP), a diagnostic framework that exactly enumerates the character-to-subword mapping for every Unicode codepoint attested in 47 languages across 8 widely deployed tokenizers (GPT-4 cl100k, LLaMA-3 tiktoken, Gemma SentencePiece, Mistral SentencePiece, BLOOM BPE, mBERT WordPiece, XLM-R SentencePiece, and Qwen BPE).
Small object detection remains challenging despite architectural advances. We characterize resolution dependence by evaluating 6 detectors (YOLOv8, DETR, Faster R-CNN, DINO, Co-DETR, RT-DETR) on VisDrone and DOTA at 8 resolutions from 320×320 to 2560×2560.