The Detect Law: Zero-Shot Detection of Machine-Generated Text with an Integer-Exact, Heterogeneity-Aware Sequential Test

Abstract

We present The Detect Law, a zero-shot detector of machine-generated text that combines three per-token signals from two small open language models with an exact 32-bit integer sequential decision rule. A base model (Llama-3.2-1B) and its instruction-tuned twin supply a surprise signal (how much more predictable each token is than the base model expects), a contrast signal (how much more the instruction-tuned model prefers the chosen token), and a repetition signal (whether tokens are reused less often than the base model predicts). Each signal is centred and scaled by constants measured on human-written text only; no detector is trained on machine-generated text. The null model gives every human text its own persistent stylistic bias, which keeps a human text's statistic bounded as the text grows, and the decision rule combines a fixed-length end-of-text test with anytime-valid early stopping derived from Ville's inequality, under a design false-positive budget of 1%. The ranking score is the one-sided chi-bar-squared statistic. On the official RAID test set (672,000 texts: 11 generators, 8 domains, 4 decoding settings, 11 adversarial attacks), RAID's evaluation service reports that The Detect Law detects 92.33% of machine-generated text at a 5% false-positive rate without attacks (86.54% at 1%) and 88.99% when attacks are included (AUROC 96.48). This is the highest score among the zero-shot detectors evaluated on RAID; Binoculars, the strongest previous one, scores 78.98% and 69.54%. The detector needs one forward pass of each of two 1.24B-parameter models per token, and it scored the full RAID test set in 5.6 hours on a single NVIDIA A30 GPU.