Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Refined Detection for Gumbel Watermarking

Tor Lattimore

Abstract

We propose a simple detection mechanism for the Gumbel watermarking scheme proposed by Aaronson (2022). The new mechanism is proven to be near-optimal in a problem-dependent sense among all model-agnostic watermarking schemes under the assumption that the next-token distribution is sampled i.i.d.

Refined Detection for Gumbel Watermarking

Abstract

We propose a simple detection mechanism for the Gumbel watermarking scheme proposed by Aaronson (2022). The new mechanism is proven to be near-optimal in a problem-dependent sense among all model-agnostic watermarking schemes under the assumption that the next-token distribution is sampled i.i.d.

Paper Structure

This paper contains 26 sections, 10 theorems, 66 equations, 3 algorithms.

Table of Contents

  1. Introduction
  2. Detection
  3. Contribution
  4. Related work
  5. Notation
  6. Null and alternative hypotheses
  7. Entropy-like quantities
  8. Exponential detection
  9. Power law detection
  10. Step 1: Setup and main argument
  11. Step 2: Case-by-case argument
  12. Lower bounds
  13. Step 1: Setup and entropy inequalities
  14. Step 2: Bounding the chi-squared divergence
  15. Step 3: Finishing up
  16. ...and 11 more sections

Key Result

Theorem 2

If alg:detect is run with input $(A_t)_{t=1}^n$ sampled using alg:water and using the same key and $\delta \in (0,1)$ and $\epsilon = \log(1/\delta) / n$, then where $C > 0$ is a universal constant and $\tau = \Theta(\sqrt{n \log(n) \log(1/\delta)})$ is defined in lem:null.

Theorems & Definitions (29)

  • Remark 1
  • Theorem 2
  • Lemma 3: fernandez2023three
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • Lemma 6
  • proof
  • proof : Proof of \ref{['thm:upper']}
  • ...and 19 more