claudini/claudini/methods/original/mc_gcg

name, full_name, reference, paper_url, code

name	full_name	reference	paper_url	code
MC-GCG	Multi-Coordinate GCG	jia2025improved	https://arxiv.org/abs/2405.21018	https://github.com/jiaxiaojunQAQ/I-GCG

MC-GCG — Multi-Coordinate GCG

Paper: Jia et al., "Improved Techniques for Optimization-Based Jailbreaking on Large Language Models" (ICLR 2025) Links: arXiv | Code \cite{jia2025improved}

Algorithm

MC-GCG extends GCG with a progressive multi-coordinate merging strategy (called "automatic multi-coordinate updating" in the paper). Instead of keeping the single best candidate per step, it:

1. Generates B single-token candidates (standard GCG sampling)
2. Evaluates all B candidates and sorts by loss
3. Takes the top-K best candidates
4. Progressive merge: greedily merges token changes from the top-K candidates to create K merged candidates with increasing numbers of changed positions
5. Evaluates the K merged candidates and keeps the best

The merging works as follows: starting from the current suffix, iterate through the top-K candidates (best first). For each candidate, wherever it differs from the original suffix, apply that change to the running merged suffix. This creates K candidates that accumulate more and more beneficial single-token changes.

The paper also proposes diverse target templates and easy-to-hard initialization, which are jailbreak-specific and not implemented here.

Hyperparameters

Parameter	Default	Description
search_width	512	Number of single-token candidates (B)
topk	256	Top-k tokens per position for gradient sampling
n_replace	1	Tokens replaced per candidate (standard GCG)
merge_k	7	Number of top candidates to merge (K)

The paper uses K=7 as the default merge depth.

Notes

• The paper calls the full method "I-GCG" but we use "MC-GCG" to avoid confusion with the existing i_gcg package (Li et al. 2024, LSGM/LILA), which is a different paper.
• The progressive merge adds K extra forward passes per step (for evaluating merged candidates), which is negligible compared to the B candidate evaluations.
• The merge can change up to K positions per step, but the actual number depends on how many of the top-K candidates change different positions.