Mixed-precision quantization (MPQ) assigns a different bitwidth to each linear layer of a large language model (LLM) to minimize the quantization-induced quality loss under a fixed budget, but Mixture-of-Experts (MoE) models contain these layers in every expert of every MoE block, so the allocation space grows far larger than in a dense model. Existing methods either allocate within each block under a uniform per-block budget, or allocate across blocks through an additive proxy, and neither directly optimizes a model-level objective over the choices that couple the blocks. We propose Q-Strata, a bi-level allocator that ranks within-block assignments with a cheap proxy and allocates across blocks with a model-level objective evaluated on the assembled quantized model. Its inner stage caches a Pareto frontier of candidates per block over finely spaced budgets, leaving the outer stage to set one budget per block instead of a bitwidth for every linear layer. With the search reduced to one budget per block, the outer stage optimizes this model-level objective directly, capturing the inter-block coupling that additive proxies miss. On Mixtral-8x7B-Instruct, Qwen1.5-MoE-A2.7B, and DeepSeek-V2-Lite, Q-Strata consistently achieves lower WikiText2 perplexity than uniform-bitwidth GPTQ and the state-of-the-art MoE MPQ methods MxMoE and GEMQ in the low-bit regime. The code is available at https://github.com/snu-mllab/Q-Strata/tree/main.

The deployment of large-scale generative models is often restricted by their potential risk of causing harm to users in unpredictable ways. We focus on the problem of black-box red teaming, where a red team generates test cases and interacts with the victim model to discover a diverse set of failures with limited query access. Existing red teaming methods construct test cases based on human supervision or language model (LM) and query all test cases in a brute-force manner without incorporating any information from past evaluations, resulting in a prohibitively large number of queries. To this end, we propose Bayesian red teaming (BRT), novel query-efficient black-box red teaming methods based on Bayesian optimization, which iteratively identify diverse positive test cases leading to model failures by utilizing the pre-defined user input pool and the past evaluations. Experimental results on various user input pools demonstrate that our method consistently finds a significantly larger number of diverse positive test cases under the limited query budget than the baseline methods.The source code is available at https://github.com/snu-mllab/Bayesian-Red-Teaming.