Large language model (LLM) services face rapidly rising serving costs. To sustain free or affordable access for a broad user base, alternative monetization mechanisms are needed. Native advertising offers a promising approach, as it creates economic value by aligning user intent with merchant offerings. Yet how to integrate sponsored content naturally into LLM responses remains largely underexplored. Existing approaches primarily rely on prompt-level injection, multi-pass rewriting, or fine-tuning, which can compromise response quality or introduce additional computational costs. We propose AdSteer, a lightweight decoding-time advertising framework that adaptively adjusts token probabilities to integrate contextually appropriate advertisement into responses. AdSteer calibrates the strength and duration of advertising influence, making sponsored content a natural part of the response. Experiments on GEM-Bench across three application scenarios show that AdSteer achieves an average improvement of 14.1% in overall score over the strongest baselines and 22.5% fewer total tokens on average than rewrite-based methods. These results demonstrate that AdSteer provides an effective and practical solution for native advertising in LLMs.
Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning large-scale models by avoiding backpropagation. However, ZO optimization has a fundamental tension between accuracy and query efficiency. In this work, we show that ZO optimization can be substantially improved by unifying two complementary principles: (i) a projection-based subspace view that reduces gradient estimation variance by exploiting the intrinsic low-rank structure of model updates, and (ii) Muon-style spectral optimization that applies gradient orthogonalization to extract informative spectral structure from noisy ZO gradients. These findings form a unified framework of subspace gradient orthogonalization, which we instantiate in a new method, ZO-Muon, admitting a natural interpretation as a low-rank Muon optimizer in the ZO setting. Extensive experiments on large language models (LLMs) and vision transformers (ViTs) demonstrate that ZO-Muon significantly accelerates convergence and achieves a win-win improvement in accuracy and query/runtime efficiency. Notably, compared to the popular MeZO baseline, ZO-Muon requires only 24.7% of the queries to reach the same SST-2 performance for LLM fine-tuning, and improves accuracy by 25.1% on ViT-L fine-tuning on CIFAR-100.