Large Language Models (LLMs) are powerful text generators, yet they can produce toxic or harmful content even when given seemingly harmless prompts. This presents a serious safety challenge and can cause real-world harm. Toxicity is often subtle and context-dependent, making it difficult to detect at the token level or through coarse sentence-level signals. Moreover, efforts to mitigate toxicity often face a trade-off between safety and the coherence, or fluency, of the generated text. In this work, we present a targeted subspace intervention strategy based on gradient signals for identifying and suppressing hidden toxic patterns from underlying model representations, while preserving the overall ability to generate safe, fluent content. On the RealToxicityPrompts, our method achieves strong mitigation performance compared to existing baselines while imposing minimal impact on inference complexity. Across LLMs, our approach reduces the toxicity of state-of-the-art detoxification systems by 8-20%, while maintaining comparable fluency. We further validate cross-benchmark generality on ToxiGen, where the same gains hold under adversarial, implicitly toxic prompts. Through extensive quantitative and qualitative analyses, we show that our approach achieves effective toxicity reduction without impairing generative performance, consistently outperforming existing baselines.

Multi-agent debate improves the reliability of large language models (LLMs) through iterative peer critiques. However, fixed topologies often introduce persistent positional biases, amplify unreliable agents, and cause high sensitivity to role assignments. We introduce Permutation-Equivariant Adaptive Routing Multi-Agent Debate (PEAR), an inference-time protocol that dynamically reconfigures communication roles and sparse topologies across consecutive debate rounds. By strategically switching agent-to-role assignments based on evolving agent states, PEAR prevents any agent from permanently occupying a privileged network position or distributes influence more evenly across the debate. We theoretically characterize PEAR as an equivariant sparse router: it preserves accuracy under agent relabeling while reducing routing complexity and improving generalization. Comprehensive empirical evaluations across four reasoning benchmarks and six diverse LLM backbones demonstrate PEAR significantly improves average accuracy over the strongest debate baselines. The code is at https://github.com/EVIEHub/PEAR.

The application of span detection grows fast along with the increasing need of understanding the causes and effects of events, especially in the finance domain. However, once the syntactic clues are absent in the text, the model tends to reverse the cause and effect spans. To solve this problem, we introduce graph construction techniques to inject cause-effect graph knowledge for graph embedding. The graph features combining with BERT embedding, then are used to predict the cause effect spans. The results show our proposed graph builder method outperforms the other methods w/wo external knowledge.