This paper identifies that misinterpreting the context can be a significant issue during the reasoning process of large language models, spanning from smaller models like Llama3.2-3B-Instruct to cutting-edge ones like DeepSeek-R1. We introduce a novel, post-training approach called **Stick to the Facts (SIFT)** to tackle this. SIFT leverages increasing inference-time compute to ground LLM reasoning in contexts. At the core of SIFT lies the Sticker, which is generated by the model itself to explicitly emphasize the key information within the context. Given the Sticker, SIFT generates two predictions—one from the Sticker alone and one from the query augmented with the Sticker. If they differ, the Sticker is sequentially refined via forward optimization (to better align the extracted facts with the query) and inverse generation (to conform with the model’s inherent tendencies) for more faithful reasoning outcomes. Studies across diverse models (from 3B to 100B+) and benchmarks (e.g., MATH, AIME) reveal consistent performance improvements. Notably, SIFT improves the pass@1 accuracy of DeepSeek-R1 on AIME2024 from 78.33% to **85.67%** and that on AIME2025 from 69.8% to **77.33%**. Code will be public after acceptance.

Mixture of experts (MoE) has become the standard for constructing production-level large language models (LLMs) due to its promise to boost model capacity without causing significant overheads. Nevertheless, existing MoE methods usually enforce a constant top-k routing for all tokens, which is arguably restrictive because various tokens (e.g., "<EOS>” vs. “apple”) may require various numbers of experts for feature abstraction. Lifting such a constraint can help make the most of limited resources and unleash the potential of the model for downstream tasks. In this sense, we introduce **AdaMoE** to realize token-adaptive routing for MoE, where different tokens are permitted to select a various number of experts. AdaMoE makes minimal modifications to the vanilla MoE with top-k routing—it simply introduces a fixed number of *null experts*, which do not consume any FLOPs, to the expert set and increases the value of k. AdaMoE does not force each token to occupy a fixed number of null experts but ensures the average usage of the null experts with a load-balancing loss, leading to an adaptive number of null/true experts used by each token. AdaMoE exhibits a strong resemblance to MoEs with expert choice routing while allowing for trivial auto-regressive modeling. AdaMoE is easy to implement and can be effectively applied to pre-trained (MoE-)LLMs. Extensive studies show that AdaMoE can reduce average expert load (FLOPs) while achieving superior performance. For example, on the ARC-C dataset, applying our method to fine-tuning Mixtral-8x7B can reduce FLOPs by 14.5% while increasing accuracy by 1.69%.Code is available at [this link](https://github.com/CengZihao/AdaMoE).