In post-training large language models (LLMs), supervised fine-tuning (SFT) provides expert guidance but can overfit, while reinforcement learning (RL) enables exploration but often suffers from cold-start and sparse-reward issues. Although combining SFT with RL is intuitive, naively mixing off-policy expert data into on-policy RL can induce distribution shift and destabilize optimization. We propose APEX, a framework that harmonizes off-policy guidance and on-policy exploration via a Cognitive State Awareness mechanism. Specifically, APEX leverages a perplexity-based Student’s -test to compare the sequence-level perplexity distributions of on-policy generations against candidate offline data. This comparison diagnoses whether failures reflect sampling stochasticity or missing knowledge. Guided by this diagnosis, APEX adaptively gates GRPO optimization and modulates SFT supervision. The framework preferentially selects offline samples that are statistically consistent with the current on-policy distribution to guide RL updates, while filtering out high-shift data and verifiably incorrect samples that could destabilize training. APEX also uses a dynamically weighted SFT loss when needed. Extensive experiments show that APEX improves over SFT-then-RL by +7.10 points in average pass@1 on six math benchmarks and by +15.50 points on three general reasoning benchmarks.

Reasoning-driven universal multimodal embedding has advanced rapidly by introducing Chain-of-Thought (CoT) reasoning into the embedding pipeline. Despite the strong performance across both general and complex tasks, this paradigm suffers from two core limitations: (i) autoregressive CoT reasoning incurs high computational cost, making it impractical for low-latency retrieval; and (ii) embedding performance is heavily coupled with CoT annotation quality, making large-scale training unreliable. These raise fundamental questions:Is textual CoT the optimal form of reasoning for embedding, and can effective embedding reasoning be accomplished in latent space? To this end, we propose LaME (Latent Reasoning Multimodal Embedding), which formulates embedding-oriented latent reasoning as a weakly supervised information bottleneck. LaME employs K learnable reason tokens as a fixed-capacity bottleneck, completing all reasoning within a single forward pass. The two weak supervision signals structurally decouple contrastive from autoregressive objectives and eliminate dependence on CoT annotations, while a two-stage training pipeline ensures stable convergence. Experiments on MMEB-v2 and MRMR show that LaME achieves competitive performance, surpassing some explicit CoT-based models, while delivering 60× faster inference than explicit CoT methods and 2× faster than latent baselines with throughput comparable to discriminative embedding models. The code is available at https://github.com/PeppaWu/LaME.

Speculative decoding (SD), where a small draft model is employed to propose draft tokens in advance and then the target model validates them in parallel, has emerged as a promising technique for LLM inference acceleration. Many endeavors to improve SD are to eliminate the need for a draft model and generate draft tokens in a retrieval-based manner in order to further alleviate the drafting overhead and significantly reduce the difficulty in deployment and applications. However, retrieval-based SD relies on a matching paradigm to retrieve the most relevant reference as the draft tokens, where these methods often fail to find matched and accurate draft tokens. To address this challenge, we propose LogitSpec to effectively expand the retrieval range and find the most relevant reference as drafts. LogitSpec is motivated by the observation that the logit of the last token can not only predict the next token, but also speculate the next next token. Specifically, LogitSpec generates draft tokens in two steps: (1) utilizing the last logit to speculate the next next token; (2) retrieving relevant reference for both the next token and the next next token. LogitSpec is training-free and plug-and-play, which can be easily integrated into existing LLM inference frameworks. Extensive experiments on a wide range of text generation benchmarks demonstrate that LogitSpec can achieve up to 2.61× speedup and 3.28 mean accepted tokens per decoding step.