Key-Value (KV) cache eviction—which retains the KV pairs of the most important tokens while discarding less important ones—is a critical technique for optimizing both memory usage and inference latency in large language models (LLMs). However, existing approaches often rely on simple heuristics—such as attention weights—to measure token importance, overlooking the spatial relationships be-tween token value states in the vector space. This often leads to suboptimal token selections and thus performance degradation. To tackle this problem, we propose a novel method, namely AnDPro ( An chor D irection Pro jection), which introduces a projection-based scoring function to more accurately measure token importance. Specifically, AnDPro operates in the space of value vectors and leverages the projections of these vectors onto an “Anchor Direction” —the direction of the pre-eviction output—to measure token importance and guide more accurate token selection. Experiments on 16 datasets from the LongBench benchmark demonstrate that AnDPro can maintain 96 . 07% of the full cache accuracy using only 3 . 44% KV cache budget, reducing KV cache budget size by 46 . 0% without compromising quality compared to previous state-of-the-arts.
Zijie Geng, Jie Wang, Ziqi Liu et al.· Advances in Neural Informati...· 6 citations
Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning. Unlike statement-level formalization, proof autoformalization is a long-horizon challenge requiring coordination of claims, contexts, and dependencies across many proof steps, yet has only recently come under focused study. Current approaches either rely on costly model training or apply excessive, unguided repair at inference time. To this end, we introduce ToMap, a multi-agent framework that structures proof autoformalization as a Decomposer-Formalizer-Prover pipeline with efficient test-time optimization guided by formal verification and semantic rubrics for proof quality. Rather than distributing test-time compute across all agents, we perform bottleneck analysis and identify the Decomposer as the critical bottleneck: the quality of its atomic, self-contained proof units directly determines whether downstream agents can successfully formalize and prove each step. ToMap therefore treats the Formalizer and Prover as downstream executors and efficiently focuses test-time compute on Decomposer refinement. This refinement follows a loop inspired by GEPA, evolving prompts over candidate decompositions and using formal verification progress together with semantic proof rubrics to define a Pareto frontier that guides the next decomposition update. Experiments on ProofFlowBench show that ToMap improves over the best previous method by 19.0% when evaluated by both syntactic correctness and semantic faithfulness, while requiring lower test-time cost. Scaling analysis shows that most gains emerge within a few iterations of decomposition evolution, guiding test-time budget selection.
We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.
Zelin Tan, Zhouliang Yu, Bo-Cheng Lin et al.· arXiv.org· 4 citations
