Ningyuan Li

Xiaotie Deng, Hanyu Li, Ningyuan Li · pku

In this work, a convergence lemma for function $f$ being finite compositions of analytic mappings and the maximum operator is proved. The lemma shows that the set of $δ$-stationary points near an isolated local minimum point $x^*$ is shrinking to $x^*$ as $δ\to 0$. It is a natural extension of the version for strongly convex $C^1$ functions. However, the correctness of the lemma is subtle. Analytic mappings are necessary for the lemma in the sense that replacing it with differentiable or $C^\infty$ mappings makes the lemma false. The proof is based on stratification theorems of semi-analytic sets by Łojasiewicz. An extension of this proof presents a geometric characterization of the set of stationary points of $f$. Finally, a notion of stability on stationary points, called convergence stability, is proposed. It asks, under small numerical errors, whether a reasonable convergent optimization method started near a stationary point should eventually converge to the same stationary point. The concept of convergence stability becomes nontrivial qualitatively only when the objective function is both nonsmooth and nonconvex. Via the convergence lemma, an intuitive equivalent condition for convergence stability of $f$ is proved. These results together provide a new geometric perspective to study the problem of "where-to-converge" in nonsmooth nonconvex optimization.

Ningyuan Li, Haiyang Shen, Mugeng Liu et al.

Recent advances in large language models and tool-using agents have expanded the range of benchmarked web tasks. Yet an important class of specialized retrieval tasks remains undercharacterized. On many specialized data-retrieval websites, answer-bearing evidence becomes accessible only after establishing the correct site-specific retrieval state through filters, views, hierarchies, or scopes. We term this capability state-gated retrieval (SGR). We introduce SGR-Bench, a benchmark for this setting containing 100 expert-curated tasks spanning six source families and 12 public data ecosystems. Each task requires discovering the appropriate website and configuring its site-specific retrieval state to produce a structured answer. SGR-Bench pairs constraint-guided and goal-oriented formulations of the same underlying problems, enabling controlled comparisons between explicit and implicit guidance for state-gated retrieval. We evaluate eight CLI-based agentic LLM systems and three commercial search-agent products. On SGR-Bench, the strongest system reaches only 66.18% item-level F1, while row-level F1 remains much lower. A manual audit of 156 analyzable failed CLI trajectories shows why: agents often reach a relevant web source, but establish the wrong site-specific retrieval state. Retrieval-scope drift (37.2%) and criterion mismatch (27.6%) dominate, whereas final answer composition accounts for only 10.3%. The dataset and single-case evaluation instructions are available at https://huggingface.co/datasets/PKUAIWeb/SGR-BENCH.

Xueyuan Lin, Chengjin Xu, Haihong E et al.

Multi-hop logical reasoning over knowledge graph (KG) plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding (CQE) methods for reasoning focus on static KGs, while temporal knowledge graphs (TKGs) have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set. To bridge this gap, we define the multi-hop logical reasoning problem on TKGs. With generated three datasets, we propose the first temporal CQE named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. We utilize vector logic to compute the logic part of Temporal Feature-Logic embeddings, thus naturally modeling all First-Order Logic (FOL) operations on entity set. In addition, our framework extends vector logic on timestamp set to cope with three extra temporal operators (After, Before and Between). Experiments on numerous query patterns demonstrate the effectiveness of our method.

Xueyuan Lin, Haihong E, Gengxian Zhou et al.

Current best performing models for knowledge graph reasoning (KGR) introduce geometry objects or probabilistic distributions to embed entities and first-order logical (FOL) queries into low-dimensional vector spaces. They can be summarized as a center-size framework (point/box/cone, Beta/Gaussian distribution, etc.). However, they have limited logical reasoning ability. And it is difficult to generalize to various features, because the center and size are one-to-one constrained, unable to have multiple centers or sizes. To address these challenges, we instead propose a novel KGR framework named Feature-Logic Embedding framework, FLEX, which is the first KGR framework that can not only TRULY handle all FOL operations including conjunction, disjunction, negation and so on, but also support various feature spaces. Specifically, the logic part of feature-logic framework is based on vector logic, which naturally models all FOL operations. Experiments demonstrate that FLEX significantly outperforms existing state-of-the-art methods on benchmark datasets.