arXiv subjects
Publications and source records attributed to Jing Yu.
For every $δ>0$, we construct infinitely many pairwise combinatorially distinct convex three-dimensional polytopes whose dihedral angles are all less than $π/2+δ$.
In this paper, we investigate monoidal derived equivalences between tensor categories with infinitely many isomorphism classes of simple objects. We introduce the notion of a simple-shifted monoidal derived equivalence and prove that a simple-shifted monoidal derived equivalence gives rise to a tensor equivalence. In addition, we investigate which tensor categories have the property that every monoidal derived equivalence between them is necessarily simple-shifted, and we establish some sufficient conditions for this property. As a corollary, we prove that if a tensor category is monoidally derived equivalent to the finite-dimensional representation category of either the quantized enveloping algebra $U_q(\mathfrak{g})$, the quantized Borel subalgebra $U_q^{\geq 0}(\mathfrak{g})$, or the quantized coordinate ring $\mathcal{O}_{q}(G)$ (for a suitable $q$), it is tensor equivalent to the corresponding category.
Agentic recommendation pursues shopper goals through sequences of context-dependent decisions. Developing and evaluating such policies requires faithful recommendation world models that capture both the interactive shopping environment and users' behavioral responses over long interactions. Existing resources rarely provide long-horizon, fine-grained real-user trajectories or support trajectory-level evaluation and offline validation against production A/B results. We introduce UserArena, a real-world e-commerce interactive benchmark containing 64,729 session trajectories from 11,010 users, spanning 566,102 items and 13 action types. UserArena pairs these trajectories with an interactive environment and supports offline validation against outcomes from a controlled production A/B test, enabling five-level evaluation from output validity and local decisions to sequential behavior, personalization, and outcomes. To improve simulator fidelity over these long-horizon interactions, we further propose On-Policy Trajectory Distillation (OPTD), which uses trajectory-level intent to provide dense teacher targets on student-generated rollouts. Experiments show that OPTD achieves the strongest overall fidelity among the evaluated simulators under UserArena's evaluation protocol and most closely reproduces the production policy effect in offline simulation.
The Student-led Threatening Asteroid Reconnaissance of Tsinghua (START) marks the inaugural mission of the Tianxing Program, a deep-space exploration initiative led by students at Tsinghua University. Conceived as a low-cost, rapid-response small-satellite mission, START will investigate the near-Earth asteroid (99942) Apophis during its close approach to Earth in April 2029, when significant terrestrial tidal forces will offer a rare opportunity to observe the physical and dynamical response of a rubble-pile asteroid in real time. The 300 kg spacecraft is scheduled for rideshare launch into low Earth orbit in early 2028 and will then use solar electric propulsion to transfer to a circular mission orbit with a semimajor axis of approximately 38,000 km and an inclination of 55 degrees. START will execute a high-speed flyby of Apophis from a closest distance of 7 km at the asteroid's closest approach to Earth, to capture its tidal response. The payload suite consists of a high-resolution narrow-field camera, a wide-field navigation camera, and three near-infrared multispectral imagers. By acquiring centimeter-scale imagery and meter-scale reflectance spectra, the mission will characterize the asteroid's surface morphology and composition and monitor immediate tidally induced surface modifications. Ultimately, START will provide geometrically complementary, high-cadence datasets to international flagship missions to Apophis, demonstrating a highly scalable and cost-effective architecture for future planetary defense and small-body exploration.
In this paper, we show that for any coquasi-Hopf algebra $H$ and any $H$-Majid bimodule $M$, the cotensor coalgebra $\operatorname{CoT}_H(M)$ admits a graded coquasi-Hopf algebra structure. We then define the standard filtration of a coquasi-Hopf algebra and show that the associated graded coquasi-Hopf algebra admits an embedding into a cotensor coquasi-Hopf algebra that preserves degrees zero and one. If, in addition, this coquasi-Hopf algebra is coquasitriangular (respectively, coribbon), then the cotensor coquasi-Hopf algebra is also coquasitriangular (respectively, coribbon), and the above embedding is a morphism of coquasitriangular (respectively, coribbon) coquasi-Hopf algebras. As a byproduct, we prove that the coquasi-antipode of a coquasi-Hopf algebra with the dual Chevalley property is bijective. Moreover, we establish graded quasi-coquasi-Hopf pairings between tensor quasi-Hopf algebras and cotensor coquasi-Hopf algebras.
In this paper, we develop a quiver approach to coquasi-Hopf algebras with the dual Chevalley property. We introduce a modified generalized path coalgebra $\Bbbk(\mathrm{Q},\mathcal{S})$ associated with a given quiver $\mathrm{Q}$ and a collection of simple coalgebras $\mathcal{S}=\{C_i\mid i\in \mathrm{Q}_0\}$ indexed by the vertices of $\mathrm{Q}$, such that its link quiver coincides with $\mathrm{Q}$. We prove that such a coalgebra admits a graded coquasi-Hopf algebra structure with the dual Chevalley property if and only if $\mathrm{Q}$ is a generalized Hopf quiver and $\bigoplus_{i\in \mathrm{Q}_0}C_i$ forms a cosemisimple coquasi-Hopf algebra. Moreover, we provide a classification of these coquasi-Hopf algebra structures. We then study the link-indecomposable components of a coquasi-Hopf algebra with the dual Chevalley property, and give the generalized dual Gabriel's theorem for such coquasi-Hopf algebras. As an application, we apply the quiver method to classify finite integral tensor categories with the Chevalley property of finite representation type. We also give structural characterizations of coradically graded coquasi-Hopf algebras of tame corepresentation type. Furthermore, we investigate finite braided integral tensor categories with the Chevalley property via the quiver approach.
We study probability distributions on independent sets of uniform hypergraphs with local constraints. For a positive vertex-weight function $w$ on an $(r+1)$-uniform hypergraph, define the weighted degree of vertex $v$ by \[ d_w(v):= \sum_{e\ni v} \left( \prod_{u\in e\setminus\{v\}}\dfrac{w(u)}{w(v)} \right)^{1/r}. \] For each fixed $r\geq1$, our first result gives, in every triangle-free $(r+1)$-uniform hypergraph (without a linearity assumption), a random independent set $I$ satisfying \[ \mathbb P(v\in I)\geq \left( \frac{r}{r+1}(r(r+1))^{-1/r}+o_r(1) \right) \left(\frac{\log d_w(v)}{d_w(v)}\right)^{1/r}, \qquad d_w(v)\to+\infty. \] The same result also implies that every $d$-degenerate triangle-free $(r+1)$-uniform hypergraph satisfies \[ χ_f(G)\leq \left( \dfrac{r+1}{r}(r(r+1))^{1/r}+o_r(1) \right) \left(\dfrac{d}{\log d}\right)^{1/r}, \qquad d\to+\infty. \] Our second result concerns linear Berge-$C_4$-free hypergraphs which allow Berge triangles. In this setting, for every sufficiently large threshold $D$, there exists a random independent set $I$ such that, uniformly over all vertices with $d_w(v)\geq D$, \[ \mathbb P(v\in I)\geq (1-o_r(1)) \left(\frac{\log d_w(v)}{r\,d_w(v)}\right)^{1/r}, \qquad D\to+\infty. \] It also yields \[ χ_f(G)\leq (1+o_r(1)) \left(\frac{rd}{\log d}\right)^{1/r} \] for $d$-degenerate linear Berge-$C_4$-free $(r+1)$-uniform hypergraphs. Both results are based on the ordered random pick process originated from Martinsson and Steiner. By choosing different selection functions and iteration, we prove the output of the random process gives the required random independent set.
LLM-based multi-agent systems (MAS) have shown promise in complex problem solving. As MAS methods diversify, systematic evaluation becomes increasingly challenging. However, existing benchmarks largely focus on final outcomes, leaving unclear how collaboration gains arise, are preserved, or are lost. To address this limitation, we introduce MASTraceBench, a benchmark for diagnosing collaboration gains through proposal trajectories in MAS. Across six cooperative and competitive tasks, MASTraceBench tracks and grades proposal trajectories and provides a multi-layer metric suite covering Task Score, Collaboration Gain, proposal-trajectory indicators, and Token Cost. Using MASTraceBench, we systematically compare representative MAS methods not only by final performance, but also by how agent proposals evolve and are aggregated into the final answer. This analysis reveals a recurring pattern: final MAS answers rarely surpass the strongest initial proposal; interaction often lifts initially weaker proposals toward it, while strong initial proposals are seldom further improved and may regress. To reduce this risk, we propose CLEARS, which replaces whole-proposal exchange with claim-level evaluation across agents to guide reliable synthesis. CLEARS more often preserves or improves upon the strongest initial proposal and achieves the highest Collaboration Gain on five of the six tasks.
We prove that every bounded-to-one action of a finitely generated commutative monoid has asymptotic dimension at most the torsion-free rank of its group completion, with control uniform for a fixed monoid, generating set, and generator fiber bound. The estimate is sharp. Together with the equality of classical and Borel asymptotic dimensions for these actions, it gives the sharp Borel rank bound and recovers hyperfiniteness for bounded-to-one Borel actions of countable commutative monoids.
Benjamini and Tzalik obtained an upper bound on the number of shortest paths between two vertices at distance $t$ in a multigraph of maximum degree at most $Δ$, and proposed a conjecture on the sharp bound. In this paper, we develop a probabilistic counting argument based on probability distributions induced by random walks from the two endpoints. This approach yields a sharp bound for multigraphs and confirms their conjecture. We further determine the exact maximum for simple graphs and thus answer another question of Benjamini and Tzalik. We also investigate the equality cases, describing the structure of the subgraph formed by shortest paths between $x$ and $y$ and giving tight examples.
A theorem of Dougherty--Jackson--Kechris states that any equivalence relation generated by a single Borel function is hypersmooth. A well-known open problem is whether this can be generalized to equivalence relations generated by countable families of pairwise commuting Borel functions. We give an affirmative answer in the case where the functions are bounded-to-one. This generalizes the theorem of Gao--Jackson on Borel actions of countable abelian groups.
Reinforcement learning with verifiable rewards has become the dominant recipe for improving large language model reasoning, yet it presumes large human-curated task collections. Zero-data self-play removes this dependency, but existing methods vet learnability only by probing candidates and rejecting post hoc, never learning where along an environment's difficulty axis to place a task, and credit the solver with sparse terminal rewards alone. We recast zero-data self-play as a pursuit-evasion game: in LURE, an LLM evader positions tasks along each environment's difficulty axis to stay one step ahead of a planner-executor pursuer that hunts it down through verifiable interaction. The evader is trained on a capture-frontier reward that peaks when the solver captures it on exactly half of its rollouts, turning barely catchable into a learned positioning strategy rather than a hand-tuned rejection band. The pursuer earns capture-anchored dense process credit, in which monotone verifier progress is group-normalized jointly with the terminal capture under a round-anchored KL that keeps the co-evolution stable. Across three verifiable reasoning environments and three backbone families, LURE outperforms advanced baselines under unified/specialist settings, while the unified model attains stronger aggregate OOD zero-shot accuracy than all trained baselines across nine held-out benchmarks from three task families.
We characterize infinitesimal finite forcibility for bounded symmetric real kernels. We prove that the graph-density gradients at a kernel span a finite-dimensional space if and only if the kernel is a step kernel. Combined with known finite-forcing results for step kernels, this gives a positive answer to a question of Lovász and Szegedy on whether every infinitesimally finitely forcible kernel is finitely forcible. The proof combines spectral methods with a compression argument based on book graphs.
Simulating realistic user shopping behavior underpins offline evaluation and reinforcement learning in e-commerce scenarios. While recent LLM- and VLM-based simulators have made encouraging progress, reproducing a real browsing session remains difficult for two reasons. (i) Memory Challenge: a shopping session spans dozens of pages, yet existing agents either discard long-range observation histories, losing the evolving user state, or naively concatenate them, overwhelming the context window and even degrading simulation quality. (ii) Optimization Challenge: current user simulators are typically supervised to match each logged action via imitation or step-level rewards; the resulting sessions often display unrealistic patterns, such as over-exploration or excessive passivity, which per-step supervision can neither detect nor correct. To address the above challenges, we present RecVerse, a GUI-grounded simulation agent that perceives pages through screenshots and produces faithful multi-turn trajectories. For the memory challenge, RecVerse adopts a cognitive-inspired hierarchical memory: Working Memory for short-term focus, Episodic Memory for in-session traces, and Preference Memory for high-level intent, with memory updates treated as actions so that the agent adaptively learns when and what to memorize. For the optimization challenge, RecVerse is optimized with a trajectory-level RL objective that scores entire sessions, aligning both macro-level action-type distributions and micro-level shopping intent with real users. We further release USB (User Simulation Benchmark), an interactive e-commerce GUI trajectory dataset for multi-turn user simulation. Experiments show that RecVerse significantly outperforms existing baselines in both behavioral fidelity and intent consistency.
Industrial recommender systems commonly use cascaded retrieval, ranking, and re-ranking pipelines. Although efficient, these pipelines fragment information and objectives across modules, rely on rigid rules, and have limited awareness of real-time intent, leaving session-level shifts among browsing, comparison, and purchase insufficiently addressed. We present DREAM (Developing Recommender Engine with Agentic Methods), an autonomous optimization control architecture that adds a perception-aware, orchestrable, and auditable policy layer atop existing pipelines without replacing them. DREAM has two core components. First, a three-tier Intent Engine fuses on-device signals into structured L0/L1/L2 intent representations; its edge-cloud trigger chain reduces reporting volume to approximately 8.7%. Second, a Meta Engine uses a MetaModel for layered M1-to-M2-to-M3 reasoning: intent summarization, strategy planning informed by Strategy Memory, and parameter translation. It dispatches the resulting parameters through a unified outlet with safety guardrails. A Reward Dual Loop continuously optimizes both components by combining offline simulation for strategy-space exploration with online feedback for outcome calibration, forming a cycle of generation, execution, evaluation, and experience accumulation. Large-scale A/B tests on Taobao's homepage feed show that re-ranking control alone improves IPV by 2.06%, Core IPV by 2.39%, and GMV by 0.88%. Extending control to fine ranking raises these gains to 2.71%, 3.06%, and 1.31%, respectively, while consistently improving PV by more than 1%. These gains require neither replacement of pipeline models nor compromise of serving stability, supporting agentic meta-control as a viable paradigm for industrial recommendation.
Long-term memory enables LLM agents to leverage past interactions, but dialogue histories quickly exceed the context window, forcing agents to retrieve relevant subsets at query time. Because useful evidence is sparse and scattered across verbose conversations, retrieval faces a fundamental tension: broadening recall improves coverage but floods downstream reasoning with noise, while compressing memories at write time eases retrieval but irreversibly discards details that future queries may need. We introduce LazyMem, which resolves this tension by deferring all memory construction to query time. Given a retrieved candidate pool, a lightweight model processes it in overlapping parallel windows, selectively retaining and compressing only query-relevant content. The model is trained with supervised fine-tuning followed by reinforcement learning, using a reward that jointly encourages the identification of relevant messages and the generation of compressions that are faithful to the source and useful for answering the query. On LongMemEval, LazyMem-4B achieves an LLM-judge accuracy of 0.85, outperforming the strongest non-oracle baseline while using only 213 answer-context memory tokens, 21.0 times fewer than the baseline. It further generalizes to LoCoMo without target-domain training and reduces mean latency relative to the prior query-time baseline. Code is available at https://github.com/allacnobug/LazyMem.
Large language models (LLMs) are transforming recommender systems from matching co-occurrence patterns in historical behavior toward reasoning about the intent that drives it. RecGPT-V1 pioneered this paradigm on Taobao by centering user understanding, and RecGPT-V2 scaled it via coordinated multi-agent reasoning; both are deployed in production with consistent gains in user experience and commercial outcomes. However, operating RecGPT at scale reveals three challenges: (1) stateless behavior modeling, where each request reprocesses full user history, wasting computation and discarding prior analysis; (2) a tag-to-item information bottleneck, where natural-language tags form a lossy channel between user understanding and item grounding; and (3) inefficient explicit reasoning, whose lengthy chain-of-thought incurs untenable latency and compute overhead. We present RecGPT-V3, a stateful, hybrid-modal recommender that reasons over natural language for open-world knowledge and Semantic IDs (SIDs) for concrete item grounding. A Memory Hub maintains structured, continually evolving user memory that distills long-horizon behavior into condensed units, cutting user-modeling computation by 55.8%. A Hybrid-modal Foundation Model allows the LLM jointly reason over text tags and SIDs, opening a high-bandwidth channel into the item space. Latent Intent Reasoning internalizes verbose rationales into compact learnable latent tokens that remain decodable into readable explanations, lowering output token cost by 200x. Deployed in Taobao's "Guess What You Like" feed, RecGPT-V3 achieves consistent gains in large-scale online A/B tests: IPV +1.28%, CTR +1.00%, TC +1.97%, GMV +3.97%, while cutting end-to-end serving resource consumption by 52.4%.
We prove an average-degree lower bound on the independence number of uncrowded uniform hypergraphs. For every fixed $r\geq 2$ and every $η>0$, there exists $d_*=d_*(r,η)$ such that any uncrowded $(r+1)$-uniform hypergraph $G$ with $n$ vertices and average degree $d\geq d_*$ satisfies \[ α(G)\geq (1-η)r^{-1/r}\left(\frac{\log d}{d}\right)^{1/r}n. \] The proof combines a cleaning procedure, which reduces the maximum top-layer degree to the average scale, with a random nibble procedure that repeatedly extracts independent vertices while controlling all lower-order degrees created by the process. After an initial top-layer cleaning, we run a trace nibble. Since the residual hypergraph contains traces of all sizes $2,\ldots,r+1$, we track the maximum degrees in every layer. A binomial-type recurrence for this degree profile yields the stated leading constant.