arXiv subjects

Hanqing Li

Publications and source records attributed to Hanqing Li.

At least 19 recordsLinked to original sources

arXiv2026

Extending Tardos's Theorem to Separable Convex Quadratic Programming

For an integer equality matrix $A\in\mathbb{Z}^{r\times m}$ of binary encoding length $\langle A\rangle$, Tardos's theorem solves linear programs using $\operatorname{poly}(r,m,\langle A\rangle)$ rational arithmetic operations and comparisons, independently of the right-hand side and objective coefficients. We extend this guarantee to continuous separable convex quadratic programming over $Ax=b$, $x\ge0$: the operation count is independent of the right-hand side, linear costs, and all nonnegative quadratic weights. The algorithm returns an exact optimal primal-dual pair or a certificate of infeasibility or unboundedness. All intermediate rational numbers have encoding lengths polynomial in the total input length. As an application, we obtain a strongly polynomial algorithm for continuous multicommodity flow with shared capacities and quadratic costs of aggregate arc flow, independently of demands, capacities, and cost coefficients. Objective compression and continuous-integer proximity yield a local solver returning a point close to an optimum. We relax nonnegativity on coordinates with zero optimal dual slack, minimize the largest remaining coordinate, and optimize over the relaxed coordinates. A descent LP over the recession cone provides a complementary bound. Circuit decomposition combines these bounds into a scale ensuring that each local call reveals a new coordinate. At most $m$ calls, followed by two LPs, recover an exact optimum and its dual certificate.

cs.DS↗

arXiv2026

SnakeCharmer: Orchestrating Utility, Timeliness, and Placement in GPU Prefetching

GPUs rely on massive thread-level parallelism to tolerate long memory latency, yet they still suffer severe stalls when many warps simultaneously wait for data from the memory system. Address-prediction-based GPU prefetchers can mitigate such stalls, but accurate prediction alone does not guarantee performance improvement: a predicted prefetch becomes beneficial only if it is worth issuing, arrives at the right time, and is retained without harmful interference. Because these requirements interact, optimizing any single dimension in isolation can simply move the bottleneck to another. We capture these requirements with a predicted-prefetch-to-realized-benefit perspective and propose SnakeCharmer, a unified backend prefetch-control framework for address-prediction-based GPU prefetchers. SnakeCharmer separates address prediction from prefetch realization: the frontend predictor generates prefetch candidates, while the backend control path jointly controls utility, timeliness, and placement by determining whether each candidate should be issued, when it should be issued, and where the returned data should be retained. SnakeCharmer realizes this control path with zero-value-aware filtering for utility, hierarchical feedback-driven distance tuning for timeliness, and a register-assisted prefetch buffer for placement. We design and implement SnakeCharmer primarily on top of Snake, and adapt the same backend-control principles to APOGEE to demonstrate that SnakeCharmer's benefits are not limited to a single frontend predictor. On an A100 GPU model, SnakeCharmer improves performance/energy efficiency by 12.8%/20.8% over Snake and by 1.7%/3.2% over APOGEE, with modest hardware overhead.

cs.AR↗

arXiv2026

Regional summaries of Bayesian model uncertainty

Bayesian posterior uncertainty can be spread across many models that share the same substantive pattern. Lists of individual models can obscure this structure, while marginal summaries do not describe which configurations are jointly supported. We study how to represent joint model uncertainty through a compact collection of interpretable regions, each grouping models that share a specified pattern. We formulate this task as minimizing representation complexity subject to retaining a prescribed posterior mass within an analyst-supplied family. To address unknown regional probabilities, we develop Adaptive Regional Selection (ARS), which combines adaptive exploration and regional weight estimation with conservative and optimistic selection. These complementary problems identify a summary meeting the mass target and bound how much further its complexity could improve. Under valid regional bounds, we establish guarantees for retained mass, total-variation error, and suboptimality, together with conditions for certifying optimality. We also show that, under bounded within-region weight variation, sufficient sample counts for regional estimation need not grow with the number of represented models, and construct bounds that remain valid under adaptive sampling and stopping. Empirical studies illustrate regional summaries in Bayesian model averaging and Bayesian networks, examining retained mass, representation complexity, and certification.

stat.ML↗

arXiv2026

Almost-Linear Decremental Single-Source Distance Estimates in Directed Graphs via Cut Balance

We give a deterministic reduction for maintaining simultaneous approximate single-source distance estimates in online decremental directed graphs. For positive integer weights in $[1,W]$, the algorithm maintains an explicit array of integer $(1+\varepsilon)$ upper estimates, identifies unreachable vertices exactly, and answers numerical queries in constant time. Let $N=m+n$, $S=N+\lceil1/\varepsilon\rceil$, and assume $\log W=\operatorname{polylog}(S)$. Initialization and all updates take $O(Δ)+(N+Δ_{\mathrm{eff}}+\mathcal{L}/\varepsilon)S^{o(1)}$ time, where $Δ$ counts raw updates, $Δ_{\mathrm{eff}}=O(m(1+\log W)/\varepsilon)$ counts filtered updates, and $\mathcal{L}$ measures finite distance growth weighted by the current indegrees of the reachable subgraph. Removed edges and vertices that become unreachable incur no subsequent growth charge. Consequently, the worst-case bound is $O(Δ)+(N/\varepsilon)S^{o(1)}$, which is almost linear for subpolynomial inverse accuracy. The reduction uses the dynamic minimum-ratio cut and exact reachability algorithms of van den Brand et al. (FOCS 2024). A degree-weighted clipped logarithmic potential turns constant relative cut balance into accuracy at every target; a successor cut then restores strict feasibility. A distance warm start and the energy released by decreasing return coefficients yield the refined growth bound. Return mass also amplifies the accuracy of the existing change detector. The public estimates can be monotone, with $O(n+\mathcal{J}/\varepsilon)$ array writes for an unweighted finite-growth measure $\mathcal{J}\le\mathcal{L}$. Execution uses rational arithmetic. A separate reduction extends the worst-case guarantee to nonnegative integer weights. The algorithm maintains numerical estimates and does not provide fast path reporting.

cs.DS↗

arXiv2026

Adaptive mixture variational inference for spike-and-slab regression

Correlated predictors can support competing sparse explanations with similar predictions, making joint uncertainty about variable inclusion difficult to capture with mean-field approximations. We develop an adaptive fitting procedure for mixtures of product distributions in Gaussian regression with a point-mass spike-and-slab prior. It minimizes reverse Kullback-Leibler divergence directly on inclusion indicators and active coefficients, jointly refining component parameters and weights as the mixture grows. This avoids an additional divergence penalty on unused latent coefficients under independent augmentation. Our analysis relates approximation accuracy to mixture size, support coverage and dependence within supports, and establishes contraction, selection consistency and a Bernstein-von Mises approximation under explicit conditions on the prior, posterior concentration and variational error. On all 250 simulated datasets with exact posterior references, mixtures reduce errors in inclusion probabilities, grouped support probabilities and coefficient covariance relative to multistart mean field. Comparisons at fixed mixture size and common initialization favor direct joint refinement over augmented or restricted refinement in posterior divergence. Complete stagewise fitting can nevertheless be more accurate near collinearity. The results support direct joint refinement for posterior approximation while showing that local gains do not ensure superiority of the full adaptive search.

stat.ME↗

arXiv2026

A Tight Second-Order Lower Bound for Routing Labels in Trees

In the designer-port routing-labeling problem, every vertex of a rooted tree receives a binary label and the child edges receive distinct port numbers. Given only the labels of a source and a destination, a decoder must return the first port on their path. Gawrychowski, Janczewski, and Lopuszanski gave labels of length $\log_2 n+O((\log_2\log_2 n)^2)$, whereas the previous lower bound was $\log_2 n+Ω(\log_2\log_2 n)$. We prove that every scheme for all $n$-vertex trees needs a label of length $\log_2 n+Ω((\log_2\log_2 n)^2)$ for every sufficiently large $n$. The result allows arbitrary port assignments and imposes no computational restriction on either the encoder or the decoder. Thus the second-order term in the optimal worst-case label length is determined up to constant factors.

cs.DS↗

arXiv2026

Union-Find with Constant-Time Deletions Across the Optimal Worst-Case Tradeoff

We consider union-find with deletions, where the representation and the cost of a query must depend on the current number of live elements rather than on the number of elements ever created. For every integer parameter $k\ge 2$, we give a linear-space data structure supporting $\mathsf{MakeSet}$ in $O(1)$ worst-case time, $\mathsf{Union}$ in $O(k)$ worst-case time, $\mathsf{Delete}$ in $O(1)$ worst-case time, and $\mathsf{Find}$ in $O\left(1+\frac{\log n}{\log k}\right)$ worst-case time for a set containing $n$ live elements. A deletion is given only an element handle, not the identifier of its current set. The construction separates global rank growth from local deletion repair. A logical set is represented by fewer than $k$ disjoint ranked trees. Equal-level trees are collected without physical linking until $k$ certificates are available, at which point one base-$k$ carry is performed in $O(k)$ time. Each member tree uses a strengthened form of the full/reduced local rebuilding scheme of Ben-Amram and Yoffe. A $q$-ary value argument, with $q=3/2$, couples the local trees to the base-$k$ certificates and yields the stated current-size height bound. A small but essential rule handles high-rank stars, a state that the base-$k$ carry can create but that does not arise directly in the binary-rank construction underlying the earlier local scheme.

cs.DS↗

arXiv2026

Directed Hamiltonian-Cycle Parity in $O^*((3/2)^n)$ Deterministic Time and Polynomial Space

We give a deterministic algorithm that computes the parity of the number of Hamiltonian cycles in an $n$-vertex directed graph in $O(n^4(3/2)^n)$ time and $O(n^2)$ bits of working space, improving the $O^*(φ^n)$ bound of Björklund and Husfeldt. Their local-degree formula reduces the problem to a weighted sum over solutions of structured quadratic equations. We cover the corresponding ternary state space by binary subcubes, each inducing an affine system. The Kuang--Wang cover can be regenerated within the target bound; canonical ownership resolves its overlaps, while self-loop conditional expectations bound every affine solution visit. Rollback elimination shares the work across cover prefixes. The same cover gives a Las Vegas algorithm listing all $L$ solutions of $m$ affine product constraints in $N$ Boolean variables in expected time $\operatorname{poly}(N,m)((3/2)^m+L)$ and polynomial space. Finally, we show that complete enumeration can require $Ω((3/2)^n)$ visits even on strongly connected digraphs after an optimal self-loop choice. This is a limitation of the enumeration method, not a general lower bound for Hamiltonian-cycle parity.

cs.DS↗

arXiv2026

Fast Odd-Permutation Sums in Characteristic Two and Shortest Even Directed Cycles

For a matrix $A$ over a field of characteristic two, let $Φ(A)$ be the sum of its permutation monomials indexed by odd permutations. Although determinant and permanent coincide in this characteristic, this parity sub-sum retains information that neither gives separately. We show that $Φ(A)$ and all its first partial derivatives can be computed deterministically in $O(n^τ)$ field operations for every $n\times n$ matrix, where $2<τ\le3$ is any fixed admissible matrix multiplication exponent. The result includes singular matrices and the binary field. An inversion-count identity expresses $Φ$ through complementary minors. For invertible matrices, a decomposition along two binary interval trees aggregates these minors by matrix multiplication; a Boolean border of constant size handles the remaining ranks. We also give an explicit matrix formula for the full gradient. Applied to $Φ(I+zW)$ for a randomly weighted adjacency matrix $W$, the evaluator computes the shortest even directed-cycle length in $\widetilde{O}(n^{τ+1})$ bit operations, improving the $\widetilde{O}(n^{τ+3})$ bound of Björklund, Husfeldt, and Kaski with the same multiplication exponent. The same time bound recovers the union of the arcs of all shortest even cycles with high probability, and deterministically outputs the cycle under a unique-shortest-cycle promise. For general graphs, exact maintenance of a nonzero coefficient gives an $\widetilde{O}(n^4)$ algorithm that outputs a shortest even cycle with high probability. Complementary extraction methods improve this bound for short cycles and for cycles that omit few vertices.

cs.DS↗

arXiv2026

A Deterministic $(2+\varepsilon)$-Approximation for Weighted Feedback Vertex Set in Tournaments

We study the weighted feedback vertex set problem in tournaments. For every fixed integer $k\geq 2$, we give a deterministic $(2+1/k)$-approximation algorithm with running time $n^{2^{O(k)}}$, apart from polynomial dependence on the encoding length of the weights. Consequently, for every fixed $\varepsilon>0$, weighted feedback vertex set in tournaments has a deterministic $(2+\varepsilon)$-approximation running in time $n^{2^{O(1/\varepsilon)}}$. The algorithm combines two ingredients. When the triangle graph of the tournament has bounded clique number, a chain decomposition of its transitive complement yields an exact dynamic program for a maximum-weight transitive subtournament. When the clique number is large, a structural theorem for triangle graphs supplies a constant-size strongly good cost vector. A local-ratio reduction with this cost vector gives the claimed guarantee. As a by-product, the dynamic program solves weighted feedback vertex set exactly in $\mathcal B_7$-free tournaments in time $O(n^7)$, where $\mathcal B_7$ is the family of seven-vertex tournaments with feedback vertex set number at least three.

cs.DS↗

arXiv2026

Bernstein-von Mises theorem for sparse generalized linear models

We establish an oracle Bernstein-von Mises theorem for high-dimensional sparse generalized linear models under an outcome-independent spike-and-slab prior. The posterior consistently recovers the true active set and converges in total variation to the Gaussian law that would arise if this set were known in advance, even when the active dimension grows. The result holds for both ordinary and fractional posteriors, the latter with the expected variance inflation under tempering. In fixed-design logistic regression, a sufficient lower bound on the squared minimum signal is proportional to the logarithm of the ambient dimension divided by sample size. Separate likelihood controls for model selection and oracle approximation allow the Gaussian approximation to use a weaker curvature condition. We verify the conditions for six canonical and noncanonical models under fixed and random designs, including Poisson regression with potentially unbounded Fisher weights. The results also yield oracle-rate contraction, credible regions on the recovered support and pointwise frequentist coverage.

math.ST↗

arXiv2026

C2P-Cache: Scalable GPU L1 Cache Sharing via Concurrent Candidate Pruning

Modern GPUs rely on private per-SM L1 caches and a shared L2 cache, but this organization obscures cross-SM reuse: an L1 miss is typically forwarded to L2 even when the requested line already resides in a peer L1 cache, leading to redundant L2 access. Prior GPU L1-sharing designs attempt to recover such reuse through exact or broad remote-hit searches, which become increasingly difficult to scale and can interfere with the critical L1 miss path under high concurrency. %miss handling as more caches participate and more misses arrive concurrently. We observe that eliminating redundant L2 accesses does not require exact, chip-wide knowledge of private L1 contents. Instead, it requires only sufficient visibility to sharply narrow down a small set of candidate caches, leaving exact confirmation to a much smaller number of L1s. Based on this insight, we propose C2P-Cache, a scalable GPU L1-sharing mechanism that transforms remote-hit discovery from a chip-wide exact search problem into a lightweight filtering-and-confirmation process. C2P-Cache maintains compact Bloom-filter-based snapshots of private L1 tags, performs parallel chip-wide candidate filtering, and selectively probes only a small number of likely peer caches. To sustain high concurrency, C2P-Cache organizes filtering as bit-sliced matching over a banked and replicated snapshot matrix, enabling efficient, parallel processing of many concurrent misses without interfering with normal L1 accesses. Across a wide range of GPU workloads, C2P-Cache improves instructions per cycle (IPC) by up to 49.7\% and by 23.5\% on average for applications with high remote-L1 reuse and strong sensitivity to L2 latency, demonstrating that lightweight, scalable filtering can effectively unlock cross-SM reuse with modest overhead.

cs.AR↗

arXiv2026

DecoEvo: Score-Decoupled Co-Evolution of Solver and Rubric-Generator Skills in Text Space

Text-space optimization adapts large language models (LLMs) by editing external natural-language artifacts rather than model weights, so the optimized artifacts remain inspectable and the model can be treated as a black box. However, most existing text-space methods keep evaluation fixed. On open-ended tasks, this can become a bottleneck: once the solver improves on the criteria a rubric measures, omitted dimensions remain invisible to the optimization signal. Simply evolving the rubric is also unreliable when updates are selected by the current solver's score, because apparent progress can come from making the rubric easier to satisfy. We introduce DecoEvo (Decoupled Co-Evolution), which co-evolves a solver skill and a rubric-generator skill under decoupled objectives without using gold rubrics during optimization. The solver skill is updated using criterion-level feedback, while the rubric-generator skill is revised through complementary audits of requirement coverage and response discrimination that are independent of aggregate solver score. This separation focuses generator updates on newly exposed solver weaknesses, reducing repeated emphasis on criteria the solver already satisfies. Under each benchmark's official evaluation, DecoEvo outperforms all compared methods across five benchmarks and three LLM backbones, yielding 2.8--5.0\% relative gains over SkillOpt in the five-benchmark average.

cs.AI↗

arXiv2026

Decoupled Multimodal Fusion for User Interest Modeling in Click-Through Rate Prediction

Modern industrial recommendation systems improve recommendation performance by integrating multimodal representations from pre-trained models into ID-based Click-Through Rate (CTR) prediction frameworks. However, existing approaches typically adopt modality-centric modeling strategies that process ID-based and multimodal embeddings independently, failing to capture fine-grained interactions between content semantics and behavioral signals. In this paper, we propose Decoupled Multimodal Fusion (DMF), which introduces a modality-enriched modeling strategy to enable fine-grained interactions between ID-based collaborative representations and multimodal representations for user interest modeling. Specifically, we construct target-aware features to bridge the semantic gap across different embedding spaces and leverage them as side information to enhance the effectiveness of user interest modeling. Furthermore, we design an inference-optimized attention mechanism that decouples the computation of target-aware features and ID-based embeddings before the attention layer, thereby alleviating the computational bottleneck introduced by incorporating target-aware features. To achieve comprehensive multimodal integration, DMF combines user interest representations learned under the modality-centric and modality-enriched modeling strategies. Offline experiments on public and industrial datasets demonstrate the effectiveness of DMF. Moreover, DMF has been deployed on the product recommendation system of the international e-commerce platform Lazada, achieving relative improvements of 5.30% in CTCVR and 7.43% in GMV with negligible computational overhead.

cs.IR↗

arXiv2025

Zero-shot Graph Reasoning via Retrieval Augmented Framework with LLMs

We propose a new, training-free method, Graph Reasoning via Retrieval Augmented Framework (GRRAF), that harnesses retrieval-augmented generation (RAG) alongside the code-generation capabilities of large language models (LLMs) to address a wide range of graph reasoning tasks. In GRRAF, the target graph is stored in a graph database, and the LLM is prompted to generate executable code queries that retrieve the necessary information. This approach circumvents the limitations of existing methods that require extensive finetuning or depend on predefined algorithms, and it incorporates an error feedback loop with a time-out mechanism to ensure both correctness and efficiency. Experimental evaluations on the GraphInstruct dataset reveal that GRRAF achieves 100% accuracy on most graph reasoning tasks, including cycle detection, bipartite graph checks, shortest path computation, and maximum flow, while maintaining consistent token costs regardless of graph sizes. Imperfect but still very high performance is observed on subgraph matching. Notably, GRRAF scales effectively to large graphs with up to 10,000 nodes.

cs.AI↗

arXiv2025

BEAR: BGP Event Analysis and Reporting

The Internet comprises of interconnected, independently managed Autonomous Systems (AS) that rely on the Border Gateway Protocol (BGP) for inter-domain routing. BGP anomalies--such as route leaks and hijacks--can divert traffic through unauthorized or inefficient paths, jeopardizing network reliability and security. Although existing rule-based and machine learning methods can detect these anomalies using structured metrics, they still require experts with in-depth BGP knowledge of, for example, AS relationships and historical incidents, to interpret events and propose remediation. In this paper, we introduce BEAR (BGP Event Analysis and Reporting), a novel framework that leverages large language models (LLMs) to automatically generate comprehensive reports explaining detected BGP anomaly events. BEAR employs a multi-step reasoning process that translates tabular BGP data into detailed textual narratives, enhancing interpretability and analytical precision. To address the limited availability of publicly documented BGP anomalies, we also present a synthetic data generation framework powered by LLMs. Evaluations on both real and synthetic datasets demonstrate that BEAR achieves 100% accuracy, outperforming Chain-of-Thought and in-context learning baselines. This work pioneers an automated approach for explaining BGP anomaly events, offering valuable operational insights for network management.

cs.NI↗

arXiv2025

Reverse Prompt Engineering

We explore a new language model inversion problem under strict black-box, zero-shot, and limited data conditions. We propose a novel training-free framework that reconstructs prompts using only a limited number of text outputs from a language model. Existing methods rely on the availability of a large number of outputs for both training and inference, an assumption that is unrealistic in the real world, and they can sometimes produce garbled text. In contrast, our approach, which relies on limited resources, consistently yields coherent and semantically meaningful prompts. Our framework leverages a large language model together with an optimization process inspired by the genetic algorithm to effectively recover prompts. Experimental results on several datasets derived from public sources indicate that our approach achieves high-quality prompt recovery and generates prompts more semantically and functionally aligned with the originals than current state-of-the-art methods. Additionally, use-case studies introduced demonstrate the method's strong potential for generating high-quality text data on perturbed prompts.

cs.CL↗

arXiv2024

Unsupervised Video Summarization via Iterative Training and Simplified GAN

This paper introduces a new, unsupervised method for automatic video summarization using ideas from generative adversarial networks but eliminating the discriminator, having a simple loss function, and separating training of different parts of the model. An iterative training strategy is also applied by alternately training the reconstructor and the frame selector for multiple iterations. Furthermore, a trainable mask vector is added to the model in summary generation during training and evaluation. The method also includes an unsupervised model selection algorithm. Results from experiments on two public datasets (SumMe and TVSum) and four datasets we created (Soccer, LoL, MLB, and ShortMLB) demonstrate the effectiveness of each component on the model performance, particularly the iterative training strategy. Evaluations and comparisons with the state-of-the-art methods highlight the advantages of the proposed method in performance, stability, and training efficiency.

cs.CV↗