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Hong Liu

Publications and source records attributed to Hong Liu.

At least 55 records · Page 3Linked to original sources
arXiv2026

The sharp diagonal spectral correlation inequality on the discrete cube

We prove the sharp diagonal spectral correlation conjecture of Friedgut, Kahn, Kalai and Keller, proposed in their Fourier-analytic approach to Chvátal's conjecture. For every pair of increasing Boolean functions $f,g:\{0,1\}^n\to\{0,1\}$, $$\mathrm{Cov}(f,g)\ge4\sum_{\varnothing\ne S\subseteq[n]}|S|\hat{f}(S)^2\hat{g}(S)^2.$$ Thus covariance controls the degree-weighted collision of the two nonconstant Fourier spectra, giving a sharp Fourier strengthening of the Harris--Kleitman inequality. The theorem also implies the unweighted diagonal conjecture of Friedgut--Kahn--Kalai--Keller for an increasing family and a maximal intersecting family. The factor $4$ is optimal, and we determine all equality cases. Apart from pairs whose relevant coordinate sets are disjoint, equality occurs only for a common dictatorship and, up to relabelling coordinates and interchanging $f$ and $g$, for the two-coordinate AND-OR pair $(f,g)=(x_i x_j,\,x_i\vee x_j).$ The main novelty is a correlated four-restriction induction and a sharp endpoint convolution inequality. The usual two-restriction induction behind Harris--Kleitman sees only the parallel restricted pairs and loses the mixed Fourier information needed to control the degree-weighted diagonal spectral energy. We instead couple the four codimension-one restricted pairs with correlation $1/2$; this precise correlation extracts the missing degree-weighted energy as a nonnegative square.

math.CO↗
arXiv2026

Chromatic thresholds for linear equations and recurrence

Motivated by classical problems in extremal graph theory, we study a chromatic analogue of Roth-type questions for linear equations over $\mathbb F_p$. Given a homogeneous equation $\mathcal L:\sum_{i=1}^k c_i x_i=0$ with $k\ge 3$, we study $\mathcal L$-solution-free sets $A\subseteq \mathbb F_p$ through the chromatic number of the Cayley graph $\mathsf{Cay}(\mathbb F_p,A)$. We introduce the \emph{chromatic threshold} $δ_χ(\mathcal L)$, the minimum density that guarantees bounded chromatic number of $\mathsf{Cay}(\mathbb F_p,A)$ among all $\mathcal L$-solution-free sets $A$, and determine exactly when $δ_χ(\mathcal L)=0$. We prove that $δ_χ(\mathcal L)=0$ if and only if $\mathcal L$ contains a zero-sum subcollection of at least three coefficients. A key ingredient is a quantitative chromatic lower bound for Cayley graphs on $\mathbb Z_p^n$ generated by Hamming balls around the all-ones vector. This is obtained by introducing a new Kneser-type graph that admits a natural embedding into $\mathbb Z_p^n$, together with an equivariant Borsuk--Ulam type argument. As a consequence, we resolve a question of Griesmer. We further relate our classification to the hierarchy of measurable, topological, and Bohr recurrence. In particular, we show that every infinite discrete abelian group admits a set that is topological recurrent but not measurable recurrent, extending the seminal examples of Kříž and Ruzsa.

math.CO↗
arXiv2026

Beyond Uniform Experts: Cost-Aware Expert Execution for Efficient Multi-Device MoE Inference

Mixture-of-Experts (MoE) architectures enable language models to achieve unprecedented scale via sparse activation. However, their inference performance is often limited by data movement bottlenecks. Two coupled challenges exacerbate this limtation: (1) Importance-Agnostic Cost: Low-contribution experts incur nearly uniform memory and transfer costs, resulting in a low cost-to-benefit ratio and wasting critical bandwidth; (2) System-Level Imbalance: Multi-device deployments are universally bottlenecked by the slowest device, meaning that local reductions on one device may yield no improvement in end-to-end latency. We propose Cost-Aware Expert Execution (CAEE), a hardware-guided runtime framework that jointly optimizes for token-level expert importance and system-level execution cost. CAEE uses lightweight, calibrated cost models to estimate hardware overhead, selectively prunes low-importance, high-cost experts, and redistributes their contributions via a low-overhead compensation mechanism, avoiding extra data movement. Evaluations on the 671B DeepSeek-R1 model show that CAEE can reduce end-to-end inference latency by 8\%-18\% across diverse deployment settings, including expert offloading and on-device execution on multi-device systems, while maintaining a model accuracy drop of less than 1\%.

cs.DC↗
arXiv2026

Eval-Actions: Fine-Grained Execution Quality Evaluation for Robotic Manipulation

Although Vision--Action (VA) and Vision--Language--Action (VLA) policies have advanced robotic manipulation, their evaluation remains dominated by binary success rates, which obscure process-level differences among executions that complete the same task. We introduce Eval-Actions, a diagnostic evaluation methodology and real-robot benchmark for fine-grained execution-quality assessment of learned manipulation policies. Eval-Actions combines criteria-based Expert Grading (EG), Rank-Guided (RG) labels that align measurable motion indicators with expert rankings, and Chain-of-Thought-style (CoT) annotations that explain observable quality differences. The benchmark contains 13K+ teleoperated and policy-generated real-robot episodes covering 150+ tasks and approximately 52 hours of recordings with RGB-D videos, robot-state trajectories, task descriptions, and success/failure labels. Its densely annotated subset provides EG/RG/CoT supervision for training and evaluation. We further provide AutoEval, a reference multimodal evaluator that predicts quality scores, task outcomes, and diagnostic explanations from RGB temporal evidence and compact kinematic summaries. On the annotated Eval-Actions test split, AutoEval-S achieves Spearman rank correlations (SRCCs) of 0.81 and 0.84 under EG and RG, with success detection accuracies of 90.6% and 91.0%; AutoEval-P reaches 0.70 SRCC under CoT. Analyses of expert consistency, physical-metric baselines, modality ablations, structured generalization, and offline policy ranking show that Eval-Actions provides standardized, interpretable diagnostic signals complementary to success-rate evaluation.

cs.RO↗
arXiv2026

Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity

The supersaturation problem asks, for a fixed $r$-graph $\mathcal F$, for the minimum number of copies of $\mathcal F$ in an $n$-vertex $r$-graph with $\ex(n,\mathcal F)+q$ edges. Mubayi conjectured a local form of supersaturation under a stability hypothesis: if $\mathcal F$ is non-$r$-partite and stable, meaning roughly that the extremal $\mathcal F$-free construction is unique and all near-extremal $\mathcal F$-free $r$-graphs are close to it, then this minimum should be at least $q c(n,\mathcal F)$, where $c(n,\mathcal F)$ is the minimum number of copies created by adding one edge to the extremal $\mathcal F$-free $r$-graph. We disprove this conjectured local lower bound in every uniformity. For every $r\ge2$ and every $K>1$, we construct a stable $r$-graph $\mathcal F$ such that, for all sufficiently large $n$ and every $1\le q\le δn$, there is an $n$-vertex $r$-graph with $\ex(n,\mathcal F)+q$ edges and at most $K^{-1}q c(n,\mathcal F)$ copies of $\mathcal F$. Thus the conjectured lower bound can already fail at $q=1$, and the failure can be by an arbitrarily large constant factor in every uniformity.

math.CO↗
arXiv2026

A sharp $p$-biased product bound for $r$-cross-intersecting families

We prove a sharp product theorem for $r$-cross-intersecting families in the $p$-biased measure. If $r\ge2$, $0\le p\le \frac{r-1}{r}$, and $\mathcal{F}_1,\dots,\mathcal{F}_r\subseteq 2^{[n]}$ are $r$-cross-intersecting, then $$\prod_{i=1}^r μ_p(\mathcal{F}_i)\le p^r.$$ The bound is attained by a common $1$-star, and the range of $p$ is best possible. In particular, this proves the equal-bias case of a conjecture of Frankl and Tokushige and, for $r=3$, confirms a conjecture of Tokushige. We also prove a stability theorem: for $r\ge3$, every near-extremal $r$-tuple is close, in $p$-biased measure, to a common $1$-star, with an optimal linear dependence on the product deficit. The extremal proof uses a coordinatewise coupling at the critical bias together with an isoperimetric inequality for increasing families. The stability proof uses dual families and random ordered partitions to obtain Fourier concentration, then applies biased Friedgut--Kalai--Naor theorem to force the star structure.

math.CO↗
arXiv2026

Causal-Privacy Audit Workflow for Synthetic and Distilled Data in Dropout Support

Synthetic and distilled student data are increasingly used to enable privacy-conscious learning analytics, yet their suitability for decision-facing institutional support remains uncertain. In dropout support, generated data must preserve not only predictive utility or distributional resemblance, but also the financial-status evidence used to guide advising, payment-plan assistance, and scholarship-related decisions. Method: This study introduces CaP-Eval, a decision-facing causal-privacy audit workflow for evaluating generated student data under a fixed estimand, timing-aware adjustment design, estimator set, and empirical privacy-governance screen. The workflow compares original, distilled, adversarial synthetic, statistical synthetic, and DPGNet privacy-oriented generated data on predictive utility, treatment-effect fidelity, robustness to alternative estimators, and local training-record proximity. Results: DPGNet and distilled data preserved the original financial-status treatment-effect structure more reliably than the adversarial and Gaussian Copula baselines. DPGNet preserved full direction and rank agreement across epsilon levels; epsilon = 10 produced the smallest non-original IPW and DML deviations, while epsilon = 1 and epsilon = 5 amplified several financial-status contrasts. Distilled data remained highly faithful but retained the strongest local training-record proximity signal. TabularGNet preserved qualitative directions with moderate attenuation, and Gaussian Copula compressed effect magnitudes. Conclusions: Predictive utility, privacy orientation, empirical disclosure signals, and causal fidelity diverged; generated student data require joint audits of direction, magnitude, overlap, and release-governance risk before decision use.

cs.LG↗
arXiv2026

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

Efficient and scalable agentic intelligence requires models that can deliver both low-latency responses and strong reasoning capabilities while remaining practical to train, serve, and deploy. In this report, we present Ling-2.6 and Ring-2.6, a family of models designed to address this challenge at scale. Ling-2.6 is optimized for instant response generation and high capability per output token, whereas Ring-2.6 is tailored for deeper reasoning and more advanced agentic workflows. Instead of training from scratch, we upgrade the Ling-2.0 base model through architectural migration pre-training and large-scale post-training. This upgrade is guided by a unified co-design of model architecture, optimization objectives, serving systems, and agent training environments, enabling improvements in both model capability and deployment efficiency. At the architectural level, we introduce a hybrid linear attention design that integrates Lightning Attention with MLA, improving the efficiency of long-context training and decoding. To further enhance token efficiency, we optimize capability per output token through Evolutionary Chain-of-Thought, Linguistic Unit Policy Optimization, bidirectional preference alignment, and shortest-correct-response distillation. For agentic capabilities, we propose KPop, a reinforcement learning framework designed to support stable training of Ring-2.6-1T on large-scale environment-grounded data. KPop improves training efficiency through asynchronous scheduling across coding, search, tool use, and workflow execution, enabling scalable learning from complex agent-environment interactions. Together, Ling-2.6 and Ring-2.6 provide a practical pathway toward efficient, scalable, and open agentic systems. We open-source all checkpoints in the 2.6 family to support further research and development in practical agentic intelligence.

cs.CL↗
arXiv2026

Triangle packings in randomly perturbed graphs

The longstanding Nash-Williams conjecture asserts that every $K_3$-divisible graph $G$ with $δ(G)\ge 3n/4$ admits a triangle decomposition. In the random setting, Frankl and Rödl showed that, with high probability, $G(n,p)$ contains a triangle packing covering all but $o(n^2p)$ edges whenever $p\ge n^{-1/2+\varepsilon}$. In this paper, we study near-perfect triangle packings in randomly perturbed graphs. We prove that for every $d>0$ and every $p>2d/(1+2d)$, if $G_d$ is a $dn$-regular graph on $n$ vertices, then with high probability the union $G_d\cup G(n,p)$ contains a triangle packing covering all but $o(n^2)$ edges. Moreover, this bound on $p$ is best possible for $0<d\le 1/2$, thereby determining the threshold in this range. A key ingredient in the proof is a new triangle-weighting lemma for weighted complete graphs.

math.CO↗
arXiv2026

FlexNPU: Transparent NPU Virtualization for Dynamic LLM Prefill-Decode Co-location

Modern AI serving increasingly relies on NPUs for conventional inference and large language model serving. However, current NPU deployments commonly expose physical devices directly to applications, which limits runtime control over scheduling and makes it difficult to adapt execution to phase-level workload behavior. This limitation is particularly evident in LLM serving, where the prefill phase is compute-intensive while the decode phase is often constrained by memory bandwidth and KV-cache accesses. Static prefill-decode (PD) disaggregation reduces phase interference, but can introduce resource imbalance and unnecessary data movement. We present FlexNPU, a transparent user-space virtualization layer for Ascend NPUs. FlexNPU interposes on AscendCL APIs and routes NPU operations through per-device daemons, decoupling unmodified from physical NPU devices without modifying model code, AI frameworks, or NPU drivers. This runtime boundary allows FlexNPU to virtualize NPU objects, control operator dispatch, and support phase-aware scheduling for LLM serving. In particular, FlexNPU enables dynamic PD co-location, which adapts scheduling between prefill and decode according to their complementary resource characteristics. We implement FlexNPU on Huawei Ascend NPUs and evaluate it with typical LLM workloads. Compared with direct NPU passthrough, FlexNPU introduces no measurable inference overhead and slightly improves throughput in some scenarios. On a 384-card Ascend 910C deployment of DeepSeek-R1, FlexNPU improves throughput over static PD disaggregation by 5.15% and 26.33%. On Qwen2.5-7B, compared with static PD co-location, FlexNPU maintains comparable throughput while reducing TTFT by over 92% across tested workloads with nearly unchanged TPOT. These results show that transparent NPU virtualization is a practical substrate for efficient and responsive LLM serving.

cs.DC↗
arXiv2026

Passive aerodynamic robustness reduces disturbance amplification in flight

Flight in turbulence is constrained not only by aerodynamic efficiency, but also by how strongly flow disturbances are transmitted into unsteady loads and dynamic responses. Although disturbance rejection is typically attributed to active control, birds often sustain fixed-wing gliding in disturbed air, suggesting that the wing itself may passively attenuate aerodynamic perturbations. Here, we show that avian wings reduce aerodynamic sensitivity to incoming disturbances. Compared with a geometrically matched airfoil wing, the avian wing exhibits lower lift-response gain, smoother stall transition, reduced force fluctuations, and a broader operative angle-of-attack range across turbulence intensities. These wing-level properties translate into an expanded passive stability envelope in rigid-flyer dynamics. Flow diagnostics indicate that this robustness is associated with delayed separation and redistribution of turbulent kinetic energy, which suppress large-scale flow instability and weaken disturbance transmission. This passive robustness comes at the cost of reduced aerodynamic efficiency, revealing an efficiency-robustness trade-off in disturbed flows. Our results identify aerodynamic sensitivity and control demand as essential metrics for flight performance in turbulence, and suggest passive aerodynamic robustness as a design principle for resilient flying systems.

physics.flu-dyn↗
arXiv2026

Spectral Sidorenko inequalities and edge-spectral supersaturation

We develop a spectral approach to Sidorenko-type inequalities and apply it to establish sharp edge-spectral supersaturation results. Let $H$ be a bipartite graph with $v$ vertices and $e$ edges, where $v\le e$, and write $M(G)=2e(G)$. We prove that Sidorenko's conjecture is equivalent to a spectral strengthening: $$ \hom(H,G)\ge M(G)^e |V(G)|^{v-2e} \quad \text{ if and only if }\quad \hom(H,G)\ge λ(G)^{2e-v}M(G)^{v-e}.$$ We also introduce an operator-norm certificate which, via the Riesz--Thorin interpolation, gives direct proofs of the spectral Sidorenko inequality in several cases. The converse direction in the equivalence theorem is proved by a tensor-power spectral regularization lemma. Our main result provides a unified framework to prove sharp asymptotic edge-spectral supersaturation results for degenerate bipartite graphs with the Sidorenko property, including complete bipartite graphs and even cycles. Let $S_{t-1,m}$ be the split graph with $m$ edges obtained by joining a clique $K_{t-1}$ to an independent set. For every $m$-edge graph $G$ with $λ(G)>λ(S_{t-1,m})$, $$\texttt{#} K_{t,t}(G) \ge \Big(\frac{2^{-(t-1)^2}}{(t!)^2}-o(1)\Big)m^t \quad \text{and}\quad \texttt{#}C_{2t}(G) \ge \Big(\frac{(t-1)!}{2t^t}-o(1)\Big)m^t.$$ Both constants are best possible: the first is attained asymptotically by random graphs, while the second is attained by split graphs. The supersaturation proofs combine spectral Sidorenko inequalities with a heavy-edge pruning process, a Perron-vector localized/delocalized dichotomy, and incidence-matrix inequalities.

math.CO↗
arXiv2026

Learning to Evolve: Multi-modal Interactive Fields for Robust Humanoid Navigation in Dynamic Environments

Safe manipulation-oriented navigation for humanoid robots requires scene memory that remains reliable under locomotion-induced perceptual distortion, environmental changes, and interaction-level geometric safety constraints. Existing semantic mapping and scene-graph systems are difficult to deploy directly in this setting because they often assume stable camera trajectories, static environments, or coarse object geometry. We introduce the Multi-modal Interactive Field (MIF), a humanoid-oriented system that integrates confidence-aware semantic 3D Gaussian Splatting, discrepancy-triggered spatial memory updates, and task-driven geometric reconstruction within a closed-loop perception-adaptation pipeline. MIF couples three fields: an uncertainty-aware 3DGS Appearance Field that suppresses gait-induced blur, a Spatial Field that maintains topological memory, and a Geometry Field that supports Interaction Pose Safety (IPS) before manipulation. A discrepancy detection score is introduced to separate locomotion-induced false-positive changes from persistent changes and updates only locally inconsistent regions. On a Unitree-G1 humanoid in a real dynamic office, MIF improves relocation success in non-static environments from 12% to 94% compared with static scene-graph memory, while reducing semantic memory footprint by 91.4% through feature distillation for practical online operation. Project page and code: https://ziya-jiang.github.io/MIF-homepage/

cs.RO↗
arXiv2026

MoPO: Incorporating Motion Prior for Occluded Human Mesh Recovery

Although recent studies have made remarkable progress in human mesh recovery, they still exhibit limited robustness to occlusions and often produce inaccurate poses and severe motion jitter due to the insufficient spatial features for occluded body parts. Inspired by the rapid advancements in human motion prediction, we discover that compared to occluded image features, pose sequence inherently contains reliable motion prior for estimating occluded body parts. In this paper, we incorporate Motion Prior for Occluded human mesh recovery, called MoPO. Our MoPO mainly consists of two components: 1) The motion de-occlusion module, where we propose a spatial-temporal occlusion detector to detect joint visibility, and then we propose a lightweight motion predictor to complete the occluded body parts by predicting the most plausible joint positions based on history poses. 2) The motion-aware fusion and refinement module, which fuses the completed joint sequence with image features to estimate human shape and initial human pose. Moreover, the completed joint sequence is further used to refine the final human pose through inverse kinematics, which provides the occlusion-free motion prior for regressing human poses. Extensive experiments demonstrate that MoPO achieves state-of-the-art performance on both occlusion-specific and standard benchmarks, significantly enhancing the accuracy and temporal consistency of occluded human mesh recovery. Our code and demo can be found in the supplementary material.

cs.CV↗
arXiv2026

Chromatic thresholds for pairs of graphs

The chromatic threshold of a graph $H$ is the minimum-degree density above which every $H$-free graph has bounded chromatic number. We study a two-color Ramsey analogue: for graphs $H_1$ and $H_2$, we ask for the minimum-degree density above which every graph that admits a red-blue edge-coloring with no red copy of $H_1$ and no blue copy of $H_2$ has bounded chromatic number. We give a complete answer when both $H_1$ and $H_2$ are 3-chromatic. The threshold takes exactly one of the five values \[ \frac23,\quad \frac57,\quad \frac34,\quad \frac79,\quad \frac45, \] and we characterize precisely which pairs $(H_1,H_2)$ give each value. The classification is determined by the ordinary chromatic thresholds of $H_1$ and $H_2$ and by their embeddability into a hierarchy of $C_5$-type Ramsey configurations.

math.CO↗
arXiv2026

A dichotomy for hypergraph Zarankiewicz problems on axis-parallel boxes

We study the Zarankiewicz problem for $r$-partite, $r$-uniform intersection hypergraphs arising from $r$ families of axis-parallel boxes in $\mathbb{R}^d$ with prescribed directions $F_1, \dots, F_r \subseteq \{1, \dots, d\}$. This extends the problems studied by Chan and Har-Peled on points and $d$-dimensional boxes in $\mathbb{R}^d$, corresponding to $(F_1,F_2)=(\varnothing,[d])$, as well as by Chan, Keller, and Smorodinsky on $r$ families of $d$-dimensional boxes, corresponding to $(F_1,\dots,F_r)=([d],\dots,[d])$. Our main result establishes a sharp dichotomy for the Zarankiewicz number in this setting: it is either $Θ_r(tn^{r-1})$ or at least $Ω\bigl( tn^{r-1} \cdot \frac{\log n}{\log\log n} \bigr)$, depending only on a simple set-theoretic condition on $(F_1,\dots,F_r)$, which we call $2$-coherence. Informally, $2$-coherence captures whether the configuration contains an underlying two-dimensional incidence structure, which is precisely what gives rise to the extra polylogarithmic factor. Our proof proceeds via a sequence of reductions and a geometric slicing argument that reduces the problem to planar incidence bounds.

math.CO↗
arXiv2026

Learning step-level dynamic soaring in shear flow

Dynamic soaring enables sustained flight by extracting energy from wind shear, yet it is commonly understood as a cycle-level maneuver that assumes stable flow conditions. In realistic unsteady environments, however, such assumptions are often violated, raising the question of whether explicit cycle-level planning is necessary. Here, we show that dynamic soaring can emerge from step-level, state-feedback control using only local sensing, without explicit trajectory planning. Using deep reinforcement learning as a tool, we obtain policies that achieve robust omnidirectional navigation across diverse shear-flow conditions. The learned behavior organizes into a structured control law that coordinates turning and vertical motion, giving rise to a two-phase strategy governed by a trade-off between energy extraction and directional progress. The resulting policy generalizes across varying conditions and reproduces key features observed in biological flight and optimal-control solutions. These findings identify a feedback-based control structure underlying dynamic soaring, demonstrating that efficient energy-harvesting flight can emerge from local interactions with the flow without explicit planning, and providing insights for biological flight and autonomous systems in complex, flow-coupled environments.

physics.flu-dyn↗
arXiv2026

Radiology Report Generation for Low-Quality X-Ray Images

Vision-Language Models (VLMs) have significantly advanced automated Radiology Report Generation (RRG). However, existing methods implicitly assume high-quality inputs, overlooking the noise and artifacts prevalent in real-world clinical environments. Consequently, current models exhibit severe performance degradation when processing suboptimal images. To bridge this gap, we propose a robust report generation framework explicitly designed for image quality variations. We first introduce an Automated Quality Assessment Agent (AQAA) to identify low-quality samples within the MIMIC-CXR dataset and establish the Low-quality Radiology Report Generation (LRRG) benchmark. To tackle degradation-induced shifts, we propose a novel Dual-loop Training Strategy leveraging bi-level optimization and gradient consistency. This approach ensures the model learns quality-agnostic diagnostic features by aligning gradient directions across varying quality regimes. Extensive experiments demonstrate that our approach effectively mitigates model performance degradation caused by image quality deterioration. The code and data will be released upon acceptance.

cs.CV↗