arXiv subjects

Hao Liu

Publications and source records attributed to Hao Liu.

At least 37 records · Page 2Linked to original sources

arXiv2026

CacheScope: Exact-Compute Allocation for Training-Free Diffusion Acceleration

Training-free feature reuse accelerates diffusion transformer inference by replacing full denoising computation at selected steps with cached approximations. Existing methods mainly improve the reconstruction of skipped features, but we find that once a stable first-order reconstructor is used, increasing reconstruction complexity brings limited gains, whereas the placement of exact-computation steps has a much larger effect on fidelity. More importantly, absolute shallow-probe variation is jointly affected by input-trajectory displacement and network response strength, and therefore does not directly reflect cache risk. We address this confounding by normalizing probe-output variation with the corresponding input displacement, yielding a directional gain per unit trajectory movement. Based on this signal, we propose CacheScope, which identifies high-risk reuse steps online and selectively falls back to full denoising computation while leaving the underlying cache reconstructor unchanged. CacheScope requires no additional training, gradients, auxiliary networks, or prompt-specific offline schedule optimization. Across FLUX.1-dev, Wan2.1-T2V-1.3B, and Open-Sora 1.2, CacheScope achieves up to 3.57x acceleration and reduces median LPIPS by up to 70.1% over the strongest probe-based baseline.

cs.LG↗

arXiv2026

DUDA-Bench: Benchmarking LLM Agents on Multimodal Data-Driven Urban Diagnosis

Urban diagnosis integrates heterogeneous observations to identify urban problems, localize affected areas, and investigate contributing factors, informing evidence-based urban planning and management. However, its reliance on labor-intensive, case-specific expert workflows limits scalability and reuse, motivating the exploration of agent-based execution. To evaluate this capability, we introduce DUDA-Bench, a hierarchical and interactive benchmark that formalizes data-driven urban diagnosis as a multi-stage agent workflow. It comprises 86 atomic and 22 workflow tasks spanning four analytical stages, grounded in multimodal data from 12 cities covering five urban problem types. Evaluations of seven backbone models and five agent systems reveal a substantial gap between isolated analytical competence and end-to-end diagnosis, with system benefits varying across backbones. Trajectory analysis shows that unresolved evidence gaps propagate across stages, while successful recovery involves revising assumptions and actions using feedback. These findings highlight limitations in coordinating analytical capabilities across stages, particularly adaptive planning, evidence integration, and verification. More broadly, DUDA-Bench provides a framework for translating expert analytical workflows into hierarchical agent tasks and process-aware evaluation, supporting systematic assessment of end-to-end analytical capabilities.

cs.AI↗

arXiv2026

Self-similar solutions to the steady Navier-Stokes equations in arbitrarily high dimensions

We study $(-1)$-homogeneous solutions of the steady Navier-Stokes equations in $\mathbb R^n\setminus\{0\}$ with $(-3)$-homogeneous, locally Lipschitz forces. Previous work [2] established the existence of $(-1)$-homogeneous solutions without any smallness assumption in dimensions $4\leq n\leq16$. In this paper, we remove the dimension restriction and obtain the existence of self-similar solutions in all higher dimensions. The new ingredient is a dimension-independent a priori estimate for the total head pressure on the sphere, obtained by adapting the source-flux method and the weighted identity of the pressure of Wang and Yang [28] to the homogeneous setting. This combines with the structural relation between the radial velocity and the total head pressure used in [2] to close the a priori estimates for the solutions in all dimensions.

math.AP↗

arXiv2026

Rethinking World-Action Model for Compositional and In-Context Robotic Manipulation

Long-horizon compositional manipulation has become increasingly important for real-world robot deployment, where a single task involves multiple coordinated subtasks. Existing world-action models (WAMs) jointly predict short-horizon visual futures and actions, but typically lack explicit subtask-level reasoning. We propose Visual Goal-conditioned Action Reasoning (ViGAR), a hierarchical framework that factorizes manipulation into a visual subgoal planner and a subgoal executor. Given the current observation and global instruction, the subgoal planner predicts a visual subgoal for the next subtask. The subgoal executor then jointly generates future visual trajectories and actions conditioned on the predicted subgoal. Both components share a pretrained world-model representation, enabling task-level planning and action generation to benefit from common physical knowledge. Moreover, our framework naturally supports in-context learning: using a global goal image as context can induce different subtask decompositions and behaviors without parameter updates. On the RoboTwin Clean2Random benchmark, ViGAR achieves 82.00% and 67.02% success rates under the Clean and Random settings, respectively, surpassing the strongest baseline by 12.86 percentage points in average success rate. Real-world robot experiments on five compositional and two in-context learning tasks further confirm the effectiveness of ViGAR.

cs.RO↗

arXiv2026

VLALight: A Vision-Language-Action Model for Traffic Signal Control

Traffic signal control (TSC) is essential for improving urban mobility and reducing congestion. Although roadside cameras are widely deployed at signalized intersections and provide rich visual observations of evolving traffic, existing TSC methods typically rely on manually engineered traffic states or separate perception modules, creating a gap between physical observations and control decisions. We present VLALight, the first vision-language-action (VLA) model for end-to-end traffic signal control from multi-view roadside videos. VLALight directly maps visual observations to coordinated signal actions through multi-target spatiotemporal traffic reasoning and topology-aware cooperative perception across intersections. To establish this capability, we develop a two-stage supervised cold-start training strategy for visual traffic understanding and signal decision-making, followed by cooperative agentic reinforcement learning that jointly optimizes local control and network-wide traffic efficiency. Furthermore, VLALight introduces adaptive fast and slow reasoning modes, enabling the policy to allocate deeper reasoning only when additional deliberation provides sufficient control benefits. Through balanced mode-aware rollouts and relative advantage optimization, VLALight learns to trade off decision quality and inference cost. Extensive experiments on seven real-world traffic-flow datasets across three urban networks demonstrate that VLALight consistently outperforms transportation-based, RL-based, and LLM/VLM-based baselines. Ablation studies validate the effectiveness of cooperative perception, network-level optimization, and adaptive reasoning. These results demonstrate the potential of VLA models for real-world physical traffic control. Our project is available at https://github.com/usail-hkust/VLALight.git.

cs.AI↗

arXiv2026

Hermes: Learning Contextual Reasoning Unlocks Test-Time Scaling

Test-time scaling improves model performance by allocating additional compute during inference. Using this compute effectively across multiple context windows requires deciding how to allocate fresh contexts and what information to carry between them. We call a model's ability to make these decisions contextual reasoning. Existing approaches largely prescribe these decisions through their harness; we instead shift them to the model. We introduce 1) Hermes, a family of simple, configurable harnesses that progressively varies model control over context allocation and reuse, and 2) Hermes-Learn, a two-stage framework for learning these capabilities. We find that capable models can exploit this flexibility to scale with additional inference-time compute, while smaller open-source models initially struggle to do so. Training with Hermes-Learn closes this gap, inducing adaptive contextual reasoning strategies that vary with both the problem and the progress of reasoning. These gains generalize across benchmarks and models, extrapolate beyond the inference-time compute seen during training, and transfer to complementary test-time scaling methods beyond Hermes.

cs.LG↗

arXiv2026

MILO: Automated Harness Discovery via Orchestrated Multi-Agent Evolution

Modern agentic systems combine an AI model with a harness that controls execution and environmental interactions. Harness design strongly affects long-horizon performance, yet its combinatorial search space demands substantial human effort that must be repeated as models change. Existing automated methods explore this space narrowly, optimizing only components such as prompts or skills or becoming trapped by fixed, exploitative search strategies. We introduce MILO (Meta-evolutionary Island Orchestration), a framework that co-evolves agent harnesses and the strategy used to discover them. MILO combines: (i) hierarchical lineage memory over island-based trees, using rejected mutations as negative evidence; (ii) per-island mutator agents that rewrite complete harnesses using global search history and parent-specific feedback; and (iii) an orchestrator that adapts search through lineage grafting and speciation, mutator reassignment and curriculum revision. Across Terminal-Bench 2.1, PaperBench, and DeepSWE, MILO-discovered harnesses outperform eight state-of-the-art harnesses and six search methods using frontier (Opus 4.8) and open-weight (gpt-oss-120b) models. With Opus 4.8, MILO improves resolution over its initial harness by $+12.0\%$, $+28.3\%$, and $+10.3\%$, respectively, compared with best prior-search gains of $+4.5\%$, $+18.3\%$, and $0\%$. On Terminal-Bench 2.1, it achieves $86.1 \pm 2.0\%$, exceeding the official leaderboard's top entry ($83.8 \pm 2.3\%$) while using 26\% fewer tokens than its initial harness. On EinsteinArena open problems, MILO improves best-known upper bounds for Erdős minimum-overlap ($0.3808586 \to 0.3808568$) and the first and third autocorrelation inequalities ($1.50274365 \to 1.50274360$; $1.45081 \to 1.44889$).

cs.LG↗

arXiv2026

On the Off-Policy Teacher in On-Policy Distillation

On-policy distillation (OPD) has recently emerged as a promising post-training paradigm in which the student learns from trajectories generated by its own policy under dense teacher supervision. However, OPD introduces a fundamental asymmetry: although the sampled trajectories are on-policy for the student, they are off-policy for the teacher. The teacher is typically optimized to continue from prefixes generated by its own policy, but during OPD it must instead supervise prefixes generated by the student. Empirically, we find that its continuation performance degrades as these prefixes grow longer. To address this issue, we propose Student-COnditioned Updates of the Teacher (SCOUT), a co-training framework that adapts the teacher to student-generated prefixes. Alongside standard OPD updates, SCOUT periodically optimizes the teacher's conditional ability using reinforcement learning with verifiable rewards, where the teacher generates continuations from student prefixes and learns from outcome rewards. Controlled experiments show that SCOUT improves the teacher's ability to continue from student-generated prefixes, supporting the intended mechanism of student-conditioned teacher adaptation. Across multiple teacher--student configurations, model scales, and reasoning domains, SCOUT also consistently improves the effectiveness of on-policy distillation.

cs.LG↗

arXiv2026

Efficient, Geometry-only Prediction of Advection-dominated Particle Transport through Saturated Soils

The environmental transport of microplastic particles has raised concerns because of their potential ecological and human-health impacts. A particular challenge for experiments on microplastic transport in soils is the fact that soil is a highly complex and non-transparent porous medium. Thus, our knowledge of transport mechanisms of microplastics in soils and related ecological implications is still limited and computational simulations offer an additional possibility to obtain important insights into the physical transport behaviour of microplastics. Yet, direct particle-resolved simulations in realistic soil structures for macroscopic sample sizes remain a computational challenge. We introduce an efficient pore-network model, minD-PNM, that predicts particle breakthrough curves in water-saturated soils using experimental X-ray micro-computed tomography ($μ$CT) pore geometries as the only input. The model combines an approximately $t^{-3}$ pore-scale transit time distribution with a minimum-dissipation partition of multi-inlet-multi-outlet pores, and propagates these distributions through the pore network to predict breakthrough curves. We benchmark minD-PNM against lattice Boltzmann and immersed boundary simulations for small systems, and against microplastic column experiments in quartz sediments for macroscopic sample sizes. In both cases, the predicted breakthrough curves agree well with the corresponding reference data. Because it requires only geometric information, minD-PNM scales to macroscopic sample volumes offering a practical tool for contaminant-hydrology studies of particulate pollutants.

cond-mat.soft↗

arXiv2026

Towards Mechanistically Understanding Why Memorized Knowledge Fails to Generalize in Large Language Model Finetuning

Fine-tuning LLMs to inject new knowledge faces a critical challenge: LLMs can quickly memorize new facts, yet fail to use them for downstream reasoning tasks. We formalize this failure as the Knowing-Using Gap, characterized by an accuracy gap and a temporal lag between memorization and generalization. To understand this phenomenon, we fine-tune LLMs with unseen knowledge and monitor the spatial permeation dynamics of the knowledge internally with self-patching, an adaptation of activation patching that scans all layer pairs at every fine-tuning check-point. Self-patching identifies activation locations where relocating representations substantially improves failed generalization cases. These results are consistent with a knowledge-circuit misalignment hypothesis: memorized representations can exist internally but may not be routed to computation-effective layers. Experiments are done cross-domain for the robustness of this finding. Building on this diagnosis, we propose layer-wise representation self-distillation (LRSD) that aligns knowledge representation from late storage layer to middle layer. LRSD keeps improving generalization after fine-tuning saturates and nearly doubles multi-hop chaining accuracy on Qwen, while leaving memorization intact.

cs.AI↗

arXiv2026

Isoperimetric bounds for the weighted Neumann and Steklov eigenvalues in dimensions three through six

For $3\le n\le6$, we determine the sharp isoperimetric bound for the mass-normalized first weighted Neumann eigenvalue on bounded Euclidean domains. For every finite nonnegative nonatomic measure $μ$ on $\overlineΩ$, \begin{equation*} \overlineλ_1^N(Ω,μ)\le\frac{n(n-1)}{n-2}ω_n\sin^2\vartheta_n\left(\frac{|Ω|}{ω_n}\right)^{(n-2)/n}, \end{equation*} where $ω_n$ is the volume of the unit ball and $\vartheta_n\in(π/2,π)$ is the angle at the first stationary radius of the regular rotational harmonic-map profile. The bound is attained on balls by a smooth positive radial density. In fact, we affirmatively resolve Question~1.12 posed by Vinokurov \cite{Vinokurov2026}. Furthermore, for admissible domains with finite boundary measure, we also prove the sharp strict Steklov bound \begin{equation*} σ_1(Ω)|\partialΩ|\,|Ω|^{(2-n)/n}<\frac{n(n-1)}{n-2}ω_n^{2/n}\sin^2\vartheta_n, \end{equation*} whose constant is approached by $C^1$ perforated domains.

math.DG↗

arXiv2026

Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$

Let $p_1, \dotsc, p_k$ be primes not exceeding $x$ ($k \geqslant 2$), and define the additive Mertens sum \[ S_k(x) = \sum_{p_1 \leqslant x} \cdots \sum_{p_k \leqslant x} \frac{1}{p_1 + \dotsm + p_k}. \] In contrast to Tenenbaum's generalized (multiplicative) Mertens sum, whose leading term has order $(\log \log x)^k$, the sum $S_k(x)$ has leading term of order $x^{k-1}/\log^k x$. We establish the complete asymptotic expansion \[ S_k(x) = \frac{x^{k-1}}{\log^k x} \sum_{n=0}^{N} \frac{E_{k,n}}{\log^n x} + O_{k,N}\left(\frac{x^{k-1}}{\log^{k+N+1} x}\right) \quad (\forall\, N \geqslant 0), \] where the coefficients are given by absolutely convergent multiple logarithmic integrals \[ E_{k,n} = (-1)^n \int_{(0,1]^k} \frac{h_n(\log t_1, \dotsc, \log t_k)}{t_1 + \dotsm + t_k}\, \mathrm{d}\mathbf{t}, \] with $h_n$ the complete homogeneous symmetric polynomial of degree $n$. We derive closed-form expressions for the first two coefficients $E_{k,0}$ and $E_{k,1}$ for all $k$, and obtain the closed form for the diagonal part of the third coefficient $E_{k,2}$ (with $E_{k,2}$ fully explicit for $k \leqslant 7$), together with a uniform closed form for the coefficients of the new constants $G(-1/m)$, where $G(z)=\int_0^z \mathrm{Li}_2(t)/(1+t)\,\mathrm dt$, whose genuinely new instances first occur for $k \geqslant 5$ (Proposition 5.4); consequently, the first three terms of the expansions of $S_2(x)$ and $S_3(x)$ are fully explicit. For $k = 2$, we further obtain a closed-form expression for the entire sequence $\{E_{2,n}\}_{n \geqslant 0}$, whose values are explicit $\mathbb{Q}$-linear combinations of $\log 2$ and zeta values $ζ(j)$. The proofs rely on the real-variable form of the prime number theorem, variable rescaling, and multivariate Taylor remainder estimates.

math.NT↗

arXiv2026

Planned Test-Time Scaling with Coordinated Reasoning Paths

Test-time scaling with parallel branches is widely adopted to improve performance on challenging reasoning tasks. The predominant approach, repeated sampling, draws branches independently from a single policy, which can produce redundant attempts and thereby limit the gains from additional inference compute. To address this limitation, we propose Planned Test-Time Scaling (PTTS), which replaces independent sampling with a coordinated joint policy: a planner generates a solution outline for each branch, steering the branches toward distinct reasoning paths, and an executor produces a full solution conditioned on each outline. Formally, we show that PTTS strictly generalizes repeated sampling and, in a stylized setting, provably promotes coverage of complementary reasoning modes and yields better pass@k scaling. We instantiate PTTS on top of strong reasoning models, keeping them fixed as executors while replacing repeated sampling with PTTS inference to further enhance test-time scaling. Concretely, we develop two variants: PTTS-ZS prompts a model to jointly generate outlines for all branches in a single autoregressive pass, while PTTS-RL directly optimizes the planner against the pass@k reward using truncated execution rollouts for efficient training and a sharper reward signal. Across five mathematical reasoning benchmarks with Qwen3-1.7B and 4B, PTTS-ZS improves pass@64 over repeated sampling by up to 6.7 points, while PTTS-RL further increases the gain to up to 13.4 points. Further analysis indicates that broader coverage of distinct reasoning paths contributes to these gains. Overall, PTTS provides a general framework for improving test-time scaling by coordinating reasoning branches, with zero-shot and trainable instantiations that yield substantial performance gains.

cs.CL↗

arXiv2026

Large forward discretely self-similar solutions to the two-dimensional Navier-Stokes equations with rough data

We construct forward discretely self-similar (DSS) solutions of two-dimensional Navier-Stokes equations with arbitrarily large data in $L^2_{loc}(\mathbb{R}^2\setminus\{0\})$. For such rough initial data, we first establish a sharp linear estimate under the discrete scaling, which identifies the $L^2$-norm of the initial datum on a fundamental annulus with the Dirichlet energy of its caloric lift over one period in logarithmic time. This, together with a structural cancellation between the linear profile and the nonlinear remainder over one period in logarithmic time, yields a uniform $\dot{H}^1$-bound for the remainder, where the natural $L^2_{loc}$-regularity of the initial data seems to be sharp. Since the two-dimensional Leray operator has no $L^2$-coercivity, we recover uniform energy control for the remainder by exploiting $L^p$-estimates ($1<p<2)$, together with a key bootstrap argument and periodicity. We then first construct smooth DSS solutions using further weighted estimates and a fixed-point argument as long as the initial data belong to $C^2_{loc}(\mathbb{R}^2\setminus\{0\})$. These stronger weighted bounds are not uniform under approximation of rough data. Instead, the passage to $L^2_{\rm loc}$ data relies only on the unweighted energy estimates. Finally, we use strong time continuity of the limiting periodic profile to recover the uniform spatial tightness needed to verify the initial data.

math.AP↗

arXiv2026

Rigidity of Stationary Navier-Stokes Solutions with Transverse bound in Dimensions Five and Higher

For $n\geq5$, let $(u,p)$ be a smooth solution of the stationary incompressible Navier-Stokes equations in $\R^n\setminus\{x'=0\}$, where $\{x'=0\}$ is the $x_n$-axis. We prove that the scale-invariant transverse bound $|u(x)|\leq C |x'|^{-1}$ forces $u\equiv0$. This result relies on a quantitative local regularity theorem, which shows that the transverse bound condition yields uniform control of $u$ and $\nabla u$ in a smaller ball and removes the possible singularity along the axis. The proof combines weak extension across the axis, approximate Green functions for an adjoint drift operator, a one-sided bound for the total head pressure, a localized Frehse-Růžička weighted estimate, and a finite Stokes-Morrey bootstrap. Applying the local theorem at arbitrarily large scales yields whole-space rigidity and removability of line singularities. This together with the asymptotic expansions on the exterior domains in the case $|u(x)|\leq C |x|^{-1}$ in [1], yields the same expansion in exterior domains under the condition $|u(x)|\leq C |x'|^{-1}$.

math.AP↗

arXiv2026

Practical Scaling Laws: Converting Compute into Performance in a Data-Constrained World

The scaling laws guiding modern model training were calibrated for a single regime: data-rich, single-epoch pretraining. The dominant such scaling law form, Chinchilla's $L = E + A/N^α+ B/D^β$, has three structural limitations outside that regime: it diverges as unique data shrinks instead of saturating at the uninformed baseline; it cannot represent overfitting when capacity exceeds the data; and it conflates total examples seen with unique examples available. We propose a closed-form extension, $L(N, D, T) = E + (L_0 - E)\,h/(1+h)$ with $h = a/N^α+ b/T^β+ c\,N^γ/D^δ$, that decomposes loss into undercapacity, undertraining, and overfitting terms. It saturates between the irreducible loss $E$ and an uninformed baseline $L_0$ fixed by the loss type, and reduces to Chinchilla in the data-rich, single-epoch limit. We validate it on four multi-epoch experiments spanning four architecture families (MLPs, ResNets, Fourier neural operators, and transformers) across vision, scientific ML, and language domains, and refit it to five published LLM scaling-law grids. Extrapolating to higher compute and larger unique data than seen at fit time, our form achieves state-of-the-art RMSE on every published LLM grid we evaluate and on most cells of our constructed experiments. Once calibrated, the form admits a cost-aware allocation that recovers Chinchilla's optimum when data is free and shifts toward smaller corpora and more epochs as data grows expensive.

cs.LG↗

arXiv2026

ZGCM-1: A Fully Open and Extremely Efficient Foundation Model for Math and Agentic Search

In this work, we present ZGCM-1, a fully open 7B dense foundation model trained from scratch with extreme data, system, and algorithmic efficiency. ZGCM-1 is founded on a core premise: compact models cannot passively memorize the open web, but can overcome parametric capacity limits by coupling deliberate internal thinking with active external tool use. To support this paradigm across a 256K context, we develop an end-to-end, high-efficiency open training recipe: Architecture & System Co-design: interleaved gated sliding-window and full attention, and a stable FP8 Muon optimizer; Progressive Curriculum & MDP Mid-Training: context scaling across 16K, 64K, and 256K, and the reformulation of interaction traces into Markov Decision Processes. Furthermore, we establish an AI-native R&D workflow where agent swarms autonomously manage cluster operations, data curation, and rapid diagnostic evaluation. Extensive evaluations show that ZGCM-1-7B is competitive across 7B model family on general benchmarks. On several challenging mathematical reasoning and agentic search suites, it remains competitive with frontier models orders of magnitude larger, such as Qwen3-235B-A22B and GLM-5.1. We also show that our pre-training design offers a ~4.2x efficiency improvement in 16K pre-training time-to-loss. Across the full development lifecycle, we distill eight actionable empirical findings-spanning architectural scaling, SFT quality pruning, long-context generalization, and agentic co-training dynamics. To facilitate community research, we open-source model weights from the pre-training, mid-training, and post-training stages, intermediate checkpoints, training code, per-stage data and data recipes, and W&B logs.

cs.AI↗

arXiv2026

A Thresholding Based Operator-Splitting Method for Curvature-Regularized Surface Reconstruction

Surface reconstruction from point clouds is a fundamental problem in computational geometry with broad applications in computer graphics, medical imaging, and manufacturing. In this paper, we propose an efficient method for solving a curvature-regularized surface reconstruction model. To avoid the computational cost associated with reinitialization in traditional level set methods, we represent the reconstructed surface by an indicator function. By introducing an auxiliary variable, we reformulate the original optimization problem as the computation of the steady-state solution of an initial value problem. We then develop an operator-splitting method to decompose the resulting problem into two tractable subproblems, one of which can be efficiently solved by iterative thresholding. The proposed approach combines the advantages of curvature regularization, operator splitting, and threshold dynamics. Numerical experiments show that the proposed method is computationally efficient and can accurately reconstruct sharp corners and concave features.

math.NA↗