arXiv subjects

Tianhao Liu

Publications and source records attributed to Tianhao Liu.

At least 19 recordsLinked to original sources

arXiv2026

Ranking Experiments under Sequential Sampling

We compare statistical experiments when observations are inexpensive and can be acquired sequentially until the decision maker chooses to stop. We introduce two orders. Small-cost decision dominance asks which of two equally priced experiments is eventually preferred in every decision problem as the per-observation cost vanishes; large-budget stopping dominance asks which experiment can reproduce every terminal experiment attainable from the other under all sufficiently large expected-sample budgets. Our main result shows that, for generic pairs, the two orders coincide and are both characterized by strict dominance of every pairwise Kullback--Leibler divergence. The key step is a uniform exact-conversion theorem: any finite-output stopping policy based on one experiment can be reproduced exactly using another, with first-order expected-sample requirements determined by pairwise KL rates and a square-root remainder that is uniform over policies.

econ.TH↗

arXiv2026

Joint Channel Estimation and Data Detection for Multi-LEO-Satellite Cell-Free OTFS Uplinks

Cell-free networks formed by multiple low Earth orbit (LEO) satellites offer a promising architecture for ubiquitous connectivity, but their cooperative reception is challenged by link-dependent residual delays and Doppler shifts. This paper investigates joint channel estimation and data detection (JCEDD) for multi-LEO-satellite cell-free orthogonal time frequency space (OTFS) uplinks. The JCEDD problem is formulated as a structured bilinear inference problem involving link-specific sparse beam--delay--Doppler channels and a multiuser data vector. We develop a low-complexity hierarchical JCEDD receiver in which all satellites first perform local JCEDD, and their observations and local estimates are then aggregated at a central satellite for cooperative refinement. Computational complexity is reduced by restricting channel estimation to coarse-information-aided local beam--delay--Doppler regions and evaluating the required forward and adjoint operations in a matrix-free manner. Simulation results validate the channel-estimation accuracy and data-detection reliability of the proposed JCEDD receiver.

eess.SP↗

arXiv2026

Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domains: the $L^2$-supercritical case

In this paper we investigate the existence of multiple sign-changing and semi-nodal normalized solutions for an $m$-coupled elliptic system of the Gross-Pitaevskii type: \begin{equation} \left\{ \begin{aligned} &-Δu_j + λ_j u_j = \sum_{k=1 }^mβ_{kj} u_k^2 u_j, \quad u_j \in H_0^1(Ω), &\int_Ωu_j^2dx = c_j, \quad j = 1,2,\cdots,m. \end{aligned} \right. \end{equation} Here, $Ω\subset \mathbb{R}^N$ ($N = 3,4$) is a bounded domain. The constants $β_{kj} \neq 0$ and $c_j > 0$ are prescribed constants, while $λ_1, \cdots, λ_m$ are unknown and appear as Lagrange multipliers. This is the first result in the literature on the existence and multiplicity of sign-changing and semi-nodal normalized solutions of couple Schrödinger system in all regimes of $β_{kj}$. The main tool which we use is a new skill of vector linking and this article attempts for the first time to use linking method to search for solutions of a coupled system. Particularly, to obtain semi-nodal normalized solutions, we introduce partial vector linking which is new up to our knowledge. Moreover, by investigating the limit process as $\vec{c}=(c_1,\ldots,c_m) \to \vec{0}$ we obtain some bifurcation results. Note that when $N=4$, the system is of Sobolev critical.

math.AP↗

arXiv2026

Reducing Temporal Redundancy for Efficient Vision-Language-Action Inference

Vision-Language-Action (VLA) models exhibit strong generalization for robotic manipulation, yet their high inference latency limits real time deployment. We identify two primary sources of temporal redundancy in existing VLA pipelines: repeated visual encoding of highly similar consecutive frames and multi step iterative sampling in diffusion based policies. To address this, we propose a system level acceleration strategy that reduces computation in both perception and action generation. On the perception side, we incrementally update only tokens corresponding to dynamic scene regions instead of re-encoding entire frames. On the policy side, we compress diffusion sampling into a compact 2-step schedule through efficiency oriented training while preserving action precision. Experiments on Libero, RobotWin, and Real Robot Platforms demonstrate over 2 times speedup while maintaining high performance, achieving up to 98% success rate on general manipulation benchmarks. Our codes will be released on Github.

cs.RO↗

arXiv2026

RoBoSR: Structured Scene Representations for Embodied Robotic Reasoning

Despite rapid progress, embodied reasoning under real-world variability remains challenging. Existing approaches rely on demonstration-driven sequential biases, limiting flexibility in open-ended and long-horizon tasks that require structured reasoning over evolving states. We introduce RoBoSR, an intermediate structural representation that formulates manipulation as step-wise state transitions over semantically grounded, object-centric scene graphs. By modeling object states and their spatial relations at the perception-action interface, RoBoSR disentangles high-level task reasoning from raw inputs and enables structured reasoning over preconditions, effects, and goal states. This representation endows the agent with causal reasoning capability, enforcing subtask dependencies and supporting coherent long-horizon task planning. To learn such structure-aware reasoning, we construct Manip-Cognition-1.6M, an open-world dataset that jointly supervises scene understanding, instruction interpretation, and subtask planning across diverse tasks. Across several benchmarks and real-world demonstrations, our method consistently outperforms prompting-based methods and classical TAMP baselines in zero-shot generalization and long-horizon tasks. The results underscore structured intermediate representations as a critical inductive bias for scalable embodied reasoning.

cs.RO↗

arXiv2026

Uniqueness of bound states to the logarithmic Schrödinger equation

This paper studies the uniqueness of bound states for the problem Δu + u\log u ^2=0, \quad u\in H^1(\RN), \quad n\geq 2, which arises from the logarithmic Schrödinger equation. We prove that for every integer $k\geq 1$, there exists a unique radial solution $u(r)=u(|x|)$ that has exactly $k$ simple zeros for $r>0$. This resolves an open problem posed by Troy [{Arch. Ration. Mech. Anal.} 222 (2016), 1581--1600] and confirms the Berestycki-Lions conjecture for the logarithmic nonlinearity. The proof combines the shooting method with suitable auxiliary functions introduced by Tang [{Invent. math.} 243 (2026), 245--291]. A major difficulty arises from the singular behavior of the nonlinearity $f(u)=u \log u^2$ at origin. We overcome it by establishing asymptotic convergence and sharp decay rates at infinity for any ground state or bound state. More precisely, every such solution satisfies \lim_{r\to\infty}\frac{ u'(r)}{u(r) \sqrt{\abs{ \log u^2(r)}}}=\lim_{r\to\infty}\frac{u'(r)}{ru(r)} = -1, \quad \limsup_{r\to\infty}|u(r)|e^{(\frac12-ε)r^2}<\infty, ~~\forall ε\in ( 0,\frac{1}{2}). These asymptotic behaviors are of independent interest and may be useful for other problems involving logarithmic nonlinearities.

math.AP↗

arXiv2026

PRIM-cipal components analysis

Supervised No Free Lunch Theorems (NFLTs) are well studied, yet unsupervised NFLTs remain underexplored. For elliptical distributions, we prove that there exist two equally optimal, scientifically meaningful bump-hunting strategies that are exact opposites, with no universal winner. Specifically, peeling $k$ orthogonal dimensions from $\mathbb{R}^d$ ($d \ge k$), retaining an inter-quantile region of probability $1-α$ per peeled dimension, maximizes total variance and Frobenius norm when the $k$ smallest principal components (called pettiest components) are selected, and minimizes them when the selected dimensions are the $k$ leading principal components. These optima inspire PRIM-based bump-hunting algorithms either by minimizing variance or by minimizing volume, thereby motivating an NFLT. We test our results on the Fashion-MNIST database, showing that peeling the largest principal components captures multiplicity, while peeling the smallest principal components isolates popular styles.

stat.ML↗

arXiv2026

FREE-Switch: Frequency-based Dynamic LoRA Switch for Style Transfer

With the growing availability of open-sourced adapters trained on the same diffusion backbone for diverse scenes and objects, combining these pretrained weights enables low-cost customized generation. However, most existing model merging methods are designed for classification or text generation, and when applied to image generation, they suffer from content drift due to error accumulation across multiple diffusion steps. For image-oriented methods, training-based approaches are computationally expensive and unsuitable for edge deployment, while training-free ones use uniform fusion strategies that ignore inter-adapter differences, leading to detail degradation. We find that since different adapters are specialized for generating different types of content, the contribution of each diffusion step carries different significance for each adapter. Accordingly, we propose a frequency-domain importance-driven dynamic LoRA switch method. Furthermore, we observe that maintaining semantic consistency across adapters effectively mitigates detail loss; thus, we design an automatic Generation Alignment mechanism to align generation intents at the semantic level. Experiments demonstrate that our FREE-Switch (Frequency-based Efficient and Dynamic LoRA Switch) framework efficiently combines adapters for different objects and styles, substantially reducing the training cost of high-quality customized generation.

cs.CV↗

arXiv2026

Dynamics of focusing nonlinear Schrödinger equation with partial harmonic confinement in higher dimensions

We study the following focusing intercritical nonlinear Schrödinger equation with partial harmonic confinement: \begin{equation*} \begin{cases} i\partial_t u+Δ_{z}u-y^2 u =- |u|^αu,\quad t\in \mathbb{R},\newline u(0,z)= u_0(z), \ z=(x,y)\in \mathbb{R}^d\times \mathbb{R}, \end{cases} \end{equation*} where $d \geq 1 $ is an integer and the exponent $α$ satisfies \begin{equation}\label{assumption} \frac{4}{d}< α<\begin{cases} \frac{4}{d-1}, \,\,\, \text{if} ~~ d\geq 2; \newline + \infty,\,\,\, \text{if} ~~ d=1. \end{cases} \end{equation} For this model, A. Ardia and R. Carles [Comm. Math. Sci. 19 (2021), 993-1032] established a sharp scattering result below the ground state threshold in dimensions $d \leq 4$ via the concentration-compactness and rigidity argument. However, their approach breaks down in higher dimensions due to the lack of smoothness in the nonlinearity. In this paper, we introduce a new strategy that removes this dimensional restriction and extend their results to higher dimensions by circumventing the concentration-compactness principle. The main ingredients of our work are the interaction Morawetz-Dodson-Murphy estimates and an alternative variational characterization of the ground state threshold.

math.AP↗

arXiv2026

NeuroLoRA: Context-Aware Neuromodulation for Parameter-Efficient Multi-Task Adaptation

Parameter-Efficient Fine-Tuning (PEFT) techniques, particularly Low-Rank Adaptation (LoRA), have become essential for adapting Large Language Models (LLMs) to downstream tasks. While the recent FlyLoRA framework successfully leverages bio-inspired sparse random projections to mitigate parameter interference, it relies on a static, magnitude-based routing mechanism that is agnostic to input context. In this paper, we propose NeuroLoRA, a novel Mixture-of-Experts (MoE) based LoRA framework inspired by biological neuromodulation -- the dynamic regulation of neuronal excitability based on context. NeuroLoRA retains the computational efficiency of frozen random projections while introducing a lightweight, learnable neuromodulation gate that contextually rescales the projection space prior to expert selection. We further propose a Contrastive Orthogonality Loss to explicitly enforce separation between expert subspaces, enhancing both task decoupling and continual learning capacity. Extensive experiments on MMLU, GSM8K, and ScienceQA demonstrate that NeuroLoRA consistently outperforms FlyLoRA and other strong baselines across single-task adaptation, multi-task model merging, and sequential continual learning scenarios, while maintaining comparable parameter efficiency.

cs.LG↗

arXiv2026

GSR: Learning Structured Reasoning for Embodied Manipulation

Despite rapid progress, embodied agents still struggle with long-horizon manipulation that requires maintaining spatial consistency, causal dependencies, and goal constraints. A key limitation of existing approaches is that task reasoning is implicitly embedded in high-dimensional latent representations, making it challenging to separate task structure from perceptual variability. We introduce Grounded Scene-graph Reasoning (GSR), a structured reasoning paradigm that explicitly models world-state evolution as transitions over semantically grounded scene graphs. By reasoning step-wise over object states and spatial relations, rather than directly mapping perception to actions, GSR enables explicit reasoning about action preconditions, consequences, and goal satisfaction in a physically grounded space. To support learning such reasoning, we construct Manip-Cognition-1.6M, a large-scale dataset that jointly supervises world understanding, action planning, and goal interpretation. Extensive evaluations across RLBench, LIBERO, GSR-benchmark, and real-world robotic tasks show that GSR significantly improves zero-shot generalization and long-horizon task completion over prompting-based baselines. These results highlight explicit world-state representations as a key inductive bias for scalable embodied reasoning.

cs.RO↗

arXiv2025

Infinitely many positive solutions to nonlinear scalar field equation with nonsmooth nonlinearity

This paper investigates the existence of infinitely many positive solutions for the logarithmic scalar field equation \begin{equation} \tag{$P$} \label{equ1} -Δu+ V(x) u= u\log u^2, \quad u\in H^1(\mathbb{R}^N), \end{equation} and its counterpart with prescribed $L^2$-norms \begin{align}\label{equ2} \tag{$P_N$} & -Δu+ V(x) u +λu= u\log u^2, \quad u\in H^1(\mathbb{R}^N), &\int_{\mathbb{R}^N} u^2 ~\mathrm{d}x=a^2>0, \end{align} which come from physically relevant situations. Here, $N\geq 2$, $V:\mathbb{R}^N\to \mathbb{R}$ is a non-symmetric and non-periodic potential satisfying certain decay conditions, $ a $ is prescribed constant, and $λ$ arises as an unknown Lagrange multipliers. For problem \eqref{equ1}, using purely variational methods, we establish the existence of multi-bump positive solutions with either finitely or infinitely many bumps. For normalized problem \eqref{equ2}, we prove the existence of normalized multi-bump positive solutions with a finite number of bumps. The main difficulty comes from the nonsmooth nature of logarithmic nonlinearity, which introduces some challenges to the variational framework. In particular, the corresponding energy functional is not of class $C^1$ on $H^1(\mathbb{R}^N)$, which prevents the direct application of standard critical point theory for $C^1$ functional or any reduction methods for $C^{1+σ}$ nonlinearity. The main ingredients in this paper are nonsmooth critical point theory, localized variational methods and a max-min argument. To the best of our knowledge, this paper appears to be the first successful application of the localized variational method to nonsmooth functionals.

math.AP↗

arXiv2025

A New Crossover Algorithm for LP Inspired by the Spiral Dynamic of PDHG

Motivated by large-scale applications, there is a recent trend of research on using first-order methods for solving LP. Among them, PDLP, which is based on a primal-dual hybrid gradient (PDHG) algorithm, may be the most promising one. In this paper, we present a geometric viewpoint on the behavior of PDHG for LP. We demonstrate that PDHG iterates exhibit a spiral pattern with a closed-form solution when the variable basis remains unchanged. This spiral pattern consists of two orthogonal components: rotation and forward movement, where rotation improves primal and dual feasibility, while forward movement advances the duality gap. We also characterize the different situations in which basis change events occur. Inspired by the spiral behavior of PDHG, we design a new crossover algorithm to obtain a vertex solution from any optimal LP solution. This approach differs from traditional simplex-based crossover methods. Our numerical experiments demonstrate the effectiveness of the proposed algorithm, showcasing its potential as an alternative option for crossover.

math.OC↗

arXiv2025

Revealed Information

An analyst observes the frequency with which a decision maker (DM) takes actions, but not the frequency conditional on payoff-relevant states. We ask when the analyst can rationalize the DM's choices as if the DM first learns something about the state before acting. We provide a support-function characterization of the triples of utility functions, prior beliefs, and (marginal) distributions over actions such that the DM's action distribution is consistent with information given the DM's prior and utility function. Assumptions on the cardinality of the state space and the utility function allow us to refine this characterization, obtaining a sharp system of finitely many inequalities the utility function, prior, and action distribution must satisfy. We apply our characterization to study comparative statics and to identify conditions under which a single information structure rationalizes choices across multiple decision problems. We characterize the set of distributions over posterior beliefs that are consistent with the DM's choices. We extend our results to settings with a continuum of actions and states assuming the first-order approach applies, and to simple multi-agent settings.

econ.TH↗

arXiv2025

Generative AI-driven Cross-layer Covert Communication: Fundamentals, Framework and Case Study

Ensuring end-to-end cross-layer communication security in military networks by selecting covert schemes between nodes is a key solution for military communication security. With the development of communication technology, covert communication has expanded from the physical layer to the network and application layers, utilizing methods such as artificial noise, private networks, and semantic coding to transmit secret messages. However, as adversaries continuously eavesdrop on specific communication channels, the accumulation of sufficient data may reveal underlying patterns that influence concealment, and establishing a cross-layer covert communication mechanism emerges as an effective strategy to mitigate these regulatory challenges. In this article, we first survey the communication security solution based on covert communication, specifically targeting three typical scenarios: device-to-device, private network communication, and public network communication, and analyze their application scopes. Furthermore, we propose an end-to-end cross-layer covert communication scheme driven by Generative Artificial Intelligence (GenAI), highlighting challenges and their solutions. Additionally, a case study is conducted using diffusion reinforcement learning to sovle cloud edge internet of things cross-layer secure communication.

cs.CR↗

arXiv2024

Normalized solutions for a class of Sobolev critical Schrodinger systems

This paper focuses on the existence and multiplicity of normalized solutions for the coupled Schrodinger system with Sobolev critical coupling term. We present several existence and multiplicity results under some explicit conditions. Furthermore, we present a non-existence result for the defocusing case. This paper, together with the paper [T. Bartsch, H. W. Li and W. M. Zou. Calc. Var. Partial Differential Equations 62 (2023) ], provides a more comprehensive understanding of normalized solutions for Sobolev critical systems. We believe our methods can also address the open problem of the multiplicity of normalized solutions for Schrodinger systems with Sobolev critical growth, with potential for future development and broader applicability.

math.AP↗

arXiv2024

PGN: The RNN's New Successor is Effective for Long-Range Time Series Forecasting

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to $\mathcal{O}(1)$, effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of $\mathcal{O}(\sqrt{L})$, ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: \url{https://github.com/Water2sea/TPGN}.

cs.LG↗

arXiv2024

An Enhanced ADMM-based Interior Point Method for Linear and Conic Optimization

The ADMM-based interior point (ABIP, Lin et al. 2021) method is a hybrid algorithm that effectively combines interior point method (IPM) and first-order methods to achieve a performance boost in large-scale linear optimization. Different from traditional IPM that relies on computationally intensive Newton steps, the ABIP method applies the alternating direction method of multipliers (ADMM) to approximately solve the barrier penalized problem. However, similar to other first-order methods, this technique remains sensitive to condition number and inverse precision. In this paper, we provide an enhanced ABIP method with multiple improvements. Firstly, we develop an ABIP method to solve the general linear conic optimization and establish the associated iteration complexity. Secondly, inspired by some existing methods, we develop different implementation strategies for ABIP method, which substantially improve its performance in linear optimization. Finally, we conduct extensive numerical experiments in both synthetic and real-world datasets to demonstrate the empirical advantage of our developments. In particular, the enhanced ABIP method achieves a 5.8x reduction in the geometric mean of run time on $105$ selected LP instances from Netlib, and it exhibits advantages in certain structured problems such as SVM and PageRank. However, the enhanced ABIP method still falls behind commercial solvers in many benchmarks, especially when high accuracy is desired. We posit that it can serve as a complementary tool alongside well-established solvers.

math.OC↗