arXiv subjects

Jun Liu

Publications and source records attributed to Jun Liu.

At least 19 recordsLinked to original sources

arXiv2026

Global asymptotic stability of homogeneous polynomial vector fields is undecidable

We study whether global asymptotic stability (GAS) of the origin is decidable for homogeneous polynomial vector fields with rational coefficients. Our main technical contribution is showing that, for such vector fields of odd degree $d \geq 3$ in every sufficiently large dimension $n$, the problem of deciding GAS of the origin is many-one complete for the class of recursively enumerable sets (and hence undecidable). Using the tools we have built up, we also improve on some recent work by proving a similar result for Lyapunov stability instead of GAS. The proof of our main contribution splits naturally into two parts: - In the first part we give, for every fixed dimension $n$ and odd degree $2k+1$, a computable map which sends a homogeneous polynomial vector field of degree $2k+1$ on $\mathbb{R}^n$ to a homogeneous polynomial vector field of degree three on $\mathbb{R}^m$, where $m=\binom{n+k-1}{k}$, and preserves both GAS and Lyapunov stability. As a consequence, the problems of deciding whether the origin is GAS or Lyapunov stable for rational-coefficient homogeneous polynomial vector fields of any degree, of any fixed odd degree $d \geq 3$, and of degree three are pairwise many-one equivalent. - In the second part we prove that there is a fixed dimension $n_*$ and a fixed odd degree $d_*$ such that the set of rational-coefficient homogeneous polynomial vector fields on $\mathbb{R}^{n_*}$ of degree $d_*$ whose origin is GAS is many-one complete. This is done by "transferring" many-one completeness between several different problems, starting from the solvability of a Diophantine equation and eventually arriving at our desired GAS decision problem.

math.DS↗

arXiv2026

When Does Test-Time Search Help World Action Models? An Empirical Audit of Candidate Selection and Simulator Integrity

World-action models increasingly apply test-time scaling, spending extra inference computation on candidate selection and adaptive allocation to improve control. Such gains are credible only when candidates carry exploitable signal, nominal compute savings become real speedup, and evaluation stays reliable. We audit all three on Cosmos Policy and RoboCasa with a premise-first, pre-registered methodology. On clean data, a learned value selector is 1.66 pp worse than random; a hindsight oracle gains only 1.40 pp, with an episode-level interval spanning zero; and 82% of states show identical candidate outcomes, leaving little selection headroom. Token pruning cuts per-forward FLOPs by up to 47% but yields at most a measured 1.15$\times$ end-to-end speedup on the deployed path (1.25$\times$ on a decode-excluded path), short of a 1.5$\times$ target, and our adaptive-allocation experiment is inconclusive under a power gate. We further identify and fix a silent rendering corruption whose rate rises sharply along compute-heavy planning paths while leaving the official direct-policy result unaffected, and release a detector, fix, and scripts. These findings show why test-time scaling should be audited as a chain of premises (decision signal, realized efficiency, evaluationintegrity) rather than by success rate alone. Conclusions are scoped to the tested configuration.

cs.AI↗

arXiv2026

RCR-Router: Efficient Role-Aware Context Routing for Multi-Agent LLM Systems with Structured Memory

Large language model (LLM) agents are increasingly organized into multi-agent systems for complex reasoning and decision-making tasks. However, scaling such systems can substantially increase inference cost, especially when multiple agents repeatedly process overlapping or role-irrelevant context. Many existing multi-agent frameworks focus on orchestration and role specialization, but still rely on full-context sharing or static context routing, leading to redundant token consumption, increased runtime, and inefficient memory utilization. We present \emph{Role-Conditioned Context Routing (RCR)}, an execution-time layer that allocates role-relevant shared-memory items to agents under token budgets. Given a structured shared memory and a set of role-specialized agents, RCR selectively routes task-relevant memory items to each agent according to its role, optional task-stage metadata, and token budget. RCR integrates role-conditioned relevance scoring, token-budgeted memory selection, and iterative memory updates to reduce redundant context exposure during multi-agent execution. Experiments on multi-hop QA, embodied reasoning (ALFWorld), and web-based decision-making (WebShop) show that RCR reduces token usage by 35\% on average and runtime by 38\% on average relative to Full-Context, while maintaining or improving task performance.

cs.CL↗

arXiv2026

Adaptive Residual Modeling for Scenario Learning in Probabilistic Load Forecasting

Uncertainties in weather, user behavior, and distributed energy production introduce significant variability into feeder power. Effective power system operations require both multi-horizon load forecasts and well-calibrated extreme quantiles for the forecast. Nevertheless, standard objectives that fit the full forecast distribution often underemphasize rare observations and extremes. Conversely, applying heavy tail-weighting in the distribution to capture these extremes can distort the underlying probability distribution. To address this issue, this paper proposes adaptive residual modeling for scenario learning (ARMSL), a two-stage framework. Particularly, Stage I in our framework sequentially models environmental response, history-dependent load patterns, persistent residual deviations, and the remaining innovations. Upon the modeling, we then generate joint active- and reactive-power scenarios with state-dependent dispersion. Stage II keeps the scenario model fixed and calibrates extreme marginal quantiles using a simple, channel-specific reference forecast (an anchor). Only outward deviations from this anchor are admitted, with their contribution determined by local calibration history and the current operating state. From our numerical simulations on FeederBW dataset, Stage I outperforms diffusion baselines in energy and variogram scores. Our complete framework achieves an active-power 0.99-quantile pinball loss of 0.1932 (a 30.08% to 85.33% reduction relative to three baselines) with 1.054% exceedance rate against a nominal 1%. From simulations on the Rolle dataset, we observe decreased losses by 5.39%--14.40% compared to the active-power-only anchor. Furthermore, the unchanged Stage I scenarios in the simulation yield a correlation of 0.953 between predicted and observed feeder event rates, with 90.0% of feeder errors falling within two percentage points.

eess.SY↗

arXiv2026

Dual-Grained Policy Optimization for Hallucination Reduction in Flow-Based RL

Reinforcement Fine-Tuning (RFT) on flow-based models is crucial for alignment. However, they often introduce visual hallucinations like over-optimized details and semantic misalignment. This work explains why visual hallucinations arise and shows how to reduce them. We first investigate RFT methods from a unified perspective and trace hallucinations to two mechanisms. Limited exploration from stochastic differential equation (SDE) rollouts yields detail-dominated within-group differences, leading to fine-grained optimization that over-emphasizes local details and neglects global semantics. Trajectory imitation writes reward-selected SDE noise into the velocity field, leading to inconsistent optimization that degrades cross-step consistency. Building on this, we propose DGPO, a general framework to mitigate hallucinations. Specifically, we design Dynamic Granularity Rollout (DGR) to balance global semantics and local details by dynamically scheduling noise sources. We then introduce a Consistent Policy Gradient Optimization that preserves the consistency by aligning the policy with a more stable prior. Experiments show that DGPO reduces low-/high-level hallucinations by 49%/38% and improves the average of out-of-domain (OoD) metrics by +4.9% on FLUX.1.dev, compared with the baseline's -0.7%. Project page: https://xiaofeng-tan.github.io/projects/ConsistentRFT/

cs.CV↗

arXiv2026

NDPP-Grasp: Non-Differentiable Physical Plausibility Constraint-Guided Task-Oriented Dexterous Grasp Generation

Task-oriented dexterous grasp generation aims to produce dexterous grasp poses that are both physically plausible and functionally suitable for specified manipulation tasks. Existing diffusion-based methods often address these two requirements in a decoupled manner: they first train a grasp diffusion model for task alignment and then rely on post-generation refinement to improve physical plausibility. However, this after-the-fact correction strategy applies physical plausibility guidance only once the grasp has already been generated, leaving the generation trajectory itself unguided by physical constraints and potentially leading to suboptimal grasps. To address this problem, we propose a novel framework that directly injects physical plausibility guidance into the denoising process of a task-aligned grasp diffusion model in a practical and effective manner, even when physical plausibility constraints are non-differentiable. This allows physical plausibility to shape grasp generation throughout denoising while preserving task alignment. Extensive experiments demonstrate the efficacy of our framework.

cs.RO↗

arXiv2026

Quantum query complexity of Hurwitz stability testing

Determining whether every trajectory of the linear system $\dot{x}=Ax$ converges to zero (or, equivalently, whether $A$ is Hurwitz stable) is a fundamental problem in control theory. It arises, for example, in verifying the stability of feedback controllers and state observers, as well as of linearized dynamical models. We study the quantum query complexity of deciding whether a matrix $A\in\mathbb{C}^{n\times n}$ is Hurwitz stable, given an exact normalized block-encoding of $A$. The query complexity is characterized in terms of the system dimension $n$ and a supplied lower bound $0<ν\leq ω_A$ on the imaginary-axis distance $ω_A:=\min_{t\in\mathbb{R}}σ_{\min}(A-\mathrm{i}tI)$, where $σ_{\min}(A)$ is the smallest singular value of $A$. We prove a query-complexity lower bound of $Ω(\sqrt{n}/ν)$, which holds even when $A$ is restricted to be real and diagonal. For general matrices with nonzero $ω_A$, we encode an approximation of the right-half-plane spectral projector $\operatorname{sign}^+(A):=(I+\operatorname{sign}(A))/2$ as a block of a matrix inverse, where $A$ is Hurwitz if and only if the projector is zero. To test this, we produce a quantum algorithm which determines if a $(β,b,1/(4\sqrt{n}))$-block-encoded projector matrix (like $\operatorname{sign}^+(A)$) is zero or not; for constant success probability, it has complexity $Θ(β\sqrt{n})$. When the zero test is applied to specific approximations of $\operatorname{sign}^+(A)$, this yields an upper bound of $O(\sqrt{n}ν^{-2}\log(\sqrt{n}/ν))$ queries in the general case, and $O(\sqrt{n}ν^{-1}\log n)$ when $A$ is Hermitian or normal. The latter upper bound matches the lower bound up to a logarithmic factor. Thus the dimension dependence of quantum Hurwitz testing is nearly optimal, while the remaining factor in the non-normal case isolates an open conditioning gap.

quant-ph↗

arXiv2026

Automated Theorem Generation in First-Order Logic by Construction from Triangular Standard Contradictions

Automated theorem generation (ATG) seeks to construct new theorems rather than merely prove given conjectures. Existing approaches typically generate candidate statements that require subsequent proof or formal verification. We propose a constructive framework for ATG in first-order logic based on triangular standard contradictions. The method constructs minimally unsatisfiable clause sets from selected first-order literals, then forms theorems by retaining some clauses as premises and taking the negation of one clause, or a conjunction of clauses, as the conclusion. Minimal unsatisfiability ensures that the remaining premises are satisfiable, avoiding trivial inference by explosion, while unsatisfiability of the full set guarantees the resulting entailment. Theorems are therefore correct by construction, without a separate proof procedure for each instance. Extending the previously developed $Δ_1$ generator, we introduce seven methods, $Δ_2$--$Δ_8$, forming a unified family of eight theorem-generation methods. Four generators, $Δ_1$--$Δ_4$, have been implemented and released. We also formulate a general $Δ$-class method encompassing the family. Combinatorial analysis demonstrates the capacity to generate large numbers of distinct theorems systematically. This framework offers a principled foundation for automated theorem discovery and the construction of logically guaranteed knowledge.

cs.AI↗

arXiv2026

Self-Referential $K$-SAT and the Finite Analogue of Gödel's Incompleteness Theorem

We study self-reference and solution independence in Boolean $K$-SAT as a finite analogue of Gödel incompleteness. Independence is defined through factorial moments of the solution count. Constant-width random formulas fail this criterion due to correlations among overlapping assignments. At a covering threshold, logarithmic-width random CNFs have a Poisson solution count, with positive probabilities of unsatisfiability and unique satisfiability. Replacing a redundant clause by one falsified by the unique solution yields an unsatisfiable companion preserving the unsigned incidence graph. For every permitted local view of a good uniquely satisfiable formula, an unsatisfiable companion preserves that view. Irreducibility defeats deterministic and bounded-error evaluators using $N^c$ clause queries, for fixed $0 0$, transcripts of $N^{1-δ}$ queries leave $N-o(N)$ bits of witness entropy. On typical support graphs, expansion yields linear Resolution width, linear PC/PCR and SOS degree, and exponential proof size. Bounds hold for semantic Cutting Planes under a partition condition and for Positivstellensatz with bounded product width, uniformly over unsatisfiable support-preserving signings. Structural evidence and the limits of acceleration strategies motivate the self-referential $K$-SAT exhaustive-search hypothesis (SRK-ESH): no uniform deterministic algorithm deciding the promise family achieves a fixed proportional saving in the exponent. This dual-evidence criterion combines intrinsic hardness mechanisms with algorithmic evidence. We interpret this hypothesis as a quantitative projection of the Gödel-style local--global gap. The information obstruction constrains quantum local observation and statistical learning from bounded local information.

cs.CC↗

arXiv2026

UniDG: Unified Defect Generation via Defect-Context Editing

Generating realistic visual defects is crucial for alleviating the scarcity of abnormal samples in anomaly detection, yet existing methods often rely on category-specific few-shot adaptation and struggle to generalize across objects, defect types, and domains. This limitation stems in part from the lack of paired defect editing data and the fine-grained nature of defect appearance, where subtle variations in scale, texture, and morphology must be preserved while maintaining consistency with the target scene. To address this challenge, we introduce UDG, a dataset of 300K normal-abnormal-mask-caption quadruplets curated from diverse defect-related scenarios, and present UniDG, a unified defect generation model. UniDG formulates defect synthesis as Defect-Context Editing: it extracts reference defect context with adaptive cropping, organizes reference and target inputs in a structured diptych format, and fuses multimodal conditions through MM-DiT attention. We further develop a two-stage training strategy: Diversity-SFT learns diverse transferable defect priors from paired editing data, while optional Consistency-RFT can further improve reference adherence, local realism, and defect-category consistency. Without per-category fine-tuning or using MVTec-AD/VisA for training, UniDG outperforms prior few-shot anomaly generation and image insertion/editing baselines in both synthesis quality and downstream single- and multi-class anomaly detection/localization.

cs.CV↗

arXiv2026

Laser wakefield acceleration and x-ray emission in plasma produced by the electrical explosion of an aluminum wire

Underdense plasmas used in relativistic laser-plasma interactions are conventionally produced from gaseous targets, whereas low-density metallic plasmas remain comparatively unexplored. Here, we investigate the interaction of a femtosecond petawatt laser with expanded aluminum plasma using particle-in-cell simulations based on an experimentally motivated exploding-wire density profile. Three-dimensional simulations show that the laser propagates through the low-density metallic plasma, drives a pronounced wake-like structure, accelerates electrons to near-GeV energies, and produces directional broadband x-ray emission. Charge-state-resolved diagnostics further show that electrons associated with higher aluminum ionization stages are disproportionately represented in the energetic population. Complementary two-dimensional simulations indicate that the net electron energy gain is dominated by longitudinal electric-field work and show that relativistic electron generation persists under variations of the assumed initial ionization and density conditions, although the yield remains quantitatively sensitive to the plasma state. These results demonstrate the feasibility of electrically exploded aluminum plasma as a target platform for laser wakefield acceleration and associated x-ray generation.

physics.plasm-ph↗

arXiv2026

Wave Is All You Need: A Quantum Language Model Based on Fully Connected Quantum Boltzmann Machine

This work proposes a self-attention mechanism based on the fully connected quantum Boltzmann machine (FC-QBM), and further constructs a fully connected quantum Boltzmann machine language model (FC-QBM-LM) using the mechanism as the core engine. By performing unitary evolution on semantic quantum states, the mechanism implicitly implements positional encoding and self-attention computation, eliminating the need to decompose continuous semantic streams into discrete matrices for explicit matrix multiplication, with the measurement results naturally satisfying the normalization condition. Specifically, this work rigorously derives the computational principle of the self-attention mechanism based on FC-QBM, and demonstrates that this mechanism is mathematically equivalent to the classical self-attention mechanism. The mathematical principles governing the training and generation of FC-QBM-LM are thoroughly derived, and the two corresponding algorithms are subsequently developed. An 8-qubit FC-QBM-LM is finally constructed and trained on the corpus of Tang poetry. Under the 8-qubit setting, the quantum layer implements the entire positional encoding and self-attention computation pipeline with only 44 parameters. In the noiseless scenario, the model exhibits favorable convergence. Furthermore, the quantum circuit proposed in this work, which terminates with Y-axis rotation gates, achieves better convergence than the counterpart terminating with X-axis rotation gates. Under the small-sample regime and across eight distinct noise intensity levels, the model demonstrates strong noise robustness, retaining over 99% of its noiseless convergence performance. Experiments on five-character quatrain generation reveal that the model preliminarily exhibits three core capabilities: associative and divergent thinking, content generation across imagery and human-aligned word ordering.

quant-ph↗

arXiv2026

Uni-Stream: A Unified Streaming Speech Language Model for Speech Synthesis and Recognition

Unified streaming speech language models aim to support speech recognition and synthesis within a single model, enabling real-time human-computer interaction. However, jointly supporting these two directions of speech-text conversion while preserving task-specific performance remains challenging. We propose Uni-Stream, a unified streaming speech language model built on compact pretrained speech models. Uni-Stream processes interleaved text and speech in a streaming format and achieves performance comparable to task-specific models through two-stage training. We also develop a data annotation pipeline for streaming training and will publicly release the generated transcriptions and word-level timestamps. We further examine Uni-Stream's representations across tasks and modalities and find that speech and text residence in distinct latent feature space even when trained in a unified model architecture, while representations within each modality become more task-dependent in later layers.

eess.AS↗

arXiv2026

Tempo-Zero: Recursive Self-Play in Executable Worlds for Video Reasoning

Video reasoning requires understanding how events unfold over time, yet videos with accurate temporal annotations are expensive to collect. Self-play offers an alternative by letting a model generate and solve its own tasks without manual annotation. However, existing video self-play methods train on fixed sets of recorded videos, so they cannot alter the underlying event dynamics and rely on noisy pseudo-labels derived from the model's own outputs, such as majority voting, that risk reinforcing shared model errors. To overcome these limitations, we introduce Tempo-Zero, a self-improvement framework that closes a loop of executable environments, execution-verified self-play, and environment evolution, where executing a program renders a video with the ground-truth option and interval of every question. A single policy plays both Questioner and Solver, proposing questions and answering them with timestamped evidence lines, and is trained on execution-grounded rewards instead of model consensus. The Solver's performance steers a curriculum over tasks and difficulty levels, and the policy selects rule changes that enrich the event dynamics of later rounds. Despite being trained solely on simple programs, without supervised fine-tuning or external video data which prior methods typically require, Tempo-Zero outperforms the base models and recent self-play baselines on average across twelve real-world video benchmarks at different model scales, with particularly strong gains on temporal grounding tasks. Project page: https://alchemist-jo.github.io/tempo-zero/

cs.CV↗

arXiv2026

Next Best Action: Causal Constrained Offline RL for Business Action Targeting

Next Best Action (NBA) systems must select among customer interventions (e.g., discounts, promotions, and lifecycle actions), maximize long-term economic value, satisfy complex operational constraints, and remain causally grounded. Existing approaches lack a rigorous framework for meeting these requirements jointly. We address this gap by formulating NBA as a Constrained Markov Decision Process (CMDP). We then integrate off-policy causal correction of the estimated customer dynamics directly into the Linear Programming (LP) formulation of the CMDP. The resulting policy selects actions based on customer states to maximize long-term value while explicitly enforcing business guardrails. Furthermore, the LP formulation yields shadow prices that quantify the economic trade-offs of operational constraints (e.g., fairness and user welfare), enhancing policy interpretability. We validate our proposed offline Reinforcement Learning (RL) framework on an industry case study involving rideshare coupon targeting, where customer states are defined by Recency, Frequency, and Monetary (RFM) stages. We evaluate performance using model-based off-policy evaluation, with causal dynamics estimated from a temporal holdout. Under the observed coupon budget and RFM state representation, our optimized policy improves customer lifetime value (LTV) by 19% over the estimated behavior policy and 8% over a myopic baseline. Although the demonstrated action space is binary, the proposed framework is action-agnostic, yielding a general-purpose decision module for targeting systems that manage multiple interventions.

cs.LG↗

arXiv2026

Controllability of polynomial systems is undecidable and not recursively enumerable

Sontag conjectured in 1988 that global controllability of polynomial control systems with rational coefficients is undecidable, but that the controllable systems form a recursively enumerable set. We prove the first part of the conjecture and disprove the second. For every homogeneous polynomial vector field $F$ of odd degree with rational coefficients, we construct an explicit polynomial control system $Σ_F$, with one more state than $F$, that is globally controllable if and only if the origin is \emph{not} globally asymptotically stable for $\dot x=F(x)$. By a recent result, the homogeneous polynomial vector fields with a globally asymptotically stable origin form a set that is recursively enumerable but not decidable. Consequently, global controllability of polynomial systems is undecidable, and the controllable polynomial systems are not recursively enumerable. The same conclusions hold for systems of the form $\dotξ=f(ξ)+Bu$ with a polynomial drift and a constant input matrix.

math.OC↗

arXiv2026

Measurement-Adaptive Light-Cone Transform for Robust Non-Line-of-Sight Imaging

Practical non-line-of-sight (NLOS) measurements are affected by noise and deviations from idealized light transport, which can degrade reconstruction with conventional light-cone transform (LCT) methods. We propose the Measurement-Adaptive Light-Cone Transform (MALCT), a physics-guided framework that retains the efficient Fourier-domain inversion structure of LCT. {Within a unified variational formulation, MALCT combines the analytical response with a shared learned response through measurement-conditioned weighting and predicts a measurement-conditioned, frequency-dependent regularization map.} An attention-enhanced spatio-temporal feature extraction module captures long-range temporal dependencies and local spatial correlations to support reconstruction under low-signal conditions. Experiments on synthetic data and real measurements from different NLOS systems demonstrate improved reconstruction quality. Controlled evaluations further assess robustness to temporal-response broadening and reduced acquisition time. MALCT also preserves scene structures with spatial sampling grids down to $32\times32$, supporting its potential for NLOS imaging under limited acquisition budgets.

eess.IV↗

arXiv2026

3DTCR: Vortex-following generative reconstruction improves tropical cyclone intensity prediction from global AI weather forecasts

Global numerical weather prediction (NWP) and artificial intelligence (AI) models often underestimate tropical cyclone (TC) intensity, partly because coarse grids underresolve fine-scale three-dimensional inner-core structures that influence TC intensity evolution. Kilometer-scale NWP simulations can better resolve these structures but are too costly for operational use, which also makes high-resolution TC data limited. Here we construct a 3-km, TC-centered dataset for 2018--2024 using the Weather Research and Forecasting (WRF) model and develop 3DTCR, a vortex-following generative framework that reconstructs three-dimensional TC structure from FuXi global forecasts. 3DTCR combines conditional flow matching (CFM) with two-stage training to learn a coarse-to-fine mapping from center-aligned reanalysis simulation pairs and then adapt it to forecast inputs through latent space alignment. Evaluated on 2024 western North Pacific (WNP) forecasts, 3DTCR reduces the root mean square error (RMSE) and the magnitude of the mean bias error (MBE) in maximum 10-m wind speed by 36.5% and 60.7% relative to FuXi, and by 8.9% and 28.2% relative to the European Centre for Medium-Range Weather Forecasts high-resolution system (ECMWF-HRES), respectively. Case studies suggest that reconstructions capture wind gradients between the eye and eyewall, vertical structure of horizontal winds, and vortex asymmetries, while inheriting the FuXi-predicted TC tracks. 3DTCR generates 5-day TC-centered atmospheric fields in approximately 3 minutes on one GPU, whereas a full-basin 3-km WRF simulation takes about 400 hours on 32 CPU cores. These results demonstrate that such a vortex-following generative reconstruction can add localized three-dimensional detail to global forecasts and improve TC intensity prediction without basin-wide kilometer-scale numerical integration.

cs.LG↗