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Lu Liu

Publications and source records attributed to Lu Liu.

At least 19 recordsLinked to original sources
arXiv2026

Aspects of Muchnik's paradox in restricted betting

Muchnik's paradox says that enumerable betting strategies are not always reducible to enumerable strategies whose bets are restricted to either even rounds or odd rounds. In other words, there are outcome sequences x where an effectively enumerable strategy succeeds, but no such parity-restricted effectively enumerable strategy does. We characterize the effective Hausdorff dimension of such $x$, showing that it can be as low as 1/2 but not less. We also show that such reals that are random with respect to parity-restricted effectively enumerable strategies with packing dimension as low as $\log\sqrt3$. Finally we exhibit Muchnik's paradox in the case of computable integer-valued strategies.

math.LO↗
arXiv2026

Cardinality of the K-cones below a non infinitely often $K$-trivial

Given a real $x\in 2^ω$, how many reals are there that are simpler (or equally simple) to describe than $x$. With ``simpler to describe" characterized by $K$-complexity of initial segments (hence we call such $y$ with $y\leq_K x$ a solution to $x$), if $x$ is infinitely often $K$-trivial (hence i.o. $K$-trivial), then a simple counting argument shows that the number of solutions to $x$ is countable. If $x$ is non i.o. $K$-trivial, then must it admit uncountably many solutions? Motivated by this question, we show that: (1) There is a non i.o. $K$-trivial $x$ such that most of its solution is i.o. $K$-trivial. i.e., Only countably many solution to $x$ are non i.o. $K$-trivial. In particular, the cardinality of $K$-degree of $x$ is countable. (2) There is a minimal pair of K-degree (meaning their common solutions are all $K$-trivial) so that each of the pair is non i.o. $K$-trivial, generalizing a result of Csima and Montalbán (where the pair is not required to be non i.o. $K$-trivial but non $K$-trivial). (3) There is a non i.o. $K$-trivial $x$ whose $Δ_K$ complexity grows arbitrarily slow (in a weak sense: $\inf_{m\geq n}Δ_K(x\upharpoonright m)\leq h(n)$ with $h$ a given unbounded and nondecreasing function) such that $x$ admits uncountably many solutions. (4) An ample excess lemma holds for non i.o. $K$-trivial. Namely: $$ \sum_n 2^{-(K(x\upharpoonright n)- \log_2 n)}<\infty. $$ for all non i.o. $K$-trivial $x$. Actually, this even holds for non i.o. $b$-$K$-trivial with $b$ only depends on the universal prefix free machine. The same argument also gives a constant complexity return phenomenon for $K$-trivial where this constant only depends on the universal prefix free machine.

math.LO↗
arXiv2026

Martin-Löf randomness and rK-reducibility

Can random real carry arbitrary information. In terms of (Turing) computability, Kučera and Gács addressed this question in affirmative. i.e., Every real $x\in 2^ω$ is computable from some Martin-Löf random real. This result motivated quantitative versions of coding into random reals. i.e., How many bits of the random oracle are needed to compute the first $n$ bits of $x$. Barmpalias and Lewis-Pye obtained a coding that uses $n+O(\log n)$ many bits. Is it possible for the coding to use $n$ bits exactly? This is equivalent to say, if every real is $rK$-reducible to a Martin-Löf random real. In this paper, we prove that such a coding does not exist. i.e., There exists some real that is not $rK$-reducible to any Martin-Löf random real.

math.LO↗
arXiv2026

Bayesian Offline Multi-Agent Reinforcement Learning with Latent World Models

Model-based offline multi-agent reinforcement learning (MARL) provides a promising approach to multi-agent decision-making under partial observability, where the global state is unavailable from offline data. However, limited dataset coverage can lead to substantial out-of-distribution (OOD) model errors, which may mislead policy optimization and degrade downstream performance. Existing model-based offline MARL methods typically rely on access to global states or mitigate model errors through pessimistic or conservative policy optimization, leaving the reliability and refinement of learned world models less explored. We propose a Bayesian offline MARL framework that infers latent global states from decentralized observation-action histories and iteratively refines a posterior world model using only offline data. Building on posterior information loss, we extend this criterion to the multi-agent setting as multi-agent posterior information loss (MPIL), which provides a reliability measure for world model refinement and offline evaluation. Theoretically, we establish an upper bound on policy regret that is monotonic in MPIL and further characterize its dependence on the size and state-joint-action coverage of the offline dataset. Experiments on partially observable multi-agent variants of D4RL MuJoCo tasks demonstrate competitive policy performance across diverse offline data conditions, while MPIL-guided refinement improves world model prediction and downstream policy performance. These results support a principled connection between world model reliability, offline data coverage, and policy performance in partially observable offline MARL.

cs.MA↗
arXiv2026

DyHist: Query-Aware Historical Dynamics Modeling for Temporal Knowledge Graph Extrapolation

Temporal Knowledge Graph (TKG) extrapolation aims to predict future facts from observed historical events. Existing methods usually achieve this goal by jointly modeling local historical evolution and long-range historical contexts. First, local evolution modeling often summarizes local history into an overall evolving representation, where query-relevant local deviations may not be sufficiently exploited as useful predictive features. Second, existing long-range history modeling often treats historical recurrence as a stable cue, while overlooking that its reliability may vary across relations and recent contexts. To address these issues, we propose DyHist, a query-aware historical dynamics modeling framework for TKG extrapolation. DyHist captures local dynamics by separating recent evidence from medium-range contexts and explicitly modeling their query-relevant deviations as predictive features. It further uses a relation-aware historical prior to calibrate candidate scores with time-decayed support, recent trends, and relation-specific strength, enabling recurrence signals to contribute differently across relations and recent contexts. Experiments on four benchmarks show that DyHist achieves the best MRR against recent baselines. Code is available at https://github.com/PANPANKK/DyHist.

cs.IR↗
arXiv2026

GraFT: A Training-Free Framework for Spatial Reasoning in Multimodal Large Language Models via 3D Scene Graphs

3D spatial reasoning underpins understanding and acting in the physical world, yet it remains unreliable in current multimodal large language models (MLLMs). These models falter at precise geometric measurement, at transforming between egocentric and allocentric viewpoints, and at grounding fine-grained appearance. The most common remedies fine-tune the model on large-scale curated spatial-reasoning datasets or attach dedicated encoders for 3D geometry, which typically couples the solution to costly supervision and a specific backbone. We instead introduce GraFT, a training-free framework that supplies the missing 3D structure through a compact, easily maintained 3D scene graph (3DSG). GraFT supplies the graph's 3D structure to the frozen model in three forms: as values computed by symbolic tools, as a bird's-eye-view (BEV) the model reads as an image, and as egocentric frames the geometry selects. On ScanQA, GraFT improves every metric over the same-backbone baseline, raising CIDEr by 27%. On VSI-Bench, GraFT improves frozen MLLMs by up to 65%, surpassing every proprietary and general-purpose open-source baseline, and several prominent fine-tuned spatial models.

cs.CV↗
arXiv2026

There is no maximal $K$-degree

The Kolmogorov complexity of a string characterize how complex it is to describe the string. If every prefix of a real $x$ is more complex to describe than every prefix (of the same length) of real $y$, then it is seen as $x$ is more complex to describe than $y$. It is wondered if there is a real $x$ so that no other reals are strictly more complex (to describe) than $x$. The behavior of Kolmogorov complexity functions generated by reals (namely $n\mapsto$ the minimal description length of the real) is quite chaos. Therefore, it is widely believed that there are many reals that are maximally complex to describe. For instance, it is conjectured that all random enough reals have maximal $K$-degree. In this paper, it is shown that there is no real with maximal $K$-degree. Actually, for almost all real $x$, we can uniformly computably find another real whose $K$-degree is strictly above $x$. The same construction also derives the following: (a) There is no maximal $C $-degree. (b) Every $n$-random real $x$ admits an $n$-random real $y$ such that $y>_Kx$ and $y>_C x$; moreover, the difference of $K$-complexity and $C$-complexity of $y,x$ (namely $K(y\upharpoonright n)-K(x\upharpoonright n)$ and $C(y\upharpoonright n)-C(x\upharpoonright n)$) do not tend to infinity.

math.LO↗
arXiv2026

Beyond Preset Identities: Selective Stance Accommodation and Interaction Reorganisation in Generative Agent Societies

Generative agent societies simulate people with assigned roles, preferences and relationships. As agents exchange arguments and choose partners, they can revise their positions and reorganise discussion. Understanding these changes requires examining what they accept and how they continue to interact. Stance-change scores and communication totals describe the extent of change. However, the same stance movement can preserve or reverse an assigned preference, and frequent communication can support either agreement or continuing disagreement. We therefore examine the content of changed positions and the exchanges that strengthen particular partnerships. Using Computational Multi-Agent Society Experiments (CMASE), we combine stance measures, source evaluations and temporal networks with individual answers and messages. Study 1 compares seven conditions across ten GPT-4o runs per condition, with a separate interview collection covering four models. Study 2 follows one 75-step GPT-4o café simulation. Environmental rational persuasion yields the largest mean stance departure ($1.30\pm0.08$ on a 7-point scale), whereas economic emotional persuasion yields the highest low-trust stance-shift rate ($17.3\%\pm11.2\%$, with standard deviations across runs). In the separate interviews, eight environmental agents shift from 7 to 6, acknowledge economic concerns and rate the source 3. Their partial acceptance preserves the assigned environmental preference. In the café, a pair with zero earlier exchanges becomes the most frequent final-phase partnership, with 25 messages. Its members develop coordination proposals while disputing their implementation. These results show that partial acceptance can coexist with low source trust, and sustained coordination with continuing disagreement.

cs.AI↗
arXiv2026

Handoff Curves: Initial Selection, Later Handoff, and Supervision Targets in Multi-turn LLM Routing

We study how initial model selection, later handoff, and training targets affect success and cost in LLM tasks that span multiple turns. We compare several router architectures using handoff curves, which record task success and cost as the handoff step changes. Our dataset contains 34,204 complete executions of three Qwen models across BFCL, MultiWOZ, and $τ$-retail, providing offline supervision for routing decisions. In our primary comparison, with Qwen3.5 35B-A3B as the starting model, allowing a later handoff does not establish an improvement in utility over initial selection on BFCL or MultiWOZ, and increases cost on BFCL across a range of cost weights. Changing the supervision targets improves router performance on both our dataset and TwinRouterBench. On our dataset, replacing noisy training success curves with monotone fits raises success by 0.2 to 4.1 percentage points at the same cost across the reported operating points. On TwinRouterBench, we construct targets that describe the model capability needed for the remaining work and difficult steps ahead. Compared with training on the benchmark's per-step labels, these targets raise trajectory pass scores by 7.8 percentage points and cost savings by 6.3 percentage points on the full static bank. A live deployment of the router trained with these targets resolves 79 of 100 instances at a router cost of 0.59 US dollars per instance.

cs.AI↗
arXiv2026

LifelongCrossNav: Persistent 3D Semantic Memory for Cross-Floor Multi-Object Navigation

Object-goal navigation has made substantial progress in semantic perception and exploration, yet persistent memory for multi-object navigation and cross-floor navigation are still commonly addressed separately. We present LifelongCrossNav, a framework for sequential multi-object ObjectNav in unknown multi-floor indoor environments. Within each episode, the agent receives an ordered sequence of object-goal queries while continuously maintaining a shared sparse 3D semantic voxel memory. This memory incrementally accumulates geometric structure, traversability states, and vision-language features, allowing subsequent object-goal queries to retrieve previously acquired scene information without rebuilding the map. To support persistent search across floors, LifelongCrossNav combines support-aware 3D traversability mapping, stair-specific perception, and direction-aware stair traversal. A unified navigation policy coordinates same-floor frontier exploration, live and historical point-of-interest retrieval, stair navigation, and target-object search and approach. We further introduce HM3D-MFMON, a benchmark for sequential Multi-Floor Multi-Object Navigation built on HM3D scenes, including a dedicated subset in which completing the full sequence of object-goal subtasks requires at least one floor transition. Experimental results show that LifelongCrossNav consistently outperforms a representative planar persistent semantic-map baseline on HM3D-MFMON, demonstrating that persistent 3D semantic memory and cross-floor traversability modeling effectively support sequential multi-object navigation in multi-floor environments.

cs.RO↗
arXiv2026

Offline Multi-Agent Reinforcement Learning with a Physics-Informed World Model for Cooperative Mixed Traffic Control

This study investigates cooperative control of connected and automated vehicles (CAVs) at partially observable highway bottlenecks in mixed traffic, aiming to mitigate congestion without relying on complete global traffic states or online trial-and-error. We propose a physics-informed world model-based offline multi-agent reinforcement learning framework that reconstructs a physically interpretable global traffic state from local CAV observation-action histories, with coupled macroscopic-microscopic traffic dynamics providing physics-based supervision. A probabilistic ensemble world model learns traffic-state transitions and system rewards, while model disagreement quantifies epistemic uncertainty. Multi-step imagined rollouts with pessimistic rewards and uncertainty-driven truncation are then used for offline policy learning. Experiments in a SUMO-based on-ramp bottleneck using approximately $1\times10^6$ offline transitions show that physics supervision improves state reconstruction and world-model prediction accuracy.

cs.MA↗
arXiv2026

SAIN: Structure-Aware Interactive Navigation with Active Dialogue Grounding for Mobile Robot

Most existing vision-language navigation tasks assume that instructions are complete and unambiguous. However, real-world robots often encounter natural human instructions that are ambiguous, underspecified, or incomplete, requiring them to resolve such uncertainties through active questioning. Interactive Instance Goal Navigation (IIGN) requires an embodied agent to find the specific instance under an ambiguous category-level instruction through active dialogue. However, existing dialogue-enabled methods often consume oracle answers as transient textual context for immediate decisions, rather than persistent spatial or object-centric structured state. We present SAIN, a zero-shot framework that turns active dialogue into persistent navigation state. Instead of consuming oracle answers as one-step text hints, SAIN compiles them into target evidence, route-level corridor memory, and object-candidate labels. These states are stored in structured value, room, graph, and object memories, then consumed by a unified policy for frontier ranking and final target approach. On the VL-LN IIGN benchmark, SAIN improves SR from 20.2 to 25.4 and SPL from 13.07 to 14.17 over the strongest reported dialogue-enabled baseline, while requiring no task-specific policy training. The results support dialogue-to-state conversion as an effective zero-shot mechanism for long-horizon interactive instance navigation. Project website: https://zorattc.github.io/SAIN/

cs.RO↗
arXiv2026

Effective-Geometry Rescaling and Universal Critical Behavior in the Anisotropic Three-State Potts Model on the Square Lattice

We study the two-dimensional anisotropic three-state Potts ferromagnet on the square lattice using Wolff single-cluster Monte Carlo simulations and finite-size scaling. For coupling ratios $λ=J_y/J_x=0.5$, $0.75$, and $1$, finite-size scaling of the correlation ratio yields critical behavior consistent with the two-dimensional three-state Potts universality class. The scaling of the leading Fisher zeros gives a correlation-length exponent consistent with $ν=5/6$, while their cumulative density is consistent with the expected specific-heat exponent $α=1/3$. We further characterize the anisotropy at criticality using directional correlation ratios $R_x$ and $R_y$ together with directional FK wrapping probabilities. For $λ=0.5$ on a physically square lattice, $R_x$ and $R_y$ approach distinct critical values while yielding a common correlation-length exponent. From the wrapping probabilities, we independently determine an effective aspect ratio $ρ_e^\square=0.6413(5)$, in close agreement with the theoretical value $ρ_e^{\square,\mathrm{th}}\simeq0.64150030$ obtained from the isoradial representation. Using the theoretical value to set the physical aspect ratio restores directional equivalence, $R_x\simeq R_y$, and brings the overall correlation ratio toward the isotropic-square reference. The results show that spatial anisotropy changes the effective critical geometry without altering the bulk three-state Potts universality class.

cond-mat.stat-mech↗
arXiv2026

When to Rethink: Learning Multi-Perspective Self-Verification for Vision-Language Models

Vision-language models (VLMs) have achieved strong performance in multimodal reasoning, yet they remain prone to generating plausible but incorrect answers. Self-verification offers a practical way to improve answer reliability without relying on external judges, but existing methods typically depend on a single verification criterion or fixed prompt, resulting in incomplete and unstable reliability estimates. We first systematically analyze how verifier capability and prompt design affect verification performance. Our findings show that stronger verifiers provide more reliable judgments, while verification performance is highly sensitive to prompt choice, with no single prompt consistently dominating across tasks. Guided by these findings, we propose \texttt{MOTIVE}, a \textbf{M}ulti-View Self-Verificati\textbf{O}n wi\textbf{T}h Rel\textbf{I}ability-Guided Selecti\textbf{VE} Rethinking framework for reliable multimodal reasoning. \texttt{MOTIVE} evaluates each candidate answer from complementary verification perspectives and learns a correctness-aligned reliability score through correctness-grounded multi-view verification learning. During inference, this score governs an accept-or-rethink decision, allowing reliable answers to be returned directly while uncertain ones trigger history-guided rethinking. Extensive experiments across diverse multimodal benchmarks and VLM backbones demonstrate that \texttt{MOTIVE} consistently outperforms strong self-verification and self-correction baselines. Further results show that reliable verification improves accept-or-rethink decisions and reduces unnecessary reasoning turns, enabling more reliable and efficient self-verification without an external judge.

cs.AI↗
arXiv2026

Continue, Abort, or Fall: Viability-Aware Policy Selection (VAPS) for Safe Humanoid Acrobatics

Dynamic humanoid motions such as flips risk hardware damage due to suboptimal policies, disturbances or sim-to-real gaps. A motion tracking policy offers no way out once the maneuver leaves its reference, and a backup policy needs to take over to protect the hardware for a minimum-damage landing. Which backup to use matters as much as when to switch. We present Viability-Aware Policy Selection (VAPS), which treats safety as a policy-conditioned, receding-horizon decision. Besides a protective fall policy, we also train an abort policy which can abort the motion at any time, landing on its feet. At every control step, learned predictors estimate whether the nominal tracking policy and the abort policy remain viable over a short horizon, and a least-sacrificial hierarchy keeps the most task-ambitious behavior that remains viable. In simulation with randomized disturbances, VAPS sharply reduces head contact and hand contact, which are the dominant sources of hardware damage, with both a Unitree G1 and a LimX Oli; on the LimX Oli, we validate the viability predictors and the full VAPS controller for side-flip motions. VAPS Pareto-dominates the strongest single-network alternatives we could train, including an end-to-end safe-tracking policy and students distilled from VAPS's own oracle-routed decisions, in both task success and head impact. We also show that VAPS is a powerful framework to supervise undertrained policies and protect the hardware.

cs.RO↗
arXiv2026

Bearing-Only Formation Tracking Control for Euler-Lagrange Multi-Agent Systems Without Inter-Agent Communication

This paper investigates communication-free bearing-only formation tracking control for multi-agent systems governed by Euler-Lagrange dynamics. Distinct from existing results that can only stabilize a stationary formation, this work considers a scenario where the leaders move with time-varying velocities while the inter-agent communication is absent. In this setup, the leaders' states (position and velocity) are unavailable to all followers and cannot be estimated via distributed observers. A novel adaptive distributed control scheme is developed to address this problem. The design exploits the fact that bearing rates contain the projected relative-velocity information, which, together with bearing rigidity, provides a rigidity-based damping mechanism for compensating the unavailable velocity error. Moreover, this damping mechanism is incorporated into a bearing-driven auxiliary variable to construct a surrogate velocity error, facilitating the adaptive control design for EL dynamics. Furthermore, since this damping mechanism necessitates sufficient bearing rigidity, we characterize a rigidity-preserving set and establish its forward invariance, thereby guaranteeing such rigidity via initial conditions. Via a Filippov-based Lyapunov analysis, the proposed scheme is shown to achieve local practical formation tracking in the sense that the velocity error converges to zero and the position error is uniformly ultimately bounded. As a corollary, for the constant-velocity case, asymptotic tracking is achieved without initial-condition restriction. The simulation results verify the effectiveness of the proposed control law.

eess.SY↗
arXiv2026

Decoupling the Magnetic Field Operator as an Independent Operator Class in Stochastic Series Expansion Quantum Monte Carlo

The Stochastic Series Expansion (SSE) quantum Monte Carlo method with loop updates is among the most powerful approaches for quantum spin and boson systems. In the standard formulation, the magnetic field term is routinely absorbed into the Heisenberg interactions---a strategy that has proven highly efficient across a wide range of field strengths. In this work, we propose a more general SSE framework in which the magnetic field operator is treated as an independent operator class, enabling it to participate in Monte Carlo updates on an equal footing with all other operators. Importantly, the field operator and other interaction operators can transform into one another during the update process. We demonstrate this algorithm using the two-dimensional antiferromagnetic Heisenberg model in a magnetic field as a concrete example. The simulation results agree with those of the conventional algorithm, confirming the correctness of the new formulation. A comparison of the integrated autocorrelation time shows that the new algorithm is competitive. This flexibility not only facilitates measurements of observables associated with operators but also offers potential computational advantages for a broader class of problems.

cond-mat.str-el↗
arXiv2026

VideoReloc: Long-Term Indoor Video Relocalization against a Kilobyte-Scale Semantic Scene Graph

Given a compact semantic scene graph, long-term indoor video relocalization estimates a map-frame trajectory after lighting and furniture changes. Visual methods rely on appearance and become unreliable under these changes; localizing one frame at a time from object classes and geometry instead leaves sparse, ambiguous evidence. We introduce VideoReloc, whose adaptive clips use odometry to gather spatial evidence until object and motion criteria are met, adapting query length to the observed scene. Its run-level decision rechecks conflicting placements using evidence accumulated across connected clips, stabilizing the trajectory beyond adjacent-clip tracking. Hypothesis-first registration proposes poses from object triplets and verifies each using clip-wide object centers and box surfaces. Orientation-aware refinement uses box faces, gravity and wall directions to resolve ambiguity in camera orientation and refine the full pose. This reframes sparse-map relocalization as verification of spatially extended video queries, moving discriminative support from stored appearance to temporal context and permitting a 100 kB map of class-labelled boxes. On RIO10 and ReplicaCAD, the all-frame localization success rate at 1 m/10$^\circ$ is 73.5% and 61.1% under causal evaluation, rising to 90.6% and 74.8% with clip closure. The evaluated per-frame scene coordinate regressors reach up to 47.6% and 49.8%, respectively, with maps of 12.6-42 MB. Project page: https://videoreloc.github.io

cs.CV↗