Papers

Gravitational-wave (GW) observations offer a powerful probe of new fundamental fields. One well-motivated source is black hole (BH)–boson cloud systems, in which an ultralight scalar field forms a cloud around a rotating BH via superradiance and emits long-lived nearly monochromatic GWs. In this work, we compute the stochastic GW background (SGWB) from such systems, extending previous work by including scalar self-interactions, and discuss its detectability with next-generation ground-based GW detectors. We find that self-interactions can suppress the SGWB and thereby relax existing LIGO-Virgo-KAGRA constraints inferred from null searches. Namely, the LIGO detectors at design sensitivity are insensitive to a SGWB produced by scalar fields with a decay constant $f_\mathrm{s} \lesssim 3\times 10^{17}$ GeV, independently of the scalar field mass. Looking ahead, we show that a moderately self-interacting cloud can still produce a detectable SGWB with next-generation detectors. Under conservative assumptions, for a decay constant $f_\mathrm{s} = 10^{17}$ GeV, the Einstein Telescope (ET) will be sensitive to scalar masses in the range $\sim[10^{-13.0},10^{-11.8}]$ eV, while Cosmic Explorer (CE) will be sensitive to scalar masses in the range $\sim[10^{-13.2},10^{-11.7}]$ eV. We also find that the minimum decay constants that still yield a detectable SGWB for ET and CE are $f_\mathrm{s}\sim 6\times10^{16}\,$GeV and $\sim 3\times10^{16}\,$GeV, respectively.

Joint-embedding world models enable visual planning by learning action-conditioned dynamics in latent space. Yet they are commonly trained for one-step prediction on encoded states, while planning recursively applies the learned transition to its own predictions. One-step accuracy therefore does not capture how prediction errors propagate under recursive rollout. We decompose multi-step rollout error into the errors introduced at individual steps and their propagation through subsequent transitions. We show that state-affine dynamics are precisely the differentiable transitions with state-independent Jacobians, eliminating the nonlinear propagation residual and making the error propagation operators depend only on the action sequence. Guided by this result, we introduce SALT (State-Affine Latent Transition), an action-conditioned state-affine dynamics model in which the action modulates both the state transformation and the additive update. We train SALT through recursive multi-step rollout supervision, feeding each predicted latent state back into the transition so that training matches how the model is used during planning. Across four visual planning environments, SALT exhibits $1.48$–$2.19\times$ higher one-step prediction error than the matched LeWM baseline, yet improves closed-loop success in every environment by $10.0$ percentage points on average. On OGBench-Cube, the fraction of episodes that fail with a sharp rise in model-predicted cost after execution decreases from $23.3%$ to $2.0%$.

Large Language Models (LLMs) have shown promising capabilities in scientific reasoning, yet scientific discovery ultimately requires deriving precise laws directly from observational data, known as Symbolic Regression (SR). This poses a challenge for LLMs due to the gap between probabilistic text generation and the exact structural requirements of SR. Existing approaches rely on complex external scaffolds, which are computationally expensive and separate symbolic reasoning from the model itself. To address this limitation, we propose to directly equip LLMs with symbolic regression capabilities through dedicated numerical-symbolic and physical supervision. We introduce PhysSymbArena, a large-scale benchmark containing over 160,000 equations and 1.8B tokens of numerical-symbolic data with physical descriptions, enabling systematic training and evaluation. Based on PhysSymbArena, we develop SymbolicLM, which enhances the symbolic regression ability of LLMs through mathematical and physical supervision. During inference, we further introduce SymbolicSGA, a refinement framework that leverages quantitative feedback to iteratively improve generated equations. Experiments on multiple symbolic regression benchmarks show that SymbolicLM substantially improves structural recovery while maintaining competitive numerical fitting performance. These results demonstrate that symbolic regression can be explicitly learned as an intrinsic capability of LLMs.

Color enhancement of 4K images must meet a quality target under a tight compute budget. Three-dimensional lookup tables (3D LUTs) dominate real-time enhancement because they decide at low resolution and apply a per-pixel lookup at full resolution. A single global LUT, however, is spatially invariant, so an underexposed shadow and a well-exposed region that share a pixel value receive identical corrections. Spatially heterogeneous demands cannot be expressed by such a mapping. We propose LoopLUT, a region-cascaded 3D LUT with progressive refinement. A global LUT performs the overall correction, followed by K-1 loop iterations. In each iteration a gating head predicts at low resolution the region that still needs correction, then builds a residual LUT from the color statistics of that region alone. The cascaded gates form a partition of unity, so the output is a per-pixel convex combination of the K lookup results. Fusion is therefore performed by the gates themselves, with no separate fusion module and no interpolation error accumulating across rounds. The decision stage runs at a fixed 256x256 resolution, independent of output resolution, so a 4K image costs only K pure lookups. Extensive experiments across four benchmarks show that LoopLUT improves PSNR by up to 2.81 dB over the strongest prior method, while keeping real-time throughput at 4K. The same decomposition also generalizes well to underwater enhancement datasets.

In systems where controllers operate remotely and communicate with actuators over shared communication channels, it is crucial to efficiently schedule the control data transmission to reduce bandwidth usage and actuator effort. In this article, we investigate a novel scheduling mechanism that jointly coordinates control actions across different controllers and different time steps. We propose an algorithm based on the alternating direction method of multipliers (ADMM) to solve the resulting optimization problem. While ADMM is often treated as a black-box solver, the proposed algorithm offers a clear physical interpretation, ensures convergence to a stationary point, and is computationally efficient. Simulation results validate our theoretical results and demonstrate the effectiveness of our proposed algorithm.

Low-precision Transformer systems increasingly quantize attention matrix multiplications, while softmax often remains at higher precision. During pretraining, an approximate softmax changes the gradients that train the model as well as its forward computation. We study this interaction with K-interval attention, which approximates the exponential using K+1 grid values. We vary per-row grid calibration, interpolation versus hard rounding, and the placement of a straight-through surrogate relative to normalization. We derive the corresponding backward rules, including calibration derivatives, and compare these choices in pretraining experiments matched on model, data, and optimizer. Detaching the row extrema leaves the forward computation unchanged but produces a delayed increase in validation loss. With hard rounding at K=4, min-max calibration and a pre-normalization surrogate incur a large loss gap; changing either choice substantially reduces it. At 124M parameters and 2.5B training tokens, fixed-window calibration with a post-normalization surrogate yields a validation loss gap of +0.019 nats relative to softmax at K=4, and with a pre-normalization surrogate yields +0.004 nats at K=16.

We study the ergodic integrals for linear flows on the infinite staircase, a translation surface with infinite area, and deduce detailed information on the bias properties of local discrepancy functions for irrational numbers of bounded type.

Efficient exploration often remains a central bottleneck in reinforcement learning with verifiable rewards (RLVR). Although temperature control and test-time scaling strategies can increase rollout diversity of large language models (LLMs), they either expand the sample budget at rollout time or leave the benefit of exploration unquantified. To this end, we propose Temperature-Grouped Reinforcement Learning (TGRL), which turns temperature-induced diversity into an explicit training signal. For each prompt, TGRL partitions its rollout group into low- and high-temperature subsets, estimates exploration gain through their reward contrast, and allocates this group-level signal as token-level credit using Jensen–Shannon (JS) divergence between the corresponding temperature-scaled next-token distributions induced by the same logits. Notably, TGRL reaches equivalent accuracy up to 36% faster than strong RLVR baselines without expanding the rollout budget. Across 11 benchmarks from diverse domains, TGRL broadly improves over strong RLVR baselines: it improves the six-benchmark math average by 1.6% at 32B, raises CodeForces rating by 196.7 points and LiveCodeBench Pass@16 by 4.4%, and improves ALFWorld/WebShop success rates by 6.3%/4.9%. Comprehensive ablations and wall-clock analysis confirm the efficacy of all proposed components. Code is available at https://github.com/1229095296/TGRL/tree/main.

We consider allocation of indivisible goods to agents with equal entitlements and subadditive valuations. As an ex-post fairness notion we consider the maximin share (MMS), and as an ex-ante fairness notion we consider the maximum expectation share (MES), which is always at least as large as the MMS, and sometimes much larger. We present a simple transformation that for every $0 < \rho \le 1$, given any algorithm that produces $\rho$-MMS allocations, transforms it into a randomized allocation algorithm that offers $\rho$-MMS ex-post simultaneously with $\eta$-MES ex-ante. We prove several new properties of MES, and use them to show that $\eta \ge \min[\frac{\rho}{2 + \rho}, \frac{1}{4}]$. We also present cases in which the transformation results in a higher value of $\eta$. Applying our transformation to currently known allocation algorithms shows for subadditive valuations the existence of randomized allocations that are simultaneously $\Omega(\frac{1}{\log\log n})$-MES ex-ante and $\Omega(\frac{1}{\log\log n})$-MMS ex-post, and for XOS valuations the existence of randomized allocations that are simultaneously $\frac{4}{27}$-MES ex-ante and $\frac{4}{17}$-MMS ex-post.

We develop a Hopf-algebraic theory of graph coefficients arising in the quantum Magnus expansion. At the classical level, the expansion is governed by directed trees, whereas its quantum counterpart involves loop graphs, multiple edges, and several types of edge data. We introduce a contraction Hopf algebra of mixed quivers containing these diagrams and closed under contraction. On this algebra we define a character $e$ from normalized linear-extension data, directed-tadpole factors, and a prescription for undirected edges, and let $\omega$ be its convolution inverse. Our main result is a universal closed formula for the connected function $\omega_c$ on every finite mixed quiver, expressed as a finite sum over ordered set partitions of the vertices. We also construct a weighted vertex-splitting Hopf structure on the unlocalized mixed-quiver algebra, with convolution $\star_V$ and canonical edge-weight character $\zeta_V$, such that $\omega_c=\log_{\star_V}\zeta_V$. Compatibility of the two coproducts and an explicit identity between their characters explain this equality. We further prove that the two-vertex contraction identity, tadpole factorization, vanishing on disconnected graphs, and boundary data uniquely determine $\omega_c$. For acyclic quivers, the formula reduces to a permutation formula with coefficients depending only on descent numbers. We derive this formula independently from the quantum Magnus expansion using operator products and Wick contractions, showing that the physical graph coefficients are governed by the convolution structure of the contraction Hopf algebra. Further consequences include a refined quantum Murua formula and orientation-sum identities related to Tutte and chromatic polynomials.

On NVIDIA Blackwell B200, tensor-core throughput outpaces special-function exponential throughput by more than two orders of magnitude, exposing exponential evaluation in fused attention kernels. A pretrained Transformer, however, may not need it evaluated accurately at every element. We characterize what a pretrained model does need by approximating softmax at inference in ten frozen decoder-only models (0.5B-72B). The number of positions the softmax map assigns probability to and within-row resolution can be cut substantially, yet uniform weighting of the same positions is damaging. Where a fixed resolution budget is placed matters as much as its size, with resolution near the row maximum consistently favored. Perturbations matched on scalar distortion produce model-dependent responses of opposite sign. These findings motivate Rowmax-PoT, a coarse logarithmic weight representation anchored at each row maximum, and Rowmax-H15, its hardware specialization in FlashAttention-4. On B200, the patched FP8 attention forward is 12.4% faster at causal 8K and 25.8% faster at non-causal 8K in host-side call-latency measurements; board energy per forward falls by 8.4% at causal 16K. Measured separately on the BF16 kernel path at 2K, Rowmax-H15 increases perplexity by 0.091-0.492% across five models from three families.

The rapid proliferation of highly realistic AI-Generated Content (AIGC) necessitates robust and interpretable detection mechanisms. However, existing detectors are predominantly confined to single modalities and provide binary outputs without reasoning. While Multimodal Large Language Models (MLLMs) present a promising solution, their development is constrained by the scarcity of multimodal reasoning data and the reasoning-detection optimization dilemma, where explicit reasoning supervision can compromise detection accuracy. To this end, we introduce IVT-Set, a comprehensive dataset comprising over 152K diverse image, video, and text samples equipped with multi-granularity Chain-of-Thought (CoT) reasoning trajectories. Based on it, we propose IVT-Guard, a pioneering framework for unified and interpretable AIGC detection across image, video, and text modalities. Furthermore, to overcome the aforementioned optimization dilemma, we design a novel three-stage training paradigm: Artifact-Aware Pre-training, Artifact-to-Evidence Supervised Fine-Tuning via artifact-aware injection, and Evidence-Verdict Consistency Group Relative Policy Optimization. Extensive experiments demonstrate that IVT-Guard achieves state-of-the-art detection performance across in-domain, out-of-domain, and cross-dataset settings while delivering faithful reasoning. Code and data will be released.

For a line arrangement $\mathcal{A} \colon f=0$ in $\mathbb{P}^2$, let $\nu(\mathcal{A})$ be the maximal dimension of a graded piece of the Jacobian module of $f$. We study the conjecture that $\nu(\mathcal{A})$ depends only on the intersection lattice of $\mathcal{A}$. It is known that $\mathcal{A}$ is free if and only if $\nu(\mathcal{A})=0$, and hence this conjecture is a strengthening of Terao's conjecture for line arrangements. We show that the conjecture holds for arrangements of at most $13$ lines, except possibly for arrangements of exactly $13$ lines whose intersection points have maximal multiplicity $5$.

Let $1<m<n$ and $0<q<m-1$. We classify positive, locally bounded weak solutions of \[-\Delta_m u=u^p|Du|^q\quad\text{in }\mathbb R^n,\qquad p=\frac{m-q}{n-m}\left(n+\frac{q}{m-1-q}\right)-1.\] Every solution is constant or belongs to an explicit family of radial solutions, up to translation and scaling. No global bound, decay, or finite-energy assumption is required. The proof is based on a scalar differential identity and a maximum principle that remains valid at critical points. These lead to a sharp gradient bound, classification of normalized solutions, and a first-contact argument for arbitrary entire solutions. Local regularity and the behavior at critical points are treated throughout in the weak solution class; global $C^2$ regularity is not assumed.

Recent real-world image super-resolution (SR) methods often adapt text-to-image (T2I) backbones with ControlNet-style branches or spatial conditioning tokens, which increases memory and computes with resolution and often constrains training to a fixed scale. We propose Fill2SR, which repurposes a masked-inpainting Diffusion Transformer for SR without extra spatial branches. Our Inpainting-Interface Evidence Adapter (IIEA) writes the low-quality (LQ) observation into the native masked-image slot under a full-image mask, turning inpainting into a reverse-degradation conditional rectified flow trained with LoRA-only tuning. We further introduce RCDT, an offline pipeline that distills degradation descriptors from unpaired real images and transfers them onto clean targets using frozen open-source models. Fill2SR supports mixed-resolution training up to QHD and yields stable performance across $512/1024/2048$ outputs. On synthetic benchmarks, our base model with IIEA achieves the best LPIPS on DIV2K and LSDIR; adding RCDT trades a small LPIPS drop for consistently stronger no-reference quality on RealLQ250 and RealPhoto60. Fill2SR remains memory-predictable, running $1536^2$ inference on a single 32GB GPU and extending to multi-megapixel outputs via tiled restoration.

Aerial Vision-Language Navigation (AVLN) requires UAVs to maintain reliable instruction following over long trajectories in complex 3D environments. However, existing AVLN approaches are predominantly reactive or limited to single-horizon prediction, overlooking complementary future cues across different temporal horizons. To address this limitation, we propose ForeFly, a dual-horizon latent world action model that predicts both a proximal future for local continuity and an adaptive route-critical future for long-range guidance. Horizon-specific foresight queries are primed with recent and route-critical visual memories, providing history-aware context for future prediction. To exploit their distinct roles in action generation, we introduce Foresight-Guided Action Refinement (FGAR), which asymmetrically exploits proximal foresight for local action enhancement and route-critical foresight for feature-wise correction and route-level guidance. Experiments on the TravelUAV and UAV-ON benchmarks show that ForeFly consistently outperforms strong baselines across seen and unseen settings, validating the effectiveness of dual-horizon foresight and FGAR learning. The code is available at: https://github.com/kunhuiW/ForeFly

Learning-augmented algorithms for metrical task systems (MTS) can exploit predictions of canonical dual values, but existing formulations typically require a prediction for every state. We study whether these predictions can be compressed to a small set of representative states while retaining their algorithmic value. We introduce landmark-compressed value predictions, in which the predictor reports predicted dual values only at $m$ landmarks and the remaining values are reconstructed by a Lipschitz extension. Our algorithm achieves additive excess cost $O(T\,r(L) + \sum_t \delta_t)$, where $r(L)$ is the covering radius of the landmarks and $\delta_t$ measures prediction error up to additive shifts; local and value-dependent bounds refine this guarantee. For sparse landmark sets on unit-spaced finite lines, we prove a matching $\Omega(T r_m)$ lower bound for every randomized algorithm using fixed landmarks, even with advance access to their entire exact absolute-value table. The prediction interface also matters: on two states with one landmark, exact absolute values permit horizon-independent excess, whereas exact relative values force worst-case expected excess linear in $T$. We give PAC guarantees for learning compressed prediction tables, with efficient empirical-risk minimization for fixed landmarks. Our results connect metric coverage, prediction interfaces, and learning guarantees for compressed predictions in online MTS.

Open-search fact checking is not merely retrieval followed by classification, but a sequential decision problem in which every query, source visit, and stopping decision reshapes the evidence available for verification. Yet existing systems often distribute these decisions across predefined pipelines or separately prompted modules rather than learning them as a unified task-specific policy. We introduce OpenFC, a unified verification-policy training framework that post-trains Qwen3-8B as a compact next-action controller over reasoning, evidence acquisition, and stopping. OpenFC learns this policy in two stages. Stepwise-Calibrated Cold Start (SCCS) uses a strong training-time supervisor to review post-initial reasoning, tool-use, and stopping proposals before execution, producing reliable trajectories for supervised fine-tuning without access to gold verdicts. Verification-Aware Reinforcement Learning (VA-RL) then improves the cold-start policy on unresolved claims through budget-aware tool rewards, label-aware advantage reweighting, and localized response masking. Across six fact-checking benchmarks, OpenFC achieves 70.39% average accuracy and 63.30% macro-F1, the highest overall averages among the evaluated methods. Stage-wise ablations further show that SCCS and VA-RL provide complementary gains, supporting the design of the two-stage training framework. These results position OpenFC as a strong and effective framework for open-search fact-checking. We will open-source our code and release the model checkpoints to support reproducibility.

For the 2D incompressible Euler equations on the half-plane, we establish Lyapunov stability of the Lamb dipole without sign condition on the vorticity. The main challenge arises from growth of the $x_{2}$ weighted norm for mixed sign vorticities, whereas this norm is conserved and responsible for dipole stability in the single signed vorticity case. This difficulty is handled by a Lagrangian bootstrap argument, based on carefully dividing the solution into several pieces and analyzing interactions among them, with the most delicate interaction involving vorticity drifting to infinity in the vertical direction. We expect that the strategy developed here will provide a starting point for the stability analysis of more general vortex configurations, including interactions among multiple vortex dipoles and among multiple vortex rings in settings involving mixed-sign vorticity.

This paper investigates the boundary pointwise regularity of solutions to the p-Laplace equation. By treating curved boundaries as perturbations of flat ones, we establish the boundary pointwise Lipschitz regularity under the exterior $C^{1,\mathrm{Dini}}$ condition and the Hopf lemma under the interior $C^{1,\mathrm{Dini}}$ condition. We also establish the boundary pointwise $C^1$ regularity under the $C^{1,\mathrm{Dini}}$ condition by a compactness argument.

We study three particles on the two-dimensional square lattice with contact interactions of infinite strength, in every sector of total quasimomentum, for three statistics: identical bosons, two identical fermions with a distinguishable third particle, and two identical bosons with a distinguishable third particle. The atom-dimer sector associated with the infinitely degenerate eigenvalue of the pair-contact operator is analysed on the whole Brillouin zone. A Feshbach-Schur reduction gives explicit effective Hamiltonians built from the Dirichlet Laplacian and a rank-four exchange operator, and a spectral transfer theorem with explicit error bounds identifies the atom-dimer threshold of the three-body operator with that of the effective one; the eigenvalue counting function below the threshold is squeezed between those of the effective operator, so that the number of atom-dimer states bound uniformly in the coupling equals the number of bound states of the effective Hamiltonian. The threshold problem reduces to a four-by-four Hermitian matrix whose zero-energy limit is built from the two-point resistances of the square lattice and hence to a quartic polynomial. This yields the complete atom-dimer zones in closed form; the critical hopping ratio as an explicit function on the whole Brillouin zone with two-sided bounds and closed forms at all symmetry points; at most two atom-dimer states per sector with an explicit second threshold; exact onset laws of infinite order at the corner point and linear-over-logarithmic in the pure p-wave channel; and two exact dualities relating a change of statistics to a shift of quasimomentum by half a reciprocal-lattice vector. The reduction of the three-body eigenvalue problem to the lattice Skornyakov-Ter-Martirosyan equation is proved with an explicit isomorphism of eigenspaces.

Vision-Language-Action models are increasingly effective for robotic manipulation, yet most predict actions directly from current observations without explicitly modeling future scene evolution. Recent methods introduce future prediction to improve action generation, but dense future modeling often requires expensive iterative denoising, while one-step alternatives can underperform their multi-step counterparts. To reconcile efficient future modeling with strong action performance, we present SLIP-VLA, a policy learning framework that equips VLA models with a Single-Step Latent Imagination for future-aware action prediction. SLIP-VLA obtains temporally dense future latent representations with a single denoising update, and we improve the perceptual sufficiency of these representations by aligning intermediate latents with future geometric and semantic features. We further improve their control sufficiency through action-conditioned latent world modeling and inverse dynamics modeling, explicitly coupling latent transitions with robot actions. SLIP-VLA achieves state-of-the-art performance across diverse simulation benchmarks and real-world manipulation tasks, while its single-step latent imagination takes only 12 ms.

We show that stronger interactions protect periodically driven time-crystal order against dephasing but destabilise order under random multipolar drives, and that coordination matters beyond the total interaction strength. We studied a disordered kicked Ising model of $N=12$ and $16$ spins with imperfect $\pi$ pulses and per-site dephasing by exact diagonalisation, comparing a periodic drive, random multipolar drives of order $n=0,1,2$ and the Thue-Morse sequence, and separated coupling strength from coordination by comparing a grid with a ring at equal total interaction strength $zJ$. For the periodic drive the coherence time scales approximately as $1/\gamma$, and stronger coupling reduces the transverse tilt on which dephasing acts. For multipolar drives of order $n\ge1$, doubling the coupling on a ring shortens the coherence time to $0.54$ ($n=1$), $0.37$ ($n=2$) and $0.44$ (Thue-Morse) at $N=16$, while random signs ($n=0$) are unaffected. A disorder scan supports a toggling-frame picture in which interactions spoil the block cancellation of the pulse error. At equal $zJ$ the grid outlives the ring by $2.15$ ($N=12$) and $2.78$ ($N=16$) for the periodic drive despite an identical transverse tilt, a coordination effect beyond this picture. All ratios hold under three definitions of the coherence time.

Dujella, Jak\v setić and Pe\v carić recently established in \cite{DJP}, a chain of power-sum inequalities, built from Hölder's and Cauchy's inequalities and their converse forms, and applied it to the Fibonacci sequence using the identities $\sum_{i=1}^nF_i^2=F_nF_{n+1}$ and $\sum_{i=1}^nF_iF_{i+1}=F_{n+1}^2-\frac{1+(-1)^n}{2}$. We show that this machinery applies uniformly across the one-parameter family of $k$-Fibonacci and $k$-Lucas numbers of Falcón and Plaza, via the generalized identities \begin{align*} \sum_{i=1}^nL_{k,i}^2=\frac{L_{k,n}L_{k,n+1}-2k}{k},\qquad \sum_{i=1}^nF_{k,i}^2=\frac{F_{k,n}F_{k,n+1}}{k}, \end{align*} and \begin{align*} \sum_{i=1}^nL_{k,i}L_{k,i+1}=\frac{L_{k,n+1}^2}{k}-k+\bigl((-1)^n-1\bigr)\left(\frac{2}{k}+\frac{k}{2}\right), \end{align*} which recover the classical Fibonacci and Lucas identities at $k=1$. We further exploit the cross-identity $F_{k,i}L_{k,i}=F_{k,2i}$, valid for every $k\ge1$, to obtain a Cauchy-Schwarz-type inequality linking the two families that has no counterpart in the Fibonacci-only setting. At $k=1$, this specializes to a fully explicit elementary inequality between ordinary Fibonacci and Lucas numbers, alongside the corresponding Hölder and Cauchy-conversion refinements we obtain for ordinary Lucas numbers.

Underlay spectrum sharing enables flexible coexistence between a primary network (PN) and a secondary network (SN), but inter-network interference remains a critical limiting factor. Existing mitigation strategies often rely on instantaneous channel state information (CSI), incurring high signaling overhead. This work proposes a zoning-based interference management framework that leverages large-scale channel statistics to partition the PN into interference zones and classify secondary APs (S-APs) into risk tiers. The zone-level characterization enables selective power-reduction policies with reduced coordination complexity. Simulation results confirm that the proposed framework protects the PN while preserving SN spectral efficiency (SE) in distributed cell-free deployments.

Emerging scenarios, including low-altitude economy and intelligent transportation, require ultra-reliable communi- cation and high-precision sensing, making integrated sensing and communication (ISAC) a key enabler for sixth-generation (6G) networks. The ISAC signal serves as the carrier for both communication and sensing, and its design directly affects the overall performance of ISAC system. This article presents a progressive roadmap of ISAC signal design. First, we establish a multi-dimensional performance metric framework of ISAC signal covering communication, sensing, and radio-frequency (RF) performance. Second, we introduce a three-stage ISAC signal design paradigm, namely UNLEASH POTENTIAL, EXPAND DIMENSIONS, and DEEPEN COLLABORATION. This paradigm progresses from the exploitation of existing signals, through the design of new waveform bases and multi-dimensional signal structures, to the ISAC signal design with multi-node cooperation. Finally, we propose a corresponding standardization roadmap that evolves from compatibility with existing communication sys- tems toward native and cooperation-enabled ISAC. The resulting framework provides practical guidance for ISAC signal design and the standard evolution toward 6G.

Group-relative policy optimization (GRPO) makes learner-side activations a major memory-computation bottleneck: gradient checkpointing reduces activation memory through recomputation, but fixed schedules can leave roughly 18 GB unused on a 48-GB GPU despite substantial recomputation overhead. Existing activation-management methods set state fidelity from execution cost, tensor properties, or generic compression sensitivity, without explicitly incorporating GRPO's analytic update structure into state-fidelity allocation. We formalize this dependence as policy-update exposure, linking the current GRPO loss coefficients to state-level approximation sensitivity. These coefficients are available before backward without an additional backward pass. We introduce HiLoRe, which allocates graph-attributed recovery units among high-precision storage, low-precision compression, and deterministic recomputation using measured recovery utility and update-conditioned approximation risk. It combines high-precision storage and deterministic recomputation with low-precision recovery under a calibrated risk budget. Across five model-task settings with 2K responses and memory < 1.10 times GC's per-GPU actor-update peak, HiLoRe's actor-update throughput gains reach 13.5% over GC and 7.9% over the fastest evaluated baseline, with paired mean downstream-score differences below 0.6 percentage points.

Point cloud autoencoders are fundamental components for 3D world representation and support many safety-critical downstream applications. Existing studies have extensively investigated backdoor attacks on point cloud classification, whereas backdoor attacks against point cloud autoencoders remain largely unexplored. However, their backdoor behaviors differ substantially due to the intrinsic structural gap between discriminative and generative models. Specifically, a classifier is a discriminative model that separately fits the marginal distributions of benign and malicious data. In contrast, the generative nature of an autoencoder entangles the two within a unified latent distribution, leading to information crosstalk and reduced attack controllability. In this setting, residual source geometric information in malicious data may leak into the clean inference branch, causing the reconstruction to collapse toward the source data. We then propose the Information Blackhole principle, which introduces Gaussian distribution constraints to disentangle latent representations and block interfering information. Building on this principle, we further propose Adaptive Gaussian Matching (AGM), which explicitly regularizes the latent distribution of poisoned samples. By suppressing the propagation of source geometric information from poisoned features to the attacker-specified reconstruction target, AGM improves attack controllability. Extensive quantitative and qualitative experiments on ModelNet and ShapeNetPart demonstrate that the proposed framework improves the attack performance of several standard triggers and reveals the unique operating mechanisms of backdoor attacks against point cloud autoencoders.

We investigate three-component Hubbard models on a bipartite lattice in the presence of a trans?verse field. Unlike the two-component Hubbard model, where the {\eta}-pairing symmetry survives the transverse field, the three-component model possesses neither {\eta}-pairing symmetry nor conservation of the particle number of each component. We introduce a generalized {\eta}-pairing operator, formed as a hybridization of three types of two-component pairing operators, and employ the restricted spectrum-generating algebra to construct a family of exact eigenstates. These eigenstates exhibit off-diagonal long-range order. Furthermore, we construct an exact tensor-product state whose co?herent periodic dynamics provide an exact realization of quantum many-body scar dynamics while simultaneously exhibiting long-range magnetic order. We also propose three protocols for preparing this state via quench dynamics, and verify their effectiveness through numerical simulations.

Structured quantum-state learning not only depends on an expressive ansatz but also on an operational certificate that stays meaningful with finite measurements and imperfect implementation. We study pure one dimensional states learning by an inverse binary multiscale entanglement renormalization ansatz (MERA). In the learning procedure, the qubits removed during coarse graining are controlled coherently and measured together at the terminal register. We confirm that an ideal sequential and terminal measurement schedule delivers the same complete bit string distribution under matched causal operations, while normalized postselection can amplify perturbations inversely with prefix acceptance. A noise aware theorem introduces an individual calibrated total variation implementation budget to the finite shot certificate. The protocol is estimated on an open boundary transverse field Ising ground state. A frozen 8-qubit schedule using $560$ million simulated training measurements per run achieves fidelity above $0.99$ in all $60$ held-out runs, with a mean fidelity of $0.996886$. 1080 circuit-noise cells and 6480 confidence-coverage rows are covered by fixed-circuit robustness validation without a locked soundness violation. We then address architectural fairness at $n=16$ using three new studies. In a 120-run exact-gradient multistart diagnostic, MERA has higher fidelity in 58/60 paired restarts and lower long-range error in 60/60, although no run met the prespecified stationarity criterion. Finally, a causal cone-complete, parameter matched local circuit achieves $2.62\times$ greater aggregate gate exposure yet loses all 30 paired comparisons in fidelity, long-range error, energy, and entropy.