Quantum Physics
Papers
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All of arXiv
Friday 18 September
Polarization qubits offer a direct route to fiber-based quantum communication, yet the fiber that carries them also scrambles their reference frame through uncontrolled birefringence. Active compensation commonly relies on monitoring and feedback, raising a natural question: can the link itself suppress coherent polarization drift before it reaches the receiver? We show that it can within a regime of sufficiently correlated unitary drift. Our central idea is to embed a fixed cyclic sequence of Pauli rotations along the fiber, turning propagation distance into a spatial toggling frame. Rather than estimating and inverting the unknown transformation, the sequence repeatedly reverses its leading action. We establish exact refocusing for constant generators compatible with a two-segment echo, show that a four-frame Pauli cell cancels the leading contribution of any traceless quasi-static generator, and bound the residual error for smoothly varying birefringence. We then connect these guarantees to operational BB84 quantities, including measured QBERs, the resulting secret fraction, and insertion loss. In simulations of a 50 km fiber with spatially correlated birefringence, a representative design reduces the mean QBER from 6.11% to 0.224% at a device spacing of 1.25 km. With an assumed per-device transmission of t = 0.997, this raises the asymptotic key rate per launched pulse by a factor of approximately 2.5. For this parameter set, the best design in the tested scan is not the densest one: error suppression and optical loss create a finite operating window. These results provide a loss-aware design principle for passive polarization stabilization and suggest a low-overhead complement to active tracking in polarization-encoded QKD networks.
Signal Processing
The Impact of the Cauchy Interlace Theorem on the Convergence of the RLS Algorithm
In this paper, we revisit the convergence of the RLS algorithm in view of the Cauchy Interlace Theorem. It states that the eigenvalues of a Hermitian matrix $A$ and of the rank one updated matrix $\hat{A} = A + u\,u^H$ interlace. We analyze the impact of this theorem on the convergence of the RLS algorithm and its suitable initialization. The results suggest an improved initialization for speeding up the convergence time. Moreover, a novel proof of the theorem is given based on the Sherman Morrison Woodbury formula.
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Computer Vision
RobotEQ-Video: A Video-Centric Benchmark for Social Proactive Intelligence with World-State Taxonomy
Social Proactive Intelligence (SPI) extends proactive assistance beyond task completeness to consider social appropriateness in diverse embodied scenarios. However, prior SPI research faces two key limitations. First, existing work focuses on static images, whereas dynamic videos provide crucial cues for inferring human states and needs, offering richer information than isolated images. Second, prior work often relies on free-form data collection pipelines, which fail to guarantee comprehensive coverage of diverse scenarios. To address these gaps, we introduce RobotEQ-Video, shifting the focus from image-centric to video-centric analysis. To ensure comprehensive video coverage, we construct a hierarchical world-state taxonomy organized into a four-level coarse-to-fine structure, comprising 6 domains, 20 dimensions, 142 level-1 attributes, and 816 level-2 attributes. The resulting benchmark comprises 2K+ videos with 100K+ human annotations and 16K+ labels for assessing behavior properness. Benchmark evaluation reveals that current systems remain unreliable and fall short of human performance. We further explore how world models can help tackle this task. This work advances SPI research from static images to dynamic videos and ensures more comprehensive scenario coverage during benchmarking.
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High Energy Physics (Theory)
Entanglement entropy in holographic CFTs with generic boundaries
Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.
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Robotics
ProTracer: Proprioception-Guided Failure Diagnosis in Robot Manipulation
This paper presents a comprehensive framework for robot manipulation failure analysis that includes binary failure detection, failure categorization, explanation generation, and the additional capability of failure onset localization, which aims to identify the earliest moment at which a robot execution deviates from a valid task-completion trajectory and is ultimately followed by task failure. To address these tasks, we propose ProTracer, a training-free framework that leverages existing Vision-Language Models (VLMs) together with proprioceptive signals for failure analysis. Our method uses proprioceptive dynamics to identify temporally informative action boundaries and converts richer robot-state signals into structured natural-language descriptions that can be jointly analyzed together with visual observations by the VLM. This design combines the temporal precision of proprioceptive signals with the multimodal reasoning capabilities of modern VLMs without requiring additional model training. We further introduce FailTime, a benchmark with synchronized visual and proprioceptive observations for evaluating conventional failure diagnosis tasks as well as failure onset localization. Experiments demonstrate that ProTracer achieves strong performance across both conventional failure diagnosis tasks and the newly introduced failure onset localization task, highlighting the importance of proprioceptive reasoning for fine-grained temporal failure analysis.
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Operator Algebras
Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups
In this paper, we establish a quantum Cheeger inequality for primitive KMS-symmetric quantum Markov semigroups in terms of projection conductance. We discuss both projection conductance and classical conductance for graph-based KMS-symmetric quantum Markov semigroups. We show that hypercontractivity and the logarithmic Sobolev inequality hold for primitive KMS-symmetric quantum Markov semigroups. We also present applications of the quantum Cheeger inequality to logarithmic Sobolev inequalities, hypercontractivity, and complete modified logarithmic Sobolev inequalities.
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Combinatorics
A solution to a conjecture on the signless Laplacian spectral radius for $t$-color-critical graphs
An induced matching is a matching that forms an induced subgraph. A graph is $t$-color-critical if removing some induced matching of size $t$ lowers its chromatic number, but removing any $t-1$ vertices does not. Let $F$ be a $t$-color-critical graph with $\chi(F)=r+1$. For sufficiently large $n$, Simonovits determined the unique edge-extremal $F$-free graph on $n$ vertices. Recently, Zheng, Li and Li [Linear Algebra Appl.\ 730 (2026) 546–565] conjectured that, for $t\ge 2$ and $r\ge 3$, the join $K_{t-1}\vee T_{n-t+1,r}$ uniquely maximizes the signless Laplacian spectral radius among all $n$-vertex $F$-free graphs when $n$ is sufficiently large. In this paper, we prove this conjecture. In contrast to the usual spectral arguments, our proof of this conjecture relies on two techniques of a rather different flavour. Our first technique is an analogue of Zykov symmetrization for the signless Laplacian matrix. Our second technique is an induction on $n$, from which we obtain the lower bound on the smallest entry of the Perron vector of a signless Laplacian spectral extremal graph rather than a structural statement.
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Distributed Computing
TokaGLINT: A Scalable GPU-Tailored Implicit Solver for Full 3D Tokamak Electromagnetic Simulations
We introduce TokaGLINT, a GPU-accelerated implicit solver for electromagnetic field computations in full 3D tokamak simulations, aimed at efficient large-scale parallel GPU computing. Its central innovation lies in the co-design of hierarchical domain decomposition and a fast exact local solver, where hierarchical partitioning is tailored to match fine-grained intra-card subdomains and exploit the tensor-based solver dedicated to curvilinear-coordinate symplectic CN-FDTD-discretized 3D Maxwell equations. Backed by automated operator fusion and batching customized for the intra-card multi-subdomain structure, the solver decouples unknowns through discrete transformations and leverages tensor-structured computations to achieve high hardware utilization, while preserving the long-time stability characteristic of symplectic discretizations. TokaGLINT scales the electromagnetic field solve beyond 10,000 GPUs, achieving 90.1% weak and 53.9% strong scaling efficiency, while delivering a 2.67X single-node speedup over an unpreconditioned BiCGStab baseline (HIP-enabled HYPRE). It is validated in EAST tokamak simulations within the SymPIC plasma simulation code, enabling high-fidelity long-duration modeling.
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Robotics
MicroHookACT: Monocular Microscopic Vision Guided Visuomotor Policy for Flexible Microelectrode Hooking
Automated needle-loop hooking is a critical step in flexible microelectrode (FME) implantation. This paper presents MicroHookACT, an imitation learning-based visuomotor policy for automated 3D hooking under monocular microscopic vision. First, a unidirectional hooking strategy exploits defocus cues and optical-axis guidance to enable palpation-free precise alignment and contact-rich threading. Second, an action-supervised object attention module built on a frozen ViT backbone learns to focus on the micro-needle tip and micro-loop directly from human demonstrations, without requiring manual visual annotations for training. Third, attention-centered global coarse and local fine features are dynamically weighted according to predicted action progress, enabling a single ACT policy to adapt to changing defocus blur and visual requirements throughout the operation. In the experiments, visuomotor policies were trained on 60 human demonstrations and evaluated under five setups with varying difficulties. Our MicroHookACT framework achieved the highest overall success rate of 96.7% with an average execution time of 11.5 s. These results demonstrate the potential of visuomotor policy learning for micron-level control under varying operating conditions.
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Cryptography and Security
Batched Paillier-Based Hamming-Distance Computation over Binary Embeddings
Additively homomorphic encryption supports outsourced computation on encrypted binary embeddings, but large-integer arithmetic and data movement can limit throughput. We describe a Paillier-based client that combines a carry-separated binary encoding, table-based encryption, reduced-exponent decryption, CUDA/CGBN arithmetic, persistent device state, and batched retrieval integration. We establish the encoding's correctness and characterize four CPU and GPU client configurations. The lookup configuration uses a 280-bit exponent-size parameter. Across 3 warm-state trials on batches of 10,000 random 512-bit embeddings, the lookup GPU configuration achieved median-batch throughputs of 43,091 encryptions/s and 28,983 Hamming- distance decodes/s. Its amortized costs were 0.0232 ms and 0.0345 ms per vector, corresponding to factors of 453.8 and 200.9 relative to the measured CPU baseline. These implementation- specific results demonstrate the throughput benefits of combining cryptographic precomputation, batched accelerator execution, and persistent runtime state. The study distinguishes warm-batch performance from isolated-request latency and identifies the remaining costs of initialization, transport, and retrieval integration.
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Computer Vision
Hiding in Plain Sight: A Diffusion-based Mitigation of Geolocation Privacy Leakage in Vision-Language Models
Multimodal large reasoning models (MLRMs) have demonstrated remarkable capabilities in complex visual understanding. However, this very power introduces a critical yet underexplored privacy threat: adversaries can exploit MLRMs to precisely infer users' geographic locations from casually shared photographs, by performing structured reasoning over subtle visual cues such as architectural styles, vegetation, and lighting conditions. In this work, we present a systematic study of MLRM-driven geolocation privacy leakage. We first reveal that refusal-based safeguards are critically insufficient, as carefully crafted jailbreak prompts can raise model response rates to 100%. We further identify that existing defenses, which inject imperceptible perturbations into shared images, suffer from structural limitations intrinsic to their pixel-space optimization, resulting in degraded black-box transferability and pronounced visual artifacts. Motivated by these findings, we propose a diffusion-based framework that provides targeted, proactive defense against geolocation privacy leakage. By injecting perturbations into the latent space of a diffusion model during reverse sampling, our method operates directly on high-level semantic representations, thereby resolving the effectiveness-utility bottlenecks by construction. We further ground our optimization with GeoCLIP, a model explicitly aligned with GPS coordinates, as a surrogate to pinpoint and disrupt the geographic signals that MLRMs exploit for location inference. This targeted semantic disruption yields significantly stronger black-box transferability while preserving perceptual image quality, offering a seamless integration on social media platforms. Code is available at https://github.com/RachelWolowitz/Hiding_in_plain_sight.
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Computation and Language
Beyond Atomic Tokens: Factorizing Syllables for Language Model Pretraining
Conventional tokenizers represent text as characters or statistically derived subwords, overlooking the internal phonological structure of syllables and often requiring large vocabularies. We introduce Phonemic Tokenizer, a linguistically motivated tokenizer for Vietnamese and Chinese that converts each syllable into IPA and factorizes it into three phonological components: onset, rime, and tone. The three components jointly occupy one contextual position, preserving syllable-level sequence length while enabling representation sharing across phonologically related syllables. Non-phonological and unsupported units are handled through character-level fallback. This deterministic design requires no corpus-dependent vocabulary learning and yields vocabularies of only 112 entries for Chinese and 256 for Vietnamese. Intrinsic evaluation shows that the tokenizer achieves substantially higher Rényi efficiency in both languages, represents every entry in a standard Vietnamese syllable dictionary with a Fertility of exactly one, and generally produces shorter Vietnamese sequences than existing pretrained tokenizers. We further instantiate the tokenizer in PhonemicBERT, which combines factorized component embeddings and reconstructs complete masked syllables using three prediction heads. Under a controlled Chinese pretraining setup, PhonemicBERT-Zh is competitive with or outperforms character, subword, and SubChar alternatives across diverse language-understanding tasks. PhonemicBERT-Vi also achieves competitive or superior results to established Vietnamese and multilingual pretrained models. These results establish phonemic factorization as a compact, efficient, and interpretable alternative to atomic and statistically segmented text representations.
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Number Theory
Difference of the Sum of All Odd and Even Overlined Parts of Overpartitions
Recently, Garvan and Sarma studied sums of non-overlined parts in overpartitions and partitions without repeated odd parts. In this paper, we study the corresponding statistic for overlined parts. We define $\mathrm{OSOME}(n)$ as the sum of all odd overlined parts minus the sum of all even overlined parts in the overpartitions of $n$. We obtain a closed form for its generating function and use it to prove congruences by elementary $q$-series methods, the theory of half-integral weight modular forms, and known congruences for the overpartition function.
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Representation Theory
Minuscule Relations in Quantum $K$-Theory of Flag Varieties
We study the quantum $K$-theory of the flag variety $G/B$. For each minuscule fundamental weight $\varpi$, we construct an explicit relation in the torus-equivariant quantum $K$-theory $QK_T(G/B)$. The relation can be regarded as a quantum deformation of the character of the irreducible representation with highest weight $\varpi$.
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Probability
Limit shape, avalanches, and stabilisation of abelian sandpiles on comb lattices
We study two aspects of the abelian sandpile model on comb lattices. First, we prove that the infinite-volume limit of the stationary measures is supported on the saturated configuration. We then investigate the shape of avalanches induced by adding a particle at the origin in finite boxes of size $(2n+1)\times(2n+1)$ around the origin. In the stationary distribution on these finite boxes, we show that avalanches reach the boundary along the vertical teeth with probability tending to $1$, while the horizontal spread is of order $\sqrt{n}$. Finally, we establish that the single-source limit shape for abelian sandpiles on the comb lattice agrees with the corresponding limit shapes for the divisible sandpile, internal diffusion-limited aggregation (IDLA), and rotor-router aggregation models. This establishes limit shape universality on the comb lattice.
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Robotics
FAN: Foresight Action Normalization for Continual Adaptation of Vision-Language-Action Models
Vision-Language-Action (VLA) models pre-trained on large-scale, closed datasets have demonstrated remarkable success across diverse robotic manipulation tasks. However, their long-term real-world deployment necessitates continuously acquiring new skills while retaining previously learned capabilities. While pioneering works have explored continual VLA adaptation using techniques such as experience replay and reinforcement fine-tuning, they overlook a foundational mechanism: action normalization, which determines the underlying coordinate system in which policies perceive and execute physical actions. To bridge this gap, we systematically evaluate five normalization strategies across four real-world task streams covering single-arm and bimanual manipulation. Our analysis reveals that existing protocols induce severe failure modes due to inter-task coordinate drift, limited motion coverage, or train-test coordinate mismatches. Motivated by these insights, we formulate three core design principles: consistency, coverage, and causality (3C), and introduce foresight action normalization (FAN). FAN estimates normalization statistics once from a small, task-independent calibration set prior to continual learning and freezes them throughout adaptation. Across all evaluated streams, FAN achieves the highest performance and demonstrates consistent robustness, providing insightful guidance for building stable action representations in achieving effective lifelong VLA adaptation.
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Metric Geometry
The disjoint disks property for Busemann $G$-spaces
We prove that every finite-dimensional Busemann \(G\)-space of dimension at least five has the disjoint disks property (DDP). For a sufficiently small metric sphere \(L=S(c,r)\), we show that every embedded arc contained in an exact distance level is a homotopical \(Z_2\)-set in \(L\). It follows that \(L\) has the disjoint arc-disk property and the disjoint homotopies property. Daverman's product theorem then gives DDP for \(L\times\mathbb R\), and a local avoidance argument at the center yields DDP for the ambient \(G\)-space. Since finite-dimensional Busemann \(G\)-spaces are generalized manifolds, in dimensions at least five the remaining obstruction to the Busemann conjecture is the resolution problem.
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Algebraic Geometry
Double shuffle relations via the Hodge defect
We interpret the convolution constructions of [arXiv:2604.26357] in Hodge-theoretic terms, extending the Hodge defect calculation of [arXiv:2609.19341]. For Hodge–Tate modules on $\mathbb C^*$ smooth outside $1$, the defect is the action of an element of the Deligne–Terasoma transport algebra expressed through the Drinfeld associator. For convolutions of iterated Kummer extensions, comparison of mixed Hodge structures produces a beta factor and yields the regularized double shuffle relations.
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Quantum Physics
Weighted Berry curvature and global geometry of mixed quantum states
We examine the geometric interpretation of the quantum geometric tensor proposed in [Phys. Rev. B 110, 035404 (2024)] for mixed quantum states, focusing on its imaginary part, which is proportional to a weighted sum of the Berry curvatures of the eigenstates of the density operator. While the real part naturally decomposes into Fisher–Rao and weighted Fubini–Study contributions, we show that the imaginary part does not, in general, coincide with the curvature of a connection on a globally defined U(1) line bundle whose holonomy yields a mixed-state geometric phase. Using a two-level system as an explicit example, we demonstrate that its surface integral depends on the choice of surface bounded by the same closed path, with ambiguities that are not integer multiples of $2\pi$.
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Computer Vision
Field Tracking of Insects Using a Stereoscopic Event-Based Camera Setup
High-speed tracking of small, fast-moving organisms in their natural environments is important to better understand their behavior and ecology. Traditional frame-based imaging suffers from motion blur due to low temporal resolution, and data storage limitations, propelling a search for more adaptive solutions. Event cameras, which capture changes in brightness at pixel level instead of entire frames, have emerged as a promising solution by increasing temporal resolution and data efficiency. Here, we demonstrate the use of event-based imaging with standard video-based processing methods by converting the asynchronous events into conventional video formats, allowing us to leverage the event camera's enhanced temporal detail to capture intricate insect flight movements and apply established image analysis techniques. Coupling this conversion process with a stereoscopic configuration provides continuous, low-latency, three-dimensional tracking of fast-moving subjects in field conditions. As a result, we substantially mitigate motion artifacts and achieve more accurate representations of animal movements. By making event-based imaging more readily applicable in natural field settings, our method support broader applications across animal behavior and ecological research, agricultural management, and other fields requiring high-fidelity object tracking in the wild.
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Applied Physics
Multiplexing approaches to thermoradiative signatureless communications
Using mid-infrared emission from semiconductor devices for covert communications remains a relatively unexplored and yet promising opportunity. The phenomenon of negative luminescence allows for a method of signatureless covert communications where the net infrared emission of an emitting optoelectronic device is balanced to be identical to the ambient thermal background. In this work we provide a practical demonstration of covert data transfer over a thermoradiative channel with data rates up to 100 kbps. In addition, we demonstrate several additional multiplexing techniques that make the proposed thermoradiative communications method more secure against interception by achieving zero instantaneous optical emission, while remaining detectable if a sufficiently spatially or spectrally discerning observation is utilised. Finally, we discuss various application scenarios in which the proposed methods can be used to achieve secure signatureless communications.
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Materials Science
Strain-Induced Relaxor Multiferroicity at Room Temperature in Hexaferrite BaFe12O19 Thin Films
Multiferroic materials that combine magnetic and electric order at room temperature are rare. Here, we demonstrate strain-induced room-temperature polar order in the ferrimagnetic hexaferrite BaFe12O19. First-principles calculations reveal a strain-tunable energy landscape with multiple competing dipolar configurations and predict that compressive strain favors polar distortions. Using an isostructural Sr1.03Ga10.81Mg0.58Zr0.58O19 substrate, we grow coherently strained BaFe12O19 films with 1.1% in-plane biaxial compression. Second-harmonic generation measurements demonstrate inversion-symmetry breaking and establish a strain-stabilized polar phase that persists to at least 1000 K. Multislice electron ptychography directly reveals enhanced off-centering of Fe3+ ions within the trigonal-bipyramidal sites of the strained films and spatially varying local polarization, demonstrating the formation of polar nanoregions. Path-integral Monte Carlo simulations further show that compressive strain suppresses quantum fluctuations and stabilizes these local polar distortions. Together, these results establish strain-engineered BaFe12O19 as a room-temperature relaxor multiferroic, in which robust ferrimagnetism coexists with nanoscale polar order. Our work demonstrates a route for transforming an incipient ferroelectric ferrimagnetic into a polar magnetic material through epitaxial strain.
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Computer Vision
PrismAlign: Prior-Steered Multi-View VLM Alignment for Hallucination-Robust Table OCR
Table extraction suffers from frequent structural errors and semantic hallucinations. We propose PrismAlign, a multi-VLM framework aligning diverse visual perspectives to resolve ambiguity. It integrates priors of table logic to assess output plausibility, decoupling structural alignment from cell content alignment. A Bayesian decision strategy maximizes alignment accuracy by exploiting the correlation between extraction errors and computable rule violations. Evaluated on open-source and custom VLMs, PrismAlign reduces hallucinations and achieves state-of-the-art performance on OmniDocBench 1.5, as well as on the table category of CC-OCR and PureDocBench.
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Astrophysics of Galaxies
From Observation to Ground Truth: Reconstruction Losses of Galaxy Imaging Under Heteroscedastic Noise
Deep learning is widely used to analyze galaxy images, and the reconstruction loss determines which image features a model prioritizes during training. Mean squared error (MSE) and mean absolute error (MAE) correspond to homoscedastic Gaussian and Laplace likelihoods, respectively, whereas the inverse-variance-weighted $\chi^2$ loss accounts for the spatially varying uncertainties of heteroscedastic astronomical noise. Comparing how closely these objectives recover the underlying signal requires a ground truth (GT), which real observations cannot provide. We therefore generate noise-free galaxy images with IllustrisTNG, SKIRT, and GalaxyGenius, convolve them with a point-spread function (PSF) to define the GT, and construct noisy simulated observations. We train otherwise identical variational autoencoders (VAEs) with the three reconstruction losses and evaluate their outputs against the GT. Over most of the evaluated signal-to-noise ratio (SNR) range, the $\chi^2$-trained model yields lower relative reconstruction errors than the MSE- and MAE-trained models, indicating that inverse-variance weighting improves galaxy-image reconstruction under the heteroscedastic noise considered here.
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Computation and Language
From Memory to Behavior: A Behavior-Aware Role-Playing Framework for Social Media Influencers
Large language models have shown strong potential as role-playing agents for real individuals, yet faithful impersonating remains challenging. Existing in-context learning-based methods fail to capture how individuals react under different situations. In addition, LLM-based evaluation is difficult for obscure individuals. To address these challenges, we propose Situation–Internal state–Behavior Persona method to incorporate situation-dependent behavioral strategies. We further design an evaluation protocol that provides LLM evaluators with references about the impersonated individual. We evaluate our approach on a newly constructed dataset for the task of generating replies on social media. Experimental results show that our proposed method outperforms state-of-the-art ICL-based baselines, while our evaluation protocol achieves moderate correlation with human judgment. Besides, experiments on fictional-character benchmarks demonstrate that our proposed method is applicable beyond the social media setting. These findings suggest that incorporating behavioral information broadly improves the fidelity of role-playing for real individuals on social media or fictional characters.
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Data Structures and Algorithms
The Cube-Root Phenomenon in Online Carpooling
We consider the online carpooling problem, where edges arrive online and must be oriented immediately while keeping the discrepancy between the indegree and outdegree at each vertex small. We prove that the natural Greedy algorithm incurs discrepancy $O(\min\{T^{1/3},n\})$ after $T$ arrivals. This resolves a question of Ajtai et al., who showed that any deterministic algorithm must incur $\Omega(\min\{T^{1/3},n\})$ discrepancy, and gave an algorithm with $O(\min\{T^{1/2},n\})$ discrepancy. We also show a similar square-root to cube-root improvement in the stochastic setting, where $O(n)$ edges are sampled independently from an underlying $n$-vertex graph $G$. Formally, we show an $O((\log n)^{1/3})$ bound for random arrivals from any $\Delta$-regular graph $G$. When $\Delta = \Omega((\log n)^3)$, we show the more refined bound of $O((\log n/\log \Delta)^{1/3}+\log\log n)$ on the discrepancy. We show that the cube-root term in the previous bound is essential, while the $\log\log n$ term is already known to be necessary for random arrivals from complete graphs. The previous upper bounds here were $O((\log n)^{1/2})$, which follow from the breakthrough works on online discrepancy due to Kulkarni, Reis, and Rothvoss, and Aden-Ali. Our techniques for proving such cube-root-type bounds may be of independent interest, as the standard quadratic-potential and subgaussian analyses underlying the previous general bounds appear inherently unable to go below square-root-type guarantees.
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Computer Vision
Cube-Splat: High-Fidelity 360{\deg} Gaussian Splatting SLAM via Cubemap Factorization and Adjoint-Consistent Optimization
Recent progress in 3D Gaussian Splatting (3DGS) has enabled dense visual SLAM with pinhole cameras, yet most pipelines are not designed for panoramic imagery. We present Cube-Splat, the first panoramic GS-SLAM framework that factorizes each 360{\deg} frame into a cubemap of four fixed-orientation virtual pinhole views sharing a single optical center. By designating the front face as the primary pose state, we accumulate gradients from all faces via an adjoint mapping, thereby enabling multi-face observations to coherently update a single state while strictly preserving cross-view geometric consistency. Concurrently, our mapping module densifies and optimizes anisotropic Gaussians using aggregated cubemap rays for high-fidelity, dense reconstruction. Furthermore, to rigorously evaluate panoramic SLAM under diverse and challenging conditions, we introduce SynPano, a highly scalable, photorealistic synthetic dataset featuring parameterized complex trajectories and multi-modal ground truth. Extensive evaluations on two public benchmarks (PALVIO and OmniBlender) and our SynPano dataset, collectively encompassing both indoor and outdoor scenes, demonstrate that Cube-Splat achieves state-of-the-art (SOTA) performance in tracking accuracy and reconstruction fidelity. Both the source code and the SynPano dataset are available at https://github.com/guoxf304/CubeSplat.
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Machine Learning
IntBMoE: Integrating Block-Level Conditioning into Expert Composition for Full-Participation Mixture-of-Experts
Mixture-of-Experts (MoE) scales capacity, but existing designs cannot set three quantities independently. For a single token, participation is how many experts contribute knowledge to its output, execution is how many are actually computed (compute cost), and materialization is how many expert-sized parameter sets must be built and stored (memory cost). Sparse routing keeps execution and materialization low, but shrinks participation: for each token, only a few experts contribute. Dense output-mixing restores full participation, but its execution grows with the number of experts. Parameter-merging keeps execution at one expert, but its materialization grows with the number of routing decisions. We propose IntBMoE, a block-conditioned MoE that decouples all three by pairing dense expert composition with sparse block execution. Its blocks come from a small learned codebook, one per entry. At each internal layer, a lightweight hypernetwork merges all expert bases in that layer's pool into one composed expert. Participation is full, because every composed expert draws on the entire pool. Execution stays sparse, because a router sends each token to only a few blocks. Materialization is bounded, because the codebook, not the input, fixes how many blocks exist. Dual-Path Residual Gating (DPRG) further couples two independently composed paths through multiplicative gating. Experiments on image classification show consistent gains over representative sparse and dense MoE baselines. Additional experiments on language modeling and sequential recommendation validate its generalization beyond vision. IntBMoE is fully deployed in AMap's generative recommendation system, serving hundreds of millions of users under a 60ms latency budget, with a 2.4% relative UVCTR gain in online A/B testing. Our code is available at https://github.com/AMAP-ML/DreamX-Rec/.
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Probability
Small-time asymptotics of heat kernels of one-dimensional diffusions in a random environment
We establish the Varadhan small-time asymptotics for the quenched and annealed heat kernels of one-dimensional diffusions in a random environment with generator $\mathcal L_W f(x)=e^{-\rho(x,W)}(e^{a(x,W)}f'(x))'$. The coefficients $a$ and $\rho$ are continuous in space and satisfy a local exponential moment condition. We assume that the law of the intrinsic coordinate map $\Lambda_W$ has compact support $\mathscr L$ consisting of strictly increasing functions. Let $q^W(t,x,y)$ and $q(t,x,y)=\mathbb E[q^W(t,x,y)]$ denote the quenched and annealed heat kernels with respect to Lebesgue measure, respectively. We prove that, for almost every environment $W$, $\lim_{t\downarrow0}t\log q^W(t,x,y)=-\frac12|\Lambda_W(y)-\Lambda_W(x)|^2$, and that $\lim_{t\downarrow0}t\log q(t,x,y)=-\frac12\min_{\Lambda\in\mathscr L}|\Lambda(y)-\Lambda(x)|^2$. Both limits hold uniformly on compact subsets of $\mathbb R^2$. The framework includes Brox diffusion, formally described by $dX_t=dB_t-\frac12\dot W(X_t)\,dt$, where $B$ is a standard Brownian motion and $W$ is an independent two-sided Brownian motion.
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Cryptography and Security
CESBench: Benchmarking Large Language Models on Cryptographic Engineering Security for IoT Devices
For Internet of Things (IoT) devices, a secure algorithm alone is not enough: an attacker with physical access can attack the implementation directly, and its flaws are hard to fix once deployed. Large language models (LLMs) are now used to build and analyze such implementations. LLM benchmarks exist for cryptography and general cybersecurity, but none covers cryptographic engineering. In this paper, we present CESBench, 380 expert-written items across six sub-domains of cryptographic engineering security for IoT devices: side-channel, fault injection, implementation, countermeasures, evaluation, and integration. Four task types target different competences: 209 multiple-choice items test recall, 67 judgment items require a security verdict and its justification, 63 scenario items require an engineering diagnosis, and 41 code tasks are graded by 572 test cases. To validate the benchmark, 11 open-weight and proprietary LLMs answer every item. Multiple-choice and code responses are scored automatically, and judgment and scenario responses by an LLM judge, whose scores are checked against a second judge from another model family and human re-scoring. Composite scores range from 54.4% to 83.6%. The top score on each task type is 98.6% for multiple choice, 95.1% for code, and 88.4% for scenario diagnosis, but only 58.8% for judgment. Across models, 88.5% of verdicts are correct, yet their justifications earn only 53.4% of the rubric marks. Multiple choice is near its ceiling for the strongest models and most code tasks are solved, whereas justifying a security verdict remains the weakest competence. The benchmark, prompts, and per-item results are public.