Papers

End-to-end autonomous driving models are typically trained on real-world driving logs, which record only the trajectory actually executed in each scene. This provides limited supervision for learning alternative valid behaviors. Multi-target supervision can mitigate this limitation, but broader trajectory coverage makes safe candidate selection more challenging. We propose FPD-Drive, an end-to-end planner that distills privileged future knowledge into a visual driving policy to improve both multi-trajectory supervision and safety selection. Specifically, we introduce Future-Privileged Multi-Target Distillation to transfer diverse, high-quality trajectory targets from a teacher with access to recorded future observations to the student. These targets extend supervision beyond the single recorded human trajectory. For candidate selection, we further introduce Safety-Aware Score Correction to correct ranking errors between nearby safe and unsafe candidates and raise underestimated safety scores of safe candidates. At deployment, the student requires neither future observations nor teacher inference. Our base model achieves 94.9 PDMS on NAVSIM v1 navtest and 55.9 EPDMS on NAVSIM v2 navhard. The scaled FPD-Drive-Pro improves these scores to 95.5 PDMS and 58.1 EPDMS, respectively, achieving SOTA performance among the compared methods on both benchmarks. Zero-shot closed-loop evaluation on HUGSIM further yields an HD-Score of 45.1 and RC of 55.3.

We explore the possibility of non-resonant flavoured leptogenesis in the framework of the aligned two-Higgs doublet model augmented with two right-handed neutrinos. Considering the lightest heavy neutrino mass between 10 TeV-100 TeV, we calculate the baryon asymmetry of the universe by solving fully flavoured coupled Boltzmann equations and find that the observed baryon asymmetry can be successfully generated for lightest heavy-neutrino masses in this range without relying on resonant enhancement. We compute the flavour-dependent CP asymmetries and washouts as well. Unlike conventional analyses based on only one Higgs doublet, in this framework, both Yukawa structures associated with the scalar doublets contribute to the CP asymmetry, and their combined effect plays an essential role in realizing the observed lepton asymmetry. We find that the flavoured lepton asymmetry survives if the washout in that direction is weak. The CP asymmetries in the other flavour directions suffer strong washout. The surviving flavour-dependent lepton asymmetry becomes the main contributor to the final baryon asymmetry. We perform a comprehensive numerical analysis to identify the allowed regions of the multi-dimensional parameter space compatible with neutrino oscillation data, perturbativity of the Yukawa couplings, charged-lepton flavour violation and the observed baryon asymmetry.

We apply a two-layer thermophysical model, with water sublimating from below a dust-crust with dynamically varying depth, to simulate the water outgassing rate, dust-ejections, and non-gravitational forces and torques of comet 67P/Churyumov-Gerasimenko. The dust-depth is determined at each time-step by the balance of dehydration and subsurface pressure, leading to alternating ejections and crust build-up. This model is the first stage of implementing a fully coupled activity-fallback model that self-consistently incorporates dust-fallback into the ejection depth calculation, but already a number of conclusions can be drawn from these results. The two-layer model with only dehydration and ejections is able to reproduce much of the Rosetta outgassing, dust-ejection data and non-gravitational dynamics, particularly in the comet's more primitive southern terrain. Best agreement is found for nucleus material made up of small aggregates ($d_{agg}\sim1$ mm) with not-too-high dust-to-ice ratios ($\delta\sim2-8$) and low average strengths ($\lesssim1$ Pa) that decreases with depth. Disagreements between the observations and model are greatest for the northern-facing and dust-covered terrains, suggesting the importance of surface modification by fallback and material processing here, which will be the subject of investigation in the next paper.

Polynomial first-order projective differential moment invariants are investigated. The main result establishes an exact correspondence between such moment invariants and symmetric polynomial multipoint relative projective differential invariants of weight $-1$. This correspondence describes each homogeneous component with respect to moment degree and allows previously obtained results on relative projective invariants to be used for systematic construction. It is also proved that passing from the formal algebra of moments to their integral definitions introduces no additional algebraic relations among the constructed invariants. For low moment degrees, the absence of nontrivial invariants of degrees $1$ and $2$ is established, and a complete description of degree $3$ invariants is obtained. The ten cubic differential moments are naturally identified with the coefficients of a ternary cubic, connecting the construction with classical invariant theory. In particular, the Aronhold invariants $S$ and $T$ yield projective differential moment invariants of degrees $4$ and $6$. One of the known moment invariants of Wang et al. is shown to be proportional to $S$. The algebra of polynomial moment invariants is proved not to be finitely generated. The field of rational moment invariants coincides with the field of fractions of the polynomial invariant algebra. For the explicit constructions, compact multipoint representations define the corresponding moment polynomials without requiring their full expansions. These representations provide a basis for algorithmic construction and software computation of the invariants.

We present an explicit quantum circuit that constructs a block encoding of a generator-representable semiseparable (one-pair) matrix directly from its two generators. For an $N\times N$ semiseparable matrix with $N=2^{n}$, the circuit uses $2n+2$ ancilla qubits and has $O({\rm polylog} N)$ depth, and it realizes a $(2\sqrt{N},\,2n+2,\,2 \sqrt{2}\ \varepsilon)$-block encoding, where $\varepsilon$ is controlled by the accuracy of the state-preparation routines that load the generators. The building blocks of the circuit are cyclic shifts, swaps, and Hadamard gates, each admitting an efficient implementation through the binary decomposition of the relevant indices.

Agent skills extend the capabilities of AI agents by bundling instructions, code, and resources into reusable packages. During skill execution, agents may produce or modify artifacts, such as files, configurations, and cached data, that are reused by other skills in later sessions. Since these artifacts can persist across sessions and later be accessed by other skills, they introduce a new attack surface that can be exploited to influence subsequent executions. However, the security risks arising from such cross-session skill interactions remain largely unexplored. In this work, we investigate cross-session composition attacks in skill-based AI agents and develop a runtime defense against them. Specifically, we characterize three attack mechanisms, namely Instruction Propagation (IP), Data Boundary Violation (DBV), and Evidence Poisoning (EP), through which malicious effects propagate across skill executions via persistent artifacts. To evaluate whether existing agents can resist these attacks while completing legitimate tasks, we construct SkillRelayBench, a benchmark of 270 adversarial cases drawn from 30 cross-session skill-composition scenarios across ten domains. Our evaluation of seven models across Codex CLI, Gemini CLI, and Claude Code reveals attack success rates (ASR) ranging from 46.7% to 77.4% and attack chain success rates (ACSR) ranging from 35.6% to 61.1%. Successful attack chains cover all five target security consequence categories, highlighting the broad impact of these attacks. To mitigate these risks, we propose SkillRelayGuard, which restores artifact provenance context and provides pre-execution advisory review while leaving the final execution decision to the agent. Evaluation across three agent settings shows that SkillRelayGuard reduces overall ASR from 69.5% to 10.9% and ACSR from 54.8% to 10.0%, while increasing legitimate task completion from 79.6% to 87.5%.

In this paper, we prove global pointwise estimates on the decreasing rearrangement \(u^{\ast}\) and \([H(\nabla u)]^{\ast}\) of SOLAs \(u\) of an elliptic Poisson equation driven by the anisotropic \(p\)-Laplace operator \(\Delta_p^H\) for given \(L^1\)-data and equipped with either homogeneous Dirichlet or Neumann boundary conditions. Here, we assume that the dimension \(n\ge 2\), \(1<p<n\) and \(H\) is norm on \(\R^n\). In the degenerate range \(2 \leq p <n\), this gives an anisotropic extension and a full-interval completion of the rearrangement theory of Cianchi-Maz'ya [JEMS, 2014]. In particular, we obtain a new rearrangement estimate for gradients by decomposing the data for singular range \(1<p<2\), where the nonlinear interpolation method aren't available. Moreover, the endpoint weak-type gradient estimate is obtained for all \(1<p<n\). In the range \(p_*(n)<p<n\) with \(p_*(n):=\frac{3n-2}{2n-1}\), we prove a stability estimate for differences of gradients. These results extends the known ones in the literature to the singular range \(p_*(n)<p<2\).

Generative modeling for discrete data has been significantly advanced by learning continuous vector fields on the statistical manifolds to transport simple priors to target discrete distributions. However, because these continuous-time flows are not constrained to follow geodesics on the statistical manifold, thereby requiring multi-step numerical integration for simulation and leading to substantial computational costs during inference. In this work, drawing inspiration from the "straight and fast" properties of Rectified Flow in continuous Euclidean space, we propose the Rectified Statistical Flow (ReSFlow) model, which enables one-step categorical generation on statistical manifolds by explicitly learning geodesic trajectories that adhere to the intrinsic Riemannian geometry. By rectifying the flow on the statistical manifold, we theoretically guarantee that trajectories between prior and target distributions approximate geodesics. This rectification significantly reduces the transport cost by aligning the learned trajectories directly along geodesics on the statistical manifold, allowing the model to map pure noise to target discrete data in a single step. Through extensive experiments on diverse real-world generative tasks, ranging from image and text to biological domains, we demonstrate ReSFlow's superior one-step generation quality, which truly embodies geodesically optimal and rapid categorical generation. Our code is available at https://github.com/xiaohuanjia/ReSFlow.

Symbols and icons in archival maps represent an expansive source of evidence for historical geography. In this paper, we present a two-stage framework for (1) detecting cartographic signs in historical maps and (2) generating interpretable sign embeddings that capture both semantics and stylistic variations. We also introduce CaSiDD, an open benchmark dataset spanning multiple sign categories and diverse cartographic styles, designed for generic sign detection. Using YOLOv10-X, we demonstrate the practicality of automated sign detection on historical maps. We then present strategies for creating contrasted, informative embeddings of cartographic signs. We approach embedding design systematically, maximizing expressiveness while suppressing digitization or background material confounders. Our final method, based on an adapted RADIOv4 backbone, effectively encodes both sign form and semantics, while producing interpretable representations. This work lays a foundation for scalable evidence extraction for the comparative study of map signs within cartographic culture and geohistorical research.

This study aims to determine asteroid rotation periods from sparse, unevenly sampled, multi-observatory photometry using the Lomb-Scargle (L-S) method. The photometric measurements of the asteroids are taken from the circulars of the Minor Planet Center (MPC). Twelve asteroids, four of them with known rotation periods, were analyzed with two complementary methods. In the separate dataset analysis (S-method), each observatory dataset was analyzed separately, and the final period was obtained as a weighted average of the consistent candidate periods, with weights based on the peak power of the power spectrum, the number of measurements, and the quality of the corresponding light curve fit. In the combined dataset analysis (C-method), all measurements were corrected for the biases of the photometric band, the star catalog and the observatory, reduced to a common scale and merged into a single dataset, after which the period was derived directly from the L-S analysis of the combined time series. Both methods produced consistent results, and they reproduced the known periods of the four test asteroids within 0.05%. The results show that the L-S method is well suited for finding rotation periods in sparse observations with uneven sampling over long time intervals. New rotation periods were found for asteroids 2968, 2971, 3081, 3473, 3716, and 4303. The period of 2968 remains ambiguous because of daily aliasing. For 3716, the most likely period is 10.474 hours, but its daily alias at 13.405 hours cannot be excluded completely. For 3173, the strongest peaks at 22.99 and 45.98 hours are probably daily aliases of a slower brightness variation. For asteroid 2607, the period agrees with a recently published value and is more precise. The approach is therefore promising for automated searches for unknown asteroid rotation periods.

Extended-domain spectral collocation expands the solution of a boundary value problem in the Laplacian eigenbasis of an enclosing box and collocates at as many nodes as modes. The square system is exponentially ill-conditioned, and the impossibility theorem for equispaced data rules out stable geometric convergence; yet such solvers converge geometrically to a few orders of magnitude above the unit roundoff. We explain why in one dimension. The collocation solution is the solution operator applied to the interpolant of the data in an operator-dependent test space whose Lebesgue constant must grow exponentially for geometric convergence, so exact solutions can amplify data errors exponentially. In floating-point arithmetic the error of any coefficient vector is bounded by its nodal residual, its distance to a competitor and two frame constants, a leakage and a restricted Marcinkiewicz–Zygmund constant, bounded uniformly in the number of modes at a fixed positive threshold; for a backward-stable solve, under a condition on the perturbed matrix, the bound is uniform in the conditioning for suitably analytic data and, with computed constants, within a factor of about ten of the error floor of a direct solver. For the Poisson operator the rate of the two constants along the tail of the spectrum is given by a constrained equilibrium problem of logarithmic potential theory. For an interval of length $L$ extended by $\delta$ at each end, the problems for $\delta$ and $L^2/(4\delta)$ are dual, the rate is linear for $\delta = L/2$, and it starts with slope minus the fraction of the extended domain occupied by the extension, so for $\delta < L/2$ the leakage constant obeys no power law with the exponent of the end of the spectrum. In experiments, convection–diffusion operators behave like the Poisson operator at moderate Péclet numbers.

Cancer diagnosis and treatment increasingly rely on multi-modal diagnostic technologies that generate high-dimensional datasets. Although these datasets are rich in pathological information, they pose considerable challenges in interpretation, dimensionality reduction, and clinical applicability. Conventional machine learning approaches often fail to extract meaningful cross-modal features, thereby limiting predictive accuracy in patient risk stratification. To address these limitations, this paper proposes an unsupervised machine learning framework that integrates feature extraction, tensor decomposition, and clustering to improve cancer risk prediction. The framework employs tensor decomposition to fuse heterogeneous genomic and clinical data, enabling the extraction of latent, biologically meaningful features that outperform unimodal feature sets. Multiple feature extraction strategies are investigated, and the resulting features are subsequently clustered using a range of clustering algorithms. Comparative evaluations based on internal and external metrics are then used to identify the most effective configurations. The framework is validated on LinkedOmics data comprising 11,158 patients across 32 cancer types. For patient risk stratification, clinically relevant attributes such as tumor purity, pathological stage, and survival outcomes serve as ground-truth indicators. Experimental results demonstrate the superiority of tSVD+GMM, which consistently outperforms other configurations across clinical benchmarks.

The unmanned aerial vehicle (UAV)-based maritime surveillance is becoming an important part of maritime Internet of Things (IoT) and intelligent transportation systems. It provides a flexible and cost-effective way to large-scale maritime traffic monitoring. However, achieving robust situational awareness remains challenging in practical maritime environments. The main challenges arise from heterogeneous sensing modalities, adverse imaging conditions, and spatial misalignment caused by UAV motion. To address these problems, this paper proposes an airborne multi-modal graph learning-driven framework, termed AMGT, for vessel identification and tracking in UAV-assisted maritime IoT. Specifically, visible and infrared images are first aligned and fused through a multi-parameter perspective transformation model. This improves visual perception under low visibility and complex illumination conditions. Automatic identification system (AIS) messages are then temporally synchronized using interpolation and linear prediction. To detect small and oriented vessels, we develop a mixed-modality MAir-YOLOv8-OBB detector, followed by the MAir-SORT algorithm for stable vessel tracking. We further design a graph learning-driven association network to model temporal dynamics and spatial dependencies among vessels and between vessels and UAVs. A motion-aware coordinate unification (MCU) strategy is also introduced to reduce nonlinear misalignment caused by UAV motion. Experiments on the MAP-M2UAV50 dataset show that AMGT achieves high accuracy and efficiency. The results demonstrate its potential for UAV-assisted maritime IoT applications, including vessel monitoring, traffic situational awareness, and intelligent maritime transportation services. The dataset and code will be available at https://github.com/MAPGroup/AMGT.

The discrepancy induced by surface reconstruction in a distorted point cloud is jointly influenced by its intrinsic structural complexity and signal degradation. This observation motivates a referencefree point cloud quality assessment (PCQA) strategy that estimates and compensates for the complexity-induced component. We implement this strategy through successive reconstruction. Specifically, reconstructing the distorted point cloud produces an input-toreconstruction discrepancy that combines the effects of signal degradation and content complexity. Reapplying the reconstruction operator with stronger smoothing produces a discrepancy between successive reconstructions, which serves as a proxy for the complexityinduced component. This proxy is then used to calibrate the inputto-reconstruction discrepancy. We apply the same strategy to 3D geometry patches and their aligned 2D regions, enabling local comparison of the resulting discrepancies. The calibrated geometric and projected-view discrepancies are then fused into a final degradation score. For both branches, the discrepancies are measured using frozen pretrained perceptual representations. Our method does not require PCQA-specific training or fine-tuning. Experiments on three public databases show that the proposed method consistently outperforms most generic baselines and achieves performance comparable to several full-reference metrics.The code is available at https://github.com/HC-W-whc/CCRD-NR-PCQA.git.

We present a spectral analysis of a large sample of low-redshift type 1 active galactic nuclei (AGNs) selected from the first data release of the Dark Energy Spectroscopic Instrument (DESI DR1). For objects at $z\le0.9$, we perform spectral fitting and ML-assisted refinement, yielding 114,754 type 1 AGNs. We use two fitting schemes that differ only in the broad-line model: the broad Balmer components are fitted with either a Lorentzian function or a sum of Gaussians. The continuum and [O III] luminosity measurements agree closely between the two schemes, whereas the Gaussians scheme generally yields larger broad-H$\beta$ full width at half maximum (FWHM) values, larger virial black hole masses, and lower accretion rates. The adopted broad-Balmer profile also changes the decomposition of narrow Balmer emission. Specifically, the anti-correlation between [O III]$\lambda5007$/narrow H$\beta$ and accretion rate is stronger under the Gaussians scheme with a Spearman rank correlation coefficient $r_{\rm s}=-0.412$, than under the Lorentzian scheme with $r_{\rm s}=-0.206$; the same tendency is observed in the narrow-line Seyfert 1 galaxies (NLS1s) subset ($r_{\rm s}=-0.435$ and $-0.259$ for the Gaussians and Lorentzian schemes, respectively), suggesting that the Gaussians scheme may provide a more self-consistent separation of the broad and narrow H$\beta$ components. Moreover, the consistent correlations recovered under both profile prescriptions favor a continuous type 1 accretion-state sequence, with NLS1s occupying its high-accretion end rather than constituting a distinct population.

Video generation supports digital content creation, with applications in virtual avatars, AI-driven filmmaking, interactive game engines, and world models. State-of-the-art systems achieve controllability primarily through image-to-video (I2V) generation, in which an injected anchor image determines the identity, composition, and style of the resulting video. In modern pipelines, this anchor is synthesized by a text-to-image (T2I) generator. This raises a largely overlooked question: Are images obtained directly from the T2I model truly suitable for current video models? Our analysis shows that anchor aesthetic and quality scores are weakly correlated with downstream video quality. The structure-and-texture score is negatively correlated with I2V video quality in both the visual and motion dimensions. Fine-tuning the T2I model on an image reward accordingly yields anchors with visibly denser structural and character detail: they score higher on image metrics, yet lower the video reward on every I2V model we test and change downstream motion unpredictably. We therefore introduce Golden Anchor Learning (GAL), to our knowledge the first framework for learning golden anchors by optimizing a T2I generator with downstream video feedback. GAL evaluates candidate anchors through the videos they induce under a frozen I2V model and converts video rewards into image-level preferences for DPO fine-tuning of the T2I generator. On all four I2V models, GAL raises the VBench average by $2.97\%$–$8.46\%$ over the untuned generator. The rendered clips also score higher under VideoReward-Overall, and their extracted frames under HPSv3 and UniPercept. GAL yields consistent motion gains across all four I2V models, as measured by a $5.62\%$–$38.24\%$ increase in VBench dynamic degree. Although GAL is trained only on HunyuanVideo-1.5 renders, these gains extend to the other three I2V models.

The rapid progress of 3D generative models has made 3D asset creation increasingly accessible. However, achieving intuitive, precise, and interactive user control, such as point-based drag editing, remains challenging. Existing 3D drag methods either rely on slow 2D diffusion priors, such as Score Distillation Sampling, or directly warp geometry, often causing multi-view inconsistency and topological artifacts. In this paper, we present 3DRAG, a training-free framework that executes precise drag editing natively within the explicit 3D latent space of large-scale generative models, without SDS-based optimization or iterative point tracking. To ensure geometrically plausible deformations, 3DRAG explicitly extends the drag displacement field into 3D space, incorporating an Occupancy-Aware Winner-Takes-All (OA-WTA) strategy to robustly handle sparse geometries. Furthermore, we introduce a generative editing pipeline that explicitly transforms latent representations via the 3D displacement field. By fully leveraging the model's generative capabilities, it achieves smooth geometric deformations while maintaining the object's identity. To further transfer original geometry and texture with high fidelity, we propose Logits-Level Token Fusion, which accurately injects source information into the destination region. To evaluate 3D point-based editing, we construct a novel dataset featuring diverse 3D assets and complex multi-point drag instructions. Quantitative and qualitative experiments demonstrate that 3DRAG achieves state-of-the-art performance, surpassing existing baselines in drag accuracy, geometric fidelity, and unedited region preservation.

Learning new tasks in multimodal continual instruction tuning can cause catastrophic forgetting of previously acquired knowledge. Although multi-expert LoRA distributes learning across experts, updates to a dense low-rank expert can still affect many output features. We introduce Monarch-MoE, which replaces the dense factors in LoRA experts with block-diagonal factors connected by a fixed permutation. This structure provides blockwise gradient isolation: individual block-pair updates affect only one output block, while connections between all input and output blocks are maintained. To make these compact experts practical on memory-limited hardware, we combine batched computation, fused forward operators, and an optimized backward pass. Across three continual-learning methods evaluated on MLLM-DCL and UCIT with LLaVA-1.5-7B, Monarch-MoE improves first-task retention while reducing adapter parameters by approximately 75% and 50%, respectively. In the main comparison, first-task forgetting is as low as 0.52 percentage points on MLLM-DCL and 0.10 on UCIT, with method-dependent trade-offs in final performance. Our implementation supports fine-tuning and inference on a single 24 GB RTX 4090, with lower measured memory use and competitive runtime in the evaluated settings. Together, these algorithmic and systems improvements make structured experts a practical option for continual adaptation on memory-limited hardware.

We classify all nonconstant smooth harmonic maps $\mathbb{S}^2\to \mathbb{CP}^n$ and $\mathbb{S}^3\to \mathbb{CP}^n$ whose 0-homogeneous extensions are minimizing: they are, respectively, isometric embeddings or holomorphic isometric embeddings composed with a Hopf map.

Let $\hbar$ be a non-zero real number and put $q= e^{-\pi i \hbar}$. Let $G$ be a semisimple split real Lie group of classical type, with Lie algebra $\mathfrak{g}$ and associated Borel subalgebra $\mathfrak{b} \subseteq \mathfrak{g}$. We show that there exists a locally compact quantum group $(L_{\hbar}(B),\Delta)$ which integrates the Borel part $U_q(\mathfrak{b})$ of the Drinfeld–Jimbo quantized enveloping algebra $U_q(\mathfrak{g})$, viewed as a Hopf $*$-algebra. We further compute the associated Haar weights and modular data for $(L_{\hbar}(B),\Delta)$. Up to an excess Cartan part, the Drinfeld double of $(L_{\hbar}(B),\Delta)$ can be seen as an analytic quantization of the function algebra of the totally positive semigroup $G^+\subseteq G$.

Actions specify what a robot should execute, but do not describe what those commands will achieve. Vision-language-action (VLA) policies nevertheless learn primarily by predicting action chunks from images, language, and state. We introduce Action–Future Coupled Effect Learning (AFCE), which makes a future-grounded physical Effect the policy's primary prediction target. An offline tokenizer constructs temporally ordered Effect tokens from demonstrated actions, realized robot responses, and sparse visual transitions. Reconstruction objectives encourage the representation to retain executable detail and observed physical change. A flow-matching VLA predicts Effects from current images, instruction, and robot state, while a state-conditioned decoder converts them into action chunks. Embodiment-specific interfaces allow single- and dual-arm tasks to share the Effect model. On DexJoCo, AFCE achieves $50.97\%$ overall success, improving over $\pi_{0.5}$ and UVT by 11.82 and 15.21 percentage points, respectively. It leads on all five bimanual tasks, highlighting the value of Effect supervision for coordinated dexterous manipulation. The project page is available at https://afceproject.github.io/AFCE-Web/.

Generative machine learning has shown remarkable results across a wide range of interdisciplinary tasks, motivating significant efforts toward Quantum Generative Models as a path to beyond-classical performance, given their capability of generating classically intractable distributions. However, comparatively little attention has been paid to securely delegating such computations to a powerful remote quantum server. In this work, we propose a blind and verifiable protocol for sampling that can be used for the inference phase of such quantum models. Such a protocol inherits blindness from Universal Blind Quantum Computing and achieves verifiability by exploiting known approaches based on trapification schemes. Alongside, to delegate the training phase, we discuss an extension of the previously proposed verifiable end-to-end Delegated Variational Quantum Algorithms (Inajetovic et al., Phys. Rev. Research, 2026). Beyond the usual Accept/Abort outcome characterizing verification protocols, the sampling protocol for inference also provides, even against a malicious server, an estimation of the amount of corrupted generated samples, i.e., a fine-grained feature describing the quality of the outcome connecting verification protocols and application-level benchmarking.

We construct an action of the positive half of the Witt algebra on colored $\mathfrak{gl}_N$-Khovanov-Rozansky homology and prove that this action is compatible with the functoriality of colored link homology. To establish this result, we use Bar-Natan's framework of canopolies to formulate and prove the relevant statements at the level of tangles.

We derive the noncommutative open WDVV equations for the open Gromov-Witten superpotential introduced in joint work of the author and Solomon, extending the Solomon-Tukachinsky equations to noncommutative differential graded algebras. The resulting recursive formulas facilitate the computation of open Gromov-Witten invariants with multiple boundary point constraints for even-dimensional Lagrangians. We apply the open WDVV equations to compute all open Gromov-Witten invariants for the real loci of even-dimensional complex quadrics of dimension greater than two. These computations show that open Gromov-Witten invariants with multiple boundary point constraints can be nontrivial in arbitrary dimensions. We also construct a character for a natural subalgebra of big quantum cohomology associated to a Lagrangian endowed with a point-like bounding cochain. The character is in the spirit of the Kodaira-Spencer map of Fukaya-Oh-Ohta-Ono. Applying the character construction to the even-dimensional quadric illustrates how point-like bounding cochains refine the information about closed quantum cohomology obtained from weak bounding cochains of Floer theory. Open Gromov-Witten invariants with three boundary point constraints determine the two extensions of the character from the subalgebra to big quantum cohomology.

Time-series foundation models use the same network depth for every input, although forecasting windows differ in structure and difficulty. We test whether whole Transformer blocks can be removed at inference time in two pretrained models: Chronos-Bolt and TimesFM 2.5. Our bypasses avoid the original block computation and preserve the dense model exactly when all blocks are enabled. Masks are selected only on calibration windows and evaluated on 1,088 held-out windows from ETTh1, Traffic, Weather, and Exchange. At moderate sparsity, Chronos-Bolt with 7/11 candidate blocks and TimesFM with 16/20 blocks show little change in mean relative forecasting quality across datasets while reducing median A100 batch-1 latency by 11.2% and 13.4%. More aggressive TimesFM skipping accelerates inference further but substantially harms Traffic and Weather. Across both models, different equal-budget masks win on different windows, and a retrospective oracle significantly improves over the best static mask on every dataset. However, dataset-specific masks transfer inconsistently, and Chronos representations do not support reliable unseen-domain routing. These results establish cross-architecture structured redundancy and input-dependent opportunity, but not a deployable dynamic inference method.

Fake news detection under low resource conditions is challenged by the scarcity of labeled data and the difficulty of capturing subtle deceptive patterns. In this work, we focus on low resource fake news detection, where only a small labeled set is available for training, while evaluation is performed under a fixed and unchanged test protocol. This setting is motivated by costly, ambiguous fact-checking and emerging topics and domains that are poorly covered by existing benchmarks. Existing data augmentation methods, such as synonym substitution, generative adversarial networks, and large language model (LLM)-based generation, often produce fluent but overly generic content, lacking the task-specific relevance needed for accurate detection. To address this, we propose SharP, a boundary-aware text generation framework guided by soft and hard prompts, which leverages LLMs as tools adapted to produce task-specific synthetic samples. SharP employs a dual prompt mechanism: hard prompts provide structured guidance and factual constraints, while soft prompts introduce learned semantic patterns from the data. These two types of prompts are combined to guide the generation process, enabling the model to produce samples that closely align with the characteristics of news. To further enhance detection performance, we incorporate a boundary-aware strategy that steers generation toward areas where the classifier is less confident, helping to clarify subtle distinctions between real and fake content. In addition, we adopt a dual objective optimization that balances semantic alignment with the source data and classifier feedback. This encourages the generation of samples that are both domain-consistent and helpful for refining decision boundaries, ultimately improving model robustness and generalization in low resource fake news detection.

We present what are, to our knowledge, the first 3D numerical-relativity evolutions of wormhole binaries: pairs of massive Ellis-Bronnikov drainholes held open by a ghost scalar field. Each throat is an unstable fixed point whose e-fold time matches the González-Guzmán-Sarbach linear rate to within 1.9%. Two throats obey a charge-sign rule: like scalar charges repel and opposite charges attract, with a measured attraction-to-repulsion ratio of $1.462\pm0.022$ against the predicted 3/2, so only opposite-signed pairs merge. A head-on collision forms a common MOTS around both still-open throats, born with about their combined area. The horizon then loses 28% of its area as it swallows the phantom field, and by $t=100$ lies within 1.4% of the Schwarzschild radius of the pair's mass, still shrinking. Fly-by pairs form no horizon and both mouths inflate, the one nearest capture radiating the most gravitational-wave energy measured. A lone collapsing throat sheds its seeded quadrupole as a burst ringing at the Schwarzschild frequency of the black hole it becomes, and every encounter radiates its own burst of gravitational waves and a scalar dipole of comparable energy and negative sign. A throat survives at most a few orbital periods for any plausible perturbation, and the negative-energy dipole would pump rather than drain the orbit, so these binaries have no inspiral.

On-policy distillation (OPD) trains a target policy on its own rollouts using token-level supervision from a stronger teacher, but typically relies on the teacher being substantially more capable than the target. Recent work relaxes this requirement by transferring the relative policy difference between an expert and a reference policy rather than the expert's absolute distribution. Yet it remains unclear which differences provide useful supervision and which targets can benefit from them. We develop a unified view in which the log-probability ratio between a proxy expert and a proxy reference defines an implicit reward for KL-regularized policy optimization. This formulation induces an on-policy update for the target, recovers conventional OPD as a special case, and enables any-to-any transfer across models that differ in scale, training stage or generation. Our systematic experiments yield three findings. First, a stronger expert is not necessarily a better source of supervision: differences induced by task-specific training, including reinforcement learning and supervised fine-tuning, transfer consistently, whereas those arising from model scale alone transfer weakly or not at all. Second, the expert and reference serve complementary roles: the expert provides the capability to be transferred, while the reference filters out shared behavior and isolates the relevant residual. Third, even a useful difference does not transfer to every target: success requires the induced update to move the target toward the expert and generalize beyond sampled rollouts. Raw policy distance does not predict transferability, whereas an appropriate reference can rescue otherwise unsuccessful transfer. These results characterize when relative policy differences provide effective supervision for OPD.

We prove that any subset $A \subseteq \{1, \dots, N\}$ lacking non-trivial polynomial progressions $(x, x + y, x + y^2)$ satisfies $\lvert A \rvert \le CN \exp\bigl(-c(\log \log N)^\beta\bigr)$ for effective absolute constants $C, c, \beta > 0$. The argument develops a density increment framework localized to anisotropic quadratic Bohr sets. To handle mixed linear and quadratic frequencies, we establish a multilinear transference principle coupled with a relative quadratic inverse theorem based on Balog–Szemerédi–Gowers additive energy rigidity. Boundary stability across increments is maintained via semi-algebraic model regularization using cylindrical algebraic decomposition and Cauchy–Crofton estimates, while dimension growth is controlled by dissociated basis reduction and multidimensional Erdős–Turán–Koksma equidistribution.

Heyer's left adjoint to derived parabolic induction gives rise to higher mod $p$ Satake transforms \[ \mathcal S_V^i: \mathcal H_G(V) \longrightarrow \mathcal H_M\bigl(H^i(K_U,V)\bigr), \] whose extreme degrees recover Herzig's invariant and coinvariant transforms. For $G=\mathbf G(F)$, where $\mathbf G$ is a connected reductive group defined over a finite extension $F/\mathbb{Q}_p$, we describe these maps explicitly using Mackey decompositions and corestriction in group cohomology. For $G=\mathrm{GL}_n(F)$, we evaluate them on the standard Hecke generators, showing that their support lies in a single Weyl orbit and that their values on the individual support cosets are concrete corestriction operators. For $G=\mathrm{GL}_2(F)$, we determine the image in every cohomological degree for each non-Steinberg Serre weight. The endpoint images are the classical polynomial Satake images, while every interior image is of the form \[ k[x,y^{\pm1}]/(x^r) \] for some positive integer $r$. Thus, every interior image is a finite nilpotent thickening of the Laurent polynomial algebra $k[y^{\pm1}]$. We give explicit bounds for its thickness, prove that they are sharp, and show that in the unramified case every interior image is either reduced or a square-zero thickening.