Papers

Image retargeting aims to resize images while preserving salient content free from distortion and stretching. Recent learning-based solutions reduce reliance on traditional hand-crafted features and optimization procedures, leading to more efficient and generalizable performance. Nevertheless, existing approaches still struggle to preserve global structure and content fidelity. To address these limitations, we propose AttenIR, an unsupervised image retargeting framework requiring no manual labels, based on content-aware mesh warping, which ef- fectively couples dense visual attention with sparse mesh constraints. We for- mulate the mesh deformation as a vertex displacement regression task. Guided by saliency priors, our method jointly optimizes scale, structure, and geometry preservation losses. By combining dense visual attention with semantic features, it achieves robust, unsupervised retargeting without manual annotations. Our primary contributions include (1) a lightweight unsupervised method for image retargeting that ensures content fidelity and preserves global structure, and (2) a coarse-to-fine projection strategy to align dense visual attention priors with sparse mesh constraints, enabling content-aware deformation at the pixel level. Experiments demonstrate that our method achieves competitive and superior performance compared with both traditional and state-of-the-art learning-based methods.

Dimensionality reduction can preserve the average performance of text embeddings even when a substantial fraction of their dimensions is removed. Aggregate metrics, however, do not reveal whether degradation is distributed uniformly across examples. We study per-example neighborhood stability under PCA truncation across static word embeddings and modern sentence encoders. Per-item neighbor retention varies widely and is predictable from geometric properties of the representation and its alignment with the retained PCA subspace. The fraction of centered-vector energy retained by the truncated subspace is strongest for CBOW and RI, with neighborhood contrast leading on SkipGram and the modern/Matryoshka settings (GTE approximately tied), while local density is associated with retention in marginal analysis but adds little unique information once energy and contrast are controlled (R-squared increments 0.001 to 0.010). Local intrinsic dimensionality accounts for more variation than density on modern sentence encoders in pairwise comparison. On SciFact, query density predicts retrieval degradation under aggressive compression; on NFCorpus the primary 32d association does not replicate, and a direct variance-restriction test leaves that null unresolved. Average compression performance conceals systematic per-example variation that geometry makes visible.

We present the first targeted Einstein Probe (EP) X-ray observations of any planetary nebula (PN). Using the onboard Follow-up X-ray Telescope (FXT), we detect X-ray emission within the central region of IC 1297. The spectral analysis yields a plasma temperature of $kT = 0.086^{+0.054}_{-0.058}$ keV ($T\sim1.0 \times 10^{6}$ K), characteristic of shocked wind bubbles in PNe, whereas there is no evidence that its Wolf-Rayet central star emits X-rays. The absorption-corrected X-ray luminosity in the 0.3–2.0 keV energy band is $L_{\mathrm{X}} = 2.8 \times 10^{32}$ erg s$^{-1}$, also consistent with a hot bubble. At an adopted distance of $\sim3.8$ kpc, IC 1297 is the most distant X-ray emitting PN found to date, opening up a new observational window on hot-bubble formation and evolution. It is also among the most luminous known X-ray-emitting PNe. Our results demonstrate the capability of the EP FXT for detecting and characterizing faint, extended X-ray sources in the soft X-ray band for distant PNe, extending the known spectral properties of detectable X-ray emitting PNe. We also compiled the X-ray properties of all 41 known Galactic XPNe, finding a clear correlation between distance and X-ray luminosity that reflects an observational bias toward detecting the brightest sources at large distances. The compilation also shows a separation in X-ray luminosity between hot bubbles powered by H-rich and [WR]-type central stars, with the latter reaching luminosities up to an order of magnitude higher. The ten most luminous XPNe all host [WR]/PG 1159 central stars.

Large language models (LLMs) are increasingly used to discover scientific equations from experimental data. Such a discovery system has two parts that must work together: a library of executable computational tools and the model's tool-use policy. The tools supply the solving capability, from diagnosing structure in the data to fitting candidate equations; the policy plans and orchestrates their use. Yet existing systems adapt only one part, keeping either the toolset or the model fixed, which leaves the corresponding failures uncorrectable. We develop a coupled evolution framework that improves both parts from the same verifiable fit-error signal. In the tool-evolution phase, an agent grows an executable tool library from a small set of generic numerical operations by diagnosing its own failures: it authors a new tool when a capability is missing and revises its selection rules when the right tool went unused. In the policy-evolution phase, a small open model (roughly 3B active parameters) is fine-tuned on successful tool-use trajectories collected with the frozen library, on training formulas screened to be disjoint from all evaluation benchmarks. Ablations show the two phases are complementary: with no tool library at all the same model solves almost nothing, the tools account for most of the gain, and trajectory training adds a further gain that is largest on the most difficult problems. The full system solves 79.1/71.3% of LSR-Synth problems at fit tolerances $10^{-2}$/$10^{-3}$, reaches 63.8% pooled accuracy on the distributionally different SRSD-Feynman panel, and obtains a normalized CP3-28 aggregate of $-7.27$. These results suggest a broader recipe for scientific agents: let the model and its instruments improve each other under verifiable feedback.

Estimating potential outcomes under alternative treatment sequences is essential for personalized decision-making, but remains challenging with high-dimensional covariates and time-varying confounding. In this study, we propose HiSTOR (High-dimensional Structured Treatment-Outcome Representation), an end-to-end framework that integrates nonlinear dimension reduction with longitudinal counterfactual prediction. The central idea is to learn structured low-dimensional representations of both current patient states and evolving histories, according to their shared and distinct relationships with treatment assignment and outcomes. This extends latent-space covariate adjustment to longitudinal settings, jointly addressing covariate dimensionality and historical complexity. The resulting framework supports one-step and multi-step outcome prediction under specified treatment sequences. Experiments on CVSim and CancerSim demonstrate the superiority of HiSTOR across varying covariate dimensions, confounding strengths, and prediction horizons compared to state-of-the-art methods. To sum up, HiSTOR offers a unified approach to connecting high-dimensional covariate adjustment with longitudinal potential-outcome prediction.

End-to-end (E2E) full-duplex spoken language models (FD-SLMs) enable simutanous listening and speaking continously, requiring models to take appropriate interaction actions as conversations unfold. However, existing benchmarks lack a structured action-level formulation, often evaluate action occurrence rather than success, and provide limited coverage of diverse real-world conversations. We introduce DuplexAct, a benchmark for evaluating interaction action taking in E2E FD-SLMs. DuplexAct defines a three-level action taxonomy spanning eight interaction actions and 24 corresponding interaction conditions. We further characterize successful action-taking through immediate execution and subsequent follow-through, and develop action-specific evaluation metrics for both. DuplexAct contains 4,691 test instances spanning casual conversation, meetings, customer service, and interviews, including 2,531 instances derived from real-world conversational recordings. Together, DuplexAct provides a structured and real-world-grounded framework for systematically assessing how E2E FD-SLMs participate in ongoing spoken interaction.

Let $\mathfrak p$ be the $(-1)$-eigenspace of a complex semisimple symmetric pair. For every $r\ge2$, we prove $\dim C_r(\mathcal N(\mathfrak p))\le \lfloor r\dim\mathfrak p/2\rfloor$ and show that every irreducible component is isotropic for a natural family of alternating forms. For a nonzero Hermitian pair with $\mathfrak g$ simple and $\mathfrak p=\mathfrak p^-\oplus\mathfrak p^+$, put $d=\dim\mathfrak p^+$ and $\ell=\operatorname{rk}(\mathfrak g,\mathfrak k)$. Then \[ \dim C_r(\mathcal N(\mathfrak p))=rd,\qquad \dim C_r(\mathfrak p)=\max\{rd,\,2d+(r-1)\ell\}. \] In this case we also determine the maximal-dimensional components of $C_r(\mathfrak p)$; for $r\ge3$, the only maximal-dimensional nilpotent components are $(\mathfrak p^+)^r$ and $(\mathfrak p^-)^r$. For arbitrary symmetric pairs, $\dim C_r(\mathcal N(\mathfrak p))=ra+m$ for all large $r$, where $a$ is the largest dimension of an abelian subspace of $\mathfrak p$ consisting of nilpotent elements and $m$ is the dimension of the variety of such subspaces. Applications give dimension and component formulas for equivariant punctual Quot schemes under explicit framing conditions, and bounds for punctual Gorenstein loci refined by socle parity.

We investigate whether Rényi divergence can sharpen McDiarmid's inequality and its distribution-dependent refinement induced by KL divergence. Starting from Marton's transportation proof, we show that its transport inequality fails in general when KL divergence is replaced by Rényi divergence of order $0<\alpha<1$. For sums of independent bounded random variables, however, the additivity of Rényi divergence allows us to adapt the argument and derive concentration bounds. For Bernoulli sums, these bounds strictly improve on the distribution-dependent bound induced by KL divergence over a range of deviation thresholds. We also establish a distribution-dependent refinement of Gilardoni's inequality relating total variation to Rényi divergence, providing explicit constants for our general concentration bounds.

Multi-sample reasoning measures candidate coverage, the probability that at least one of $K$ candidates is correct. However, minimizing the average loss of individual attempts does not directly optimize candidate coverage. We therefore formulate finite-$K$ posterior learning, which trains a distribution over solver parameters to reduce the probability that all $K$ independently generated candidates fail. To optimize this objective efficiently, we propose a Fenchel-Bregman (FB) approach that requires only one posterior draw per update, rather than the $K$ used by direct Monte Carlo optimization. FB first uses an exact Fenchel reformulation to separate problem-specific weights from the posterior update, enabling one-draw posterior updates. It then applies a closed-form Bregman update to track these weights through an exponential running average of observed failures, reusing the same draw. We instantiate FB with IVON, a variational optimizer for Gaussian posteriors over solver parameters, yielding Fenchel-Bregman IVON (FBI). Across diverse recursive and autoregressive reasoning tasks, FBI improves candidate coverage. In a matched comparison, it achieves comparable Pass@10 using 12.3% of the direct Monte Carlo baseline's measured training time per update.

Exploration bounds learning efficiency in reinforcement learning with verifiable rewards (RLVR). Current methods explore mostly through independent sampling, without fully using the information gathered along the way, such as known wrong answers and environment feedback. We propose LEAF, which injects a dynamic, problem-specific memory into the context before every rollout. The memory contains the most recent response, its reward, and other environment feedback. It is updated after every verifier call. We decouple policy updates from rollouts and update the policy through self-distillation. On four benchmarks and two open models, LEAF accelerates exploration by about 4x compared with a random sampling baseline. On unseen test sets, it improves accuracy over the strongest baseline by 1.59 and 1.83 percentage points on the two models, while using less compute than any RL baseline. These results highlight the potential of LEAF in improving both exploration and learning efficiency. Code is available at: https://github.com/on1262/LEAF

Rubric-based reinforcement learning (RL) evaluates responses against explicit criteria to construct rewards, offering a viable way to train large language models on open-ended tasks. However, standard methods compress criterion-level feedback into scalar rewards and assign uniform token advantages, leaving structured rubric supervision underutilized. Recent work seeks finer-grained guidance by treating rubrics as privileged information to derive self-distillation targets, but the resulting learning signal is not grounded in criterion outcomes and can lead to reward degradation. This motivates us to reframe the problem as criterion-aware credit assignment, where privileged rubric information serves as a relevance cue for credit allocation rather than a source of imitation targets. Accordingly, we propose CoCA, which derives criterion-level credits from group-relative outcomes and allocates them across tokens based on criterion-induced distribution shifts, yielding both outcome-grounded and fine-grained learning signals. Empirically, CoCA achieves an average gain of +4.2% over standard rubric-based RL across medicine and science benchmarks, demonstrating more effective learning on open-ended tasks.

We propose a structured continuous-time stochastic volatility model for one-day-ahead integrated-variance forecasting. The model introduces a jointly evolving realized-measure state that feeds directly into latent variance dynamics, while correlated Brownian innovations capture return-linked dependence. Parameters are estimated through simulation-based predictive learning, and Monte Carlo simulation forecasts integrated variance. Across 17 equity indices, the proposed model shows strong out-of-sample performance relative to GARCH, GARCH-Itô, Realized GARCH, HAR, and HEAVY benchmarks under QLIKE, MSE, and MAE. Ablation results show that realized-measure feedback provides substantial incremental forecasting value within the proposed framework, while return-linked Brownian dependence contributes more modest complementary gains. The results support incorporating measurement-driven information directly into continuous-time latent volatility dynamics to improve integrated-variance forecasting.

As foundation models enter creative industries, understanding their aesthetic preferences becomes an important step toward AI-assisted creative decision making. In this work, we investigate how foundation models evaluate creative content and characterize their “machine taste” using K-pop songs and music videos as a testbed. We formulate aesthetic evaluation as a pairwise ranking problem and systematically examine pairwise inter-model agreement, group-level consensus, and cross-modal preference alignment. Our results reveal stronger pairwise inter-model agreement and group-level consensus in visual evaluation than in audio evaluation, while preferences across the two modalities remain weakly aligned. We further examine how visual consensus rankings relate to real-world popularity using historical YouTube viewership data, finding positive but varying correlations across artist groups. These findings provide initial insights into machine aesthetic preferences and lay the groundwork for future AI-assisted creative decision making that considers creative content, artist identity, audience preferences, and market dynamics.

Low-rank adaptation (LoRA) often underperforms full fine-tuning. We investigate this performance gap through a tangent-space lens: factorized updates are confined to the tangent space of the current low-rank factors, leaving gradient components outside this space unexploited. An analysis of ten representative LoRA variants reveals that these residual components account for most of the gradient energy and exhibit strong spectral concentration. Motivated by this finding, we propose Dynamic Tangent LoRA (DT-LoRA), which partitions a fixed rank budget into a stable branch and a dynamic branch to capture the principal residual gradient directions. We show that these directions define the optimal update of a local quadratic model under orthogonal-complement and rank constraints. Matrix-free randomized SVD recovers them without materializing the residual gradient, while controlled write-back preserves accumulated updates and stabilizes training within the allocated rank. DT-LoRA adds no trainable parameters or inference cost over LoRA. Experiments across computer vision and natural language processing tasks demonstrate consistent improvements over LoRA and its variants. Moreover, despite being a general-purpose adaptation method, DT-LoRA outperforms task-specific approaches to open-vocabulary domain generalization for semantic segmentation, achieving state-of-the-art results. Code is available at https://github.com/Snipine/DT-LoRA.

The pentablock is a domain in $\mathbb C^3$ arising in the study of the $\mu$-synthesis problem and is defined by \[ \mathcal P = \left\{ (a_{21},\operatorname{tr}(A),\det(A)): A=[a_{ij}]_{i,j=1}^2\in M_2(\mathbb C),\ \|A\|<1 \right\}. \] We introduce the Hardy space $H^2(\mathcal P)$ associated with the canonical measure $\mu$ on the distinguished boundary $b\mathcal P$. We identify $H^2(\mathcal P)$ with a closed subspace of $L^2(b\mathcal P,\mu)$ and show that it is a reproducing kernel Hilbert space. We establish a new description of $\mathcal P$ and its closure and obtain a uniqueness set. In particular, we prove that $\mathcal P$ is the interior of the polynomial convex hull of $\Psi(\overline{\mathbb D}^3)$, where \[ \Psi(\xi,\lambda_1,\lambda_2) = \left( \frac{\xi(\lambda_1-\lambda_2)}{2}, \lambda_1+\lambda_2, \lambda_1\lambda_2 \right) \] is the parametrization map for $\mathcal P$. We also show that $H^2(\mathcal P)$ embeds isometrically as a closed subspace of $H^2(\mathbb D^3)$. We then obtain a Brown-Halmos type characterization of Toeplitz operators on $H^2(\mathcal P)$ and a commutant lifting theorem for $\mathcal P$-isometries and their minimal $\mathcal P$-unitary extensions. As consequences, we determine the commutant of the coordinate multipliers, characterize the compact Toeplitz operators and show that the coordinate multipliers have no nontrivial joint reducing subspaces. Finally, we characterize $\mathcal P$-unitaries as images of commuting triples of unitaries under $\Psi$ and present a class of $\mathcal P$-contractions from triples having $\overline{\mathbb D}^3$ as a spectral set.

Egocentric multimodal assistants see through the user's eyes and guide what the user does next, so their outputs directly shape physical actions, including those that affect bystanders. Yet existing safety evaluations do not distinguish whom a response would harm, and score only whether a model refuses. Pooling all harms into one refusal rate hides two failures: a model may protect one target but not another, and it may refuse without understanding the risk, or understand it and comply anyway. We present STOU, a benchmark of 2,902 egocentric video-audio and video-text queries whose potential harm targets the user (Self), co-present individuals (The Others), or society at large (Others). Our evaluation decouples safety understanding from refusal behavior: beyond refusal, we score whether the model recognizes the user's intent, the presence and target of harm, and its downstream consequences. Across 10 open and closed source omnimodal and multimodal LLMs, we find that refusal varies systematically with the harm target, and that models often recognize a harm yet still assist with it. These results show that refusal rates alone cannot certify an assistant as safe, and that safety alignment must account for who would be harmed. Project page: https://onedayoneyeah.github.io/safety-for-whom

Agent skills turn natural-language instructions into actions, creating a security challenge: legitimate automation and malicious behaviour can look deceptively similar. A practical screen must catch nearly every attack while keeping the review load manageable. We present SkillScreen, a compact decision model trained to score skill maliciousness directly from SKILL$.$md in a single forward pass. On MaliciousSkillBench, SkillScreen flags 20-25% of benign skills at 99% recall on unseen attack families, substantially fewer than the word-level classifier and prompted LLM judges tested. Under the same training protocol, it also generalizes better than a fully fine-tuned encoder to unseen sources. Yet unfamiliar benign sources sharply increase false positives, showing that recognizing new attacks does not ensure reliable screening of new skill collections. Our results demonstrate the value of task-trained decision models for high-recall skill screening. Project page: https://jerroldh.github.io/SkillScreen-webpage/

Large language model (LLM) agents excel at complex, multi-step tasks but suffer from catastrophic forgetting during continual learning–acquiring new skills often degrades previously mastered capabilities. Existing post-training paradigms face a fundamental trade-off: Supervised Fine-Tuning (SFT) is sample-efficient but prone to severe forgetting, while Reinforcement Learning (RL) preserves prior capabilities but converges slowly without expert guidance. To bridge this gap, we introduce Trigger-based Supervised Reinforcement Learning (TSRL), a framework that integrates the strengths of both paradigms through an adaptive, state-dependent expert supervision mechanism. TSRL employs RL as the optimization backbone, activating SFT selectively on "hard states" where the policy fails. Theoretically, we show that restricting supervision to failure states derives an upper bound on the cumulative parameter updates, thereby reducing forgetting compared to full SFT. Empirically, TSRL achieves consistent gains across three agent benchmarks (ALFWorld, WebShop, and Deep Search) at both 7B and 32B scales. In continual learning scenarios, our method retains up to 9.6 points more capability on prior tasks than SFT->RL baselines, while matching or exceeding target-task performance.

Transformer-based network intrusion detection systems (NIDS) have shown strong potential for detecting multi-stage cyberattacks, yet most methods construct input sequences using fixed temporalization schemes rather than treating sequence construction as a systems design decision. In flow-based intrusion detection, timestamp-based windowing often fragments related attack activities while merging unrelated communications, reducing the behavioral context available to transformers. We present a unified pipeline abstraction that decomposes transformer-based NIDS into four design dimensions (traffic representation, temporalization, transformer backbone, and prediction aggregation) and propose session-coherent temporalization, which constructs sequences from communication sessions instead of fixed time windows. Experiments on three complementary intrusion detection datasets show that temporalization is the dominant factor governing transformer performance: session-coherent temporalization more than doubles Macro-F1 over timestamp-based windowing, enabling lightweight transformers to achieve up to 0.95 Macro-F1 at substantially higher inference throughput than pretrained models. We further vary the transformer size from 0.65M to 3.38M parameters and find that larger transformer models provide no measurable accuracy improvement despite substantially higher computational cost, while zero-shot cross-dataset evaluation shows only modest gains under domain shift. These results indicate that preserving communication-session semantics, rather than scaling transformer capacity, is the key to accurate and efficient transformer-based intrusion detection.

Long-horizon, semi-verifiable agentic tasks often rely on rubric-based evaluation, but the evidence needed to assess these tasks can be spread across the environment state and the execution trace. A judge may overlook this evidence or accept unsupported claims, including an agent's own reports of success. When rubric verdicts serve as reinforcement-learning rewards, such errors can reinforce undesirable behavior. We introduce Sauron, an evidence-first agentic verifier that investigates both state and trace and relies on a claim only after independently validating it against its source. Bounded queries and joint investigation of related criteria reduce context use and redundant work, and each verdict carries an auditable receipt of its supporting evidence. Across 2,586 human-labeled criteria from 100 personal-assistant episodes, Sauron achieves the highest F1 of five verifiers on all eight backbones tested while costing less than Gandalf, the strongest baseline. With GPT-5.6 Sol, it reaches 0.96 F1 versus Gandalf's 0.92 at 23% lower cost, with a wider margin on process criteria. On a paired fault-injection suite covering 13 families, several of which simulate reward hacking, Sauron detects 97% of injected failures while flagging only 2% of clean controls, outperforming baselines even when they are given the full trace. On TRAIL, a benchmark for detecting and localizing real agent errors, Sauron leads both Gandalf and TRAIL's own judge on all three quality metrics.

People act on evaluative judgments produced by LLM agents, and in multi-agent systems those judgments pass through several agents before reaching a person. We show that a workflow's information architecture—source access, handoff format, and which model reads the untrusted content—governs how much of a coordinated manipulation reaches the end. On 32 Taiwan~2025 recall cases, ten authentic Threads comments shown to one agent move its stance by $+0.171$ toward the injected position, and a mirrored set moves it the other way. Passing that judgment down a chain removes more than half of the shift by the third agent; keeping the comments in front of every agent sustains more of it. The reduction is not attrition in transit: each receiver discounts the inherited stance in proportion to how far it sits from its own reading of the evidence, returning to what that evidence implies for the case rather than to neutrality—consistent with partial re-anchoring. Handoff format is a second lever: a stance relayed without its reasoning is largely discounted. Susceptibility at the exposed seat varies fourfold across models, while the chain's arrangement does not matter at all. None of this is visible in the transcripts—the injected claims are almost never restated, so reasoning-trace audits miss the attack.

Quantum Machine Learning (QML) has a theoretical advantage over classical algorithms for specific synthetic data that is computationally hard. However, it remains unclear whether such theoretical advantages play a meaningful role for realistic classical data, such as natural images. Quantum structural properties induced by unitary operations or entanglement introduce inductive biases that differ from those of classical models, potentially leading to distinct learning behavior on real-world data. In a fully quantum learning pipeline, classical real-world data are first encoded into quantum states via a quantum feature mapping, analogous to a classical feature extractor, and a quantum classifier then classifies the resulting states. Quantum feature mappings generate representations that are difficult to realize classically, while also inducing representation-level biases that do not necessarily match the structure of realistic data. To enable a fair comparison at the classifier level, we focus on the classifier and use classical feature extractors that already provide powerful representations for natural images. By controlling the data scale and supervision strength, we analyze how the unitary structure of quantum classifiers affects generalization, and show that their effectiveness depends strongly on the geometry of the input representations. These results indicate that quantum classifiers benefit from classical features that are aligned with quantum feature spaces. Our analysis shows that kernel alignment identifies representations compatible with quantum feature spaces, providing insights into translating classical models into quantum algorithms.

Chiral perturbation theory is a power tool for studying the low-energy strong interactions. In the conventional chiral expansion, according to the power counting rule, the higher-order corrections for physical observables are expected to decrease order by order as the chiral dimension increases. However, most previous study of $\pi K$ scattering lengths by different references showed that the $\mathcal{O}(p^6)$ correction to the scattering lengths is anomalously large and even exceeds the $\mathcal{O}(p^4)$ one. It poses a serious challenge to the convergence of chiral expansion. In order to explore the underlying origin of this phenomenon, the contributions of two-loop diagrams, one-loop diagrams and tree diagrams for the $\pi K$ scattering amplitude are detailed analyzed. The reducible two-loop integrals, sunset integrals and vertex integrals from the $\mathcal{O}(p^6)$ order all violate the power counting rule. The sunset and vertex integrals can be largely canceled numerically, but not enough. Furthermore, $\pi K$ scattering is compared with $\pi\pi$ scattering, which seems not violate the power counting rule. The analysis indicates that $\pi\pi$ scattering contains a higher symmetry, although each $\mathcal{O}(p^6)$-order part also violates the power counting rule, but the violation is much smaller than the one from $\pi K$ scattering. Large kaon mass also makes a contribution to the power-counting breaking, but it is not a major origin. Hence, it needs to pay more attention to the many-loop low-symmetry diagrams in future work. These diagrams may give large contribution and cannot be ignored.

We derive a recurrence for logarithmically weighted Möbius sums by combining Möbius inversion with the Euler–Maclaurin summation formula. Consequently, starting from estimates of orders zero, one and two, we obtain polynomial approximations for these sums for every nonnegative integer exponent of $\log$. We then extend these estimates to sums with coprimality conditions via a convolution identity and to sums weighted by the reciprocal of the sum-of-divisors function. We also establish the nonnegativity of the latter sums for every positive integer logarithmic order, proving that they never change sign.

Agents build knowledge graphs as memory, and building them has become easy. Maintaining them has not. When a source is retracted, overruled, or erased, everything built on top of it (entity merges, entailed edges, community summaries) must be re-examined, and the maintainer must choose between deleting too much and too little. Deployed pipelines delete only the directly extracted facts: on our corpus that reduces contaminated queries from 32.2% to 28.0% under a real retraction and changes nothing under predicate revocation. Rebuilding is no repair for a constructor that samples: two builds of the same 300-document corpus differ in 29,475 artifacts, five times the 6,248 that removing the 61 retracted documents changes. PolyGraph instead asks the constructor for receipts: for every artifact, alternative bundles of source evidence, each claimed sufficient on its own, emitted in the call that creates it. Cleanup is then set arithmetic over the receipts, with no model calls. Because receipts are the model's own self-report, a re-derivation audit checks them by deleting the cited evidence and testing whether the constructor still produces the artifact. The audit finds that a receipt is trustworthy when it is shaped like the claim it backs. Merge receipts, each backing one narrow claim, agree with re-derivation 68% and 85% of the time. Summary receipts, elicited per sentence but stored as one flat list for the whole text, are wrong about two thirds of the time, almost always by keeping dead content. One receipt per sentence instead is 100% and 88% faithful and lets cleanup keep 33 of 35 touched summaries. The result holds under a second oracle model, a claim-blind prompt, ten further deletions, a second domain and a second constructor. Distrusting the summary layer cuts contaminated queries to 0.4% and 0.8% at 99.8 to 100% of the recall a perfect maintainer would return.

Electrocardiogram (ECG) models need supervision that targets evolving weaknesses and remains faithful to waveform evidence. We introduce ECG-RSI, a recursive self-improvement framework combining verified waveform synthesis with feedback-guided intervention search. Signal remeasurement verifies waveform edits; construction errors guide generator repair, while learner errors motivate interventions compared on a separate selection set. Across seven benchmarks, three rounds raise Qwen3.5-35B-A3B's mean question-answering accuracy from 34.57% to 56.04% and mean classification F1 from 24.27 to 34.03. Across the retained trajectory, the preferred supervision shifts from direct reinforcement to confusion-focused contrasts. Continued feedback correction yields diminishing external gains. These results motivate separating error diagnosis from intervention selection and checking whether gains on the feedback set transfer to independent benchmarks.

We prove that the simulated annealing algorithm efficiently samples from the Sherrington-Kirkpatrick model at inverse temperature $\beta < 1$ to an arbitrary inverse polynomial accuracy in total variation.

Electrolaryngeal (EL) speech suffers from severe acoustic mismatches with normal speech, resulting in degraded naturalness and intelligibility. These mismatches also make sequence-to-sequence voice conversion struggle to learn robust intermediate representations, hindering EL-speech-to-normal-speech conversion (EL2SP) performance. To address this, we propose a novel multimodal contrastive representation learning framework to 1) achieve richer multimodal-representation learning, and 2) facilitate the transferability of multimodal representations to speech-only EL2SP. First, EL speech and text representations are fused to learn multimodal representations for target speech generation, during which cross-modal contrastive learning is employed to encourage a semantically consistent speech–text representation space. Next, the fused representations are treated as a fixed target to guide speech-only representation learning through cross-stage contrastive learning, enabling multimodal knowledge to be transferred to the EL2SP task while preserving architectural and inference simplicity. Experimental results demonstrate that the proposed method consistently outperforms both the speech-only and multimodal-based baselines.

Flow matching has emerged as a powerful alternative to diffusion models for generative modeling, but standard conditional flow matching is fundamentally misaligned with partially observed time series: starting from an uninformed Gaussian source forces the model to transport even already-observed entries from noise to the target, wasting capacity on trivially known regions. We propose MissPath-FM, a partial-observation-aware flow matching framework that redesigns the source prior and probability path for incomplete time series. MissPath-FM employs structured source priors (interpolation priors and Gaussian process posterior priors) to initialize the flow close to the observed signal, paired with a missingness-aware smooth path that allocates transport asymmetrically between observed and missing regions. We evaluate systematically across four datasets, four missingness mechanisms (MCAR, block, MNAR, irregular), two missing ratios, and three sequence lengths (T in {24, 48, 96}), totaling 48 settings against eight baselines. MissPath-FM wins 29 of 32 settings at T=48 and 45 of 48 overall (93.8%). Our ablations reveal a regime-dependent design hierarchy in which no single component suffices: under random missingness the source prior yields a large initial gain, but under structured block missingness it can fail entirely and the learned flow becomes indispensable; the missingness-aware path contributes a further 12%-26% across all regimes. Mechanistically, structured priors shorten observed-region transport by up to 15x, concentrating the velocity field on genuinely uncertain entries. Project page: https://zgp110.github.io/misspath-fm/

Clouds and disequilibrium chemistry shape the observable properties of substellar and planetary atmospheres, and JWST time-resolved spectroscopy now enables direct tests of their three-dimensional structures. We present an update to the 3D atmospheric framework ADAM, coupling the dynamical core to a miniature kinetic chemistry scheme (mini-chem) and a saturation-relaxation tracer cloud module. Using this framework, we investigate the atmosphere of the brown dwarf orbiting the white dwarf ZTFJ0038+2030 in a 10-hour orbit. The brown dwarf receives stellar irradiation comparable to its internal heat flux, placing the atmosphere in a regime where the circulation is characterized by a standing Matsuno–Gill wave response and equatorial superrotation. Rapid rotation confines these structures closer to the equator, producing more symmetric broadband light curves with smaller hotspot offsets than canonical hot Jupiters, in agreement with recent JWST observations of this system. Although most species are globally homogenized, rapid rotation limits global-scale horizontal mixing and allows circulation-driven vertical transport to maintain strong CO and CO$_2$ inhomogeneities in the photosphere. These chemical inhomogeneities produce asymmetric phase curves in the CO and CO$_2$ absorption bands, which could qualitatively explain the observed CO$_2$ light-curve asymmetry. When clouds are included, Na$_2$S clouds dominate the photosphere and weaken the large-scale circulation, lowering photospheric CO and CO$_2$ abundances, while MgSiO$_3$ and Fe clouds rain out at deeper levels. Because the dominant Na$_2$S clouds reside mostly above the quench region, cloud-driven convection has limited impact on the quenched abundances, which are instead regulated mainly by large-scale circulation.