Papers

Large language models (LLMs) demonstrate strong individual task performance, yet still struggle to collaborate with users over extended, multi-turn interactions, for example by attempting solutions before understanding the user's needs or by failing to revise mistaken assumptions after receiving feedback. We propose Collaborative Theory of Mind (CToM), a framework that addresses these challenges by explicitly training LLMs to anticipate user responses and to use those predictions to improve their own behavior. CToM drafts a response, predicts how the user will respond, and uses this prediction to guide internal revision before presenting a response. During training, the user's reply to each draft serves as the target for predicting the next turn, and we train the assistant to minimize the negative log-likelihood of that reply. We combine this prediction objective with group-relative policy optimization (GRPO) to optimize both task performance and interaction efficiency. Across mathematical reasoning, coding, and writing tasks, CToM achieves higher collaborative task performance than all baselines; for example, on a collaborative mathematical reasoning task, it improves final accuracy from 74.1% to 79.6% compared with naive GRPO. Ablations show that predicting user responses also makes collaboration more efficient: under the same reward, adding prediction supervision reduces the number of user replies by 8% on coding and 17% on writing while improving task performance. Behavioral analyses of interaction trajectories show that user-response predictions become more accurate after training, and that more accurate predictions are associated with larger improvements in collaborative task performance through self-revision.

When a query must be matched against a database built with a different sensor or processed by a different encoder, the independently trained encoders impose distinct coordinate systems on the feature space. No canonical reference frame exists to which all encoders can be aligned, and no single training procedure has fully closed this gap. We show that the relative transformation between any two such systems is a spatially preserving rotation in whitened feature space, whose angular velocity exhibits white-noise characteristics: large in norm, temporally uncorrelated, and unpredictable from the features themselves. However, the cross-covariance between encoder outputs has low effective rank, constraining only a small fraction of the rotation parameters, therefore local alignment is tractable. ROSETTA is a training-free calibration layer that estimates the local rotation via an expectation-maximization procedure, requiring no coobservation at query time. We validate ROSETTA on three public driving datasets spanning LiDAR, camera, thermal, and event modalities in cross-modal, cross-device, cross-representation, and cross-backbone settings, with milliseconds overhead per query.

Practical ship design requires localized refinement and performance evaluation. This paper presents a reward-directed diffusion framework for localized hull optimization. Parametric masking during dataset generation restricts geometric changes to selected variables, including the bulbous bow and forebody, while preserving full-hull continuity. Surrogate-assisted sequential Monte Carlo sampling targets reduced predicted calm-water resistance, with stability retained through training data and displacement matched during screening. An automated viscous free-surface CFD pipeline, validated against measurements for two benchmark container ships, evaluates a generated variant and GenHull E, a hull refined by a naval architect within the same representation. At matched KRISO Container Ship (KCS) displacement, the generated variant has comparable total resistance at $F_n=0.195$ but 45-50% higher resistance at $F_n=0.250$ and $0.260$, missed by empirical screening. GenHull E achieves 6-8% lower total resistance up to $F_n=0.240$ but higher resistance above $F_n=0.250$ as opposing friction and pressure trends reverse the gains. Aggregating resistance across this crossover can conceal tradeoffs that emerge when friction and pressure components are evaluated separately. The assessment reveals an inability to represent a faired bulbous bow and a reward lacking viscous pressure and stability terms. These findings show how high-fidelity assessment informs improved representations and objectives for physically realizable generative designs.

Let $\lambda$ be the Liouville function. In this paper we prove an average form of Chowla Conjecture for even $k $. that is, for every fixed even integer $k\geq 2$, we prove that \[ \lim_{\min\{M,N\}\to \infty}\frac{1}{MN}\sum_{m=1}^M\sum_{n=1}^N\lambda(m)\lambda(m+a_1n)\cdots\lambda(m+a_kn)=0. \] We construct a stationary model for both averaging variables, derive the finite conditional-entropy estimates. A comparison of overlapping intervals on the logarithmic axis then forces this function to vanish.

The global fruit and vegetable industry confronts severe post-harvest sorting challenges for small and medium-scale growers. Large intelligent sorting systems are too costly, while manual sorting suffers from low efficiency, inconsistent standards, and high labor demand. To bridge this gap between expensive equipment and inefficient manual work, this study develops a low-cost, high-efficiency, lightweight fruit sorting system driven by deep learning, suitable for small and medium growers. We propose the Selective Spatio-Temporal Fruit Inspector (S$^2$FI) architecture, which combines a 3D convolutional encoder with a Mamba-based backbone.It efficiently extracts spatiotemporal features, adaptively weighs informative frames during fruit rotation, and models long-range dependencies with linear complexity, reducing motion blur and occlusion. The hardware uses a dual-conveyor and curved rail design, supporting household power, fast deployment, and lightweight embedded deployment to improve affordability. We also built a conveyor-based fruit quality video dataset with 6,460 samples. Experiments on the held-out test set show that our method achieves the best trade-off among accuracy, efficiency, and practicality, outperforming the compared baselines on the test set, achieving an excellent balance of accuracy, speed, and practicality for real-world sorting.

Electro-optic (EO) frequency combs convert microwave signals to the optical domain with deterministic repetition rates, enabling applications in optical telecommunications, microwave photonics, and LiDAR. However, generating flat EO combs has remained a long-standing challenge due to exponential decay of the spectral envelope inherent to bidirectional frequency coupling within conventional schemes. Here we reveal the inherent correspondence between flat-comb generation and the topological energy bands of non-Hermitian nonreciprocal frequency lattices, and experimentally realize ultra-flat combs with topologically controlled spectral flow. We derive the exact analytical condition for flat-comb generation, and find that it maps precisely onto the complex energy band, thereby establishing a direct connection between comb-envelope engineering and non-Hermitian topology. Experimentally, we observe an ultra-flat comb whose frequency evolution direction is governed by the topological winding and remains robust against detuning and phase fluctuations. This scheme can be further extended to long-range coupling and multi-lattice architectures, underscoring its versatility for flat dual- and multi-comb generation. Our work establishes a topologically steerable approach for achieving ultra-flat EO combs, paving the way for chip-scale spectral engineering via non-Hermitian topology.

Modern reasoning CAPTCHAs require fine-grained perception, compositional relation reasoning, and grounded browser interaction. End-to-end vision-language model agents remain brittle in this setting because a missed object, incorrect count, or confused relation can propagate directly to the final action. To address this problem, we present CaptchaAgent, a structured visual reasoning framework for interactive CAPTCHA solving. Instead of predicting an action directly from a screenshot, CaptchaAgent first constructs a visual intermediate representation (V-IR) that explicitly records entities, attributes, and spatial or topological relations. A symbol-only ASCII protocol further requires the parser to commit to a concrete object set and count. Building on this global representation, localized evidence refinement revisits ambiguous regions at higher effective resolution, while counterfactual consistency verification tests whether the resulting action remains stable under task-preserving transformations. Across three proprietary backbones on Open CaptchaWorld, CaptchaAgent improves Pass@1 by 21.3-25.8 percentage points over a commercially available browser agent baseline evaluated with the same backbones. On the separate offline Oedipus-data benchmark, it further improves average Pass@1 by 9.2-12.3 percentage points over the Oedipus solver across three matched backbones. The intermediate traces show that exact counting, continuous geometry, and ordered execution remain major sources of automation difficulty for the evaluated agents, providing practical guidance for designing more resilient compositional CAPTCHAs.

Existing convergence guarantees for non-log-concave sampling with stochastic gradient Langevin Monte Carlo (SG-LMC) typically assume globally Lipschitz gradients and uniformly bounded noise variance. Both assumptions can fail even in elementary sampling problems, and relaxing them better reflects practical applications such as Bayesian fine-tuning of large language models (LLMs). We relax both assumptions through generalized smoothness and our proposed state-dependent heavy-tailed oracle with finite $p$-th moments, $1<p\leq 2$. The oracle permits infinite variance when $p<2$ and includes the Blum-Gladyshev (BG-0) condition. We study these relaxations separately and jointly, proposing three methods. Under globally Lipschitz gradients, robust LMC (R-LMC) handles the proposed oracle through geometric-median centering and residual clipping. With exact gradients, adaptive LMC (A-LMC) controls discretization error under generalized smoothness. Robust adaptive LMC (RA-LMC) addresses both relaxations through robust estimation and a noise-aware step size. For all three methods, we establish non-asymptotic convergence guarantees in Fisher information (FI) without assuming dissipativity or a functional inequality. Synthetic experiments demonstrate FI convergence and the benefit of each mechanism. Bayesian fine-tuning experiments with LLMs and vision-language models support our oracle model and show that RA-LMC matches or outperforms state-of-the-art baselines in accuracy and uncertainty quantification.

Existing sequence models share a critical limitation: they lack an explicit, interpretable mechanism for content-aware temporal recall. LSTMs compress everything into a single hidden state, thereby losing information about specific past events. Transformers attend to all tokens indiscriminately at quadratic cost, while state-space models like Mamba compress history into a fixed-dimensional state without explicit content-addressable memory. To address this gap, we introduce a novel framework grounded in nonlinear time-delay systems, in which the effective delay is dynamically estimated based on the semantic similarity between current and historical inputs. Our approach features three key innovations: (i) a differentiable semantic lag estimator that computes content-aware soft attention weights over history, producing a weighted historical context and similarity score; (ii) a diagonal state space with closed-form cumulative sum solution, achieving O(1) per-step complexity with no sequential loops; and (iii) an interpretable fuzzy semantic modulation mechanism that learns context-dependent rules for balancing instantaneous processing versus historical recall, where rule centers correspond to prototypical semantic contexts. Experimental results on text classification and generation outperform state-of-the-art methods.

Satirical news is a unique form of misinformation: it is intended to be humorous by the original publication source but can be misinterpreted. Explanation of satirical news articles is challenging because recent and local context needs to be incorporated. This is a pilot study that explores explanation generation for satirical news articles from Australia and compares them alongside those from USA. The paper demonstrates that framing explanations on unreliable narrator theory on open-weights models can be a feasible, cost-effective alternative to frontier models. We find that models identify the satirical tropes more accurately on the American source than the Australian one. This work results in a novel dataset and an evaluation benchmark for satirical explanation.

Knowledge bases are essential to agents for high energy physics (HEP), supplying few-shot evidence for previously unseen tasks. Their principal utility lies in strategic guidance for novel analyses rather than ready-made answers or reusable code. Prevailing systems, however, treat all retrieved evidence as equally trustworthy and fail to accrue knowledge from the analyses under assistance. In this paper, inspired by the standard HEP treatment of uncertainty, we propose \textbf{\textsc{\underline{HepUKE}}}: an \textbf{\underline{U}}ncertainty-aware \textbf{\underline{K}}nowledge \textbf{\underline{E}}volution system for \textbf{\underline{HEP}} that repurposes information entropy to unify statistical uncertainty from LLM generation and systematic uncertainty from HEP methodological choices. Upon it, we construct a self-evolving domain-specific-language (DSL) knowledge base and release a large-scale expert-annotated HEP physics-analysis benchmark. Per-evidence confidence is quantified via the information entropy of sampled DSL generations: high-confidence precedents constrain program synthesis, whereas analyses lacking close precedents are validated and written back, sustaining continual knowledge evolution. To handle the highly redundant yet logically stringent nature of HEP knowledge, we introduce an early-stopping controller that fuses a backward stationarity test on the answer posterior with a forward marginal information gain estimate. On the 1,000-pair BESIII PhysicsQA benchmark, HepUKE reduces retrieval rounds by 43.0% while preserving most answer quality, and on the out-of-domain HotpotQA benchmark, it reduces retrieval rounds by 14.5% with a similar quality–efficiency trade-off. The code and datasets used in this work are available at https://anonymous.4open.science/r/HepUKE-32FF.

In the practical deployment of vision–language–action policies, handling long-tailed task distributions is a common challenge due to the highly imbalanced composition of robot demonstration datasets. To investigate this issue, we study the head-task action bias in shared robot policies, particularly focusing on its relationship with task-specific visual evidence. Our experimental analysis shows that, when the visual evidence required by a tail task is insufficient, the policy increasingly falls back on action patterns reinforced by data-rich head tasks, resulting in degraded performance on under-represented tasks. Motivated by this observation, we propose Evidence-Guided Counterfactual Learning, a training framework for long-tailed robot policies. Our method identifies decision-relevant visual evidence using instruction-related and action-related signals, and constructs counterfactual observations by removing the selected evidence. The resulting counterfactual predictions are used to strengthen the association among task instructions, visual evidence, and actions, with the supervision adaptively adjusted according to the number of demonstrations available for each task. The proposed framework requires neither additional training data nor region-level annotations and incurs no additional computation during deployment. Extensive experiments across simulated benchmarks, different VLA architectures, and real-world robot platforms demonstrate that our method robustly and consistently improves long-tailed robot policy learning, particularly for tail tasks, while maintaining reliable performance on head tasks.

Multivariate longitudinal count data arise in biological studies, where responses may be over-dispersed, correlated within subjects and over time, measured at irregular times, and exhibit unobserved subgroup structure. Our goal was to develop a model that can accommodate over-dispersion, longitudinal dependence, cross-outcome dependence, covariate effects, irregular observation times, and covariate-dependent latent-class membership. We propose a latent-class Poisson-lognormal mixed model for clustering heterogeneous multivariate count trajectories. Estimation is performed using a variational EM algorithm designed for scalable inference. Simulation studies show accurate parameter estimation, strong latent-class recovery, and reliable selection of the number of classes, as compared to state-of-the-art approaches. We also applied the proposed approach to longitudinal neutrophil RNA-seq data from hospitalized COVID-19 patients as an illustration. The proposed framework provides a flexible approach for clustering complex longitudinal biological count data. Implementation code is available at https://github.com/PengqiLiu-Mc/latent-class-mpln-mixed-models.

Reliable electrode-level degradation diagnosis is essential for accurate health estimation and non-destructive monitoring in advanced battery management. Diagnosis models developed under controlled laboratory conditions can fail when operating conditions change, while acquiring sufficient full-lifespan data in new target domains remains prohibitively time-consuming and practically unfeasible. Here, we propose a closed-loop domain generation framework to enable cross-domain battery health diagnosis under dynamic conditions. Physics-constrained domain generation is achieved through Variational Autoencoder-based latent extrapolation, which maps the source data and few-shot early-life target domain data into a shared latent space and generates cross-domain samples within physical boundaries. Bayesian optimization closes the generation-diagnosis loop by automatically calibrating the sampling, latent regularization, extrapolation, perturbation, and generation-volume hyperparameters using leakage-free development validation, thereby strictly excluding later-life target data from optimization and ensuring the quality and quantity of generated data. Numerical results demonstrate that, across four cross-domain cases, the proposed framework achieves average root mean square errors of 1.53%, 2.15%, and 2.02% for positive electrode active material loss, negative electrode active material loss, and lithium inventory loss, respectively, whereas traditional methods suffer from notably higher errors or even complete failure. This framework provides a general pathway for onboard and physics-consistent electrode-level degradation diagnosis, independent of downstream diagnosis models.

"Security by obscurity," or the idea that hiding how a system works helps protect it from adversaries, has long been poorly regarded in the security community. Yet its intuitive appeal persists, and it has resurfaced repeatedly in industry practices and public debates over the years. The logic, on the one hand, is that open scrutiny of systems is the best way to find and respond to problems; and on the other hand, that too much openness can increase risk by giving adversaries a roadmap for attack. This isn't purely a technical question, but a human one: it's about how attackers and good-faith security researchers respond to openness in the real world. As such, security experts base their stance on decades of community experience; however, the field lacks empirical or theoretical foundations to back up these long-standing beliefs. We provide the first rigorous modeling of "security by obscurity," aiming to capture how rational actors will respond to openness or obscurity in fallible systems. We prove that in equilibrium under realistic model conditions, "obscured" systems are more likely to suffer successful attacks than "open" systems — establishing theoretical support for the longstanding received wisdom.

In 1970, P. R. Halmos raised ten open problems on operator theory. The third problem of Halmos is the following: if an intransitive operator has an inverse, is its inverse also intransitive? This question is reduced to the case of conjugate bi-geometric operators in arXiv: 2610.11202. In the framework of conjugate bi-geometric operators, using tools from complex geometry, operator theory, and function theory, this paper gives an affirmative answer to the third problem of Halmos in the following cases: (a) bundle-preserving operator;(b) subexponential growth of operator norms. These two cases cover a large class of operators.

We study half-line CMV matrices whose Verblunsky coefficients are decaying perturbations of periodic sequences. We quantify the stability of fine properties of the absolutely continuous spectral measure under such perturbations. More precisely, we establish Hölder continuity of the perturbed spectral measure and derive sharp time-averaged Fourier estimates governing the associated quantum dynamics. These results remain valid up to the edges of the absolutely continuous spectrum. Since the spectral measure of a half-line CMV matrix is precisely the orthogonality measure for the corresponding orthogonal polynomials on the unit circle (OPUC), our results also yield new statements for OPUC whose Verblunsky coefficients are decaying perturbations of periodic sequences.

On-Policy Self-distillation is a self-improvement paradigm that enables large language models (LLMs) to improve their capabilities by leveraging the same model as both teacher and student under different conditioning contexts. However, we find that OPSD methods can progressively degrade previously acquired capabilities: queries that are correctly responded at earlier training stages may become incorrectly responded as optimization proceeds, even the overall performance continues to improve. Further analysis reveals that this degradation coincides with a deterioration of the geometry of hidden representations, characterized by reduced intra-cluster compactness and diminished inter-cluster separation. Motivated by this observation, we propose Representation Geometry Regularization (RGR), which preserves representation geometry during post-training by encouraging compactness within cluster and separation across cluster. RGR can be seamlessly integrated into existing OPSD methods without altering their core optimization procedures. Extensive experiments on multiple OPSD methods and benchmarks show that RGR generally alleviates capability degradation while retaining capability improvements. Our code is available in https://github.com/supermachinelearner/RGR.

Let $C$ be a smooth hyperelliptic curve of genus $g\ge2$ over an algebraically closed field of characteristic zero. We prove that the normal bundle of the embedding of $C$ in $\mathbb{P}^n$, $n\ge3$, by the complete linear series of a general line bundle of degree $n+g$ is semistable if and only if $n\ge3g+1$. By openness, general complete embeddings of general curves of genus $g$ also have semistable normal bundle when $n\ge3g+1$. We then show that a general nonspecial curve of genus two and degree $d$ in $\mathbb{P}^n$ has semistable normal bundle except when $(n,d)$ is $(3,5)$, $(4,6)$, $(5,7)$ or $(6,8)$. The degenerations used in genus two extend to every genus $g\ge3$: semistability in all nonspecial degrees and dimensions follows from the cases $0\le d-n-g\le4g-4$. Together with a separate estimate for large $n$, this reduces semistability in each fixed genus to finitely many cases. The proofs combine degenerations to reducible nodal curves, explicit bounds on the degrees of subsheaves, and, in genus two, finitely many exact computations, which are provided as ancillary files.

We derive an explicit zero-side formula for the imaginary part of a smooth truncation of the logarithmic derivative of the Riemann zeta-function. The resulting kernel is the odd companion of the Fejér kernel in Montgomery's pair-correlation identity. Motivated by the recent breakthrough of Anthropic's Claude \cite{Claude26}, we also give an expository account of how the real-part identity can be turned into a matrix problem, overcoming the clustering obstruction for zeros off the critical line. Finally, we discuss how the new imaginary-part identity may contain additional information about such clustering.

We prove a sharp Zhong-Yang type lower bound for the first nonzero eigenvalue of the $p$-Laplacian on closed manifolds with small integral Ricci curvature for $p \geq 2$. The proof combines a global elliptic estimate obtained by Sobolev truncation with strict perturbations of one-dimensional comparison profiles.

This work studies an entropy-based estimator of Kullback-Leibler (KL) divergence constructed from normalized importance weights. We prove a universal finite-sample bound showing that its expectation can exceed the target-proposal KL divergence by at most $\log 2$ for any sample size. We then characterize the KL divergence between the distribution induced by importance-weighted resampling and the proposal, showing that it is upper bounded by both the expectation of the entropy-based estimator and the target-proposal KL divergence. Importantly, these bounds require neither bounded importance weights nor finite higher moments. We apply these results to test-time alignment of generative models via Soft Best-of-$N$ sampling, an importance-sampling-based scaling technique proposed by Verdun et al. (2025), and to relative entropy coding, obtaining finite-sample policy-divergence certificates and moment-free bounds on coding cost.

Bayesian simulation-based inference (SBI) can struggle to recover increasingly concentrated posteriors as observation size grows. We consider learning sufficient summary statistics jointly with the posterior as a general principle for scalable inference in various SBI methods. A common measure taken in SBI is dimension reduction through predetermined summaries, which may partially discard posterior information. Our approach instead imposes structure on how the posterior learner depends on a learned summary (e.g., affinity), and learns the summary simultaneously with the posterior. We identify an important mechanism named two-way guidance: under a structural restriction on the summary, the posterior sufficiency of the learned summary simplifies posterior learning, whereas a suitable posterior objective guides the learned summary towards posterior sufficiency. This mechanism explains a counterintuitive finding that the structural restriction on the summary statistics improves posterior learning, rather than limit its performance. We establish theoretical guarantees on both posterior estimation error and the learned summary's departure from sufficiency, thus identifying conditions on the simulation budget for recovering increasingly concentrated posteriors as observation size grows.

Current software engineering agents are evaluated predominantly inside isolated sandboxes against synchronous local tests. However, deploying features in collaborative repositories requires modifying continuous integration (CI/CD) pipelines, containers, and provisioning manifests alongside application logic. Because agents lack deployment awareness, attempting cross-domain modifications introduces unverified dependencies into asynchronous integration pipelines. To isolate the causal integration overhead of dual-scope pull requests (PRs)-modifying both application code and deployment infrastructure-we evaluated 26,999 PRs across two large datasets (AIDev v5 and MOSAIC-3M) encompassing six agent architectures and an aligned human baseline. Using a deterministic four-tier file taxonomy and an exact 4D strata-matching framework, we isolated integration metrics under conditional exchangeability while controlling for application volume. We find agents operate primarily as application coders or chore workers, with maintenance tasks capturing 17.70% to 25.41% of agent PRs. Dual-scope modifications represent only 4.48% to 4.55% of agentic PRs, yet trigger bimodal integration outcomes. In the first mode, explicitly reviewed contributions experience protracted delays, adding a median penalty of +13.13 hours and multiplying time-to-merge by 3.24x, driven mechanically by CI/CD and provisioning manifests. In the second mode, maintainer gatekeeping exhibits a structural bypass: even for external contributors lacking repository write access, agent identity reduces the odds of human review by 63.7% compared to human peers. Consequently, 43.1% to 56.2% of dual-scope PRs bypass inspection to merge silently in a median of under 31 minutes. These uninspected modifications compromise build verification, demonstrating the need for deployment-aware benchmarks and strict path-based access controls.

In maximum entropy and behavior-constrained reinforcement learning (RL), the optimal policy is given by a Boltzmann distribution. Generating samples from this distribution can be challenging, as it is often complex and multimodal. While flow policies trained with flow matching provide a powerful framework for representing such distributions, they traditionally rely on access to training data, which is generally unavailable in online RL. To address this limitation, we propose fixed-point flow matching (FFM), a data-free procedure for training and fine-tuning flow policies in RL. FFM leverages the target flow identity to formulate the actor update as a fixed-point iteration, utilizing a flow-matching-style regression objective where the critic's action gradients serve as regression targets. We show that the optimal policy is a fixed point of this iteration. Through extensive experiments, we demonstrate that FFM effectively fine-tunes pretrained flow policies in the offline-to-online setting and enables efficient and accurate training of flow policies from scratch in online RL. These results establish fixed-point flow matching as a principled approach for learning expressive flow-based policies without requiring training data.

A simulator summarizes an environment in a state that users can read and change. Generative models learn representations of the world without explicit specification, but offer no built-in way to edit that world's state. We investigate the conditions under which a generative model can act as a simulator through $\textit{editability}$: whether changing a model's latent representation produces the next-step outputs we get by editing a simulator's state. Plainly stated, our goal is to find a mapping between a generative model's latent state and the simulator state, where the model is trained on observations alone and the mapping is learned afterward. We test two kinds of mappings, both learned from observations paired with simulator states. In one, we train probes to decode the simulator state from the model, then steer along them. In the other, we learn the mapping directly with an inverse map, which can succeed even where steering fails. We study both in two contrasting environments: the discrete board game Othello, and Rayworld, our own continuous world of moving discs seen through partial renderings, closer to physical scenes and video. We find that which mapping succeeds depends strongly on the environment, even though the state is decodable in every variant. In Othello, editability falls smoothly as the game is simplified, and even small rule changes have large consequences. In Rayworld, probes fail to steer along the simulator's continuous state, yet an inverse map sets the model from that state anyway. A model can therefore be driven by a simulator it may have never learned.

This paper investigates an abstract viscoelastic wave equation in a separable Hilbert space, in which the damping term depends on a power of the velocity norm. Depending on whether the power exponent is zero or nonzero, this damping corresponds to friction damping or nonlocal damping, respectively; the equation also contains a viscoelastic damping represented by an integral term with a relaxation function. We establish global well-posedness for initial data in \(\mathcal{H}_1\) by combining monotone operator theory with the Faedo–Galerkin method, and prove uniqueness for all exponents greater than \(-1\), with the singular range between \(-1\) and \(0\) handled through the monotonicity rather than the Lipschitz continuity of the nonlocal damping operator. We then study the long-time behavior of the energy via integral inequalities, multiplier techniques, and Nakao's method, and obtain explicit decay estimates showing that the energy decays exponentially in the friction case and polynomially in the nonlocal case. To the best of our knowledge, this is the first work to consider the combined effects of viscoelastic damping and nonlocal damping in such an abstract framework, and it is also the first to analyze nonlocal damping with negative exponents.

Despite extensive research, computational creativity still lacks a conceptually grounded, practically relevant, and empirically applicable formal definition across contexts such as art, scientific research, and games. Existing approaches to creativity often focus on proposing informal conceptual definitions without providing formal computational concepts. Alternatively, they propose formal definitions without carefully examining their underlying assumptions or providing validation of these definitions by testing their performance in specific application settings. To address these problems, this paper proposes several formal postulates of creativity grounded in prior psychological work on creativity, especially as related to Boden's three core criteria of creativity: newness, value, and surprise. Furthermore, we propose a conceptual mathematical definition of creativity that aligns with these postulates. We also validate our proposed creativity formula in two applications: determining the creativity of particular chess moves, and assessing the creativity of paintings by some artists, such as Picasso, Renoir, and other painters. Experimental results demonstrate that our formula of creativity successfully captures creative patterns across both the chess and the art domains. This suggests that creativity can be effectively characterized through a unified mathematical structure based on three fundamental criteria, namely newness, value, and surprise, whose specific measurements are adapted to the particular domains.

We give a polynomial-time randomized classical algorithm that approximates the largest eigenvalue $\lambda_{\max}$ of a traceless quartic fermionic Hamiltonian $H$ on $n$ modes. The algorithm achieves energy at least $\lambda_{\max}/O(\sqrt n)$ and outputs either a fermionic Gaussian state or a polynomially sparse state in the Fock basis. This is achieved through a new upper bound on $\lambda_{\max}$ in terms of the maximum energy of a Gaussian state and $\sqrt{2^{-n}\operatorname{Tr}(H^2)}$.

Fewer latent tokens promise cheaper diffusion. Yet aggressive latent compression creates a reconstruction-generation dilemma: adding channels improves reconstruction but makes generation harder. We introduce APEX, short for Asynchronous Prefix denoising for EXtreme compression, which pairs a hierarchical latent space with asynchronous denoising over channel groups. Our autoencoder orders channel prefixes from structure to detail, while one shared denoiser generates them at staggered local times without adding tokens. On ImageNet-512, APEX outperforms existing methods at every evaluated channel count under 64x and 128x compression. At matched training and guided sampling compute, it also outperforms a 256-token model at every evaluated budget, with larger gains at lower compute. Code is available at https://daviddinkevich.github.io/APEX.