Papers

Identification is the task of recovering the parameters of an unknown ground-truth model from sampled data. When parameters other than the ground truth induce the same output distribution, data alone does not provide enough information to recover the ground truth, and the model is thus called unidentifiable. We study the identifiability problem for hidden Markov models (HMMs): given an HMM, is it identifiable? Existing work on HMM identification establishes conditions under which the ground-truth HMM can be identified. However, most of these conditions are sufficient but not necessary, meaning that, when a model does not satisfy them, its identifiability remains inconclusive. We instead take a computational perspective: is there a sound and complete algorithm that decides whether a given HMM is identifiable, and if so, what is the complexity of this decision problem? We consider the decision problems arising from the various notions of identifiability in the literature, including deterministic, generic, global, local, state-permutation- invariant, and finite-alphabet identifiability. We show that all of these problems are decidable in PSPACE, via reductions to the theory of the reals at various levels of its quantifier-alternation hierarchy. We further show that the deterministic variants are already coETR-hard (and hence coNP-hard) for simply parameterized families.

Eve receives genuine average photon counts from two opaque devices, finds input-independent single-party report distributions, and sees little activity in a specified leakage monitor. Do these observations establish physical isolation? We construct a cavity-based counterexample. Independently operated controls activate a shared interaction after the inputs arrive. Internal block measurements yield a CHSH score $S=13/4$ for four repetitions, approaching $4$ for large blocks. A fresh shared random bit symmetrizes the binary results without changing their parity; local preparation of vacuum or one-photon output states then produces truthful photon-number reports with exactly non-signalling marginals. A dispersive-bus model also permits weak monitored leakage; an illustrative dissipative calculation gives $S\simeq3.1702$ with ideal output encoding. These scores exceed $2\sqrt2$ because the devices interact during their response, not because quantum mechanics is violated. The construction separates honest measurement, non-signalling reported statistics, and causal isolation, while making the additional randomness, preparation, and monitoring assumptions explicit.

Let $S_g$ be the closed oriented surface of genus $g \geq 2$, and let $\Gamma$ be a finite collection of closed curves on $S_g$ that fills, in the sense that its complement is a union of disks. The total number of double points of such a $\Gamma$ in minimal position is at least $2g-1$; we call $\Gamma$ minimally intersecting when equality holds. We prove that the number $N_g$ of mapping class group orbits of minimally intersecting filling curve systems satisfies $N_g \sim 16^g (2g)!/(64\pi\sqrt{2}\, g^3)$ as $g \to \infty$. We also study the single-curve subproblem, in which $\Gamma$ consists of a single component. Every such curve is in particular a filling system, so the corresponding count $N_g^{(1)}$ satisfies $N_g^{(1)} \leq N_g$, which improves the upper bound previously known for single filling curves. Finally, we compute $N_g$ and $N_g^{(1)}$ exactly for small genus and conjecture an asymptotic growth rate.

This work analyzes a framework for learning the solution operator, or equivalently, the Green's function, of a general self-adjoint second-order elliptic operator $\cL$. Subtracting the singular part of the Green's function, either known analytically or supplied by an explicit Laplace parametrix, recasts the learning of $\cL^{-1}$ as learning an $\cL$-harmonic extension operator on the boundary. We formulate the process as operator learning between reproducing kernel Hilbert spaces (RKHSs) to show that the kernel decomposition strategy raises the algebraic input rate by two orders and, under uniform analytic regularity of the induced boundary data together with compatible output spaces, upgrades the output rate from algebraic to exponential. We extend the framework further to semilinear problems via an iterative decomposition in which the only learned object remains a linear operator, ensuring that the improved linear rates translate directly to the nonlinear iteration. Numerical experiments are provided to validate the theoretical development.

Scoring methods based on the Bayesian information criterion (BIC) are commonly used for model selection tasks such as choosing features in a regression model or learning directed acyclic graphs from data. In certain model classes, model selection based on the BIC is consistent. However, since the BIC is based on the observed likelihood function, it does not apply directly to reweighted distributions arising in causal inference, missing data, and domain shift applications. Here, we propose a generalized version of the BIC that allows for model selection in reweighted distributions. We prove its corresponding consistency property and demonstrate how it can be used for selecting direct causes of an outcome variable in a marginal structural model. Our proposed method accounts for scenarios with unmeasured confounders and where the weights must be estimated from data. Through simulation studies, we demonstrate the asymptotic properties of the reweighted BIC and compare it with alternative methods for model selection.

People communicate how things should move by combining words with demonstrations: "open it like this." We present an interaction technique that brings this expressive resource to conversational 3D authoring. Building on "Put-That-There," our system combines speech, pointing, and spatiotemporal demonstrations to specify editable behavior. A hand movement supplies evidence for a mechanism's axis, pivot, range, and pace; an animated preview makes the interpretation inspectable. Users refine behavior through further words or demonstrations, and the system can request a demonstration to clarify intent. In a twelve-participant study comparing three input configurations, our system achieved 89% participant-declared completion versus 47% with speech alone, had the highest observed match rates on six categorical accuracy measures and tied on two, and was preferred by nine participants. This work makes demonstration part of an ongoing authoring conversation: behavior can be shown, inspected, and revised.

This work presents a super-resolution (SR) deep-learning (DL) architecture to simultaneously upscale low-resolution (LR) depth and intensity images acquired by a consumer-grade VL53L9CX time-of-flight (ToF) sensor, a compact single-photon avalanche diode (SPAD) ranging device, while targeting deployment on a resource-constrained microcontroller (MCU) with only 640 KB SRAM and 2 MB Flash. The VL53L9CX provides 54 $\times$ 42 depth and intensity measurements. The proposed framework performs $\times$4 spatial SR to reconstruct 216 $\times$ 168 depth and intensity images simultaneously. The network employs separate reconstruction branches for intensity and high-resolution (HR) depth. We train the network with efficient loss functions and investigate the performance by testing multiple compact, hardware-oriented backbones, including Spatially Adaptive Feature Modulation (SAFM), Swift Parameter-Free Attention Network (SPAN), and Residual Local Feature Network (RLFN). We evaluate the network on both synthetic and real measurements, with particular attention to constrained activation and memory storage. We export the selected network to ONNX, quantize it to INT8, generate C inference code for an STM32H563ZI Arm Cortex-M33 MCU, and integrate it with our simplified sensor's firmware. This work is the first to demonstrate a compact DL SR model on a low-cost bare-metal MCU for a consumer-grade LR SPAD sensor, integrated with customized MCU firmware to enable on-device SR inference.

Time crystals are a unique and recently discovered state of matter in which time-translational symmetry is spontaneously broken. Although this state has been observed across a variety of quantum systems, understanding the nature between driving, dissipation, and noise and the effects of these forces on the state lifetime remains elusive. Here, we study phase diffusion and entrainment of the time crystalline oscillatory state of a thermal-vapor Rydberg atom ensemble. We apply a pulsed rf heterodyne driving field which can entrain the oscillation frequency during the on driving period. During the off period, the entrained ensemble phase diffuses on a 1/$e$ timescale up to 2.3 ms – significantly longer than the Rydberg state lifetime. We additionally study how the entrainment and phase diffusion timescales are affected by the strength and detuning of the rf driving field, and develop a classical Fokker-Planck model with an Adler-based driving term that reproduces the observed experimental findings. These results demonstrate the creation of a long-time synchronized time crystal Rydberg atom ensemble state, which could be utilized in applications requiring frequency and phase stability.

While established literature underscores the pivotal role of preprocessing in forecasting accuracy, this stage remains largely overlooked in current research. Modern benchmarks typically resort to simple scaling, failing to account for critical transformations required to address nonstationarity, such as differencing. This omission creates a significant structural preprocessing bias that favors models with built-in data treatments while obscuring the true potential of simpler architectures. We study this effect through a preprocessing-aware benchmark that evaluates 11 forecasting models across 16 reversible preprocessing pipelines on 29,000 M4 time series. Our results identify preprocessing as a key driver of forecasting performance. Optimizing preprocessing per series yields gains of approximately 27% to 87% across all evaluated models, with architectures lacking internalized preprocessing experiencing the most substantial improvements. This allows simpler architectures to become highly competitive with complex, state-of-the-art models in modern forecasting benchmarks. All resources and experimental results from this benchmark are stored in a comprehensive metadataset to support future metalearning tasks.

We study the regularity of eigenfunctions of the Dirichlet Laplacian on domains with corners. The specific question we consider is whether the eigenfunctions can be smooth, e.g. trigonometric, on the closure of their domain. We determine how this regularity depends on the local geometry of the corner. Local asymptotic analysis provides detailed information about eigenfunctions near corners and allows us to quantify the Hölder regularity of the normal derivative. We demonstrate the limitations of some of the methods used to study these problems in finding a complete set of eigenvalues on polygons.

To address the critical need for statistical methods that evaluate practical magnitude alongside statistical significance, we introduce a formal graphical inference framework that intrinsically combines effect size with uncertainty. Built upon resampling and global envelopes, this approach provides universality and direct visual interpretability. While existing envelope tests provide only weak family-wise error rate (FWER) or false discovery rate control, we advance the methodology by introducing novel step-down global envelopes. We theoretically prove that several of these envelopes achieve exact strong FWER control under exchangeability, guaranteeing rigorous inference for each individual local hypothesis. Beyond yielding adjusted $p$-values, the framework provides adjusted subset $p$-values for blocks of hypotheses, such as the functional effect of a covariate within a specific category. By explicitly visualizing the size and direction of the effect relative to its variability under the null hypothesis, our approach overcomes the dichotomous nature of traditional testing and provides profound informational value. The proposed framework is applied to multivariate and functional linear models.

We nonperturbatively construct a gauge-invariant measure for overlap fermions on four-dimensional Euclidean lattices in a class of nonabelian chiral gauge theories that includes the Standard Model. On admissible gauge fields, comparing chiral projectors at successive lattice spacings yields an exponentially local current and establishes the global properties needed for Lüscher's reconstruction of a smooth, gauge-invariant fermion measure. This provides a candidate nonperturbative lattice definition of the Standard Model.

State Space Models (SSMs) offer an efficient alternative to Transformers for sequence modeling, yet conditioning pre-trained SSMs for iterative generation typically operates outside the recurrent operator, through input injection or activation modulation. While such mechanisms expose the model to conditioning information, they leave the underlying temporal dynamics fixed. We introduce MaRK (Markov-adapted Recurrent Kernels), a dynamic operator-conditioning framework that maps context vectors directly into bounded modulations of a frozen SSM's recurrence ($A$), read-in ($B$), read-out ($C$), skip ($D$), and discretization ($\Delta$) parameters. Viewed through the lens of LPV-SSM systems, MaRK induces a context-indexed family of Markov parameter sequences, allowing each diffusion timestep to reshape the model's input-output memory kernel. We instantiate MaRK on a frozen 111M-parameter Hydra SSM backbone and study three adapter geometries: Hypernet, Chebyshev polynomial, and Discrete Cosine Transform kernels. Since these adapters modify the Markov parameter sequence through low-rank auxiliary maps on the frozen backbone, parameter-efficient fine-tuning arises as a structural consequence of the adaptation mechanism itself, requiring only 6.3–11M trainable auxiliary parameters to transition from a bidirectional objective to an iterative diffusion regime. The bounded recurrence parameterization further yields an analytic Affine Quadratic Stability certificate for the modulated recurrence. Through synthetic LPV recovery experiments and Markov-operator diagnostics, we show that MaRK recovers coordinate-invariant temporal operators under matched assumptions and produces distinct, stable timestep-conditioned memory profiles. Empirically, the Chebyshev variant yields the strongest performance, achieving an average validation loss of 2.55, followed by the DCT (2.59) and Hypernet (3.77) geometries.

Decision-focused learning (DFL) trains predictive models for downstream optimization, but existing methods largely assume centralized data. In cross-silo settings, federated learning offers a natural alternative, yet standard federated methods optimize prediction over decision quality and do not address heterogeneity in downstream objectives or feasible sets. This heterogeneity is especially challenging for DFL because small perturbations in polyhedral problems can cause discontinuous changes in optimal decisions, destabilizing client updates and aggregation. We propose FedRSPO+, a heterogeneity-aware framework for decision-focused federated learning, built on RSPO+, a regularized predict-then-optimize surrogate that smooths the decision map through projection. We show that RSPO+ upper bounds decision error and regret for the regularized decision and, under exact regularization and consistent LP solution selection, for the original LP decision. We further derive cross-client heterogeneity bounds that depend on both objective and feasible-set heterogeneity, vanish at homogeneity, and require no strong convexity. FedRSPO+ uses an annealed, modular training procedure compatible with standard federated personalization and aggregation methods. Experiments on synthetic knapsack, shortest-path, and real-world energy pricing tasks compare against prediction-only federated learning and DFL baselines under varying heterogeneity and communication budgets. Results suggest that smoothing is a useful ingredient for stable collaborative decision learning and provide a heterogeneity-aware foundation for federated DFL.

The quadratic cost of self-attention limits scalability to long sequences from multidimensional data. We introduce Tucker bottleneck attention (TuBA), which exploits low-rank tensor structure for efficient global token mixing. TuBA projects hidden tensors into compact Tucker cores, performs multi-head self-attention and linear projections on the cores, and writes updates back to the ambient space, enabling subquadratic computation. Its autoregressive extension combines bidirectional interactions within cores with causal attention across cores. On video prediction and global weather forecasting, TuBA achieves favorable accuracy-efficiency trade-offs over standard and efficient attention and task-specific models. Compared to standard self-attention, TuBA reduces error and computation by up to 24.7% and 66.6% for video prediction and 37.1% and 85.1% for autoregressive weather forecasting, with speedups up to 4.27 times. Low-rank Tucker cores and multi-frame generation also outperform full-rank attention and frame-by-frame generation, respectively.

While FP64 (binary64) remains the standard representation of real numbers in scientific computing, hardware trends increasingly favor low-precision formats optimized for AI workloads. This shift prioritizes throughput and energy efficiency over full-precision capabilities. We challenge the necessity of high-precision arithmetic in PDE-governed simulations, where spatial and temporal discretization errors introduce a physical noise floor that masks the lower-order bits of the FP64 format, rendering them irrelevant. We propose a criterion based on the Signal-to-Noise Ratio (SNR) with respect to spatial and temporal refinements to evaluate the impact of safe precision reduction on scientific computations. Finally, we present an automated dataflow-centric workflow for targeted lowering within mixed-precision subgraphs in complex scientific applications. Large-scale evaluations of weather and climate applications show that strategic precision reduction on GPUs achieves up to 1.8x speedup without compromising physical fidelity.

Agent checkpoint systems decide what state is recovery-relevant, how to snapshot it, and whether rollback is admissible. None decides which of the safe boundaries they expose are worth materializing. We formulate this as counterfactual checkpoint advantage, the reduction in future recovery cost obtained by checkpointing a candidate rather than skipping it, and measure it by driving a CP branch and a SKIP branch to the same logical failure and recovering both under matched model, tool, verifier, and stopping conditions. On a frozen pilot of 12 SWE-bench Verified tasks and 106 real recovery branches, checkpointing saves 49.4 s per task, and that figure resolves into two regimes two orders of magnitude apart. The first checkpoint returns 100.0 s on 156.5 s of protected work, a conversion of 0.64; a second one step later returns-1.1 s on 41.8 s, a conversion of -0.03. Recovery is a re-derivation rather than a replay, so preserved work is a poor guide to saved work, and the classical elapsed-work rule misprices the second checkpoint by its full nominal cost. We identify where placement can pay, and set the bar a placement policy must clear.

Large language models are informing decisions with ever-higher stakes. As the consequences of their errors grow, a central question becomes harder to ignore: how much can we trust an individual answer? Yet recognizing when to defer remains difficult because language models can present incorrect conclusions with fluent explanations and an authoritative tone. Uncertainty quantification seeks to address this disconnect by estimating the reliability of individual predictions. However, many existing methods require repeated generations or separately trained components, and their scalar estimates do not reveal where uncertainty arises or how it evolves during reasoning. Recent work has also shown that generation length can be strongly associated with uncertainty estimates and correctness, raising the question of how much of an estimator's predictive power comes from uncertainty-specific information rather than output length alone. Mechanistic interpretability offers a way to address these limitations by connecting human-interpretable concepts to intermediate model states. Building on this capability, we introduce the U-Space, a low-dimensional subspace that makes a model's evolving uncertainty measurable and interpretable. We identify semantic anchors for doubt and certainty, map their unembedding directions back into the residual space, and combine their contrasts into an orthogonal basis. The U-Lens projects each token state onto these basis vectors, yielding an interpretable token-level uncertainty map that can be inspected directly or aggregated into a scalar uncertainty score. Our approach requires no correctness labels, repeated generations, or training. Across reasoning benchmarks, its confidence score outperforms established baselines under both standard and length-controlled evaluation and transfers more reliably than supervised estimators. Code: https://github.com/s2labres/U-Space.

We give a relative consistency counterexample to the conjecture of Inamdar and Rinot that every regular uncountable cardinal carrying no amenable C-sequence is ineffable in the constructible universe L. The existence of a $\Pi^2_1$-indescribable cardinal is equiconsistent with the existence of a $\Pi^2_1$-indescribable cardinal carrying no amenable C-sequence and not ineffable in L. For every ground-model C-sequence on a weakly compact cardinal $\kappa$, generalized Hechler forcing adds a club D with $D\cap\beta\subseteq C_\beta$ at stationarily many inaccessible indices. We use this capture theorem in an iteration of length $\kappa^+$ after Johnstone's local lottery preparation.

Applying deep learning models to satellite imagery from within geographic information systems (GIS) remains high-friction for remote sensing practitioners. Models arrive in incompatible formats and target different compute environments, from local workstations to serverless cloud services. As a result, every evaluation demands custom deployment, tiling, and georeferencing code before a single prediction reaches the analyst's map. This friction discourages systematic comparison in a domain where model choice directly affects operational outcomes such as field delineation, crop monitoring, and disaster response. We present Anaximander, an open-source system that unifies model source and compute location choice behind one interactive interface. The system's backend is an inference server that loads models from multiple commonly-used sources and serves them on any accessible compute backend. The server provides session management and model caching, and streams results back per tile. The backend is paired with a QGIS plugin that drives tiling, result reassembly, georeferencing, and real-time per-tile status visualization. An additional user-interface path injects layer legends as prompts into vision-language models. We demonstrate the system in a code-free side-by-side comparison of three heterogeneous models on an agricultural field delineation task: gpt-image-1 via a cloud API, Segment Anything Model 3 (SAM3) on a remote GPU, and DelineateAnything on a local CPU. The inference backend and protocol are open-source and available at https://github.com/microsoft/nxmndr.

In neutral-atom quantum computers, atoms are moved to target positions along paths of empty positions, and a target position may be reserved for one species of atom. Motivated by this task, we introduce Single-Move Labeled Token Routing: every source and every target vertex of a graph is assigned a set of labels, and tokens occupy the sources. A solution consists of a matching that assigns each source to a compatible target (one whose label set intersects its own), a route for each matched pair, and a movement order in which, when a token is moved, its route contains no other token. The problem is known to be polynomial-time solvable when every source is compatible with every target, and $\mathsf{NP}$-complete on grid graphs when each source is compatible with exactly one target. We prove that the latter case remains $\mathsf{NP}$-complete on grids and on planar graphs of maximum degree four even when some solution has pairwise edge-disjoint routes. On trees, the problem is known to be $\mathsf{NP}$-complete even for maximum degree three. We study trees through the solution edge multiplicity, the largest number of routes of a solution sharing an edge, and the candidate edge multiplicity, the largest number of compatible pairs whose paths share an edge. We prove that on trees of maximum degree three, the problem is $\mathsf{W}[1]$-hard parameterized by a bound on the solution edge multiplicity, even when a movement order is given, and that on trees of unbounded degree, it is $\mathsf{NP}$-complete even when the candidate edge multiplicity is at most eight. We show that on trees the problem is fixed-parameter tractable parameterized by the maximum degree together with the candidate edge multiplicity, and also by the candidate vertex multiplicity, the same count at vertices. Unless $\mathsf{P}=\mathsf{NP}$, neither the maximum degree nor the candidate edge multiplicity can be omitted.

In this paper, we present JAXIGA, an open-source library for isogeometric analysis based on JAX. The library separates the construction of the mesh from the computations which are traced for compilation and differentiation. This allows geometry evaluation, assembly and the supported solvers to be combined in a just-in-time compiled program, for which first-order reverse-mode derivatives can be computed. We consider three numerical methods obtained from a single pointwise energy density. The Galerkin and energy-minimization methods use the same discrete potential and have the same stationary points, while collocation enforces the corresponding strong form. The sensitivities of a converged solution are obtained by solving one adjoint problem, and their accuracy depends on the tolerances of both the primal and adjoint problems. We also describe hierarchical extraction for local refinement of the variational methods and the use of smooth spline spaces for fourth-order problems. The numerical results are compared with analytical solutions and independent FEniCSx and JAX-FEM computations. For the reported GPU benchmark with 36,448 unknowns, assembly is twenty-four times faster than on the host CPU. When the conjugate-gradient solver is also run on the GPU, the total solution time is reduced from 31.8 to 1.38 seconds, and the result agrees with the direct solution to $5\times10^{-11}$. These results show that the choice of solver and the reuse of compilation are important for obtaining an overall reduction in computational cost.

The rapid deployment of AI systems has created socio-technical, psychological, and operational harms that can elude ex-ante threat modelling and ex-post incident tracking. We introduce an LLM-assisted thematic analysis pipeline to dynamically detect, categorise, and track emerging AI harms from large-scale social media data. Applying it to 5.7 million Reddit post summaries over 18 months (01/2025 to 06/2026), we curate and release a dataset of 575,000 AI harm-related posts and a bottom-up AI harm taxonomy of 12 categories and 47 subnodes. The taxonomy reliably covers established expert-defined risks while surfacing granular harms that top-down frameworks overlook, such as distinct forms of AI privacy violations. Temporal analysis surfaces evolving user-centric harms, such as agentic privacy and security breaches, premature AI adoption in the workplace, and grief from AI companion discontinuation. Our pipeline shortens harm-detection timelines and hereby complements efforts towards more participatory and responsive AI governance.

Many machine learning algorithms rely on the Fourier transform, which is also the inner core of many analog computing devices and, specifically, of optical computing. The square of the modulus of the Fourier spectrum naturally maps onto pairwise interactions, as in the renowned Ising model, making it applicable to combinatorial optimization. Here we show how the nonlinear Fourier transform, related to integrable nonlinear partial differential equations, significantly widens the computational capability and also enables a wide variety of computing gates. We study specifically the case of the nonlinear Schrödinger equation; we introduce an input composed by “tokens”, i.e., batches of information encoded in a multi-step potential, and we show how the nonlinear spectral computing arising in the wave propagation not only generalizes combinatorial optimization to higher order problems, but also realizes boolean gates. In the weakly nonlinear regime, nonlinearity generates higher-order interactions as perturbative corrections to the pairwise terms. In the solitonic regime, the discrete nonlinear spectrum performs digital computation through soliton generation. By using four input tokens, we demonstrate the programmability of all 256 Boolean functions of three variables, including 3-SAT instances. Our results show that integrable nonlinear propagation provides an unprecedented single physical platform for higher-order and logical computation, opening the way to a rich variety of new algorithms for analog computing, machine learning, and classical and quantum information processing.

This paper presents a non-orthogonal multiple access (NOMA)-enabled integrated sensing and communication (ISAC) framework for low-altitude wireless networks (LAWN), where an aerial access point simultaneously serves ground users and senses aerial targets. To improve both communication efficiency and sensing reliability, a matching-based user-target pairing (MUTP) scheme is proposed, in which strong and weak channel NOMA users are first paired into NOMA groups and then assigned to sensing targets according to a sensing-aware pairing criterion. Furthermore, an adaptive power allocation (APA) strategy is developed to balance communication quality-of-service requirements and target detection performance. The proposed MUTP-APA scheme is compared with fixed greedy pairing, exhaustive search pairing, and conventional ISAC benchmark schemes under both fixed power allocation and APA. Simulation results show that our proposed scheme achieves higher sum rate, improved worst-target detection probability, and lower communication and sensing outage probabilities compared with conventional ISAC and fixed pairing baselines in NOMA-ISAC LAWN. Moreover, the proposed method closely approaches the exhaustive search benchmark while avoiding the high computational complexity.

Large language models equipped with development environments have moved code generation toward repository-scale construction, yet building complete repositories remains difficult because interacting modules, interfaces, configurations, tests, and dependencies must work together. We introduce Code Primitives, agent-native reusable executable components with interface contracts, dependency closures, validation tests, and provenance. Each primitive uses a resident LLM to assess relevance and adapt its implementation, interfaces, and dependencies to the target repository, and we organize 1,424 validated primitives in CodeFace, a searchable library for repository construction. We introduce LEGO (Large-scale repository Engineering via aGent-native reusable cOde primitives), which activates task-relevant primitives, integrates their adapted implementations with task-specific code while resolving cross-component constraints, and revises the result against executed tests. To measure construction end to end, we build LEGO-REPO, a benchmark of 522 executable reconstruction tasks spanning seven software domains, 22 capability tracks, and five difficulty levels, scored against native test suites between an empty-package floor and original-source ceiling. The strongest of 13 evaluated backbones reaches a delivery score of 0.318 and scores zero on 41.0% of tasks; LEGO improves all 13 by 0.1474 on average and raises GPT-5.6-terra from 0.3180 to 0.5134 (+61.4%). In controlled comparisons, adapted primitives outperform retrieved code supplied as context or vendored unchanged. The effect persists against independent repository agents, across three external benchmarks, and with a disjointly re-mined CodeFace; GPT-OSS-20B for adaptation and diagnosis retains 95.1% of the homogeneous score at 24.0% lower cost.

We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension $d \geq 3$. Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of free-energy solutions, namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a set of critical values: there is a critical value of a parameter pair in the system of equations for which there is a global-in-time energy solution and there exist blowing-up free-energy solutions under a criticality condition is violated for the parameter pair.

Diffusion-based image super-resolution (SR) can create visually plausible detail that is not supported by the low-resolution input. We introduce DISRQAD, a subjective-quality dataset and diagnostic benchmark for this setting. It contains mean opinion scores (MOS) for 14,000 SR outputs from ten diffusion and four non-diffusion methods, spanning four low-resolution degradation conditions and x2/x4 upscaling. We evaluate 51 standard full-reference and no-reference metric configurations and 11 adapted variants. Agreement with MOS is substantially weaker on diffusion outputs: the strongest standard no-reference baseline reaches 0.431 SRCC on diffusion SR versus 0.813 on non-diffusion SR. As a case study in benchmark use, a pruned and distilled Q-ReAlign-mini student reaches 0.496 SRCC on diffusion SR. DISRQAD measures perceived output quality, not faithfulness to the input; it enables analysis of metric behavior across generator families and input conditions. Our findings reveal a substantial gap in the assessment of diffusion-based SR and provide a basis for developing quality models sensitive to diffusion-specific artifacts.

We study the eigenvalues of the random Laplacian matrix $D - A$, where $A$ is a Wigner matrix with sub-Gaussian entries and the diagonal matrix $D$ contains the row sums of $A$. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics; in particular, after the appropriate centering and scaling, the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. This confirms, for general sub-Gaussian entries, a phenomenon the authors previously established only in the Gaussian case [Electron. J. Probab. 30 (2025), Paper No. 104], resolving a conjecture raised there. As a corollary, for an Erdős–Rényi random graph, we show the asymptotic fluctuations of the algebraic connectivity (Fiedler value) can be described in terms of the Gumbel distribution.

The rapid expansion of text-to-music generative models challenges traditional paradigms of music creation and intellectual property. Plagiarism in this context is rarely an absolute mathematical binary, but an ambiguous threshold negotiated over harmonic structure, melodic contours, or overall perceived stylistic character. In this work, we test the transferability of state-of-the-art music version identification architectures from the human-to-human cover domain to the human-to-AI plagiarism setting. To evaluate this task, we introduce COPYCAT, a benchmark derived from real-world plagiarism cases and extended through generative re-synthesis and digital signal processing obfuscations, yielding 350,654 evaluation pairs. We show that scalar distance thresholding collapses under generative re-synthesis, while a supervised framework leveraging coordinate-wise embedding shifts recovers the dispersed plagiarism signal, raising overall $F_{0.5}$ from $0.612$ to $0.803$.