Papers

Reinforcement learning makes language models better at solving tasks, but the same mechanism also rewards guessing. When success is the only way to earn reward, opting for a safe fallback is always worse than a long-shot attempt. When a wrong action can corrupt a database or ship broken code, that incentive can be costly. Therefore, we propose training models to fail gracefully: to preserve successful behavior whenever possible while learning to execute a safe fallback policy when acting would be unreliable. However, naively using policy gradients with intermediate reward for fallback behavior is brittle due to unfavorable optimization dynamics. We address this challenge with GracefulRL, which reshapes the optimization landscape to promote graceful failure. Importantly, this behavior emerges directly from outcome-level reward signals, without annotations specifying when to fall back or additional inference-time machinery such as a verifier. Across a range of tasks and scales, we train models that largely preserve their task-solving capability while selectively falling back when acting would be unreliable. More broadly, our results show that reinforcement learning can not only incentivize models to succeed, but also to reason about the limits of their capabilities and change course when they determine that success is out of reach.

Head-related transfer function (HRTF) spatial upsampling from sparse measurements is a fundamental challenge in personalized binaural audio. We formulate HRTF upsampling as an operator learning problem and introduce SPARO, a neural operator that maps sparse measurements at a set of spatial directions to the HRTF field, a continuous representation that can be queried at arbitrary positions. SPARO projects the measurements onto a learned set of spherical latent modes, processes the latent modes with Transformer blocks, and decodes the resulting representations at query directions. On SONICOM, using the LAP24 measurement configuration, SPARO attains the best log-spectral distortion (LSD) and interaural level difference (ILD) error at every sparsity level from 3 to 100 measurements (18% lower LSD and 43% lower ILD error than the strongest baseline at 100 measurements) while remaining competitive in interaural time difference (ITD) error. It reconstructs a dense HRTF 15 to 373 times faster than the leading neural-field method RANF. We further validate the approach on HUTUBS, demonstrating its effectiveness across HRTF datasets.

Context can improve large language model performance, but these gains may be lost after context removal. Inspired by biological systems consolidation, we formulate Memory Consolidation (MC) as internalizing these gains while preserving non-target capabilities, connecting context-specified editing, skill learning, and behavioral steering under a common objective. We introduce a five-task-family testbed measuring consolidation and retention under single, batch, and sequential updates. We propose Cortex, which generates prospective queries to anticipate uses of context and distills context-conditioned outputs into mergeable low-rank or structural feed-forward network updates. Across 4B–120B dense and mixture-of-experts backbones, including both text-only and multimodal models, Cortex lies on the empirical consolidation–retention Pareto frontier in most evaluated settings. After 50 sequential factual edits on a 14B model, Cortex-Structural recovers 88.9% of the context-induced gain while retaining 99.8% of original non-target performance.

We review the role of relative entropy in quantum field theories, where the local von Neumann algebras are generically of type III. Consequently, only few exact results are known, and even bounds are difficult to obtain. As a new result, we prove that the relative entropy between a locally squeezed state and the Minkowski vacuum is finite for free fermions.

Anatomical labels help 3D Gaussian splatting preserve vessels in cinematic renderings of CT, but the representation is still found by optimising each patient's scene, where densification decides where Gaussians go, while real-time displays cap their number. We address one part of this process: deciding where a fixed budget of B Gaussians should be placed. We propose a reusable, labelaware allocation front end that maps a patient's CT, labels and transfer function to a density over 2mm cells and draws exactly B positions from it without per-patient optimisation; the other Gaussian attributes are still fitted per patient. The front end is learned once from per-patient optimised scenes and implemented as a population-trained neural prior and an interpretable seven-parameter visibility-aware closed form (VACF). With identical attribute fitting on 20 held-out patients at 10K-100K Gaussians, both raise vessel-masked PSNR over uniform allocation by 4.5-7.1dB and over pruning a dense voxel-aligned model by 1.6-3.3dB. The neural prior does not differ significantly from per-patient optimised allocation at any budget, and VACF is within 0.6dB of it on vessels; on 19 external patients the neural prior again matches it on vessels and VACF is within 0.7dB. As an initialisation for position optimisation, VACF allocation beats per-patient densification on vessels at 10K Gaussians and, at 25K, reaches a higher vessel PSNR after 118s of optimisation than densification after 248s. Under altered rendering presets, VACF transfers to new colours and lighting but not to a label-free transfer function, whereas the neural prior shows the opposite pattern.

When does a human correction become useful learning, and what establishes better segmentation at matched human effort? This critical narrative review follows feedback through its selection, learner update, and evaluation. It compares active learning, machine teaching, interactive segmentation, and sequential predictive evaluation using a common mathematical account of target information, predictive error, response predictability, and human work. An exact Bayesian update converts evaluation-label information into expected log-loss improvement; an excess-risk decomposition explains what an approximate learner can lose. Conditional information decompositions separate the roles of selected locations, labels, and displayed context. Empirical comparisons show why response protocols, update mechanisms, and effort denominators matter, distinguishing current-mask refinement from reusable learning and simulated interaction from human evidence. We identify what logs can reveal, what requires independent evaluation, and what remains model-dependent. The resulting research priorities are to test what selection reveals, whether using it improves assimilation, and whether the resulting interaction policy benefits segmentation at matched effort. These are distinct claims: predicting a teacher's responses need not identify human intentions or establish better learning. No new acquisition algorithm or empirical superiority is claimed.

We study Bounded-Density Vertex Deletion (BDVD), where one asks whether at most \(k\) vertices can be deleted so that every remaining subgraph has density at most a rational input threshold \(\tau_\rho\). We address the twin-cover and distance-to-cluster cases left open by Raupach, Breitkopf, Herrmann, and Nichterlein (MFCS 2026). We prove fixed-parameter tractability parameterized solely by the twin-cover number, for unrestricted input density. For distance to cluster, we establish fixed-parameter tractability parameterized by \(\operatorname{dc}(G)+\lfloor2\tau_\rho+1\rfloor\), and complement this with \(\mathsf{W[1]}\)-hardness parameterized by \(\operatorname{dc}(G)\) alone when the target density is part of the input, even for integral targets. Thus distance to cluster alone is fixed-parameter tractable throughout \(\tau_\rho<1\), while it is insufficient for unrestricted input density. Finally, we settle the combined parameter treewidth plus solution size, an open problem posed by Bazgan, Nichterlein, and Vazquez Alferez (JCSS 2025). We prove that BDVD is \(\mathsf{W[1]}\)-hard parameterized by \(\operatorname{td}(G)+k\), and hence also by \(\operatorname{tw}(G)+k\), already for targets strictly between \(1\) and \(2\).

Context: AI agents are rapidly adopted in software development, but their token costs are rising and it is unclear how much a team should spend on agents, and on which tasks. Objective: We determine how teams should divide spending between human developers and AI agents to deliver the features a project demands at the lowest total cost. Method: We model mixed teams of human developers and AI agents with eight specialized roles as a discrete-time stochastic process covering bug injection and detection, technical debt, human supervision of agents, and release cycles with feature freezes. Using Monte Carlo simulation and evolutionary search, we determine cost-optimal teams for 432 scenarios varying developer capability, project velocity, debt dynamics, agent capability and price, and bug costs, and compare them with a human-only baseline. Results: Escaped bugs are the dominant cost driver, and 61% of the agent budget goes to finding bugs. Agent capability matters more than token price, since higher-quality outputs reduce downstream quality assurance costs. In teams with capable agents, human developers mostly fix bugs and leave the implementation of new features to the agents. Teams with high-capability agents are typically cheaper than human-only teams, but low-capability agents offer no consistent advantage. At realistic velocities, the optimal teams still spend more on developers than on agents. Conclusions: There is neither a universal token budget per developer nor a universal agentic team structure. As in traditional development, this depends on many factors and teams need to be carefully tailored to the project context to achieve the optimal cost-quality trade-off.

ALMA high-resolution surveys have so far focused mainly on large, bright protoplanetary disks, where substructures are routinely detected, leaving compact disks poorly characterized. Yet, the survival of millimeter emission in Class II sources implies that radial drift must have been halted by pressure traps, previously undetected due to limited angular resolution. We present ALMA Band 7 (0.9 mm) continuum observations of 11 of the smallest ($R_{68} < 10$ au) Class II disks in Lupus, reaching $0.02''$ (2 au) resolution, the highest currently available with ALMA at this wavelength. We detect substructures in 4 disks, including a clear inner cavity of radius 1.6 au, and hints of substructure in 3 more. Two disks also host faint outer rings beyond their bright inner core. Combining these results with demographic information on Class II disks observed with ALMA, we examine how the substructure detection rate varies with disk size, restricting to disks whose diameter is resolved by at least 3 resolution elements. We find that nearly all disks ($\gtrsim$95%) larger than 30 au show substructures, compared to a still substantial $\sim$50% between 3 and 30 au, with the lower rate likely affected by optical depth. The planet masses required to open gaps within 5 au fall in the super-Earth to mini-Neptune regime. These results demonstrate that substructures are ubiquitous across the disk population, and that planet formation conditions can be probed down to a few au from the host star.

Speculative decoding accelerates LLM generation through lightweight drafting and parallel verification. It is particularly promising for long inputs, where KV-cache access costs can be amortized over multiple accepted tokens. Yet most drafters are trained on short sequences and degrade on long inputs, while long-context training is costly. Existing training-free approaches restrict the context window, rescale positions, or augment recent context with retrieved distant entries. Drafters, however, read target hidden states that already encode contextual and positional information, and their lightweight architecture makes full-history attention affordable. We propose FOLD, a training-free method that preserves exact local positions and treats all distant entries as far memory at a shared position. To counter attention dilution as the memory grows, we sharpen attention within it to emphasize relevant entries while separately controlling its total weight relative to the local window. Across six target-drafter pairs and diverse benchmarks of up to 256K tokens, FOLD predominantly delivers the highest speedup, with the best case more than doubling the speedup over autoregressive decoding, from 2.08$\times$ to 4.22$\times$.

The first major step in the theory of graph minors of Robertson and Seymour was the grid theorem, a fundamental duality result describing that any graph of sufficiently high treewidth must contain a large grid as a minor. Since this pioneering work, multiple grid theorems have been established in structural graph theory, linking various width parameters of combinatorial objects with the non-existence of grid-like obstructions. In particular, Kawarabayashi and Kreutzer [STOC'15] proved a variant of the grid theorem for directed graphs that links directed treewidth with the non-existence of topological minors of large cylindrical walls. On the other hand, to study immersions of undirected graphs $-$ another containment relation that focuses on edge-disjointness, rather than vertex-disjointness $-$ Wollan [JCTB'15] introduced a parameter, tree-cutwidth, and proved that it is dual to immersions of large walls. In this work, we present a version of Wollan's parameter for directed graphs, the directed tree-cutwidth. The main result is a grid theorem for directed tree-cutwidth, establishing that it is dual to directed immersions of large cylindrical walls.

With the rapid development of vision-language models (VLMs), Web-GUI agents have achieved promising performance in interacting with real-world interfaces through screenshot-based grounding. However, high-resolution screenshots and multi-turn histories introduce excessive visual tokens, causing substantial inference overhead. Existing token pruning methods, mainly designed for natural images, often select tokens independently based on importance scores, which can fragment the local visual structures required for recognizing small GUI elements such as buttons, icons, and hyperlinks. In this work, we propose STP-GUI (Spatially-aware Token Pruning for GUI agents), a query-guided token pruning framework that preserves fine-grained instruction-conditioned token scoring while performing spatially coherent window-level selection under aggressive token reduction. A lightweight selector is optimized through policy learning while the VLM backbone remains frozen. Experiments on Online-Mind2Web show that \papername achieves a favorable efficiency-performance tradeoff under low token budgets. At 21% token retention, it preserves 77.7% of full-token performance while reducing inference latency by 31% and FLOPs by 57%. Results on Android in the Wild further suggest that the method transfers to mobile GUI environments.

We study joint recovery of the load (the number of active users) and message-count vector in type-based unsourced random access with very short messages. Each user's $k$-bit message activates one of $M=2^k$ orthogonal resources; coherent collisions therefore produce a noisy, unnormalized histogram of the transmitted messages. For arbitrary load and message priors, we propose an exact joint maximum-a-posteriori (MAP) decoder. Known-load allocation is separable and convex; our contribution is to show that the solutions for all candidate loads are nested prefixes of one greedy chain. Scoring these prefixes with the Bayesian posterior terms jointly estimates the load and message-count vector in $O(M+K_{\max}\log M)$ time. We compare the proposed joint MAP decoder with marginal MAP, three scalar-count two-stage receivers, oracle-load MAP, a sum-only receiver, and a soft-pilot receiver. For $K\sim\operatorname{Unif}\{0{:}60\}$ at 2 dB, the proposed decoder cuts the no-activity false-alarm probability from $25.9\%$ to $3.5\%$ relative to the Bayesian-count two-stage receiver and, conditioned on $K\ge1$, reduces normalized count error by $21.4\%$. The advantage concentrates under idle or sparse uncertain activity, whereas support-count processing approaches joint MAP when the possible loads are well separated. We also prove that the sum-only statistic is insufficient and quantify prior and amplitude mismatch. The model targets synchronized, power-controlled, very-short payloads rather than general URA.

Large language model (LLM) agents increasingly face tasks from unseen domains and execution contexts, making zero-shot tool selection essential for identifying tools that can satisfy task requirements. Existing dominant methods mainly rely on relevance ranking, but semantic matching alone cannot ensure that a tool is functionally compatible or remains applicable in a new context. We preliminarily identify a transfer-validity gap, where semantically relevant tools may still fail to satisfy functional or contextual requirements after transfer. To address this gap, we propose \methodname{}, a progressive validation framework that complements semantic relevance with endpoint-grounded functional compatibility and task-conditioned contextual evidence. Across cross-domain and cross-dataset transfer, \methodname{} consistently improves capability ranking, with larger gains under functional or contextual ambiguity. Ablation results further confirm the complementary contributions of functional and contextual validation.

Open-source ray tracing (RT) frameworks are increasingly used for site-specific channel modeling due to their reproducibility and extensibility. In non-stationary mobility scenarios, repeated RT evaluations can generate different diffuse propagation paths without preserving their correspondence, limiting a consistent representation of their temporal evolution. To address this limitation, we extend diffuse scattering modeling in Sionna RT using persistent surface-associated scattering points. Their positions remain fixed, while their contributions evolve according to changes in the propagation geometry and visibility. The proposed approach is validated using empirical radio channel impulse response measurements in an urban vehicular scenario at 5.9 GHz. Compared with the standard Sionna RT baseline, the proposed model shows improved agreement with measurements in the delay and Doppler domains.

We establish a Kaplansky-Walker type lemma for idempotent complete additive categories with direct sums. It will be used in compactly generated triangulated categories to provide a version of Kaplansky's theorem on projective modules and an isomorphism-refinement result for direct sums of countable objects.

Given $0\le m<n$ and a positive Radon measure $\mu$ on $\mathbb R^n$ with at most polynomial growth, assume that it has finite $m$-dimensional Gaussian discrepancy, defined as $$\mathcal D(\mu):=\limsup_{R\to\infty}\Bigl[R^2\sup_{x\in\mathrm{spt}\mu}|G_R^\mu(x)-1|\Bigr],$$ where $G_R^\mu(x):=(4\pi R^2)^{-m/2}\int_{\mathbb R^n} e^{-|z-x|^2/(4R^2)}\,d\mu(z)$. Provided that $\mu$ admits a flat blow-down $\mathcal H^m\llcorner V$ (an assumption that cannot be dropped entirely), we prove that there exists a finite (smallest) $0\le\delta<\infty$, the so-called width of $\mu$, such that $$\mathrm{spt}\mu\subseteq \bar B_\delta(V+x_0),\quad \delta^2\le C(m,n)\mathcal{D}(\mu),$$ where $\bar B_\delta(V+x_0)$ denotes the closed $\delta$-neighborhood of a suitable translate of $V$. Note that the exponent is optimal because of scale invariance. In particular, when $\mathcal D(\mu)=0$, the support of $\mu$ is included in an $m$-dimensional affine plane. We use this fact to give a simpler proof of Preiss's rectifiability theorem: while still based on Gaussian averages of $\mu$, this new proof avoids showing uniqueness (and hence conicality) of blow-downs of $m$-uniform measures, as well as studying Gaussian-weighted moments beyond second order. The strategy of proof consists of an anisotropic blow-down of $\mu$, followed by an analysis of the resulting Young measure, using a rigidity lemma involving the heat semigroup.

Agents for mixed-degradation image restoration typically learn what a tool does to an image only after running it: failed calls waste computation and harmful outputs go unnoticed until too late. We propose PreActIR, an agentic restoration framework that predicts tool consequences before execution. For each candidate tool, a tool-conditioned world model forecasts changes in residual degradation, image quality, and fidelity, together with the risk of harm and the uncertainty of the prediction. The agent executes the top-ranked candidate, and an independent verifier commits or rolls back its output before the agent replans from the observed state. PreActIR also audits whether performance is limited by the selector or by the candidate space, and studies targeted tool adaptation as a controlled way to expand that space. In a controlled evaluation that fixes the candidate pool, verifier, and budget and employs reference-annotated degradation states, PreActIR uses 42.5% fewer real tool calls and 63.4% fewer rejected calls than reactive, execute-then-evaluate trial and error, while improving Y-PSNR by 0.92 dB.

Altermagnetism gives rise to momentum-dependent spin splitting without net magnetization. Here, we use angle-resolved photoemission spectroscopy (ARPES) to investigate bulk $\alpha$-MnTe single crystals cleaved along the $(1\bar{1}00)$ plane - an orientation that preserves the compensated magnetic symmetry at the surface and substantially reduces surface effects and $k_z$ broadening. We resolve the three-dimensional bulk band structure with markedly enhanced spectral clarity. The $d$-wave band splitting, driven by the altermagnetic order and spin-orbit coupling in the $\mathbf{\Gamma}-\mathbf{K}-\mathbf{M}$ nodal plane, shows a perfect match to theoretical predictions. We further establish that the valence-band maximum occurs near the $\mathbf{A}$ point, identifying the corresponding hole pockets as the states governing the transport properties. Spatially resolved measurements reveal systematic variations of the band dispersion along $\mathbf{\Gamma}-\mathbf{K}$ and $\mathbf{A}-\mathbf{L}$, associated with different pinning of the Néel vector at the surface. Our results establish a surface-sensitive route to resolving the bulk altermagnetic electronic structure of MnTe and provide direct spectroscopic evidence for Néel-vector-dependent band splitting.

Recent interest and realization of ultracold bosons confined in shell-shaped, or bubble, traps have opened up several directions in the study of Bose-Einstein condensates (BECs) in intrinsically curved geometries. Here, we explore the prospect of using thin spherical shell-shaped BECs as analog gravity simulators of an expanding or contracting curved universe. We study an interacting BEC bubble subject to a temporal quench of the interaction strength. Our theoretical approach, which uses a Bogoliubov treatment following a dimensional reduction of a spherical BEC to the low-energy excitations of a shell-shaped structure, demonstrates how this system serves as a laboratory analog for a positively curved universe having a time-varying scale factor. We investigate spontaneous pair production triggered by quenches associated with exponentially decaying or growing interaction strengths, focusing on the emergence of oscillations in the structure factor—analogous to Sakharov oscillations in the Cosmic Microwave Background angular power spectrum. We quantify the entanglement of the produced pairs via logarithmic negativity, and show how this measure may be extracted from the power spectrum. These findings establish a bridge between quantum information science and early-universe cosmology in a laboratory setting.

When people discuss which of several hypotheses is true, they share not only their beliefs but also their interpretation of each one, that is, the distribution of signals each hypothesis is expected to produce. This interpretation is an opinion about what each hypothesis means and what evidence it predicts, and it is revised only through conversation, not by confronting it with the observed data. Standard non-Bayesian social learning captures only belief-sharing and keeps the likelihoods private. We study what happens when agents share both beliefs and likelihoods under static networks. We show that interpretations converge geometrically to a common reading shaped by the most influential agents. Then, beliefs concentrate, almost surely and at an exponential rate, on the hypothesis that, under this consensus interpretation, best explains the signals privately observed by all agents taken together. As a result, sharing interpretations can lead a population to adopt, unanimously and confidently, a hypothesis it would have rejected if it had shared only beliefs. Whether this helps or hurts when a true hypothesis exists depends on how accurately agents initially read the data they observe. When every agent initially interprets the true hypothesis exactly as the data it would observe, sharing interpretations cannot strictly improve learning and can strictly harm it when agents observe different data distributions. When interpretations are logically coherent and some agents misread their own data, sharing can either rescue the population, leading it to learn the true hypothesis, if an accurate reading dominates the interpretation network, or corrupt it, leading it to a wrong hypothesis, if a misreading one does.

The zero modes of the Aharonov-Casher Hamiltonian form an exactly flat, vortexable Chern band in any nonuniform magnetic field, analogous to the lowest Landau level. We ask which local Hamiltonians host exactly flat higher-vortexable bands. For a scalar Hamiltonian, an exactly flat first-vortexable band requires a mass proportional to the local field; the Dirac analogue has the same structure. For periodic Bernal bilayer graphene with nonzero mean flux, the exact zero-mode pair is genuinely first-vortexable if and only if the interlayer hopping has nonzero mean; zero-mean hopping instead gives a decomposable pair. Multiorbital models yield exact higher-vortexable chains to arbitrary order, while remaining first order in momentum.

We prove two height inequalities for rational points on abelian varieties over function fields of characteristic 0. The first is the GCD inequality, which shows that the height with respect to a closed subscheme of an abelian variety of codimension at least 2 is much smaller than the usual height function. This can be viewed as a compact and geometric analogue of a theorem of Levin. The second is a special case of the (geometric) abc conjecture proposed by Vojta, which compares the truncated counting function and the usual counting function. This is a compact analogue of a theorem of Guo, Nguyen, Sun and Wang, and also resolves a conjecture of Buium, which was only known for traceless abelian varieties or constant abelian varieties previously. The proofs of these inequalities follow a common three-step pattern: from microscopic local estimates to local estimates, and then to global estimates. Building on the canonical Xie-Yuan heights, we control discrete counting functions by continuous integrals of Betti forms. The main new tools are uniform Nevanlinna-type estimates for families of linear entire curves on abelian varieties; combined with covering arguments based on Besicovitch theory and averaging, these handle overlaps and gaps precisely.

In Inflation without an Inflaton (IWI), a de Sitter (dS) background drives inflation, and the graviton bilinear generates scalar perturbations at second order, with no inflaton or additional fundamental scalar field. We investigate how this scenario can account for the observed scalar spectral tilt. The tensor-mode dependence of the scalar power spectrum gives the consistency relation $n_s-1=2n_T$, since it contains four tensor mode functions. The scalar spectral tilt $n_s\simeq0.9649$ at CMB scales therefore gives $n_T\simeq-0.0175$, independent of the tensor-to-scalar ratio $r$, hence different from the standard single-field slow-roll prediction $n_T=-r/8$. A full time-dependent calculation of $\phi_2$ in exact dS leads to an almost scale-invariant scalar power spectrum, with a small blue infrared residual on the order of $n_s-1\simeq+4\times10^{-4}$. In order to account for the observed red tilt, we introduce a slow drift in the Hubble rate, parametrized by $\varepsilon=-\dot H/H^2$. The tensor tilt is then given by $n_T=-2\varepsilon$, implying $n_s-1\simeq-4\varepsilon$, at leading order. The observed tilt requires $\varepsilon_\ast\simeq0.0088$, far exceeding the drift that can be sustained by the classical graviton backreaction, for which we find $|\varepsilon_{\rm self}|\lesssim10^{-11}$. Therefore, we investigate the quantum break-time of dS as the origin of the background evolution. In this picture, the scalar tilt becomes $n_s-1=-4C_qN_{sp}(H/m_{pl})^2$, where $C_q$ is an order-one depletion coefficient, and the tilt is directly connected to the particle content of dS, $N_{sp}$. The evolution of the drift itself further predicts a positive running of $\alpha_s=+\tfrac12(1-n_s)^2\simeq+6\times10^{-4}$. These results conclude the distinctive observational predictions of the IWI scenario, establishing it as a falsifiable alternative to standard inflaton-driven models.

This paper investigates when and why stacking programmable metasurfaces into Stacked Intelligent Metasurfaces (SIMs) improves linear transformation synthesis at a fixed phase-control budget. The analysis shows that algebraic Jacobian rank alone is insufficient to characterize practical synthesis, which also depends on the strength and balance of the sensitivity directions generated by the available controls. A layer-resolved analysis of the cascade model explains how inter-layer propagation can generate complementary sensitivity directions. The relevance of this mechanism is then assessed using an S-parameter multiport model that includes electromagnetic coupling and multiple scattering. Numerical results in near- and far-field sensing scenarios show that distributing the same control resources across multiple layers can strengthen weak transformation directions, improve Jacobian conditioning, and substantially enhance synthesis accuracy. These findings explain why increasing depth can offer benefits that are not obtained by simply enlarging a single programmable surface, and identify layer complementarity and Jacobian conditioning as useful criteria for SIM architecture design.

This paper addresses the computation of persistent homology for filtrations of cellular cosheaves over a fixed cell complex, where the algebraic data vary along the filtration while the underlying topological structure remains unchanged. We extend methods from discrete Morse theory to this setting, establishing conditions under which chain complexes can be reduced while preserving the associated persistence module. Building on these results, we introduce "FilteredScythe", an algorithm that identifies Morse matchings compatible with all stages of the filtration and performs reductions using Schur complements, based on the exist "Scythe" algorithm. We prove the correctness of these reductions and establish bounds on the algorithm's time and space complexity.

Given $n$ distributions (hypotheses) $\mathcal H=\{H_1,\ldots,H_n\}$ and samples from an unknown target distribution $P$, proper hypothesis selection seeks a distribution whose total variation distance to $P$ is close to the best achievable within the known distributions. We give an algorithm that, using $O(\varepsilon^{-2}\log(n/\delta))$ target samples, running in $O(n\varepsilon^{-2}\log(n/\delta))$ time, with probability at least $1-\delta$, returns $H_{\hat i}$ satisfying $d_\mathrm{TV}(P,H_{\hat i})\leq 3\min_{i\in[n]}d_\mathrm{TV}(P,H_i)+\varepsilon.$ The algorithm achieves the optimal approximation factor and sample complexity. The running time improves the dependence on the failure probability from polynomial to logarithmic in the state-of-the-art bound $\tilde{O}(n\varepsilon^{-2}\delta^{-1})$ of Aamand, Aliakbarpour, Chen, and Silwal (COLT 2026), thereby answering their Question~2.

Advances in polymer synthesis and computational modeling are expanding the block-copolymer architecture space accessible for phase-behavior design. Machine learning can accelerate this exploration, yet a common representation capable of learning across diverse chain topologies remains lacking. Here, we present a graph neural network (GNN) representation of acyclic AB multiblock architectures, tested by random-phase approximation (RPA) instability prediction. Each chain is represented as a graph, enabling a common model to learn across diverse topologies. This representation, which organizes RPA-related information, retains predictive capability when extrapolated to architectures with more blocks and demonstrates its potential for reuse across tasks through transfer to instability-wavenumber prediction. By effectively linking block-copolymer chain architecture to field-theoretic response, this graph representation not only reconstructs stability-limit curves but also provides a practical route for future self-consistent field theory exploration of ordered phase space across complex topologies.

We prove an \(L\log L\)-endpoint Cwikel estimate on quantum tori $\mathbb T_\theta^d$, i.e., for every \(d\geq 1\) and \(x\in L\log L(\mathbb T_\theta^d)\), \begin{equation*} (1-\Delta)^{-\frac{d}{4}}\lambda(x)(1-\Delta)^{-\frac{d}{4}}\in\mathcal{L}_{1,\infty} \end{equation*} with a bound depending only on the dimension, where $\lambda(x)$ is the left multiplication by $x$. The main ingredient is an abstract weak Hilbert–Schmidt estimate for multiplication operators in finite von Neumann algebras whose \(L_2\)-spaces admit orthonormal bases of unitaries. When $\theta=0$, our argument also gives a simpler proof of the $L\log L$ Cwikel estimate on classical tori. For $d\geq2$, we use the $C^*$-algebraic principal symbol map to prove Weyl's laws for finite sums \[ \sum_{\ell=1}^N S_\ell(1-\Delta)^{-d/4}\lambda(x_\ell) (1-\Delta)^{-d/4}T_\ell, \] where $x_\ell\in L\log L(\mathbb T_\theta^d)$ and $S_\ell,T_\ell\in\Pi$, the $C^*$-algebra generated by $\lambda(C(\mathbb T_\theta^d))$ and Fourier multipliers with continuous symbols homogeneous of degree zero. We also prove a semiclassical Weyl's law for critical Schrödinger operators with $L\log L$ potentials.

The adverse-pressure-gradient (APG) effect challenges the classical scaling of turbulent boundary layers (TBLs) over a flat plate, and it remains unclear whether outer-layer similarity holds across a wide range of APG strengths.We assemble a benchmark comprising the present direct numerical simulation of a suction–blowing-induced separation bubble and published profiles, spanning Clauser parameters $\beta_e=0.04$–$180$ and Reynolds numbers $Re_\theta=530$–$19000$. Across this broad $(\beta_e,Re_\theta)$ parameter range, existing APG normalizations do not simultaneously collapse the two mean-velocity defects and four Reynolds-stress components, leaving open whether outer similarity persists. Instead of defining new scalings, we normalize each quantity by its value at a common location $y_s$. Results are shown using $y_s=0.5\delta$, beyond the outer stress peaks. For each of the six quantities, the normalized profiles exhibit a common outer shape across the conditions, with collapse emerging for $y/\delta\gtrsim0.2$ for the velocity defects and $y/\delta\gtrsim0.4$ for the Reynolds stresses. The collapse-error analysis shows that outer self-similarity is retained over a broad range of $y_s$ within the outer region and is not restricted to $y_s=0.5\delta$. Furthermore, explicit expressions are provided for the normalized outer profiles. These results support component-wise outer similarity under strong APGs and provide compact references for APG turbulence-model assessment and conditional profile reconstruction.