Papers

We study the eigenvalues of the negative Dirichlet Laplacian $-\Delta$ in domain $D_{\epsilon,N}$ obtained by removing $N$ Euclidean balls of radius $\epsilon$ from a bounded open set $D\subseteq\mathbb R^d$ ($d\ge2$). It is known that, for the balls centered at points drawn independently from a distribution with probability density $\rho$ and for $N\to\infty$ and $\epsilon\downarrow0$ so that the aggregate Newtonian capacity of the removed balls tends to some $\kappa>0$, the eigenvalues of $-\Delta$ in $D_{\epsilon,N}$ homogenize to those of the Schrödinger operator $-\Delta+\kappa\rho$ in $D$. Here we prove that, for the eigenvalues that are simple in the limit, a multivariate Central Limit Theorem holds in all $d\ge2$ under centering by expected values. Unlike earlier work in $d=3$ by Figari, Orlandi and Teta and, independently, Ozawa from 1980s that was based on resolvent expansions, we rely on martingale representations and one-ball perturbation asymptotic controlled by methods of harmonic analysis.

Ground-based cosmic microwave background (CMB) experiments filter their time-ordered data to remove $1/f$ noise and ground pickup, which removes or mixes the large angular scales where primordial $B$ modes peak. A common remedy is a pseudo-$C_\ell$ estimator with harmonic $B$-purification and a transfer function measured from simulations. Another applies it after a matrix-based $E/B$ purification of the maps. We extend the quadratic maximum-likelihood (QML) estimator of CosmoForge to filtered maps, treating the filter exactly: a linear filter conjugates the estimator's ingredients without altering its structure. The same holds for the pixel-based likelihood of CosmoForge, which gives the smallest error bar achievable on the same maps. We compare all methods in a simplified setup under several map-level filters through the error bars on bandpowers and on the tensor-to-scalar ratio $r$. QML sits $2$ to $4\%$ above the pixel-likelihood bound on $\sigma (r)$ in every filter state. At low noise, the pure pseudo-$C_\ell$ $\sigma (r)$ is $1.21$ times QML's without filtering, $3.0$ times under a scan filter along stripes of constant declination, and $3.7$ times under one from a toy constant-elevation scan. The matrix-purified pseudo-$C_\ell$ $\sigma (r)$ is at most $1.03$ times QML's except under the constant-elevation filters, where it reaches $1.10$. These factors shrink towards unity at higher noise. The pure pseudo-$C_\ell$ gap comes from apodisation and from harmonic $E/B$ separation; pixel-space separation closes it, except under the constant-elevation filters, which attenuate modes rather than remove them and widen the gap. QML stays within a few per cent of the optimal error bars without the tuning and simulated transfer functions of the pseudo-$C_\ell$ pipelines. Thus, CosmoForge provides a robust framework for power-spectrum estimation and inference on filtered maps. (Abridged)

On-policy distillation (OPD) trains a student on its own rollouts under a frozen teacher, mitigating the distribution mismatch of off-policy supervision. While prior work has primarily trained on problems a student can largely solve, we ask whether OPD can improve a student when training is restricted to problems it currently fails. We evaluate five representative OPD mechanisms with Qwen-3 and Phi-4 models under a unified competition-mathematics protocol. We find that OPD does not improve accuracy on this hard subset, with most mechanisms instead degrading performance despite continued decreases in training KL divergence. All eight configurations show a decline, and the two-sided sign test gives p=0.0078. In contrast, the same pipeline improves accuracy by 4.6 percentage points when training is not concentrated on failures, showing that the failure is conditional on the training regime rather than systematic. These findings suggest that OPD is effective when supervision is dominated by correct student prefixes, but can reinforce existing errors when training is concentrated on problems the student currently fails.

We introduce Fish Audio Drama 3, an open-source speech generation model that turns text into directed performances, built on a 35B-parameter mixture-of-experts backbone that activates 3B parameters per token. It clones voices from multiple references, follows natural-language direction, revises a take when the next turn gives a note, voices multi-character scenes, edits existing speech by infilling, and synthesizes long-form and streaming audio. Multi-turn revision, scene dubbing, editing by infilling, and streaming text input are new in Drama 3, all in one model. Drama 3 pairs the hybrid linear-attention backbone with a new codebook multi-token-prediction audio decoder that predicts the acoustic codebooks of each frame in dedicated layers that attend over the entire sequence. The model is trained with a three-stage pre-training recipe, instruction fine-tuning, and large-batch reinforcement learning whose only reward is a single learned model of human preference. Its inference engine decodes a single stream at 271 frames per second on one H200, against 177 for Fish Audio S2, although Drama 3 has more than seven times as many parameters. The model weights are available on GitHub (https://github.com/fishaudio/fish-speech) and Hugging Face (https://huggingface.co/fishaudio/drama-3), and inference is available through SGLang-Omni (https://github.com/sgl-project/sglang-omni). We highly encourage readers to visit https://fish.audio to direct their own performances.

Modern distributed training is costly to debug, tune, and analyze because faithful analysis often requires repeated target-scale executions. We observe that many analysis tasks depend on the original distributed execution path, but not on full all-rank execution. We present RankLens, a single-rank emulation system that runs one survivor rank on a single GPU while preserving the target job's distributed semantics. The survivor rank executes the original training program and performs real local computation. At communication boundaries, the system replaces real multi-rank communication with task-dependent semantics, selectively restoring recorded communication results and recorded or estimated completion timing while preserving the asynchronous dependencies required for analysis. This enables replay from real executions and supports analysis, debugging, and tuning with existing debuggers and performance analysis tools. We evaluate the system on DeepSpeed and Megatron-LM across 8-64-GPU target configurations. RankLens achieves 100% training-tensor communication-structure match, keeps emulation timing error below 5%, supports local anomaly reproduction and execution analysis, and reduces the resource requirement of these analyses from target-scale clusters to a single GPU.

For every von Neumann algebra \(\M\), we prove that each bounded sequence in the Haagerup space \(L_1(\M)=\M_*\) admits either a norm-convergent subsequence or a \(2\)-co-lacunary subsequence. This answers an open problem of Parcet and Randrianantoanina \cite[Remark~3.11]{ParcetRandrianantoanina2006} and removes both hyperfiniteness and semifiniteness.

LLM agents now act as delegated communication intermediaries: they read private context, draft messages, and send externally visible emails on behalf of a user. Existing checker-repair defenses can reduce inappropriate disclosure, but they rely on repeated calls to a remote action LLM (the model that drafts and repairs the email) and a remote checker LLM whenever a draft fails validation. This creates a cost problem as well as a privacy problem, especially when a requester strategically asks for exact values, raw records, source evidence, or other details that induce leakage-heavy drafts. We propose local contract-conditioned rewriting as a cost-efficient enforcement layer for email-generating agents. The mechanism intercepts an outgoing draft, constructs an information-release contract that specifies what to preserve, generalize, and forbid, rewrites the draft with a local Gemma rewriter, and selectively invokes a final PrivacyChecker. Across extensive email tasks under normal prompts and attack prompts that operationalize strategic information requests, Gemma + Checker reduces normal-prompt leakage from 11.41% to 4.03% while improving UsableRate (satisfied or partially satisfied outputs) from 85.2% to 92.6%. Under the strategic attack-prompt condition, it reduces leakage from 28.19% to 18.79% and reduces checker-only cost amplification from 1.32x to 1.02x. Offline replay ablation shows that the full contract reduces leakage relative to generic Gemma rewriting by 36.3% under normal prompts and 54.1% under attack prompts. These results support a local-first privacy enforcement design: move repair to a cheaper trusted local layer when possible, but retain the checker as the final semantic gate for high-risk sends.

We study a truthful facility location problem in which agents have private positions in a metric space and known approval preferences over two distinct facilities. Each agent incurs a cost equal to her total distance from the facilities she approves. The goal is to locate the facilities at a given set of candidate locations so as to approximately minimize either the social cost or the max cost, while incentivizing the agents to report their positions truthfully. This problem was previously studied for line metrics and deterministic mechanisms. We first settle the approximation ratio of deterministic mechanisms for the social cost on the line by establishing a lower bound of $7$, matching the upper bound from previous work, and show that randomization leads to a strict improvement. For the max cost, we show that the previously known optimal deterministic guarantee of $3$ remains tight even for universally strategyproof mechanisms. We then turn to general metric spaces. For deterministic strategyproof mechanisms, we obtain tight approximation ratios of $2n-1$ for the social cost and $5$ for the max cost. We also show that randomization yields substantial improvements for both objectives: for the social cost, we obtain a tight characterization, while for the max cost we establish nearly matching upper and lower

Surface reconstruction from range scans is challenging in the presence of noise and outliers, as fidelity to observations must be balanced against sensitivity to measurement errors. Yet, most neural approaches discard the sensor positions and corresponding visibility information, compensating for this loss with geometric priors or regularization terms. We instead formulate surface reconstruction as robust regression of the predicted first surface intersection along each acquisition ray against its measured depth, which penalizes predicted surface intersections within the segment between the sensor and the observed point. We represent the surface as the zero set of a 1-Lipschitz multi-layer perceptron, allowing the use of linearly convergent sphere tracing to compute the first hit, and use a robust Huber loss for regression. Our formulation requires neither oriented normals, sampled off-surface points, nor an eikonal loss. Comparisons with the state of the art on synthetic and real data with varying levels of noise and outlier contamination demonstrate competitive performance on clean data and much improved fidelity and robustness under even moderate corruption. Our analysis further confirms a trade-off between fidelity and robustness: greater fitting capacity improves data fidelity in the clean case but increases sensitivity to the measurement errors inherent in real acquisitions, with a sweet spot typically emerging at intermediate capacity.

Coding agents use generated tests to decide whether a proposed patch satisfies an issue's requirements. A suite that fails on the buggy program and passes after applying the reference patch can still accept an incorrect patch or reject a correct patch. We introduce SWEPATCHTEST, a test-generation benchmark with 619 tasks from SWE-bench Pro, SWE-bench Multilingual, and DeepSWE and 82,579 candidate patches collected from coding-agent trajectories. By replaying each suite on the buggy and patched codebases, \benchmark jointly measures issue reproduction, acceptance of correct patches, and rejection of incorrect patches. Joint Validation Rate (JVR), which requires all three criteria on the same task, exposes failures hidden by single-reference evaluation: the best-performing configuration achieves only 9.21% JVR despite reproducing the reference transition on 59.29% of tasks. We further use validation scores to select and scale demonstrations for supervised fine-tuning (SFT). The resulting training recipe approximately triples JVR and improves downstream repair across three SWE-bench benchmarks. Patch discrimination thus provides both a diagnostic measure of test quality and an execution-based signal for curating agent training data.

Compromised UAV reporters can poison latency telemetry and attract offloaded tasks to degraded servers. We present FleetGuard, an identity-capped conformal offloader for local, edge, and cloud execution. With equal buffers of m scores and a cap of K compromised identities, a Km rank correction retains one-sided fixed-level coverage without an honest-reporter majority. A deterministic repair scheduler allocates task-specific risk under fleet, capacity, and deadline constraints. Heavy-tailed simulations with eight reporters, four edges, 30 independent seeds, and 20 batches per seed and condition yield 2.08% deadline misses under seven low-score compromised reporters (95% clustered interval: 1.94-2.24%), compared with approximately 9.6% for pooled conformal, reporter-median, and mean rules. FleetGuard saves 22.3% energy over fixed-risk BRC and approaches adaptive exact assignment within 1.1%, with 2.6x lower mean scheduling time.

We study minimizers of the optimal Sobolev quotients for the critical embeddings $D^{1,p}(\mathbb R^N;\mathbb R^m)\hookrightarrow L^{p^*}(\mathbb R^N;\mathbb R^m)$ and $W^{1,p}(\Omega;\mathbb R^m)\hookrightarrow L^{p^*}(\Omega;\mathbb R^m)$. In the whole space, we classify all minimizers as $\boldsymbol u=\boldsymbol c\,U_{\delta,x_0}$, where $\boldsymbol c\neq\boldsymbol0$ and $U_{\delta,x_0}$ is an Aubin–Talenti bubble. On bounded domains and for $\lambda>0$, we equip $W^{1,p}(\Omega;\mathbb R^m)$ with $ \|\boldsymbol u\|_\lambda^p :=\int_\Omega \bigl(|D\boldsymbol u|^p+\lambda|\boldsymbol u|^p\bigr) $. Using scalar attainment results, we establish existence and synchronization of vectorial minimizers. At resonance, we consider the pure Neumann problem $ -\boldsymbol\Delta_p\boldsymbol u =|\boldsymbol u|^{p^*-2}\boldsymbol u\ \text{in }\Omega. $ For the associated quotient, we prove existence and global $C^1(\overline\Omega)$ regularity of minimizers. Finally, we prove synchronization of radial solutions and deduce symmetry breaking on balls.

Diffusion language models (DLMs) enable flexible parallel generation by resolving tokens according to the model's evolving predictability rather than a fixed left-to-right order. This flexibility, however, introduces training choices absent from standard autoregressive teacher forcing: which reference tokens are visible when a target is supervised and how much generation space is allocated. Standard supervised fine-tuning (SFT) typically makes these choices through random masking, independently of inference. Our analysis shows how this training-inference mismatch can misdirect supervision. Random masking can conceal prediction errors or penalize uncertainty that decoding would otherwise resolve, while the attention-visible input length can change which response formulations the model favors, even when the underlying solution is unchanged. Motivated by these findings, we propose Predictability-Aware Canvas Selection and Supervision (PACS), an SFT method. PACS uses the model's own predictability to select each example's attention-visible input length and supervises reference tokens immediately before their confidence-guided revelation. Across reasoning and code-generation benchmarks, PACS consistently achieves the highest mean accuracy among the compared SFT methods, with gains of up to 12.84 percentage points over vanilla SFT on individual benchmarks. Code will be released upon publication.

Noise characterisation not only enables error mitigation but also provides valuable information about the intrinsic performance of a quantum device, identifying dominant error contributions and bounding noise stability well beyond the aggregated calibration data. Deploying such methods on a specific hardware topology must combine efficiency and accuracy, assess noise stability, and validate the reconstructed noise model. Here we develop and implement these methods on a superconducting processor with square-lattice topology. First, we revise the cycle-benchmarking protocol and reduce the bias arising from unlearnable degrees of freedom via a regularised cost function. Second, we extend a previously developed tensor-network tomography method to match the device layout and show how its accuracy can be improved by repeated layer execution. Both methods allow approximate sublayer noise models to be extracted from parent ones. Using noise characterisation as a tool, we map the noise structure, track drift, and validate the adequacy of the learnt noise models against experimentally observed noisy estimations in benchmark physical and chemistry circuits. These results inform further improvements in the underlying technology and provide estimates of the size of noise-mitigated circuits that the device can support.

Humanoid behavior foundation models (BFMs) enable diverse whole-body control, but adapting a pretrained controller to a new embodiment remains challenging because of kinematic and dynamic mismatch. We present TRACE, a framework for efficient cross-embodiment adaptation that preserves pretrained motion representations while specializing feedback control to the target robot.TRACE first injects kinematic priors into input and output projection layers and aligns nominal joint dynamics to reduce embodiment mismatch and support stable fine-tuning. It then combines encoder distillation with low-rank reinforcement learning on a compact, quality-screened motion set, using a two-phase curriculum to establish stable tracking before refining difficult motions. We apply TRACE to transfer SONIC from Unitree G1 to Unitree H2 using 10 million motion frames and approximately eight hours of training on a single RTX PRO 6000 GPU, at less than 0.1% of the GPU-hour cost of training SONIC from scratch. The adapted controller achieves 96.08% success on 67,953 evaluation motions under a height-scaled tracking criterion. Real-robot demonstrations span dynamic motion tracking and whole-body teleoperation, with collected demonstrations supporting downstream vision-language-action policy post-training. These results demonstrate practical reuse of a pretrained humanoid controller across robots with different body scales and dynamics.

Spiking Neural Networks (SNNs) are promising for energy-efficient neuromorphic computing, but they still suffer from catastrophic forgetting when learning tasks sequentially. This work investigates the integration of Experience Packing and Replay (EPR) as a memory-efficient continual learning strategy for deep SNNs under low-latency constraints. The proposed framework combines Batch Normalization Through Time stabilized VGG9 SNNs with Spike Activation Maps (SAM), which provide forward-only explanations based on spike activity. These explanations are temporally aggregated into spatial attention maps and used to select the most informative image patches for replay, instead of storing full images. Experiments on Split CIFAR10 and Split CIFAR100 show that SAM-guided EPR improves the accuracy-memory trade-off under tight memory budgets, and remains competitive while requiring substantially less storage.

Research evaluation has developed around quantity, citation impact and, more recently, the accumulation of research excellence, but these dimensions remain largely dependent on citations, which describe how research is received rather than what it contains. We propose uniqueness as a complementary dimension and measure it with the Research Uniqueness Index (RUI), which asks how far a university's research sits from what is typical in its field, using no citations but the content of the research itself. Each researcher is represented by an embedding of their abstracts, and an unbalanced version of Optimal Transport returns the share of that work which cannot be matched into a random sample of same-field researchers, the standard population; that unmatched share is the score. Because every researcher is scored, a university is a distribution rather than one number, and we treat that distribution as the indicator: it shows whether uniqueness is spread across an institution or concentrated in a few groups. Quantiles summarise it and, being quantiles, do not reward size. Since uniqueness is defined only relative to a field, we demonstrate the index within one, neuroscience (Scopus, 2021-2025; 9,861 reference researchers). All ten universities studied sit well above the standard (RUI_median 0.40-0.53 versus 0.27) and five specialised institutes higher still (0.57-0.73), the most unique work often confined to a narrow niche that the same scores name. RUI is uncorrelated with citation impact, and a controlled test confirms that it tracks displacement from the field rather than topical concentration; results are robust to an alternative embedding and replicate in computer science and economics. The index is not intended as a league table: the gap above the standard and the researcher-level niche structure are stable, whereas the order among adjacent universities is not.

Sugarcane leaf diseases severely impact crop yield and quality, making accurate and timely detection critical for sustainable agriculture. Conventional deep learning models for plant disease detection depend on large annotated datasets, which are expensive to obtain and challenging to prepare due to challenges commonly observed across crop disease detection tasks, including (i) high intra-class variation caused by diverse symptom expressions across growth stages, (ii) subtle inter-class similarities between diseased and healthy tissues, and (iii) the risk of noisy labels degrading model reliability. To handle these challenges, we presented an Uncertainty-aware Mean-Teacher based Semi-Supervised Learning Disease Detection Network (U-SSDNet) that leverages unlabeled data while maintaining robustness. First, discrete wavelet transform preprocessing is applied to enhance lesion visibility and reduce intra- class variation. Subsequently, the KL divergence is employed to refine the pseudo-labels and reduce the impact of confirmation bias. At the same time, supervised contrastive learning is applied to make the features more distin- guishable and improve the separation among different classes. Experimental evaluations on sugarcane leaf disease datasets, considered a representative case study, demonstrate that the proposed approach achieves performance close to that of fully supervised models while requiring far fewer annotated samples and consistently outperforms state-of-the-art supervised and semi-supervised approaches.

We study the two-dimensional non-rotating primitive equations with anisotropic viscosity and no thermal diffusion. For doubly periodic perturbations of a hydrostatic equilibrium with an affine temperature profile, we establish local Hadamard well-posedness in Sobolev spaces under strict stratification. The initial horizontal velocity and temperature have sufficient regularity and vanishing vertical means, but need not be small. The estimates close at the same Sobolev order for these variables despite the horizontal derivative loss in the diagnostic vertical velocity. Stratification-weighted energy estimates and a horizontal compensation argument avoid an additional temperature derivative while retaining the full vertical dependence and the vertically homogeneous velocity component determined by periodic compatibility. A one-sided comparison places higher-order norms of the more regular solution only in terms involving lower-order differences. This structure allows the Bona–Smith method to yield continuous dependence in the original Sobolev topology. We obtain a unique maximal strong solution in the strictly stratified class, together with continuous dependence of the diagnostic vertical velocity and pressure in their natural Sobolev spaces and lower semicontinuity of the maximal lifespan.

Symbolic regression is the problem of finding an expression that fits a dataset. Solving it requires searching a combinatorial space of candidate expressions. Neural symbolic regression can amortize that search by training a model once on synthetic data and then predicting expressions for a new dataset. But existing models still underperform genetic programming on real, noisy data. We argue that the deficit lies in the training rather than in the paradigm, and present RASR (Reinforced Amortized Symbolic Regression), a method with two key changes to the training recipe. First, we design a synthetic prior that narrows the gap with real-world data: inputs come from the prior of a tabular foundation model; constants are sampled bottom-up, conditioned on the data; targets carry heteroscedastic and structured noise; and everything is standardized. Second, we split training into two stages. Supervised pre-training maximizes the token-level likelihood of a reference expression. This is followed by reinforcement-learning post-training that aligns the model with its inference-time use by rewarding held-out fit and penalizing expression size. On the black-box track of SRBench 2.0, RASR achieves the best mean test $R^2$ rank of all evaluated methods. Three RASR variants, trained with different size penalties, make up most of the accuracy-complexity Pareto front. On Strogatz, our method recovers more ground-truth expressions than any baseline, and on Feynman it is competitive with the best-performing methods.

Certified machine unlearning ensures the proximity between the unlearned model and a model retrained without the data to be forgotten. Extending this framework to sequential deletion requests, typically arriving as groups of variable size (e.g., all records of one user or of coordinated users), is challenging. For unlearning methods based on fine-tuning on the retain sets, this leads to either degrading performance or increasing computation as the number of unlearning requests grows. For independent successive requests, we instead certify each model release against a counterfactual unlearning trajectory in which the group being deleted never took part. With a fixed fine-tuning budget per deletion, we show that, for smooth strongly convex objectives, this approach keeps the performance loss bounded, uniformly in the number of requests. Experiments with multiclass logistic regression on FEMNIST show that the resulting algorithm needs fewer corrective steps than existing sequential methods and outperforms training-time differential privacy, particularly when group sizes are heterogeneous.

Classical Turán theory relates the asymptotic extremal problem for an ordinary forbidden graph to its chromatic number. This principle fails when a forbidden copy must respect prescribed vertex colors, as occurs naturally in multipartite extremal problems and in embeddings with prescribed clusters. We study properly vertex-colored graphs whose hosts have a prescribed density between every pair of color classes, with containment interpreted through color-preserving homomorphisms. Our main theorem gives a finite directed reduction: for every fixed $m$ and $\varepsilon>0$, every sufficiently many-colored $d$-dense host admits a colored homomorphism from an $m$-layer half-blowup $D[m]$ of a finite digraph $D$ with density at least $d-\varepsilon$, where $D$ may be chosen with $\lceil\varepsilon^{-1}\rceil$ vertices. Consequently, the colored Turán density of every non-empty finite forbidden family equals the homomorphism Turán density of its associated acyclic orientations. We then determine the complete finite value set: these densities are exactly the Lagrangians of finite loopless digraphs, and hence are rational. The main technical input is a low-resolution sampling method that preserves all pairwise bipartite degree profiles on a large subfamily of color classes while keeping the sample size independent of the number of retained classes.

Recovering high-quality images from degraded underwater observations is crucial for underwater exploration. Polarization observations show promise as an effective source of complementary physical cues for recovering target radiance under clear-water conditions. However, existing methods have yet to jointly model raw intensity information and polarization cues to enable image restoration driven by an understanding of mixed degradations (color casts, haze, and low light). To overcome these limitations, we propose PolUR, a unified multimodal language-driven framework that jointly uses polarization and RGB information to identify degradation types and severity levels through structured semantic instructions and enhances joint restoration representations under the guidance of degradation-aware semantic features to improve restoration robustness under mixed degradations. We further construct a new benchmark named MixPolar, which contains underwater images exhibiting real-world degradations and their corresponding degradation descriptions. MixPolar supports systematic evaluation of degradation perception, image restoration, and performance on downstream tasks. Extensive experiments demonstrate that PolUR effectively integrates polarization and RGB information, achieving competitive performance in degradation perception and image restoration, while also demonstrating generalization capability and utility for downstream tasks.

We use Loewner-Kufarev evolution to decompose the Brownian loop soup into a Poisson point process on Brownian bubbles which we call the Brownian bubble tea driven by $\rho$, where $\rho$ is the driving measure for the Loewner chain. The only assumption on $\rho$ is that the evolving boundaries are locally connected. This generalizes a similar disintegration result of Lawler and Werner to essentially optimal regularity, and includes foliations with finite Loewner-Kufarev energy as well as radial and whole-plane $\mathrm{SLE}_\kappa$ for all $\kappa \geqslant 0$. As applications, we give Brownian loop interpretations of the conformal distortion formula for Loewner-Kufarev energy and the relationships between the Loewner energy, Loewner-Kufarev energy, and the Schwarzian action.

A medical vision-language model may analyze a given CT scan and correctly detect both kidneys in view. Continuing this conversation, if a user provides a prescription with an opposite direction, medical VLMs often sycophantically choose to realign their diagnosis. In this work, we study regressive sycophancy under fabricated evidence, where a model abandons a correct answer when pushback comes with a fake document. We test four open VLMs on 400 VQA-RAD yes/no questions in 19,200 multi-turn conversations, with and without a fabricated prescription. Without a disclosure that documents are synthetic, the models abandon 80.1% of 6,488 correct answers. Notably, under one script each, the same prescription raises the flip rate of Qwen2.5-VL-7B from 45.9% to 89.6% and lowers that of Qwen3-VL-8B from 77.7% to 50.9%. A model rejected the prescription while still preserving the correct answer in 915 of 3,232 conversations with the prescription (28.3%), and 40% of these flipped in later turns. System-prompt sentences that disclose the documents as synthetic lower one model's flip rate from 77.8% to 47.3%. Thus, we conclude that awareness about a forgery does not prevent a model from adopting its answer.

We give two counterexamples to Stapledon's Effectiveness Conjecture. Each counterexample is a $6$-dimensional lattice polytope with an order-two symmetry whose equivariant $H^*$-series $\varphi[t]$ is a polynomial with one coefficient that is not effective. For polytopes with a symmetry of order two, the goal of this paper is to build up a picture of the landscape of results for when the Effectiveness Conjecture holds. Our main result is a criterion, in terms of the faces of $P$, that determines when the Ehrhart ring of $P$ admits an invariant linear system of parameters of the correct representation type. We use these results to reduce the space of possible counterexamples to one of two cases. A randomised computer search produced counterexamples in each case. We also give an example where the equivariant $H^*$-series is effective but admits no invariant linear system of parameters, neither for $P$ nor any invariant subdivision of it, answering a question of Stapledon in the case of groups of order two.

Energetic materials involve multiple interactions, making reliable machine-learning potentials (MLPs) difficult to construct without extensive datasets. Here, we enhance the ability of the neural network interatomic potential (NNAP) to describe molecular systems using sphmulti, a refined spherical-harmonic basis set that combines extra radial basis with element-specific chemical weighting in each radial channel. We further integrate hyperactive learning, farthest-point sampling, and iterative sufficiency criteria with knowledge-guided key events, enabling the NNAP to retain essential information for describing the material system. For 3,3'-diamino-4,4'-azoxyfurazan, the resulting NNAP is trained on only 13,680 configurations yet captures key properties, including the isomerization barrier, pyrolysis activation energy, and shock Hugoniot behavior. NNAP-driven molecular dynamics simulations further reveal that pyrolysis proceeds through furazan-ring opening followed by chain reactions, whereas shock loading induces anisotropic hydrogen transfer driven by interlayer structural deformations. This work enables efficient and reliable MLPs for energetic materials.

A common practice in instance retrieval is to grow the gallery size to improve a benchmark's discrimination capability. One prominent example is ILIAS, which adds up to 100 million distractor images. The prevailing assumption is that faithful evaluation demands web scale, and that indexing all 100M images through the backbone is the unavoidable price of a comparable number. That price is steep: hundreds of GPU-hours and ~200 GB of descriptors per model, paid again for every method or ablation. We show the web-scale indexing price is largely avoidable: evaluation itself obeys a scaling law. The number of distractors that outrank a positive is Binomial in the gallery size. We define the per-query retrieval hardness, a gallery-scale agnostic quantity that yields a retrieval metric at any scale, and demonstrate it can be derived from a small random sample. The underlying sampled-rank machinery is long established in recommender-system and biometric evaluation, but to our knowledge has never been adapted to visual retrieval. We make the law per-query and estimable, and validate it at true 100M scale on ILIAS and INSTRE, and on the full 759k-distractor Google Landmarks v2 pool. Concretely, within a 5% sample (a flat 20x less indexing), every backbone's tail-aware (EVT) estimate has converged onto the large-scale mAP, to within ~0.01 (mean absolute error 0.005), across five backbones, three benchmarks, and two distractor pools (mAP@1000 at 100M on ILIAS/INSTRE; the official mAP@100 at the full 759k pool on GLDv2); the recommender-systems count baseline over-predicts everywhere (+0.037 to +0.068). This is an order of magnitude better than naively reporting the metric on the same subset (+0.08 to +0.13). We release code and the per-query hardness to facilitate faster, cheaper, and greener retrieval evaluation.

We prove that the rational Chow ring of every connected component of the multi-scale compactifications of the genus three strata $\mathcal{H}(4), \mathcal{H}(2,2)$ and $\mathcal{H}(3,1)$ is generated by boundary-stratum classes. Our proof shows Chow-Künneth generation property of boundary strata of the multi-scale compactification by reducing the boundary analysis to lower-genus generalized strata of meromorphic differentials, including residueless loci, described through plane-quartic and plane-cubic models. As a consequence, the rational cycle-class map is an isomorphism and the compactifications have no odd rational cohomology.

Twisted bilayer graphene (tBLG) on H-intercalated SiC (twist angle of $9 \pm 1^{\circ}$) is studied by position\mbox{-}, time\mbox{-}, and angle-resolved photoemission spectroscopy (ARPES). Both graphene layers are hole doped, with a Dirac-point offset of 30~meV. Time-resolved ARPES near the van Hove singularity reveals a spectral feature within the hybridization-induced band gap, together with excited electrons in the conduction band. The in-gap feature exhibits distinct dynamics, and its binding energy and $k$-space location are consistent with the proposed non-hydrogenic “ghost-Fano” exciton arising from destructive interference between two nearly degenerate excitonic channels. Near the Dirac points, the twist separates the largely layer-polarized Dirac cones in momentum space, providing direct layer selectivity. We find markedly different peak electronic temperatures in the two graphene layers, even though their subsequent cooling dynamics are very similar. We attribute this to an ultrafast interlayer redistribution of electronic energy, driven by an interlayer electric field that arises from the different doping in the layers.