Papers

Recent work has shown that probabilistic flow matching for time series forecasting benefits from a data-matched prior. The resulting prior introduces local correlations, which a sequential architecture usually absorbs: a recurrent neural network (RNN), a structured state-space model (S4), or a Transformer. However, such a backbone costs GPU memory and time per epoch. A cheaper alternative is MLP-based latent-space flow matching: embed the time series via an invertible map to a single latent vector and learn the flow there, so a tabular MLP can treat the series as a set of features. The relationship between the prior and the choice of linear latent map is understudied in conditional flow matching (CFM) forecasting, yet we found it strongly affects performance. Fixed transforms such as Fourier or discrete cosine (DCT) are only well-conditioned for Ornstein–Uhlenbeck priors, while a principal-component (PCA) map fit to the data is a strong but training-set-dependent reference sensitive to train–test shift. Instead, we propose to use the Mercer eigenbasis of the prior kernel: it diagonalises the centred covariance exactly, decouples from training data, and adapts to non-stationary and periodic priors. On five GluonTS benchmarks (ETTh1, ETTh2, Weather, Electricity, Traffic) under a shared protocol with TSFlow, the resulting MLP matches or beats it on CRPS at about $4.7\times$ less training memory and $3.5\times$–$4.4\times$ less time per epoch.

Let $Y_{n,r,q}$ be the graph obtained from the Turán graph $T_{n,r}$ by adding $q$ pairwise disjoint edges inside a largest part, and let $c(n,F)$ be the minimum number of copies of $F$ created by adding a single edge to $T_{n,r}$. Fang, Li, Lin and Ma proved that for every color-critical graph $F$ with $\chi (F)=r+1$, there exists a constant $\delta_F>0$ such that for all sufficiently large $n$ and all $1\le q\le \delta_F \sqrt{n}$, the condition $\lambda(G)\ge\lambda(Y_{n,r,q})$ forces at least $q\, c(n,F)$ copies of $F$. The bound $q=O(\sqrt{n}\,)$ is tight up to a constant factor, in contrast to the linear order $n$ of the edge setting of Mubayi, Pikhurko and Yilma, but the exact constant $\delta_F$ remained unknown for any $F$. In this paper, building on a structural result of Fang, Li, Lin and Ma, we determine the threshold $\delta_F$ when $F$ is a clique and an odd cycle. For every $r\ge2$, we denote $\delta_r :=(1-\tfrac1r)\sqrt2$ and prove that for every $\varepsilon>0$, if $n$ is sufficiently large and $1\le q\le(\delta_r-\varepsilon)\sqrt n$, then every $n$-vertex graph $G$ with $\lambda(G)\ge\lambda(Y_{n,r,q})$ contains at least $q\,c(n,K_{r+1})$ copies of $K_{r+1}$, and $\delta_r$ is best possible. For odd cycles, the threshold is $1/\sqrt2$. For every $k\ge1$ and $\varepsilon>0$, if $n$ is sufficiently large and $1\le q\le(1/\sqrt2-\varepsilon)\sqrt n$, then every $n$-vertex graph $G$ with $\lambda(G)\ge\lambda(Y_{n,2,q})$ contains at least $q\,c(n,C_{2k+1})$ copies of $C_{2k+1}$, and $1/\sqrt2$ is best possible. Our results determine both the exact count of copies and the optimal range of $q$. The behavior in the spectral setting differs from the classical edge setting, in which the range of $q$ is of order $n$ and the threshold is $1/r$ for cliques by Lovász and Simonovits, and $1/2$ for odd cycles by Pikhurko and Yilma.

We establish complete outer-horizon thermodynamics for four exact rotating embeddings of Kerr–Newman and Kaluza–Klein seeds in four-dimensional, asymptotically flat Einstein–Maxwell–Maxwell–dilaton theory without a scalar potential. Constant-coefficient field maps determine the allowed couplings and charge variations. We obtain single-valued mass functions and verify the first law, Smarr relation, and scalar-shift identity on the stated regular branches and finite-area extremal boundaries, including magnetic patch contributions where required. For two distinct regular horizons with positive finite areas, the horizon combinations $2T_\pm S_\pm$ and $S_\pm\Omega_\pm/\pi$ satisfy a common quadratic relation with the long-range-force parameter determined by the asymptotic mass, electromagnetic charges, and scalar charge.

There has been significant recent interest in near-term qLDPC codes as high-performance alternatives to surface and color codes. One such class of codes is 2-dimensional translationally invariant (TI) codes, such as bivariate bicycle codes, which share similar properties to topological codes. Fundamental objects in the study of such codes are the materialised symmetries, which can be used for the construction of matching-based decoders. These decoders generalise the minimum-weight perfect matching decoder for toric codes and provide similar asymptotic performance guarantees that heuristic decoders such as BP and its variants lack. Despite this, the mathematical structure of symmetries along with their properties under translation and restriction to finite-sized lattices has not been well-studied. We describe a decomposition of symmetry spaces of 2D CSS TI codes on infinite lattices into translation-invariant subspaces which allow us to write an explicit basis of symmetries in a plane-wave-like form. We then describe how to adapt this infinite lattice basis so that any corresponding rectangular periodic lattice basis can be obtained by restriction to basis elements compatible with the periodic boundaries. This allows us to describe how the symmetry space varies with different rectangular dimensions. We illustrate via examples that it is often straightforward in practice to determine a basis of symmetries on twisted boundaries as well, without needing to recompute the decomposition. We comment on the applications of this framework to matching-based decoders and provide examples of symmetries of such codes as the gross code.

Recovering geometry, materials, and lighting from photographs is highly ambiguous when only static illumination is available. Active-lighting setups reduce the ambiguity but require dark rooms or specialized hardware. Instead, we synergize both static and flash lighting from casual indoor capture, with the flash on or off, each from independent viewpoints. The flash residual constrains albedo and the BRDF, while static lighting captures grazing-angle specular highlights that flash misses. With a 2DGS reconstruction framing, our key contribution is a GS-anchored diffuse field: a hash-encoded MLP is queried at the rasterized 2DGS depth. As it depends only on world position, it is view consistent in 3D and allows the flash residual to drive material decomposition instead of being absorbed by alpha-blending drift across views. At the same time, we render static lighting with deferred shading such that it can also supervise material decomposition. On five synthetic and three real indoor scenes, our method outperforms six recent baselines on diffuse color, albedo and roughness material parameters, and in relighting where PSNR improves by 4.17 dB over the next-best baseline.

We consider the fusion of lung ultrasound images with routinely-collected clinical and demographic data for the purpose of automated tuberculosis (TB) screening using deep-learning. Such deep-learning based screening tools for TB could meaningfully support the health care system in Africa, where the burden of disease is severe and resources are constrained. Beginning with an established ResNet baseline for classification of lung ultrasound images, which achieves an area under the receiver operating characteristic (AUROC) curve of 0.91 [0.86,0.96] (95% CI), we consider the incorporation of the clinical and demographic data using three fusion approaches. We find that a simple average-based fusion of the output scores of separately-trained image and clinical data classifiers consistently matches or outperforms a more complex approach where the data is fused earlier and a combined classifier is trained. Fusing the image and the clinical classifiers in this way leads to a classifier with an overall AUROC of 0.95 [0.91,0.99] (specificity of 0.76 at sensitivity 0.93) which is an improvement of 4% absolute over the image-only baseline. We also find that greedy feature selection can be used to reduce the number of clinical and demographic inputs without sacrificing classification performance. Finally, when we differentiate between clinical and demographic data that are self-reported, that require some basic measurement or calculation, and that require a point-of-care (POC) test, we find the inclusion of the POC tests included in this study to be of minimal benefit to classification performance. We conclude that the incorporation of routinely-collected clinical and demographic data is a promising way to improve the performance of lung ultrasound based automatic classification.

Oxley conjectured that a matroid with a circuit-cocircuit intersection of size $k\geq 4$ has one of size $k-2$. Using the standard polynomial representation of the classical extended binary Golay code, we construct an identically self-dual binary matroid of rank $12$ on $24$ elements. Its circuit-cocircuit intersection sizes are exactly $0,2,4,6,8$, and $12$, disproving the conjecture for $k=12$. The proof is self-contained and does not rely on the full weight distribution of the code or on an enumeration of all circuits.

Physics simulators can support the discovery of quantum experiments by predicting the states generated by experimental configurations. When these simulators are computationally expensive, repeated simulator calls can limit the search for experiments that generate a desired quantum state. Here, we develop a physics-inspired polynomial neural surrogate for PyTheus, a graph-based quantum-optics simulator, to predict quantum states and use it to design quantum experiments. Its polynomial activations are motivated by the relation between graph perfect matchings and the resulting state amplitudes. We train separate surrogate models for four-, six-, and eight-photon systems and show that they achieve higher prediction accuracy with fewer trainable parameters than standard multilayer perceptrons. We then use the trained surrogates for inverse design of GHZ, W, and linear-cluster states. For the larger systems, the surrogates also enable faster inverse design than direct optimization with PyTheus. These results suggest that incorporating the underlying physics into neural surrogates can provide an efficient approach to quantum experiment design.

Next-token prediction (NTP) is the standard pretraining objective for large language models, yet it provides an explicit training signal only for the immediate next token, which can lead models to exploit local patterns instead of capturing longer-range structure and ideas. Multi-token prediction (MTP) addresses this by training models to predict several future tokens. However, existing MTP methods often introduce a large number of new parameters with limited improvements in downstream performance. Latent MTP approaches address this efficiency issue by encoding future tokens into a vector representation. However, these approaches usually rely on external helper models for future token encoding. We propose LightMTP, a lightweight, i.e., parameter-efficient, latent MTP approach that bootstraps the future token representations from the model's own hidden states. Our two LightMTP variants extend supervision to more future tokens without requiring the additional computational overhead of conventional MTP nor the external supervision latent MTP normally relies on. LightMTP adds at most 1% extra parameters, retains better performance on general language modeling benchmarks, and achieves similar gains in planning, coding, and reasoning.

We consider Walsh's process on a star graph perturbed by the fact that its paths need to additionally pass through semi-permeable soft membranes, each located on a different edge at a small distance from the center, and each having its own permeability coefficient. We describe the limit processes as the distances converge to $0$, in terms of the characteristics of the approximating ones. The main finding is that the limit process is still of Walsh type, but its parameters need to be appropriately modified. The paper is a close companion to A. Bobrowski and A. Pilipenko “On Portenko's approximation of skew Brownian motion” (arXiv:2601.20440), and to A. Pilipenko and G. Vilmart, “Limit theorems for one-dimensional diffusions: reflected, skew, sticky, skew-sticky, and snapping-out limits.”

Direct dark matter detection with NaI(Tl) scintillators requires ultra-low-background materials. Silicone optical pads can couple NaI(Tl) crystals to photomultiplier tubes (PMTs) if they provide adequate optical transmission and radiopurity. We characterize four candidate materials for the SABRE-North experiment: commercial EJ-560, used as a reference, and three materials produced at the University of Salento (SYLGARD 184, EGel 3002 A/B, and a hybrid formulation) using different catalyst ratios and curing conditions, yielding ten samples in total. Optical transmittance was measured from 310 to 850 nm by UV/Vis/NIR spectrophotometry. Radiopurity was assessed at the STELLA facility at LNGS using high-purity germanium (HPGe) $\gamma$-ray spectrometry and, for EJ-560, high-resolution ICP-MS. At the 410 nm NaI(Tl) emission peak, EJ-560 shows an absorbance coefficient of $0.064\pm0.017$ mm$^{-1}$. The best locally produced samples reach $0.097\pm0.015$ and $0.093\pm0.014$ mm$^{-1}$ for SYLGARD 184 with a 10:2 base-to-catalyst ratio cured at room temperature and at $40^\circ$C, respectively, $0.125\pm0.015$ mm$^{-1}$ for EGel 3002 with a 2B:A ratio cured at $40^\circ$C, and $0.106\pm0.014$ mm$^{-1}$ for the hybrid 10:1 EGel A:CataSYL formulation cured at room temperature. EJ-560 exhibits detectable $^{232}$Th-chain activity at about 1.8 mBq/kg and the highest $^{40}$K activity, $(120\pm20)$ mBq/kg. The locally produced materials show no detectable Th-chain contamination but exhibit $^{226}$Ra activities of about 2.3 mBq/kg and lower $^{40}$K levels. No single material is optimal across all criteria. Additional ICP-MS screening, HPGe measurements of cured pads, and direct NaI(Tl)-PMT light-yield tests are required for a conclusive SABRE-North material selection.

The Independent Chip Model (ICM) converts the chip stacks of the players remaining in a poker tournament into finishing-place probabilities and prize equities. It is the standard model in tournament solvers, but its definition considers all possible finishing orders, and exact computation has been regarded as intractable for large fields. The same mathematics appears in other fields; for instance, the ICM is a Plackett-Luce ranking model with stacks as weights. We present DE-ICM, a deterministic algorithm that computes the placement probabilities of all $n$ players for all paid places in $O(M n^{2})$ time, where the number $M$ of quadrature nodes is fixed for the admissible inputs and the target accuracy. Its numerical scheme allows the target to be set close to the accuracy of double-precision arithmetic. The algorithm evaluates a classical integral representation in which, conditional on a player's exponential clock, the number of players ahead is Poisson-binomial. A double-exponential quadrature on a single grid evaluates every integral; its truncation errors have closed-form bounds, and the step size, which controls the discretization error, follows from the field size. A numerically stable deconvolution then recovers each player's leave-one-out coefficients in $O(n)$ time from one shared product. On exactly solvable instances with up to 4,000 players, the worst observed relative error of an equity is $4.0 \times 10^{-14}$ and the worst absolute error of a placement probability $1.1 \times 10^{-14}$. The full placement matrix for 1,000 players takes 0.2 seconds on one CPU core.

Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.

SVD-based pruning and quantization have recently emerged as a promising strategy for the ultra-efficient compression of large language models. In these methods, compression is performed in two stages: components are first truncated, and the remaining ones are subsequently quantized. Although this decoupled pipeline benefits from both pruning and quantization, it requires separate optimization for each stage and fails to fully exploit their balance, which can lead to suboptimal performance under aggressive compression. To address this limitation, we propose a new LLM compression method that co-optimizes pruning and quantization in a unified framework. Our key idea is a differentiable method for learning component-wise bit-widths, allowing less important components to be assigned 0-bit precision and pruned away. Notably, our method performs favorably against two-stage baselines, even when subjected to extreme quantization settings ($1.61$ bits) designed for ultra-efficiency. Code: https://github.com/MMAI-Laboratory/DBW.

Joint attention - the human ability to share a common visual or cognitive focus with others - enables a meeting of minds that lets us coordinate even with unfamiliar partners. In this work we investigate whether equipping AI agents with a similar mechanism can enable such zero-shot coordination. We introduce Mutual Attention for zero-shot TEaming (MATE): a novel multi-agent reinforcement learning method inspired by human joint attention. MATE encourages agents to coordinate their actions by aligning their visual attention on scene-salient objects during the interaction rather than relying on arbitrary partner-dependent conventions established during training. Unlike symmetry-breaking approaches that merely prevent brittle conventions from emerging, MATE actively promotes coordination through an environment-grounded signal that is naturally shared across partners. We evaluate MATE on three benchmarks: our Card Alignment Game, designed to isolate brittle convention formation, and the more challenging Level-Based Foraging and OvercookedV2 benchmarks. Our experiments consistently show that a joint-attention-inspired signal improves coordination with unknown partners, underlining MATE's potential as a general coordination mechanism that complements and surpasses symmetry-breaking approaches.

We prove a closed formula for DT4 invariants of one dimensional stable sheaves on the total space of $\mathcal{O}_{\mathbb{P}^2}(-1,-2)$ for all degree curve classes. During the proof, orientations of moduli spaces are chosen in a canonical way. Combining with Gopakumar-Vafa type invariants proposed and computed by Klemm-Pandharipande, we verify a conjecture proposed by the author, Maulik and Toda.

Exploiting meaningful latent structures from data to solve downstream tasks is a fundamental challenge in signal processing and machine learning. While Principal Component Analysis (PCA) and coVariance Neural Networks (VNNs) successfully leverage the covariance matrix to process data, they inherently capture both direct and indirect correlations. The precision matrix (inverse covariance) overcomes this by explicitly encoding conditional independencies, making it largely studied in graphical lasso and graph topology identification. However, finite-sample precision estimates are notoriously unstable, and regularized estimators remain task-agnostic. In this work, our principal contribution is tackling the challenging problem of task-aware graph inference. We propose Precision Neural Networks-Joint (PNN-Joint), a framework that jointly estimates a sparse, statistically grounded precision matrix alongside graph neural network weights via an alternating optimization scheme. As a foundational framework to support this, we introduce Precision Neural Networks (PNNs), a broader class of graph convolutional networks operating on precision estimators, and establish their spectral connections to PCA and VNNs alongside their stability to finite-sample errors. Extensive empirical evaluations on synthetic data, as well as real-world neuroimaging and motion sensor datasets, demonstrate that PNN-Joint yields highly interpretable task-aware graphs, exhibits remarkable robustness in low-data regimes, and consistently achieves the best or second-best performance among competitors on real-world tasks.

We present an overview of the relativistic distorted-wave impulse approximation (RDWIA) for lepton-nucleus scattering, with emphasis on its use as an elementary-vertex model in event generators. In the intermediate-energy regime, neutrino-nucleus event generators typically follow a two-step scheme: an elementary neutrino-hadron interaction is first generated, and the outgoing hadrons are then propagated through the nuclear medium using an intranuclear cascade (INC) model. Using exclusive and inclusive $(e,e'p)$ and $(e,e')$ data for several nuclei, we assess how nuclear effects should be distributed between these two stages. In particular, we identify which effects should be included in the elementary-vertex description and which can be treated more effectively by the INC, while addressing the consistency required between both components. We also discuss nuclear transparency in quasielastic scattering. We show that it is directly connected to $(e,e'p)$ data below the two-nucleon knockout threshold; and depends on the full nuclear density distribution and the initial position of the nucleon, therefore, it varies substantially with the shell from which the nucleon is removed. We demonstrate that this shell dependence can be incorporated straightforwardly into the INC component of event generators.

Image editing should change only the attributes specified by an instruction while preserving everything else, yet current methods often make unintended changes. We treat this minimal-change principle as an optimization objective for instruction-based editing. Latent L1 regularization is a poor proxy for output locality in modern nonlinear generators and often requires supervision unavailable at scale. We instead optimize edit outcomes with reinforcement learning. An agentic vision-language reward model audits each source image, instruction, and edited image for two failure types: unimplemented requested changes and unintended changes. A group-level rubric merges and verifies these issues to provide consistent rewards across candidate edits without per-instruction human annotations. On FLUX.1 Kontext-dev, ARRO raises average EditScore from 5.21 to 5.88 across MinEval, MagicBrush, AnyBench, and Emu-Edit. On 600 evaluation examples, it reduces off-target pixel change by 8.4% relative to the base editor. Reward and SFT controls, blinded human evaluations, and transfer to OmniGen2 provide complementary evidence. Code: https://github.com/Showwwwwwwww/ARRO

Volume electron microscopy (vEM) has emerged as an essential sensing technique in biomedical research, allowing the three-dimensional imaging of biological cells and tissues at nanometer-scale resolution. The ability to generate extensive datasets has reached the limitations of downstream analysis processes, which depend significantly on the intervention of human experts for preprocessing and annotation. We propose an efficient and reliable patch-based retrieval framework based on self-supervised learning of local image descriptors to locate self-similar structures in vEM datasets. Given a few manual annotations of a given cellular structure, our method can retrieve similar structures across the EM volume. Our framework is interactive, allowing the human expert to refine the search queries and retrieve relevant image patches quickly and using little labeled data. Experiments on real-world vEM images of biological tissues demonstrate that our framework can reliably identify relevant cellular structures, generalize across different organelles and acquisition modalities, and substantially reduce the search space for downstream analysis.

With massively parallel simulation, on-policy Reinforcement Learning methods such as PPO have become standard in many domains. However, learning from scratch is sample-inefficient and fails to exploit the potential existence of a suboptimal expert, such as a heuristic, a model-based controller, or a policy trained on a related task. Such an expert is often available and can guide early training, but its sub-optimality limits final performance. The challenge then becomes balancing expert guidance against learning from rewards. Existing methods set the expert's influence through a blending weight, a schedule, or an evaluation-driven curriculum. Alternatively, they adapt it with additional learned components such as critics over expert actions or auxiliary agents. However, none optimizes it using the same on-policy objective as the policy itself. We propose a method in which the learner and the expert alternate control within each training episode, and the expert's share of control is a single learnable parameter optimized jointly with the policy. The learner benefits from the expert early in training, but its share of control declines as the learner becomes more competent, until eventually vanishing completely. This leaves the learner acting alone and better than the suboptimal expert. We evaluate our method on 34 tasks across two benchmarks, spanning discrete and continuous action spaces, using both learned and model-based experts. Our method improves sample efficiency over guided and unguided baselines while requiring minimal hyperparameter variation. The expert's share decays to zero as the learner improves, vanishing when the expert is no longer useful.

Spatio-temporal video grounding (STVG) aims to localize objects or events described by natural language queries in both space and time. Existing STVG models are typically trained and evaluated under the assumption that each query is relevant to the input video. In this work, we challenge this assumption by studying the behavior of state-of-the-art STVG models under irrelevant queries and missing textual input. Our experiments show that current models can still produce plausible spatio-temporal predictions even when the query is unrelated to the video or removed entirely. We further analyze HCSTVG-v2 and VidSTG to identify dataset regularities that may encourage such query-insensitive behavior. Our study highlights an underexplored limitation of STVG models and motivates negative-aware evaluation protocols and architectures that explicitly assess query relevance.

Agentic buyers can cheaply fork a procurement task into many parallel negotiations, but concurrency is not free: every thread consumes resources, and simultaneous agreements create cancellation and commitment risk. We study a one-unit post-order sourcing problem with a single hard-deadline negotiation window, in which a planner jointly chooses the number of seller-facing negotiators and a common procurement price cap. The model combines a product-specific acceptance curve with fulfillment loss, per-thread cost, and excess-commitment cost. We establish three structural results. First, holding the per-thread acceptance target fixed, the marginal value of another negotiator decays geometrically, yielding a conditional concurrency threshold. Second, under a convex quantile curve, parallelism substitutes for concession: more concurrent negotiators imply a weakly lower per-thread acceptance target and price cap. Third, when prices are more dispersed, Agentic buyers benefit by searching harder for bargains, but suffer when they instead try to guarantee procurement by offering higher prices. We operationalize these results in the Concurrency-Aware Negotiation Optimizer (CANO), a deterministic optimizer that jointly determines the optimal negotiation concurrency and procurement price cap for an agentic procurement system. Across different analytic market configurations and extensive Monte Carlo, finite-data, non-Gaussian, and correlated-seller stress tests, CANO consistently outperforms common heuristic policies while validating the predicted structural properties.

We report time-resolved optical pump-terahertz third-harmonic generation spectroscopy of picosecond nonthermal many-body charge dynamics in high-purity silicon at room temperature. Although in thermal equilibrium excitons in silicon are unstable due to a lower binding energy than the thermal energy at room temperature, following pulsed non-resonant optical pumping we can identify the formation of transient excitonic states on the picosecond time scale in our high-resolution nonlinear spectroscopic measurements. In contrast to unbound electron-hole pairs, the nonthermal many-body excitonic dynamics feature a characteristic time-dependent evolution, a distinct dependence on charge density, and a nonperturbative nonlinear terahertz response.

We study the extent to which the invariants appearing in the Birch and Swinnerton-Dyer conjecture remember the elliptic curve, and we give several affirmative answers to this question. For example, the real period $\Omega_E =\frac{\Gamma(1/4)^2}{2\sqrt{\pi}\,17^{1/4}}$ and the Tate–Shafarevich group $ \Sha(E/\mathbb{Q})\cong \mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$ remember the elliptic curve $E: y^2=x^3+17x$. Let $K$ be a number field admitting a real embedding, and fix one such embedding $\sigma\colon K\hookrightarrow\mathbb{R}$. We first prove that, for an elliptic curve $E$ over $K$, the real period of $E$ attached to $\sigma$ determines the $K$-isogeny class of $E$. We then prove that an elliptic curve $E$ over $\mathbb{Q}$ is determined up to isomorphism over $\mathbb{Q}$ by its real period, the number of connected components of $E(\mathbb{R})$, and the real period of the quadratic twist $E^{D}$ by a negative square-free integer $D\equiv 1 \bmod 4$ coprime to the minimal discriminant of $E$. Moreover, over $\mathbb{Q}$, both statements already hold when the real periods are known only to sufficiently many decimal places, where the required precision depends on $E$ (and $D$).

We study two-Higgs-doublet models, extensions of the Standard Model (SM) containing two Higgs doublets rather than one. Tree-level Higgs-mediated interactions that change quark or lepton flavor are conventionally suppressed by a discrete $\mathbb{Z}_2$ symmetry. Motivated by string compactifications, we instead impose a non-invertible Fibonacci selection rule at a matching scale $\Lambda$ for that purpose. This rule also forbids the independent mass parameter that normally allows the additional Higgs particles to become arbitrarily heavy, while renormalization-group evolution regenerates it below $\Lambda$. An allowed $\mathbb{Z}_2$-breaking quartic interaction simultaneously avoids stable cosmological domain walls. In the exact alignment limit, requiring perturbative unitarity and boundedness from below up to the matching scale bounds the masses of the three non-SM Higgs states; for $\Lambda=10^{19}\,\mathrm{GeV}$, they lie below about $150\,\mathrm{GeV}$. The scanned parameter space predicts a suppressed Higgs diphoton signal strength within the projected reach of the HL-LHC. This illustrates how a stringy non-invertible selection rule can leave testable signatures in Higgs physics.

A dubbed character keeps its identity while the voice actor changes, so character identity and speaker identity are distinct properties of one recording, yet speaker verification measures only the latter. To address this gap, we propose KyaraBench, a benchmark that scores character voice directly instead of speaker voice, built from 85 human-audited identities in a dubbed anime corpus. It poses two challenging conditions: one that swaps the performer under a fixed character, and one that fixes the performer under changing characters. Listening studies with 78 participants provide human reference scores for cross-performer verification and same-actor discrimination. Speaker-verification baselines show increased errors under these character-specific conditions. We then train KyaraEmbed, a compact encoder using multilingual character supervision, same-actor negatives, and a language-alignment term. The model achieves the best performance on all character-specific conditions in the main comparison. We release the benchmark, protocol, and encoder publicly.

In this work, we study transformer attention through the lens of spectral geometry and operator theory. We view each attention head as a functional map between Hilbert spaces of functions on the token sequence and derive a Token Difference Operator, whose spectral structure controls how token-space information is routed to the output. We show that standard Euclidean spectra are structurally biased by sinks, conflating mass concentration with genuine routing capacity. By recasting token space in the intrinsic probability geometry induced by attention, the token difference spectrum disentangles sink effects from routing capacity and provides a spectral description of the dimensionality of the head output. This yields a unified framework for analyzing attention maps, explaining sinks, routing collapse, and output dimensionality within a single operator-theoretic framework. In practice, by grounding attention heuristics in spectral geometry, we develop a novel attention-based uncertainty estimator that complements probability-based scores, with the largest gains on long-context inputs.

Block diffusion accelerates speculative decoding by drafting multiple tokens in one forward pass. However, each position predicts a marginal distribution without observing earlier proposed tokens, limiting draft quality and acceptance length. We identify a concrete failure, the repetition trap, in which neighboring positions produce redundant copies of the same token. We explain this tendency theoretically and empirically examine its association with shorter accepted drafts. Recent methods refine marginal predictions with an additional causal head or a separately trained drafter, increasing parameter storage and introducing separate training objectives. We instead propose D-Loop, which introduces intra-block causal conditioning within the original diffusion drafter without additional model components. Inspired by semi-autoregressive generation and parameter sharing, D-Loop reuses the same backbone across looped passes. The first pass proposes a block, and the second conditions on a selected prefix to regenerate the suffix in parallel. A complementary prefix–suffix objective trains the shared drafter for both anchor-only prefix prediction and prefix-conditioned suffix prediction. Across eight math, code, and chat benchmarks, D-Loop can beat DFlash and DSpark on Qwen3-4B and Qwen3-8B with obvious gains.

Ultrasound visual servoing is essential for autonomous robotic ultrasound, yet 6-DoF probe control from 2D B-mode images remains challenging due to limited and ambiguous out-of-plane motion cues. Existing methods typically rely on anatomical priors or handcrafted visual features, limiting their generalizability across imaging targets. Inspired by trackerless 3D ultrasound reconstruction, we propose Recon2Servo, a visual servoing framework that learns image-to-motion inference directly from B-mode images for 6-DoF probe control. A DINOv3 encoder with low-rank adaptation and a bidirectional relation module estimate the relative probe pose between current and target images to guide iterative closed-loop target-view alignment. The framework combines supervised relative-pose learning, reconstruction-guided closed-loop adaptation, and bounded residual pose correction to improve motion inference during servoing. Evaluations on a public dataset and an in-house dataset collected from 12 healthy volunteers using different ultrasound systems demonstrate its effectiveness in reconstructed-volume servoing. Additional real-robot demonstrations of target-view alignment and dynamic tracking on a human forearm are provided in the supplementary video: https://youtu.be/qwsOdI-GMYk.