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At least 613 records · Page 34Linked to original sources
arXiv2026

Hecke structure of quaternionic modular forms mod $p$

We relate the systems of Hecke eigenvalues arising from the (mod $p$) modular forms on the Shimura curve attached to the indefinite quaternion algebra $B$ of discriminant $δ$ over $\mathbf{Q}$ to the systems of Hecke eigenvalues arising from the (mod $p$) algebraic modular forms attached to the definite quaternion algebra $D$ of discriminant $pδ$. Moreover, we discuss details of the Hecke structure on the latter spaces, following ideas of Serre. The entire setup can be seen as a Shimura curve analogue of Serre's letter to Tate on quaternions and modular forms. The bijection between the sets of systems of Hecke eigenvalues is a special case of recent work of Terakado and Yu; the novelty of this paper is the explicit nature of the construction, allowing for finer control of its behaviour with respect to weights, as well as the results on the Hecke module structure.

math.NT↗
arXiv2026

A 3-regular counterexample to the Bilu--Linial signing conjecture

We construct a finite connected simple cubic graph $F$ such that every signing of its edges yields a signed adjacency matrix with an eigenvalue outside $[-2\sqrt2,2\sqrt2]$. This disproves the Bilu--Linial signing conjecture for general regular graphs. The graph $F$ is not Ramanujan, and the conjecture restricted to Ramanujan base graphs remains open.

math.CO↗
arXiv2026

IROH: Insightful Ranking Of Humor using Multi-Stage Hybrid Retrieval with Rationale-Distilled LLM Judges for JOKER 2026 Track Task 1 English

Our team, VANGUARD, presents IROH (Insightful Ranking of Humor), a three-stage retrieval system for JOKER Task 1 English at CLEF 2026, achieving first place on the leaderboard with 0.6347 MAP. Our pipeline combines hybrid sparse-dense retrieval, cross-encoder reranking, and a LoRA-adapted Large Language Model judge ensemble. We employ Gemma 4 to generate query-aware rationales under two prompt strategies, generic and typed, and produce up to four types of structured hard negatives for training data construction. Through an ablation across three cross-encoder architectures, four dense embedders, and eight judge configurations, our key findings are threefold: (1) the rationale-distilled judge is the primary driver of ranking quality, whereas appending rationales to the first-stage index contributes negligibly; (2) structured hard negatives degrade generalisation in nearly all configurations despite inflating local validation scores; and (3) across the components we ablate, the lighter, better-calibrated model is competitive with or stronger than its larger counterpart, with the generic-rationale Qwen2.5-7B judge (0.6055 MAP) outperforming every Gemma-4-31B configuration, and the advantage of generic over typed rationales is concentrated almost entirely in the smaller model.

cs.IR↗
arXiv2026

Accelerating Transfer-Learning-Based Autotuning with Predictive LLVM IR Performance Ranking

As the complexity of High Performance Computing (HPC) ecosys- tems continually increases, achieving optimal performance becomes a challenge. Traditional performance autotuning techniques pro- vide promising means to navigate this complexity, these techniques remain computationally intensive and require many evaluations to find optimal configurations. This work proposes an autotuning framework that designs a machine learning-based ensemble LLVM Intermediate Representa- tion (IR) ranker, Neural Configuration Scorer (NCS). NCS ranks the performance of IRs sampled by a transfer-learning-based autotuner, improving the efficiency of the tuning process by reducing tuning overheads and circumventing subpar evaluations. By leveraging knowledge from related tasks, we are able to effectively exploit the transfer relationship to access high-performing configurations in fewer samples than traditional techniques that rely upon itera- tive refinement. Our framework can achieve similar performance improvements as state-of-the-art autotuning techniques with up to 61.67% fewer evaluations, averaging 27.85% fewer evaluations across various HPC benchmarks.

cs.PF↗
arXiv2026

Multiple-Mediator-Affected Ultra-High-Energy Neutrino Attenuation: Hints for 5D ${U(1)}_{L_μ- L_τ}$ in IceCube

Recent IceCube observations point to the ultra-high energy neutrino flux exhibiting a very soft spectral nature beyond tens of TeV, which is unexpected from the standard cosmic-ray neutrino connection. As a potential explanation for this behaviour, we investigate neutrino self-interactions in an extra-dimensional $ {U(1)}_{L_μ-L_τ} $ gauge theory, where symmetry breaking leads to a tower of Kaluza-Klein gauge bosons in compactified four dimensions. These multiple gauge bosons may enhance the attenuation of astrophysical neutrinos as they propagate in the C$ν$B medium. Unlike single-mediator scenarios, for example, which arise from broken $ {U(1)}_{L_μ- L_τ} $ gauge symmetries in four dimensions, the presence of a Kaluza-Klein tower of mediators produces multiple closely spaced resonances whose interference gives rise to a rich energy-dependent behaviour of the scattering cross-section over a vast range of incident neutrino energies. Alongside $s$-channel resonances, off-resonant $t$- and $u$-channel contributions also become important. We explore the possibility that repeated resonant scattering between astrophysical neutrinos and those in the C$ν$B, mediated by these new multiple gauge bosons may increasingly attenuate the former at higher energies, thereby addressing the possibility of softening its spectral nature within the consideration of a single power law.

hep-ph↗
arXiv2026

Symmetry Descent in M-theory, Part I: A Twelve-Dimensional Parent Theory

We initiate a symmetry descent procedure for M-theory engineered quantum field theories. Starting from a higher form BF theory supplemented by a cubic bulk topological interaction, we construct a gauge-invariant bulk-boundary system whose edge modes acquire generalized Maxwell--Chern--Simons dynamics after the introduction of a metric-dependent boundary action. The nonlinear contribution to the boundary equation is induced entirely by the cubic bulk interaction. In the case of twelve dimensional bulk parent, the resulting boundary conditions reproduce the local flux equations of the eleven-dimensional supergravity $C$-field, including the gravitational $I_8$ correction. Thus, the electric--magnetic pairing and the nonlinear Maxwell--Chern--Simons dynamics descend from a single 12D topological model. Using Hypothesis H, we identify the bulk equations with the Sullivan model of $S^4$ and interpret their nonlinear gauge transformations as homotopies. We then propose a twisted 4-cohomotopy quantization of the bulk fields and a homotopy pullback description of the coupled bulk--boundary field space. The construction provides both a local dynamical mechanism for M-theory symmetry descent and a candidate global characterization of its fields.

hep-th↗
arXiv2026

Redesigning the linear--quadratic--Gaussian cost function for feedback cooling of a quantum harmonic oscillator

Linear--quadratic--Gaussian (LQG) control is optimal only with respect to a prescribed cost function, the choice of which dictates the physical objective of the control. We consider feedback cooling of a continuously monitored quantum harmonic oscillator by shifting the minimum of its trapping potential. In this setting, the physically relevant cooling objective can be defined as minimizing the oscillator's energy relative to the feedback-shifted potential. In contrast, conventional LQG control evaluates the energy from a fixed origin and thus fails to directly optimize this quantity. To address this problem, we introduce a redesigned cost function that explicitly accounts for the feedback-induced shift of the potential. We then derive the corresponding optimal feedback law and obtain an analytic expression for the minimum achievable steady-state phonon occupation number. The redesigned LQG control achieves a lower occupation number than low-pass-filter (LPF) feedback formulated for the same cooling objective. While this improvement is minor at detection efficiencies currently attainable in experiments---indicating that LPF feedback already delivers near-optimal cooling performance---the advantage becomes pronounced as the detection efficiency approaches unity. In this regime, the redesigned LQG control provides an increasing advantage for reaching the motional ground state at a finite measurement strength. We clarify that the conventional and redesigned cost functions represent distinct control objectives rather than different implementations of the same optimization problem.

quant-ph↗
arXiv2026

Understanding Dynamic Scenes at Gigapixel Scale: Wide-Area Spatio-Temporal Perception from UAVs

UAV-borne imaging has advanced from megapixel to gigapixel sensors, shifting aerial perception from recognizing individual targets to understanding entire dynamic scenes. We characterize this demand as Wide-area Spatio-temporal Scene Understanding (WSTU), which requires wide-area coverage, per-target resolution, and temporal continuity at once, a combination existing datasets lack. To fill this gap, we introduce an ultra-High-resolution (12768x9564) Airborne Remote-sensing Dataset (HARD) annotated at three levels for object detection, multi-object tracking, and scene-level visual question answering. Ultra-high-resolution imagery raises per-frame processing time to seconds. At that scale latency can no longer be ignored in evaluation. Thus, we propose a latency-aware metric for multi-object tracking called streaming-HOTA (s-HOTA). Extensive baseline experiments show how ultra-high-resolution processing reshapes each task. For detection, the end-to-end pipeline affects accuracy and speed as much as the detector itself does. For tracking, high latency charges the association axis far more unevenly than the detection axis, and association is where pipelines diverge. As a result, the pipeline that performs best offline can lose its lead under s-HOTA. For VQA, vision-language models remain weak at cross-frame identity binding and cannot transfer their single-frame gains to it. Together these findings show that the baselines we evaluate fall short of WSTU. HARD provides the data and the systematic baselines to advance it.

cs.CV↗
arXiv2026

Variational computation of anharmonic ground and excited vibrational eigenstates using bound Quartic Force Fields: Application with MCTDH and ElVibRot

In this work we introduce the use of Quartic Force fields (QFF) potential expansions in the context of variational calculations. Such potentials are commonly employed in molecular Vibrational Second-Order Perturbation Theory (VPT2) studies, for which equations explicitly dependent on the QFF parameters exist. However, QFF are unbound potentials for more or less large displacements from the reference point and, most of the time, this prevents their use in conjunction with variational wavepacket-based calculations. In this work, we propose a general correction to QFFs and introduce a fully automated numerical approach to avoid their unbound character. Our corrected potentials, bound QFF (bQFF), do not exhibit appreciable modification of the local topography around the region of interest for infrared spectroscopy. As a consequence of this, we can affirm that the vibrational eigenstructure (eigenvalues, eigenstates) remains essentially unaltered by our correction. To illustrate their numerical stability, we have interfaced our bQFF routines in combination with to two well-established quantum simulation software packages MCTDH and \textsc{ElVibRot} which feature variational approaches. More specifically, our bQFFs are separable and hence directly expressible as MCTDH operators. Furthermore, concerning the size of our bQFF expansion, we show that it is possible to tensor-decompose our bQFF in Canonical Polyadic form (CP-bQFF). We use the Monte Carlo Canonical Polyadic decomposition algorithm for this. CP-bQFF results are virtually identical to uncompressed bQFF, but the computational efficiency is largely improved. Our approach paves the way for the automated variational study of anharmonic eigenstates in molecular systems within the reach of QFF-based potentials, using either time-dependent or time-independent schemes.

physics.chem-ph↗
arXiv2026

A parity obstruction to completeness of object cotorsion pairs

Fu, Guil Asensio, Herzog and Torrecillas asked whether a complete ideal cotorsion pair of object ideals in an exact category induces a complete cotorsion pair of objects. We give a negative answer in a Hom-finite, weakly idempotent complete Frobenius exact category. Our example consists of bounded complexes of finite-dimensional vector spaces with even total cohomology dimension. Two classes defined by cohomological support generate a complete ideal cotorsion pair, whereas the corresponding object cotorsion pair is neither special precovering nor special preenveloping. The obstruction is that cohomological truncations need not remain in the category, although their doubles do. Conceptually, this obstruction reflects the failure of the standard $t$-structure on the ambient derived category to restrict to the stable category of our example.

math.RA↗
arXiv2026

Decodable but Misrouted: Sparse Features Uncover a Readout Gap in Vision-Language Models for Harmful Meme Detection

When large vision-language models misclassify harmful memes, the failure may reflect missing internal evidence or an inability to route represented evidence to their outputs. We distinguish these cases in Gemma-3 and Qwen3.5 using sparse autoencoders, role-conditioned probes, causal interventions, and recovery experiments across six harmful content benchmarks, with additional Spanish and Hindi-English code-mixed evaluations. Sparse readouts outperform native prediction on all six primary binary tasks: Qwen averages $0.740$ versus $0.432$ for native macro-F1, residual reconstruction reaches $0.486$, and Gemma improves from $0.532$ to $0.714$. These gains measure how accessible the label is to a supervised readout; they do not show that the model's native generation already applies such a decision rule. Under the evaluated scales, Qwen silent-feature ablation is $24-63$ times more probe-sensitive, whereas routed-feature patching on literal yes/no tasks is $16-140$ times more output-sensitive. Native-only threshold calibration explains much, but not all of the gap: on five tasks with matched probe scores, it recovers $69.8$\% of the raw native-to-probe difference, while direct routing adds $0.094$ mean macro-F1 beyond calibrated native scoring. Joint gold-label, probe-KL, and pairwise LoRA supervision improves dedicated FHM prediction, but a gold-only adapter performs better on the shared seven-task mean. A case study of Gemma-3-12B on the Facebook Hateful Memes dataset finds a distributed rank-32 image-prompt interaction, reaching $0.756$ versus $0.685$ native macro-F1. Robustness controls show that the signal is not explained solely by accompanying OCR and depends on paired visual evidence, and that it extends beyond English. In many of the errors we study, the evidence is represented but does not reach the answer; therefore, routing is a common bottleneck in harmful meme classification.

cs.CV↗
arXiv2026

Hamming Ideals and Grobner Bases for ISD-like Syndrome Decoding

We investigate an algebraic approach to the Syndrome Decoding Problem, based on a reformulation of the Hamming weight constraint and its integration with the Information Set Decoding paradigm. We begin with a systematic analysis of the Hamming variety, deriving its defining equations in terms of elementary symmetric functions. Since these equations may have high degree, we exploit convolution identities for elementary symmetric functions, together with factorizations based on Lucas' identity, to derive an equivalent formulation with auxiliary variables and equations of bounded degree. Building on this modeling, we generalize the ISD paradigm through an ISD-like decoding strategy, implemented by the GBDecode algorithm, in which only a subset of an information set is fixed. This approach reduces the size of the combinatorial search space at the cost of solving the associated multivariate nonlinear systems. To handle this algebraic component, we employ the MultiSolve algorithm, which replaces a single Grobner basis computation with a collection of computations on simpler systems, obtained by exhaustively assigning a varying number of indeterminates over the finite field. This provides a tunable balance between combinatorial search and algebraic solving. We evaluate the resulting approach experimentally on instances of the Syndrome Decoding Problem for random binary linear codes, using parameters corresponding to the NIST Security Category 1 parameter set of the Classic McEliece cryptosystem. The experiments assess the feasibility of this combinatorial-algebraic approach and provide insights into the practical behavior of Grobner basis techniques within an ISD-like decoding framework.

cs.CR↗
arXiv2026

NeuroECG: ECGFounder-Based Deep ECG Representation for EEG-Free Neurological Prognostication After Cardiac Arrest

Neurological prognostication after cardiac arrest commonly relies on electroencephalography (EEG). However, EEG demands high clinical resources. Bedside electrocardiography (ECG) is standard and low-cost. Yet, its value for predicting neurological outcomes remains underexplored. In this study, we propose NeuroECG, an ECGFounder-based deep representation framework for EEG-free auxiliary prognostication. NeuroECG adapts a pretrained ECG foundation model via task-specific fine-tuning. We implement a gradual unfreezing strategy on single-channel bedside monitoring ECG. Multiple ECG segments per patient are encoded into segment-level deep features. These embeddings are aggregated via quantile pooling (q = 0.24) and compressed using principal component analysis (PCA). Experiments on 412 ECG-available patients from the multicenter I-CARE database show that the adapted ECGFounder backbone achieves the best performance among ECG-only backbone baselines, with a test AUROC of 0.7333. We further combine the learned deep ECG representation with static clinical covariates. The proposed NeuroECG model achieves a test AUROC of 0.8077 and an AUPRC of 0.8970. These results support deep bedside ECG representations as a useful source of auxiliary prognostic information. Their integration with static clinical covariates improves prediction in an EEG-free setting. The source code is available at https://github.com/goddream66/NeuroECG

cs.LG↗
arXiv2026

Exact logical error rates for magic state cultivation

We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$-gates are studied, not the $S$-gate proxy used for sampling. The calculation includes every fault order at several circuit-level noise strengths ($p$). We provide a series expansion form to the logical error rates, through order $(p/(1-p))^{10}$. The analytical results recover the numerical values from Clifft and SOFT at both $d=3$ and $d=5$ to within their sampling uncertainty. Then, we show that the $d=3$ and $d=5$ circuits actually have fault distances of $d_{\text{fault}}=2$ and $d_{\text{fault}}=3$ respectively, explaining the similar distance degrading effects from the companion code of [Quantum 10, 2134 (2026)].

quant-ph↗
arXiv2026

What Do Current Systematic Generalization Tasks Miss? A Reasoning-Centered Analysis

Systematic generalization, the ability to solve novel problems by recombining known atomic elements, is central to human intelligence but difficult to study rigorously under controlled settings. Existing studies therefore rely on simplifications such as elemental composition, productivity-based tests, and action-explicit goals, which make systematic generalization easier to study but omit some essential aspects of this capability. To characterize what these simplifications miss, we adopt a reasoning-centered lens and introduce TranSGrid, a testbed that brings deductive, inductive, and abductive reasoning together within a unified task. Experiments with seven Transformer models on 4,800 TranSGrid instances show that all models perform much worse on TranSGrid than on a held-out test set: the largest model solves 79.6% of the test set, but only 55.3% of TranSGrid and 15.8% of the hardest subset. The gap remains within the training length range, showing that productivity alone is not sufficient to evaluate systematic generalization. Additionally, we reintroduce the other two simplifications into TranSGrid: one variant limits interactions among action effects to approximate elemental composition (reducing the inductive demand); the other makes goals action-explicit (reducing the abductive one). In both, solve rates return to roughly the test set level, showing that either simplification alone is enough to reduce TranSGrid to an ordinary held-out test set. Together, our results show that existing tasks reduce either or both of the inductive and abductive demands of systematic generalization, and that comprehensively measuring this capability requires a task that involves all three forms of reasoning.

cs.AI↗
arXiv2026

Electroweak balls: non-topological solitons in the Weinberg-Salam theory

We construct a new class of smooth, finite-energy solitons in the bosonic $SU(2)\times U(1)$ Weinberg-Salam theory, which we dub $electroweak$ $balls$. Their localization mechanism is analogous in spirit to that of $Q$-balls: the charged vector fields possess a harmonic time dependence while the energy-momentum tensor remains time independent. We explicitly construct both spherically symmetric electric-type solutions and axisymmetric magnetic-type solutions, and show that they form families characterized by a finite frequency interval, a mass gap, and a two-branch structure. These configurations provide electroweak counterparts of Proca-Higgs balls, with the vector-boson masses generated by the Higgs mechanism rather than introduced explicitly. The construction is not tied to the measured parameters of the Standard Model. More generally, it applies to bosonic electroweak-type sectors with different gauge couplings, Higgs self-coupling and symmetry-breaking scale, and hence potentially very different characteristic particle and soliton mass scales. For the families studied here, we do not find solutions at the measured Standard Model couplings and mass ratios.

hep-th↗
arXiv2026

Scalable Simulation of Quantum Dynamics on Topological Quantum Hardware

Quantum computers offer a significant advantage in simulating quantum systems compared to classical computers for certain problems, although most current applications are limited to calculating static molecular properties using hybrid quantum-classical hardware. In this work, we establish a framework for the representation of quantum dynamics in molecular and condensed matter systems, designed for execution on topological quantum hardware. By leveraging the non-Abelian braiding statistics of Fibonacci and Ising anyons, we utilize the Solovay-Kitaev algorithm to approximate unitary propagators for a range of systems. We demonstrate the efficacy of these algorithms across a hierarchy of complexity, from two-level systems and one dimensional double-well potentials to condensed phase spin-boson models, simple molecules, and molecular reaction kinetics. These algorithms provide a scalable and robust pathway for simulating many-body condensed phase chemical physics on fault-tolerant quantum devices.

quant-ph↗