Papers

We study the phase structure of dense QCD matter by applying the flavor-dependent holographic V-QCD model to two distinct physical environments: charge-neutral, beta-equilibrated matter, and strangeness-neutral matter with a fixed charge-to-baryon number ratio, n_Q/n_B = 0.4, relevant for heavy-ion collisions. The quark sector of the model incorporates the realistic mass hierarchy of two massless light quarks and a massive strange quark. We find that the resulting phase diagram depends sensitively on both the procedure used to tune the model against lattice QCD thermodynamics and the choice of physical environment. Using our preferred fitting procedure, we find that beta-equilibrated matter exhibits a first-order phase transition terminating at a critical endpoint located at significantly lower densities than in earlier holographic studies. However, this phase transition disappears entirely under heavy-ion conditions. This pronounced environmental dependence may help explain why recent net-proton cumulant measurements from Phase II of the RHIC Beam Energy Scan have not yet revealed clear non-monotonic fluctuation signatures. We calculate higher-order baryon number cumulant ratios along the chemical freeze-out curve to quantitatively compare the model predictions with experimental data. Finally, we also present global phase diagrams obtained by matching V-QCD to Hadron Resonance Gas models implemented in the Thermal-FIST package, and argue that this comparison further supports the conclusions drawn from the V-QCD model alone.

Continuous quantum error correction (CQEC) replaces discrete syndrome measurements and recovery operations with continuous syndrome extraction and real-time Hamiltonian feedback. Here we investigate the thermodynamic resources required by this process by formulating measurement-based continuous quantum error correction as an information engine. We distinguish the system-side power associated with energy transfer between the feedback field and the protected system from the controller-side power associated with the feedback Hamiltonian. The framework is first developed for the one-qubit Ahn-Doherty-Landahl (ADL) protocol and subsequently extended to the three-qubit repetition code under continuous stabilizer monitoring. Numerical simulations show that increasing the feedback strength improves the steady-state fidelity and reduces the conditional-state entropy, while both energetic contributions continue to increase in magnitude after the fidelity begins to saturate. These results expose a direct tradeoff between logical stabilization and the energetic resources required for continuous feedback, closely related to previously established energy–precision tradeoffs in quantum measurement and quantum-Zeno stabilization.

Indoor building construction sites are demanding environments for visual SLAM, where variable lighting and repetitive, low-textured structures make the system drift over long trajectories, though structural elements such as walls remain distinguishable despite these conditions. These buildings are constructed according to their as-planned floor plans, available from the design phase, and although the actual as-built site can differ from this design, floor plans still provide a metric reference, both to localize the system in the building and to correct drift. Existing methods often use the floor plan to correct an already-built trajectory offline, and those that instead correct it online typically rely on depth sensors. We instead present MVP-SLAM, an online visual-inertial SLAM on two opposite-facing fisheye cameras that corrects drift from cameras alone by matching walls detected in its map to the floor plan, through a drift-aware policy. A multi-stage integration then turns each matched pair incrementally into a persistent correction, so the trajectory stays corrected and localized within the floor plan as it is built. MVP-SLAM was validated on the multi-floor construction sites of the Hilti-Trimble SLAM Challenge 2026, ranking 2nd of 22 teams in the Localization task (0.29 m mean RMSE) and 5th of 62 teams in the SLAM task (0.24 m), the top-ranked one in both tasks among those that operate online, integrate the floor plan, and localize within it.

Practical Muon maintains momentum and performs a small, fixed number of Newton–Schulz iterations separately for each parameter matrix, often with a Nesterov correction. We analyze these layer-wise finite-step updates jointly on a coupled nonconvex objective, rather than replacing them by exact polar factors or one global orthogonalization. Under gradient-dependent $(\mathcal L_0,\mathcal L_1,q)$-smoothness and conditionally unbiased stochastic gradients with bounded layer-wise variance, we establish an $\mathcal O(T^{-1/4})$ bound on the expected average Frobenius gradient norm. The analysis retains the Nesterov recursion and requires neither bounded stochastic gradients, symmetric noise, nor a uniform positive lower bound on the nonzero output singular values. Its constants contain no explicit matrix-dimension or rank factors when the number of blocks and problem constants are fixed. The proof follows a descent inequality and a decomposition of the momentum tracking error into initialization, noise, and drift. For the original five-step quintic, we verify the required scalar-map bounds analytically; the result also allows step-dependent coefficients satisfying the same bounds. A complementary nuclear-norm result quantifies rank dependence under a stronger spectral condition. The vanishing rate uses coupled learning-rate and momentum schedules, including the standard single-coefficient Nesterov rule.

As robots are increasingly deployed in everyday environments, ensuring their safety has become a central challenge. Existing methods often encode safety requirements as opaque mathematical/logical formulations or dense cost functions. While effective in specific tasks, they remain difficult to interpret, tightly coupled to individual tasks, and offer limited insight into why a robot action is considered safe or unsafe. To address this limitation, we propose “Neuro-Symbolic Predicate Learning for Semantic Safe Robot Control” (NEUPRO), which leverages a differentiable reasoner that can learn reusable safety representations from human-specified safety knowledge. NEUPRO allows practitioners to express task-related safety requirements as transparent symbolic rules, while enabling gradients to propagate through these rules to a feature extractor that maps raw observations to safety-relevant concepts. As a result, the learned feature extractor is (softly) grounded in human-understandable semantics, supports transparent constraint evaluation, and is transferable across tasks. By coupling interpretability with differentiability, NEUPRO moves beyond opaque cost design toward reusable safety reasoning. To evaluate NEUPRO's capability, we collect and release REASON, the first real robot benchmark dataset for interpretable robot safety specification. Experiments on REASON show that NEUPRO learns safety-critical features that generalize across tasks, mitigate the interpretability limitations of conventional black-box cost formulations, and provide explicit explanations of safety violation.

A metric space is plastic if every bijective nonexpansive self-map is an isometry. We prove that the hyperspace of nonempty compact subsets of every connected, locally finite, regular graph, equipped with the Hausdorff metric associated with the path metric, is plastic. The proof identifies the sets with smallest unit balls as the nonempty subsets of adjacent-twin classes and shows that every nonexpansive bijection induces an automorphism of the quotient graph preserving the sizes of these classes. Singletons are preserved when there are no adjacent twins, but need not be preserved in general. We also prove that $\mathcal{K}(K\times G)$ is plastic for every compact connected metric space $K$ and every connected, locally finite, regular graph $G$, with the supremum metric on the product, and give a more general criterion for such products. Further results include a plastic metric space whose hyperspace is not plastic, plasticity of every tree, and plasticity of the hyperspace of a connected, locally finite graph with only finitely many vertices of minimum degree.

We study the complexity of Local Hamiltonian problems under the restriction that every local term is an unweighted occurrence of the same fixed interaction. In the resulting Single-Interaction Hamiltonian (SIH) model, once the interaction is fixed, the Hamiltonian is specified entirely by its ordered interaction hypergraph. Our main technical tool is an exact compiler that converts any fixed finite alphabet of local interactions into a single interaction. On a designated auxiliary subspace, the compiled Hamiltonian reproduces the source Hamiltonian exactly, while the complete spectrum below a chosen separation scale is preserved with multiplicity. Combined with a finite-alphabet normalization, this gives a universal polynomial-time reduction from $k$-Local Hamiltonian to SIH$_{3k+3}$ up to a known global energy scale and inverse-polynomial approximation. Sharper constructions give QMA-completeness of SIH$_3$ and of geometrically local SIH$_8$ with bounded degree and interaction range. In the stoquastic setting, we obtain StoqMA-completeness of Stoq-SIH$_3$ and QMA-completeness of 1-Pinned Stoq-SIH$_4$. We also establish hardness results for uniformly system-size-dependent interactions and derive single-interaction formulations of the Hamiltonian quantum PCP conjecture, frustration-free, exponentially precise, and guided Local Hamiltonian problems. These results show that independently chosen local matrices and independently tunable coupling strengths are not necessary for a broad range of Hamiltonian-complexity phenomena.

Uncertainty estimation in machine learning typically decomposes uncertainty into aleatoric uncertainty (AU) and epistemic uncertainty (EU) using the standard information-theoretic framework. However, in practice, two critical issues arise: entanglement (AU and EU are highly correlated) and epistemic collapse (EU magnitude shrinks with increasing model capacity). We analyze this framework on a functional level and discover that significant portions of the assumed AU, EU range are infeasible in finite settings, and cannot be attained with any class probabilities. We characterize how this infeasible region scales with the number of classes and Monte Carlo samples $N$ (e.g., from ensembles with $N$ members), revealing it is bounded by $\text{AU} \leq \log(2)/N$. Crucially, the infeasible region's boundary helps explain epistemic collapse: when model confidence is high, $\text{AU} > \text{EU}$ is guaranteed by this fundamental structural limitation. Our findings show that increasing ensemble size mitigates epistemic collapse by reducing the infeasible area. Lastly, we caution against interpreting AU and EU as independent quantities in low AU regimes, since we show they are coupled when $\text{AU} \leq \log(2)/N$.

Compositional 3D scene generation aims to recover complete 3D object shapes and their spatial arrangement from visual observations. Recent image-conditioned 3D generators provide strong priors for producing high-quality object geometry, making the generation of complex scenes increasingly practical. A central challenge is therefore to spatially organize these generated assets into a globally coherent scene while remaining consistent with multi-view observations. Existing approaches either entangle scene layout with object generation or separately estimate spatial placement from view-specific observations, where pose hypotheses may remain ambiguous and inconsistent across views, often resulting in an incoherent object-camera soup. We introduce SPOON, a framework that reformulates multi-view compositional 3D generation as scene-level, geometry-grounded pose reasoning. Rather than treating view-specific object pose hypotheses independently, SPOON coordinates them using reconstruction-derived multi-view geometry through a Guide-Route-Reconcile paradigm. This progressively organizes object poses and camera configurations into a coherent scene-level spatial arrangement. Extensive experiments on ARSG-110K and MIDI-3D-Front demonstrate consistent improvements in object placement and scene composition across varying numbers of input views. On ARSG-110K, SPOON reduces scene-level and object-level Chamfer distances by 12.7% and 17.7%, respectively, compared with a strong baseline.

We construct efficient information-theoretic non-malleable codes for classical messages that are secure against two noncommunicating local quantum tampering operations with arbitrary pre-shared entanglement. For every sufficiently small fixed $\xi>0$ and all sufficiently large first-share lengths $n$, the codes have rate at least $1/5-\xi$, perfect correctness, and error $2^{-n^{\Omega(1)}}$. Security holds for every message, with a single message-independent simulator for each attack. This resolves the constant-rate question for worst-case classical messages in the entangled two-split-state model. Our construction builds on the permutation-based two-split construction of Batra, Boddu, and Jain, which achieves rate approaching $1/5$ for uniformly random messages. We retain their architecture but replace the uniform message input to the permutation with a prescribed message concatenated with fresh uniform padding. Our main contribution is a worst-case security reduction for this modification.

We push the frontier of large-scale spatial intelligence in Vision-Language Models (VLMs) and introduce the first benchmark that probes geographical layout understanding from real-world videos, spanning up to 1km distances. Inspired by the cognitive science literature, we evaluate models against the hierarchical stages of human spatial awareness: anchoring via landmarks, connecting them through routes, and integrating these into global mental maps. Extensive experiments reveal a fundamental divergence in how current AI models process spatial information. Instead of utilising true path integration or forming geometric survey knowledge, we find that VLMs rely almost entirely on 2D visual recognition and text-matching to bypass complex spatial reasoning. The benchmark is publicly available at https://perception-test-challenge.github.io/kilometervision.html.

We study preservation of finite gauge-energy flows under local network repair after Bernoulli edge failures. A macroscopic demand network records terminal pairs to be routed, while a microscopic physical network contains local backup routes, bypasses and shared corridors. We prove a deterministic gauge-energy repair theorem: if the usable demand network $\mathcal{B}^{\sharp}$ carries a finite $\Phi$-energy flow $\theta$, then the repaired physical network $H$ carries a lifted finite $\Phi$-energy flow $\Theta$ with $$ \mathcal{E}^\Phi_H(\Theta) \le L\,\beta_\Phi(K)\,\mathcal{E}^\Phi_{\mathcal{B}^{\sharp}}(\theta), $$ where $L$ bounds route length, $K$ bounds routing congestion, $\mathcal{E}$ marks energy, and $\beta_\Phi$ is the gauge dilation constant. We then convert this comparison into probabilistic repair criteria: finite-dependent local repair is handled via domination by product measures, and random repair lengths via a variable-cost formulation compatible with chemical-distance estimates. As a main application, we prove a finite-dependent local bypass theorem: any macroscopic network whose supercritical percolation cluster supports a finite gauge-energy flow remains gauge-energy stable after bounded-range local reinforcement, provided the local repair probability is sufficiently high. This yields reinforced lattice and wedge-type examples and provides a potential-theoretic framework for random network repair beyond tree-like or edge-disjoint constructions.

The radiative transport equation provides a powerful framework for describing wave propagation in scattering media. However, it cannot describe coherent waves whose incident wavefront is deliberately tailored. Here we establish a transport theory for wavefront-controlled waves based on a matrix transport equation. Unlike conventional radiative transport, which propagates a scalar radiance, our theory propagates a complex two-by-two matrix that retains phase information and obeys a nonlinear transport equation, despite the underlying wave dynamics being linear. We use this matrix transport equation to derive the spatial profiles of the energy and current densities of transmission eigenchannels, from closed to open channels, in arbitrary diffusive systems. Remarkably, these profiles can be expressed analytically in terms of the solution of the conventional radiative transport equation for a random wave in the same medium. The theory further extends to energy loss, including absorption and leakage into uncontrolled channels, revealing symmetry breaking of transmission eigenchannels in complex structures. Validated against numerical solutions of the wave equation, we establish matrix transport as a framework for describing and controlling coherent wave propagation in complex media.

AI video generators have not only become harder to detect but are used to generate a diverse set of scenarios from landscapes to street views to animal videos. This creates a problem where CNN-based detectors are effective but offer no insight into their inner workings, while forensics-based detectors are often pretrained for a set scenario or become too complex to derive meaningful insights. We present a novel approach to AI video detection using Sobel gradient values analysed with the first-digit law. Using linear discriminant analysis, we visualise the discriminatory signal, while a multi-layer perceptron is used for classification. The detection method has no generator- or scenespecific features, and the model has no knowledge of container formats, codec, bitrate, or compression artefacts. The model is trained and tested on GenBuster-200K, GenBusterBench, GenVA, FaceForensics++ C23, and CelebDF. We also show how zero-shot detection fails even though the feature set carries a discriminatory signal.

Edge computing has emerged as a critical computing paradigm in modern distributed systems by migrating data processing closer to end users and Internet of Things (IoT) devices. While this paradigm decentralizes processes, minimizes latency, and reduces backhaul bandwidth congestion, it exponentially enlarges the cyberattack surface. Heterogeneous, resource-constrained edge devices deployed across unmanaged administrative domains present highly vulnerable targets. To address these vulnerabilities without compromising global data privacy regulations, this paper proposes a novel Trust-Aware Federated Hybrid Intrusion Detection Framework (TA-FHIDF). The proposed framework integrates an Autoencoder, a 1D Convolutional Neural Network (1D-CNN), and a Bidirectional Long Short-Term Memory (BiLSTM) model into a unified, localized deep learning engine capable of autonomous spatial and temporal feature extraction. Model training is performed collaboratively via federated learning, ensuring raw network telemetry remains isolated at local gateways. Furthermore, to defend against adversarial model poisoning attacks, we introduce a robust server-side trust-aware aggregation mechanism that evaluates client reliability using a cosine similarity metric before global model integration. Empirical evaluations across multi-vector benchmark datasets (UNSW-NB15, CICIDS2017, and Edge-IIoTset) demonstrate the framework's superior detection accuracy, rapid convergence, and high Byzantine fault tolerance under adversarial attack scenarios.

We present the results of MADGRAV, a deep-learning-based search for high-mass compact binary coalescences, applied to the data collected by the LIGO interferometers during the third observing run and during the first and second part of the fourth observing run. The MADGRAV pipeline consists of a series of sequential convolutional neural networks that perform anomaly detection, glitch classification, coherence testing, and signal ranking. Data from the Hanford and Livingston LIGO detectors are studied (both individually and in coherence) by way of 1 second Q-transform windows. Of the candidates that survive every stage of the pipeline, 48 reach the significance threshold, and we report 47 gravitational wave detections characterised by a false alarm rate below $1\,{\rm yr}^{-1}$ with a probability of astrophysical origin $p_{\rm astro}>0.9$. Of the 47 detections, 44 are shared with the minimally modelled coherent WaveBurst search. The observed total source-frame masses, extracted from official gravitational wave transient catalogues, are in the $14-236 M_{\odot}$ range with a median of $69 M_{\odot}$, and a median SNR of 16. We note that the recovered fraction of confident detections rises with mass: for LIGO detectors network SNR $>10$ the pipeline recovers $8.1\%$ of confident catalog events below $30 M_{\odot}$, $39.8\%$ between $30$ and $100 M_{\odot}$, and $53.3\%$ above $100 M_{\odot}$, corresponding to $33.3\%$, $45.5\%$ and $53.3\%$ of the events detected by coherent WaveBurst in the same bins. These results suggest that anomaly detection pipelines can serve as an independent detection channel complementary to matched filtering in the high-mass high-SNR regime.

The increasing precision of measurements at the Large Hadron Collider requires a detailed understanding of all contributions to electroweak boson production. We estimate the impact of single-diffractive W and Z production on precision observables at $\sqrt{s}=5$, 7, 8, and 13 TeV. The non-diffractive baseline is calculated with DYTurbo, while Herwig provides the relative single-diffractive contribution and its transverse-momentum dependence. Factorization breaking is incorporated through a $p_T$-dependent rapidity-gap survival probability calculated with the dynamic multiparton-interaction model of Pythia8. The diffractive Asimov spectrum is constructed by deterministic bin-by-bin reweighting of the same high-numerical-precision DYTurbo cross section used for the non-diffractive baseline. With the non-perturbative parameters profiled, the nominal relative shifts in $\alpha_s$ are -0.0072%, -0.043%, -0.070%, and -0.067% at 5, 7, 8, and 13 TeV, respectively. Five Pythia8 Pomeron-flux and diffractive-PDF configurations give a maximum spread of $9.4\times10^{-6}$ in $\Delta\alpha_s$. In the W-mass study, the largest bias from an unmodelled survived single-diffractive contribution is 1.58 MeV, and the largest residual after applying the corresponding model-matched template correction is 1.14 MeV. These shifts are below the relevant fit precision, and no phenomenologically significant impact on $m_W$ is expected within the tested models.

Paper ECG recognition is challenging because real-world ECG images vary in layout, physical artifacts, and label availability. We introduce RobECG-CL, a rank-aware contrastive learning framework for robust paper ECG representation learning. Starting from standard 12-lead ECG recordings, we construct progressively degraded paper ECG views with heterogeneous layouts and train the model to balance same-recording invariance with degradation-aware ordering. Across synthetic stress tests on CODE-II and EchoNext, RobECG-CL improves robustness under severe degradation and few-shot transfer, outperforming contrastive learning baselines and surpassing the waveform-based foundation model, ECG-FM, in the 1% labeled setting. On 312 samples of hospital data with 37 labels, RobECG-CL achieves the best macro AUROC.

We consider the two-dimensional generalized surface quasi-geostrophic equations in $\mathbb{R}^2$, given by \[\partial_t \theta+u\cdot \nabla \theta=0,\quad u=-\nabla^{\perp}\Lambda^{\beta-2}\theta,\,\beta\in [1,2).\] When $\beta=1$, the equation defines the SQG equation and for $\beta>1$, it defines a family of more singular active scalar equations. We prove that if the interval of existence of the smooth solution to the generalized SQG equations for some $\beta_0\in[1,2)$ is $[0,T]$, then with the same initial data, the interval of existence of the generalized SQG equations for $\beta$ close to $\beta_0$ also contains $[0,T]$. To prove these results, we develop estimates for a conservation law with flux modified around the generalized SQG equations. Furthermore, we also prove some new commutator estimates with bounds uniformly bounded as $\beta\to 1$ that may be of independent interest.

Deploying vision-and-language navigation (VLN) agents in unseen environments remains challenging because unfamiliar layouts and visual conditions can cause execution to go off track. Rather than relying on continuous human supervision, a practical strategy is to selectively request corrective guidance, recover the ongoing task, and reuse corrective interactions to improve subsequent navigation. We propose Abstention-aware Visual Error Recovery and Training for Vision-and-Language Navigation (AVERT-VLN), a closed-loop framework that uses a plug-in vision-language Monitor for online human-assisted recovery and offline preference learning. The Monitor operates separately from navigation decision generation and assesses instruction-execution consistency from the instruction, visual history, and current observation. To train the Monitor for deviation recognition, we construct LOSTNAV DATASET with 20K counterfactual risk trajectories and rule-based deviation labels. The Monitor is first fine-tuned on 40K normal trajectories to assess instruction progress and then jointly fine-tuned on normal and risk trajectories to recognize semantic deviations. At runtime, Asynchronous Sidecar Monitoring evaluates execution alongside the navigation model. When the controller accepts a LOST verdict, it suspends autonomous execution and requests human guidance for recovery. For offline policy improvement, Trajectory-Anchored Preference Learning converts deviation-associated failures into decision-level preference pairs under shared decision contexts, restricting supervision to the decisions targeted for correction. Under human-assisted evaluation, the full AVERT-VLN system achieves success rates of 76.2% and 66.3% on the val-unseen splits of R2R-CE and RxR-CE, respectively. The same monitoring and human-assisted recovery interface also improves success rates across the three evaluated navigation architectures.

Agent harnesses often improve language models with human-designed workflows, but as models grow more capable, unreliable guidance can increasingly constrain their execution. We call the ability to benefit from useful guidance while overriding unreliable guidance thinking outside the box. We introduce Box$^2$-Bench, which holds the model and task fixed while varying workflow reliability to isolate how models regulate their reliance on guidance. On Box$^2$-Bench, frontier models often benefit from reliable guidance but remain vulnerable when it is misleading or becomes unreliable. To test whether this capability can be learned, we train two open-weight models using bad workflows, reserving good workflows for evaluation. We explore two complementary training strategies: counterfactual supervised fine-tuning improves robustness, while outcome-based reinforcement learning can shift the balance toward greater use of helpful workflows. We further find that this behavior extends beyond workflows to other forms of external information, improving peer correction and robustness to corrupted memory. Together, our results identify selective reliance on fallible external information as a dimension of agent reliability not captured by task performance alone.

We prove that $\mathsf{Cheq}$ is not finitely axiomatizable, resolving a longstanding open problem in intermediate and modal logics. We further prove that the undecidability of Medvedev logic implies the undecidability of $\mathsf{Cheq}$.

We present an Integrated Sensing And Communication (ISAC) framework for the joint estimation of the Doppler frequency of a passive mobile target in a bistatic scenario with clock-asynchronous nodes and where the Receiver (RX) is static but the Transmitter (TX) is mobile. In such a setup, previous geometric solutions are integrated with an Inertial Measurement Unit (IMU) device at the TX, coming up with a truly joint data fusion and estimation algorithm based on extended Kalman filtering. The approach jointly estimates the target Doppler frequency, along with the speed and direction of motion of the TX and it is robust to the unavailability of static paths between the TX and RX pair, a condition that makes previous solutions ineffective. The developed extended Kalman filter strikes a balance between the accuracy of ISAC and the IMU reliability. The proposed solution is validated via numerical simulations, obtaining a median Doppler error of 1.2% with a smartphone-grade IMU under realistic operating conditions.

Generating full-body co-speech motion for humanoid robots requires coordinating speech prosody, linguistic content, and embodiment-specific motion. To this end, we present ECHO-G, a framework jointly conditioned on speech audio and timed transcripts. Its Speech-Grounded Diffusion Transformer (SGDiT) combines frame-aligned acoustic features with token-level linguistic context, preserving their distinct granularities. Trained with rectified flow matching, it models one-to-many utterance-motion relationships directly in robot space. To support training and evaluation, we introduce a BEAT2-derived audio-text-robot dataset and a benchmark covering co-speech characteristics, robot-motion quality, and runtime efficiency. Comparative evaluation supports direct robot-space generation over the evaluated human-motion generation and retargeting pipelines, while modality ablations highlight the benefits of joint audio-text conditioning. We further demonstrate deployment on a physical humanoid robot. A complementary video-rating study also favors joint conditioning over the alternatives. The dataset and training, inference, and evaluation code are available through our project page.

We compare three approaches for computing color-summed tree-level all-gluon squared matrix elements: evaluation using direct contraction in the trace and adjoint decompositions, orthonormal multiplet bases, and fast Fourier transforms (FFT) based on the irreducible representations of the symmetric group for the trace and adjoint decompositions. The multiplet method reduces the color sum to a sum of absolute squares and utilizes an amplitude recursion labeled by SU(3) representations. The FFT exploits the relative-permutation dependence of color overlaps to replace the direct double sum with smaller independent contractions, using standard color-ordered partial amplitudes. This invokes the symmetric group at the level of gluon labels, and therefore makes maximal use of the permutation symmetry. We compare CPU time and memory use for four through eleven gluons. At eleven gluons, the direct adjoint contraction evaluates a fixed-helicity color-summed matrix element in an estimated 1.7 10${}^3$ s after initialization, compared with 19.8 s for the multiplet recursion and 0.814 s for the FFT adjoint method. The adjoint FFT is fastest from six through eleven gluons, despite its factorial scaling compared with the exponential scaling of the multiplet recursion.

As state-of-the-art text-to-image flow models achieve near-photorealistic quality, controlling their outputs, e.g., suppressing harmful content while promoting benign alternatives, has become a central challenge. The current steering paradigm consists of adding a global steering vector to selected activations. While functional, a fixed and example-agnostic vector applied uniformly along the entire trajectory cannot adapt to the changing state of the generation and often causes unintended global changes. We introduce Steering Fields, a generalization of steering vectors that adaptively re-estimates the steering direction at each step of the generative process. Steering Fields operate on the noisy states of flow models, expose a continuous trade-off between steering strength and content preservation, and are compositional, enabling the simultaneous induction and inhibition of concepts, setting a new state of the art on safety steering benchmarks. Despite using no explicit spatial masks or object priors, the trajectory-adaptive estimation naturally preserves local structure, in a manner reminiscent of image editing. In fact, Steering Fields can serve as a structure-preserving image-editing technique that achieves state-of-the-art semantic fidelity (CLIP, VQAScore), while remaining model-agnostic and inversion-free.

We analyze how lexical ambiguity and underspecification affect language model training. We create artificial homonyms and artificial hypernyms as pseudowords and analyze the generative performance of language models as they are trained with increasing amounts of these ambiguous or underspecified pseudoword types. We further analyze whether the models disambiguate ambiguous or underspecified statements and provide a first mechanistic account of how ambiguity and disambiguation are represented internally. Our main results show that both ambiguity and underspecification increase model performance in ways that scale with their influence on the language's type-token ratio. However, the accuracy of generating sequences containing ambiguous words or their synonyms decreases compared to other texts. We also show that internal representations of pseudowords reflect disambiguation of pseudo-homonyms, but underspecification of pseudo-hypernyms is maintained during the generative process.

We present a methodology for the reduction of archival spectral data together with the description of a newly developed Python-based software package featuring an interactive graphical interface. The work is primarily aimed at processing spectra obtained with electron-optical converters (EOCs), which are characterized by geometric distortions induced by the magnetic field of the registration system. Such data are preserved, in particular, in the archive of the Fesenkov Astrophysical Institute (FAI), which contains about 10,000 photographic plates. These distortions, along with the need to transform the optical density of the photographic material into relative intensity, cannot be corrected by standard astronomical packages such as IRAF and therefore require a dedicated approach. Historically, reductions at FAI were performed using a program written in the Microsoft QuickC language for computing platforms of the 1990s, rendering it incompatible with modern operating systems. The new package is implemented with the PyQt5 framework, retaining the logic of the original code while extending its functionality. The implemented algorithms include image rotation and cropping, geometric distortion correction, construction of the characteristic curve linking optical density and intensity, and direct conversion of pixel values in object spectra. The developed software ensures reproducible reduction of archival spectra and provides a cross-platform environment with potential for further extensions.

Trajectory planning is a core component of autonomous driving systems, where real-time performance and solution quality directly affect safety and reliability. Sample-Based Motion Planning (SBMP) is widely adopted for its ability to approximate near-optimal solutions through parameter space sampling. However, achieving high-quality trajectories typically requires dense sampling, leading to substantial computational overhead and significant runtime variability in complex traffic scenarios. To address this limitation, we propose a Sparse Planner (SP) that improves sampling efficiency by learning the conditional relationship between scene context and effective trajectory parameters using a Conditional Variational Autoencoder (CVAE). By modeling the structure of high-quality sampling distributions, SP directly generates cost-effective samples in the parameter space, significantly reducing the required sampling density while preserving solution quality. Experimental results show that SP achieves lower trajectory cost than the state-of-the-art FISS+ planner while using only one-eighth of the sampling density. In addition, SP demonstrates improved distance-keeping capability in obstacle-rich scenarios and maintains reduced and more stable runtime characteristics, indicating enhanced computational efficiency and predictable runtime behavior.

We develop a spouse-protected tontine in which a first death changes the household state but generates no pool transfer. The same account remains attached to the household contract until extinction and funds a spouse-only continuation phase if the retiree dies first. We derive contract-level actuarial-fairness conditions and a finite-pool mortality-credit allocation rule with exact ex post budget balance. Under a homogeneous large-pool approximation, we formulate a multidimensional decumulation problem for a representative household, with withdrawal and rebalancing controls while the retiree is alive. The objective balances expected cumulative real household payments against the Conditional Value-at-Risk (CVaR) of terminal shortfalls relative to household reserve targets, without conditioning on survival to the horizon. We develop a numerical solution method for this problem based on a global-in-time neural-network parameterization of admissible control policies. We quantify policy-induced spouse-continuation costs using expected-cost and risk-loaded payment-scale loads at both representative-contract and book levels. We characterize the large-book limit of average per-contract continuation cost as the expected representative-contract cost conditional on common market information. Numerical experiments calibrated to Australia show that the spouse-only phase is a first-order and persistent household event. In these experiments, book-level diversification removes most of the representative-contract excess upper-tail cost of spouse continuation in the large-book limit, without changing expected per-contract continuation cost. A cross-country mortality comparison indicates that the prevalence and persistence of the spouse-only phase are not specific to Australia.