Papers

Inspired by quantum metrology, we propose a coherent consensus primitive to enhance the collaborative performance of independent quantum classifiers at the decision boundary. The basic idea consists of three steps: i) prepare a Greenberger-Horne-Zeilinger (GHZ) state on $n$ qubits; ii) apply a relative phase to each qubit, which encodes the output of one classifier; and iii) undo the GHZ preparation to collect all phases onto the first qubit. The signal is amplified by a factor of $n$, which reduces the sampling error by a factor of $\sqrt{n}$ relative to incoherent majority voting, that is, the direct combination of estimates from individual classifiers. Coherent consensus is valid for general estimation and classification of phases. We derive guarantees on the resources needed to estimate phases using this coherent consensus primitive as compared to majority voting. We implement both techniques on a trapped-ion quantum computer using a given ensemble of imperfect phase gates. We observe the expected $\sqrt{n}$ gain in precision of coherent consensus, with excess dispersion at the largest $n$ consistent with device drift. Coherent consensus can thus be understood as a form of sensing inside a quantum computer.

Let $k\ge2$ be a fixed integer. Bollobás and Scott proved that every $3$-uniform hypergraph with $m$ edges admits a partition of its vertex set into $k$ parts such that each part spans at most $m/k^3+O_k(m^{6/7})$ edges. Scott later suggested that the error term should be $O_k(m^{2/3})$. In this paper, we show that every $3$-uniform hypergraph with $m$ edges admits a partition into $k$ parts such that each part spans at most $m/k^3+O_k(m^{2/3})$ edges, thereby establishing the proposed error term.

Standard information retrieval metrics, such as mean Average Precision (mAP), assess performance one query at a time, based on how the similarities between a query and its positives compare against those with its negatives. The same holds for common representation learning losses, such as InfoNCE and per-query AP surrogates. None of them considers whether similarities are comparable across queries, which any system with a single decision threshold relies on. Global Average Precision (gAP) does, by ranking all query-candidate pairs in one list and computing a single AP. We introduce gSAP, a differentiable surrogate of gAP. It needs only a similarity matrix and a binary matrix marking the positive pairs, the same input as existing losses, so it is a drop-in replacement for them and agnostic to the encoder, the modality, and the source of supervision. Since it considers all possible pairwise comparisons in the batch jointly, it also remains trainable at low temperatures, a regime where per-query surrogates run out of gradient. Swapping it into established recipes improves supervised metric learning, cross-modal alignment, and self-supervised pretraining, where, to our knowledge, it is the first ranking loss to replace the community standard InfoNCE in the latter two. Its similarities are more consistent across queries, which drives the gains under a universal threshold. gSAP retrieves up to four times as many positive pairs as the strongest AP surrogate at the same precision, and it degrades the least when queries with no positives in the database are added. Beyond thresholding, models trained with gSAP also learn better representations, with higher transfer, $k$NN and zero-shot classification accuracy.

We derive a family of sum rules for the tensor structure functions of targets with spin one or higher, rooted in exact Siegert relations. The mixed rank-two $TT$–$LT$ degeneracy combines amplitudes of opposite crossing parity and, under the superconvergence assumption, gives $\int_0^1\! d x\,[b_2(x,Q^2)-3b_4(x,Q^2)]=0$ in the Hoodbhoy–Jaffe–Manohar (HJM) basis. At large $Q^2$, the protected moment agrees with Detmold's target-mass-complete twist-two OPE; in the strict Bjorken projection, and if $b_4$ is neglected, it reduces to the Efremov–Teryaev (ET)-type condition $\int_0^1\! d x\,x\,b_1(x)=0$, whose measured-range footprint is consistent with the HERMES data. Two further rank-two combinations connect crossing-even amplitudes and determine the corresponding subtraction functions through weighted HJM moments. The protected combination can be isolated through separated tensor $LT$ and $TT$ responses, providing a direct experimental strategy for JLab and, ultimately, a future EIC.

Single-instrument automatic music transcription (AMT) has advanced substantially, yet choral applications require soprano, alto, tenor, and bass (SATB) to be transcribed as separate parts. Recent note-level choral AMT instead produces a single merged note track, limiting rehearsal, education, and score reconstruction. To address this limitation, we introduce Part-aware Choral Transcription (PawCT), to our knowledge the first end-to-end neural framework that identifies active SATB parts from choral audio and transcribes each into a separate note-level track. PawCT combines part-specific onset, offset, and frame prediction with part-presence estimation, union-level supervision, and structured training targets using a range prior (RP) based on SATB pitch ranges and its ordered-continuity (OC) extension, which adds within-part melodic continuity and cross-part pitch ordering. On YouChorale, PawCT-RP-OC achieves a macro part-aware note F1 of 0.225 at a 50-ms onset tolerance, outperforming an adapted choral baseline (0.165) by 36.4% relative and a two-stage post-hoc assignment pipeline (0.175). Its part-agnostic variant, PagCT, achieves a 50-ms onset F1 of 0.382, compared with 0.237 for the previous state-of-the-art choral AMT model. Cross-dataset evaluations on CSD and Cantoria further assess performance under dataset shift. These results demonstrate the benefit of jointly modeling note transcription and vocal-part assignment. Code and demos are available at https://hanyu-meng.github.io/Paw_Choral_AMT_Demo/.

4D point clouds acquired by permanent laser scanning (PLS) enable accurate high-frequency monitoring of surface change in dynamic topographic environments. However, existing methods remain limited in organizing detected surface activities into meaningful process types. We propose DeepTopoClustering (DTC), an unsupervised framework for deriving a hierarchical process taxonomy from object-based surface activities, so-called 4D objects-by-change (4D-OBCs). We transform each 4D-OBC into a GeoMorphogram, a distributional sequence representing the temporal evolution of topographic change within a spatially bounded surface activity. A convolutional autoencoder learns latent embeddings from GeoMorphograms, which are jointly optimized using a hierarchical deep clustering objective to organize surface activities into a hierarchy. We evaluate the learned hierarchy using expert annotations on two 4D datasets of sandy beach sites and their combination. DTC with GeoMorphograms achieves the highest agreement with expert judgment at the taxonomy level comprising eight major process types ($F_1=0.78$, match accuracy $=0.92$), outperforming dimensionality reduction and conventional flat clustering. The learned taxonomy separates major erosion- and deposition-dominated activities and distinguishes finer subtypes based on change magnitude, duration, compactness, and temporal evolution. DTC thus provides a scalable and interpretable route from 4D change detection to a data-driven, expert-supported surface process taxonomy, advancing automated knowledge derivation for understanding surface dynamics in topographic monitoring.

Accurate precipitation estimation at fine spatial scales is critical for hydrology, agriculture, and climate studies. Infrared brightness temperatures from geostationary satellites offer excellent temporal coverage over continental-scale domains. However, because these measurements primarily characterize cloud-top properties rather than precipitation processes near the surface, their correlation with rainfall intensity remains limited, making quantitative precipitation estimation challenging. In this study, we conduct a systematic inter-comparison of state-of-the-art deep learning models for high-resolution precipitation retrieval from Meteosat Second Generation infrared brightness temperatures over metropolitan France. These models include deterministic U-Nets, transformer-based architectures, conditional GANs, and diffusion models. We construct a curated dataset spanning 2008–2023, combining Météo-France radar mosaics as reference with multi-channel infrared observations, and design preprocessing and sampling strategies to address the heavy-tailed, intermittent nature of rainfall. Our results show that deterministic models provide robust mean estimates and excel in pixel-wise accuracy, but systematically underestimate extreme precipitation. In contrast, generative models better capture the full precipitation distribution, including rare and heavy rainfall events, producing more realistic spatial structures at the cost of reduced pixel-wise fidelity. These results highlight a trade-off between pixel-wise accuracy and precipitation variability, showing that generative approaches are advantageous for extreme-event detection and probabilistic applications. This work establishes a reproducible framework for evaluating infrared- based precipitation retrieval methods and provides guidance for designing models that balance precision, variability, and extreme-event representation.

Large language model agents tackle multi-step tasks by interleaving reasoning and tool calls with observations from the environment. Prior work has shown that natural-language feedback can help these agents revise their decisions during task execution. We introduce Caddie, a method for training critics to provide natural-language analysis and advice as agents work through a task. Unlike approaches that rely on step-level labels or reference critiques, Caddie learns from whether the agent ultimately succeeds after receiving the critic's feedback. We optimize the critic through reinforcement learning while keeping the base model frozen. Trained on multi-hop question answering with a single base model, our Qwen3-4B critic improves success rates across four base models of different scales and architectures, including three not used during critic training. On the MuSiQue benchmark, the trained critic improves Qwen3-4B's success rate by more than 25 percentage points, surpassing the performance of Kimi K3 without a critic. The same critic also yields gains on out-of-domain interactive benchmarks, including $\tau^3$ and DeepDive, with no additional training. Our results show that agents can decide when to seek help from a critic at inference time and that outcome-based critic training can produce guidance that transfers across base models and task domains.

Robot demonstration learning requires accurate and temporally complete end-effector localization during close-range manipulation and camera occlusion. Existing SLAM benchmarks emphasize navigation motions, whereas manipulation datasets prioritize policy learning over localization evaluation. We introduce MILD, a Manipulation-Interface Localization Dataset with real-world and simulation sequences. The real-world subset provides 86 sensor sequences from Insta360 X5 and Insight9 across 15 repeated tabletop tasks, calibration assets, and a per-execution robot end-effector reference trajectory. The simulation subset, MILD-Sim, extends task coverage in Isaac Sim for controlled manipulation-replay studies. Benchmarking visual-inertial and fiducial-aided systems on instrumented real-world recordings reveals large differences in both TCP-relative trajectory error and temporal coverage, even under the same nominal task. To support marker-augmented teaching workspaces without a pre-surveyed fiducial map, we present AprilVINS, which combines fisheye visual-inertial estimation with sequence-local AprilTag geometry and separates prior admission from guarded export of the jointly optimized state. On Insta360 AprilTag4 recordings, AprilVINS(full) under a unified protocol with sequence-specific profiles reaches millimeter-level SE(3)-aligned TCP-relative APE RMSE with high time completion and lower reported error than the tested routes under their respective protocols, whereas fisheye VIO without tag factors remains at centimeter scale. Ablations separate accuracy from exportability, and a MILD-Sim replay study provides task-specific tolerance references for interpreting those error magnitudes. Together, MILD and AprilVINS provide a diagnostic benchmarking framework for UMI-style demonstration collection. Code, datasets, and evaluation manifests will be released upon acceptance.

Self-evolving tool-integrated agents learn from tasks and feedback generated within their own training loop. A Curriculum Agent generates tasks, while an Executor Agent learns from self-consistency signals through reinforcement learning. However, relying solely on the current Executor for feedback has two limitations: group-relative advantages vanish under full consensus, while uncertainty-based curriculum rewards favor disagreement without showing whether the generated tasks support further learning. These limitations motivate an additional reference beyond the current Executor. We propose AnchorLoop, which introduces a frozen copy of the previous iteration's Executor as a historical reference and reuses it on both sides of the training loop. For the Executor, the anchor provides a cross-reference advantage that evaluates current outputs against both current and historical majority answers. For the Curriculum, it provides an agreement-based reference based on differences in sampled majority agreement. Since the Executor and anchor have identical parameters during Curriculum training, this comparison serves as a proxy for task selection rather than evidence of inter-version improvement or correctness. Across 13 reasoning benchmarks, AnchorLoop improves over Agent0 by 2.5% on mathematical reasoning and 2.8% on general reasoning tasks. It also maintains higher effective-advantage variance and continues improving in later iterations as the unanchored baseline shows diminishing gains. These results demonstrate the benefit of introducing a lightweight historical reference into self-evolving tool-integrated agents without external task or answer supervision.

Part I: Semiclassical Gravity Efficiently Solves $\mathsf{NP}$-Complete Problems Assuming the gravitational field is classical and that it couples to quantum fields via the semiclassical Einstein field equations (EFEs), we show that the weak-field dynamics of a massive and non-relativistic qubit can in principle be used to solve an $\mathsf{NP}$-complete problem in polynomial time. We attribute this vast computational power to the non-linear qubit dynamics afforded by the semiclassical EFEs. Consequently, the above two assumptions entail a violation of the Physical Extended Church–Turing Thesis, which we regard as evidence for the quantization of gravity. Part II: Spacetime Quasicrystals We generalize self-similar quasicrystals, such as the Penrose tilings, from Euclidean space to Minkowski spacetime. We construct the first examples of Lorentzian quasicrystals and identify their key novel features. We then explore possible connections to fundamental physics. First, we propose a speculative scenario in which our $(3+1)$D universe is embedded in a particularly symmetric $(9+1)$D torus $\mathbb{T}^{9,1}$, previously identified as the most symmetric toroidal compactification of the superstring. We suggest that this construction may shed light on the seesaw relation $M_{\rm Pl}M_{\rm vac} \approx M_{\rm EW}^{2}$ between the Planck, vacuum-energy, and electroweak scales. Second, we replace the random causal sets of causal set theory with ordered, highly symmetric quasi-crystalline causal sets. We find suggestive evidence that our quasicrystals outperform Poisson random sets in the number-volume correspondence in both $(1+1)$D and $(3+1)$D, where such behaviour has been conjectured to be impossible. Finally, extending hyperuniformity from space to spacetime, we show that our $(1+1)$D quasicrystal is the first demonstrated example of a spacetime-hyperuniform structure.

Ultracool dwarfs exhibit radio emission revealing strong magnetic fields and complex magnetospheric processes. Their auroral emission resembles that observed in magnetized Solar System planets, providing a framework to investigate their magnetic topology. We aim to characterize the magnetic activity, rotation, and atmospheric variability of the L3.5 dwarf LSPM J0036+1821 through a multiwavelength analysis. We conducted a long-term monitoring campaign combining radio observations from the Very Large Array and very long baseline interferometry arrays with TESS optical photometry, spanning 2019-2023. We analyzed time-series data to derive precise rotation periods and constructed light curves and radio dynamic spectra. The radio lightcurves were modeled using an auroral framework analogous to Jupiter's magnetosphere, incorporating main oval and active field line components. We detect persistent, compact radio emission with significant variability and high circular polarization. Periodogram analysis yields a rotation period of 3.07941 $\pm$ 0.00020h from radio data, consistent with the TESS optical period (3.07908 $\pm$ 0.00038h). The radio light curves display stable morphology characterized by asymmetric, rotationally modulated pulses. Our modeling reproduces the emission using a hybrid auroral scenario, with the main oval contributing a stable component and an active field line producing dominant, variable bursts. Short-term variability is explained by small changes in emission cone geometry or longitude of the active field line. The radio emission of LSPM J0036+1821 is consistent with auroral processes driven by the electron cyclotron maser instability in a structured magnetosphere. The behavior is consistent with a Jupiter-like auroral system, possibly involving companion-driven or internally-driven magnetospheric interactions analogous to those observed in the Solar System.

Pose-free feed-forward 3D Gaussian Splatting (3DGS) reconstructs a scene from sparse, unposed images in a single network pass, removing the need for camera calibration and per-scene optimization. However, camera estimation errors propagate into the predicted Gaussians and compound the geometric and photometric inaccuracies of single-pass prediction. To correct these errors, we introduce DeltaSplat, a lightweight Gaussian refinement module for pose-free feed-forward 3DGS. It iteratively renders the current Gaussians at the input context views and predicts per-Gaussian updates from the resulting residuals. A 2D residual alone, however, underdetermines the 3D correction. DeltaSplat therefore conditions each update on per-pixel Plücker rays and rendered depth as a soft geometric prior. A dual-branch convolutional mixer efficiently encodes these inputs, and per-attribute heads decode the fused features into position, opacity, and color updates. The module adds only ~2.2% parameters to the backbone and remains fully feed-forward at inference. On DL3DV, DeltaSplat reaches 26.64 dB PSNR in the pose-free setting, improving its state-of-the-art backbone by 1.75 dB and surpassing even baselines supplied with ground-truth cameras; consistent gains hold across 6-24 views and all camera regimes.

Following Macintyre's quantifier elimination result for semi-algebraic $p$-adic sets from 1976, Denef's cell decomposition from 1984 has played a catalyzing role for both motivic integration and Hensel minimality. Motivic integration has in turn been applied in the Langlands program via transfer principles to change the characteristic of the local field, e.g., for the fundamental lemma. Hensel minimality has been used to study rational points on definable sets, providing non-archimedean analogues of results by Pila and Wilkie in o-minimal structures. I will review some related results and open questions.

Affine frequency division multiplexing (AFDM) is robust to doubly dispersive channels in high-mobility 6G systems but, like orthogonal frequency division multiplexing (OFDM), suffers from a high peak-to-average power ratio (PAPR). Spreading with a discrete affine Fourier transform (DAFT) yields DAFT-s-AFDM, whose precoder and modulator chirps can be chosen independently. For a single user with zero-offset localized allocation, we show that these two chirps merge into a single residual chirp whose rate, with the other two chirp rates fixed, alone determines their effect. At the transmitter, this rate defines a circulant spreading kernel whose fourth moment quantifies the envelope fluctuation; symmetries reduce its characterization to rates in [0, 1/4]. At a linear minimum mean-square error (MMSE) receiver, the residual chirp redistributes the mean- square error across symbols without changing its total; under a Gaussian approximation, a more uniform per-symbol error lowers the uncoded bit error rate (BER). In uncoded QPSK simulations, a zero rate yields the lowest PAPR, whereas a generic rate reduces the signal-to-noise ratio required for a BER of $10^{-3}$ by 4.4 dB at a 3.33 dB PAPR cost (exceedance probability $10^{-3}$);a rate of 1/3 captures 2.8 dB of this gain for only 0.88 dB of that cost.

In this paper, we study observable sets for the one-dimensional Schrödinger equation associated with the operator $H=-d^2/dx^2+|x|$ on $L^2(\mathbb R)$. We prove that a measurable set is observable at every positive time if and only if it is thick. For each fixed observation time, the observability constant is uniform over all measurable sets with prescribed thickness parameters. The theorem answers the question concerning the relationship between thick and observable set raised by Gengsheng Wang [12] for this anharmonic oscillator.

Selecting synthetic degradations for dense prediction requires an estimate of their training utility, the generalization gain they bring under a finite training budget. Clean and degraded twins share content and labels, suggesting a score based on how much short training reduces the excess error caused by degradation. However, this gap can also shrink when clean performance deteriorates. Measuring the improvement on degraded images alone avoids that confound, but it still credits progress that the same amount of clean training would have produced. We propose the controlled Reducible Degradation Gap (cRDG) for regions defined by degradation type and severity. From a common checkpoint, cRDG runs two budget-matched probes that differ only in one augmentation slot, which holds either a synthetic degradation or a clean augmentation. The score is the gain on held-out degraded images relative to the clean-control probe. Clean harm is a separate feasibility constraint. cRDG reveals a correctable severity band in which training on the degradation yields high controlled gain under the available budget, and the band moves with the predictor, the starting checkpoint, and the training budget. Curation of Reducible Bands (\method) uses cRDG to select synthetic data without changing the predictor. On semantic segmentation and salient object detection, \method{} improves representative predictors under matched synthetic-data budgets and training schedules, extends to existing data-generation pipelines, and preserves clean performance. Code and supporting materials will be publicly released.

Inverse design in engineering often runs into a simple problem. Each labeled training sample must be produced through expensive simulation, so building a large dataset is slow and costly. This study addresses that problem for partial inverse design, where only some design variables are specified and the rest must be inferred to reach a target performance value. We propose CoNN-AL, a framework for data-efficient partial inverse design that adds stream-based active learning to the Cooperative Neural Network with Denoising Autoencoder (CoNN-DAE). The model estimates predictive uncertainty through Monte Carlo dropout and uses it to decide, in real time, which incoming candidate samples are worth labeling, so the limited labeling budget is spent on the most informative designs. We validate the framework on a real-world automotive glass run channel dataset of more than 900,000 unique simulated designs. With only 20,000 actively selected labels, about 2.3% of the training pool, CoNN-AL reaches R-squared values of 0.967 to 0.982 across all missing-variable levels, approaching the upper-bound models trained on far more data. It reaches R-squared of at least 0.95 with 30 to 40% fewer labels than random sampling at the more difficult missing-variable levels and, at the most challenging level, is the only strategy in this study to reach R-squared of 0.98. Together with this work, we publicly release the dataset to support future research on data-driven design.

We study linear perturbations of the Maldacena-Milekhin-Popov (MMP) wormhole in the parity sector that pairs axial metric perturbations with polar gauge perturbations. It contains the axial gravitational mode and the electric field along the magnetic field lines. The lowest Landau level (LLL) of the charged fermions responds through its charge. The gauge components $a_\tau$, $a_\rho$ form a two-dimensional gauge field on the worldsheet of each field line, and the fermions respond with the exact Schwinger current. Lifted over the sphere, it gives the electric field the MMP screening mass $m_S^2=\alpha q^2$, which is not small and survives in the mouth. In the throat the perturbation tilts the worldsheets, and the Casimir stress tensor acquires mixed components. Force balance then requires a current across the field lines, and charge conservation fixes an accompanying polarisation current, the counterpart of the Hall current of the polar sector. These currents close the Bianchi identities at first order in the fermionic backreaction $\alpha$. The system reduces to three coupled master equations, given in closed form and matched to the fermion-free mouth. Consistency alone does not select the fermionic constitutive relation, but locality, covariance and the index theorem do. At $\alpha=0$ the throat reduces to Poschl-Teller problems with masses $l(l-1)$ and $(l+1)(l+2)$ at $m_S^2=0$. At finite $m_S^2$ one mode is screened, one tends to the mass $l^2+l+2$, and one neutral charge-density wave stays exactly massless. The $O(\alpha)$ shifts of the massive normal frequencies are real and negative. The two parity sectors are isospectral only without fermions. The neutral channel sees an attractive region in each mouth, and a numerical solution coupled to the gravitational channel in the exact mouth potential finds no bound state. The sector has no growing mode for $l\ge2$ at this order.

Holistic co-speech animation is prone to averaging in both motion representation and speech conditioning. In coordinate-space diffusion, slow body posture, mid-frequency gesture strokes, and fast hand or facial details are entangled in one prediction target, often producing low-variance, over-smoothed motion. Meanwhile, dense rhythmic and acoustic cues can dominate sparse content-specific information under fixed multimodal fusion. We present DynaConTalk, a wavelet-constrained diffusion framework for long-form and controllable holistic co-speech motion generation. Diffusion operates in stationary wavelet transform (SWT) coefficient space, whose temporally aligned bands separate coarse posture evolution, gesture strokes, and fine expressive details. Our dynamic gating network preserves HuBERT and speaker identity as a base and selectively adds rhythm, mel, and transcript features through motion-state- and noise-aware residual gates. Attention pooling and learned depth routing deliver complementary conditions to each denoising stage, while a frame-resolution rhythm path preserves precise timing. A signed proposal-consensus update then reconciles these conditions with the evolving motion state. Matched-noise constraint injection uses the same sampling interface for history continuation and localized keypose repair, and extends to reference-guided control. Separate body-hand and facial denoisers, followed by inverse SWT and a pose-driven root regressor, produce holistic motion. Experiments evaluate generation quality, facial accuracy, temporal continuity, and controllable editing. Code, models, and the interactive editing interface are available at https://github.com/zhuyifeiabcd1/DynaConTalk.

There exist two different paradigms for records in isolated quantum systems: decoherent histories (which determines which past events leave formal records) and quantum Darwinism (which determines which current events get redundantly recorded). Neither one implies the other, and connections between the two are scarcely investigated. We unify quantum Darwinism and decoherent histories based on the insight that only redundant records about past events matter. The resulting framework of past redundancy encompasses quantum Darwinism when applied to events at the current time, and it implies the probability sum rule or decoherence of histories. The Bhattacharyya coefficient (or fidelity) plays an important role to establish this connection. Importantly, various examples show that past redundancy is a more widespread phenomenon than the fine-tuned models necessary for quantum Darwinism suggest. We thus arrive at a richer picture in which redundancy can be caused by mechanisms different from quantum Darwinism (such as macroevents or cascade structures), which emphasizes that redundancy is necessary but not sufficient for objectivity, and which, overall, allows to realistically investigate the question: how generic is redundancy in nature?

The adoption of machine learning for socially relevant tasks requires effective explainable artificial intelligence (XAI) methods to better understand the behavior of machine learning models. Attribution methods are a popular XAI approach in which input-output relationships are characterized by heat maps that reflect the relative importance of input features for a particular prediction. The quality of such maps is often assessed by measuring faithfulness based on the area under insertion and deletion curves, which measures changes in the model output as features are added and removed. In this study, we derive an objective function from this notion of faithfulness and a way to approximate its gradient. We establish the connection between insertion curves and top-$k$ feature selection, which leads to a loss function measuring the quality of attributions. Randomization of the loss allows us to efficiently approximate its gradient. To show the effectiveness of the general approach, we combine the loss function with the neural explanation mask framework. The resulting method, termed Ra-NEM, can be used with any differentiable model without affecting the model's performance. Experiments demonstrate that Ra-NEM provides accurate attributions robustly and efficiently. Compared to other algorithms, the attributions have not only higher faithfulness but also perform well in terms of other XAI metrics. The high inference speed of Ra-NEM makes the method suitable for online applications. The code is available online: https://github.com/baerminator/Ra_Nem

We study temporal fair division with indivisible goods that arrive sequentially and must be allocated irrevocably. In contrast to the usual online model, we assume that valuations and future arrivals are known in advance, and ask how unfairness evolves during the process. We introduce cumulative maximum envy: the sum, over all rounds, of the maximum pairwise envy at that round. Equivalently, this is the area under the worst-envy curve, and it captures both the magnitude and the duration of envy. For a fixed arrival order, we show that the corresponding decision problem is strongly NP-complete and that minimizing this objective admits no constant-factor approximation unless P = NP, even under identical valuations and even under binary valuations. We complement these hardness results with a dynamic program that gives pseudopolynomial-time solvability for a constant number of agents, polynomial-time algorithms in further restricted settings, and an FPTAS for fixed $n$ under identical integer valuations. We then study a sequencing variant where the algorithm may choose the arrival order. This variant remains NP-complete even for two agents with identical valuations; however, a simple greedy algorithm achieves a $3/2$-approximation for $n=2$ agents, an $n/(n-1)$-approximation for any number of agents, and an additive guarantee depending on the maximum value of any good.

In the era of interconnected data, graphs have emerged as an effective abstraction for modeling complex systems in an intuitive format, especially with the rise of Property Graphs, which offer an intuitive and scalable way of navigating non-intuitive structures. In this context, graph mining techniques have been developed for testing complex graph-based rules, as the MINE GRAPH RULE operator, which, however, require users to have prior expertise both in graph theory and formal query language. In this work, we propose to bridge the gap between users and the graph-association rule-mining process by showing how Large Language Models (LLMs) can be easily prompted to formulate, refine, and interpret complex relational rules, directly producing MINE GRAPH RULE queries.

Text-to-image diffusion models fail predictably on compositional prompts: attributes bind to the wrong objects, spatial relations invert, and multi-object scenes lose count. Recent architectures already augment CLIP with a T5 encoder precisely because CLIP's contrastive embedding loses compositional structure, yet these failures persist. We argue the binding problem is therefore not one of missing information but of misaligned information: a text encoder preserves compositional structure, but in a representation space shaped by language modelling rather than vision, and the denoising objective does not directly reward aligning the two. We show this correspondence can be supplied as an explicit training signal, that the relevant cross-modal information is concentrated in a low-rank subspace of self-supervised visual features, and that supplying it can be folded into diffusion training as a single auxiliary loss. Our method, ORCA (Orthogonal Residual Compositional Alignment), aligns the latent of a diffusion transformer with a low-rank target derived from a frozen visual encoder, through a predictor whose orthogonal basis is parameterised by a learned residual between T5 and CLIP embeddings, which provides a prompt-dependent signal for selecting the visual readout subspace. We prove that the cross-modal information recoverable at a given rank is bounded by the spectral mass of the visual encoder's covariance in the top components. Across three diffusion-transformer backbones (DiT-B/2, DiT-L/2, U-ViT-L), ORCA improves FID and GenEval over both vanilla and REPA baselines at zero inference-time cost; on DiT-L/2 it reaches FID 16.65 and GenEval 0.291 at 200K steps, exceeding the strongest 400K baseline at half the training cost, with the largest gains concentrated on attribute binding, spatial relations, and multi-object prompts.

We study $(-1)$-homogeneous solutions of the steady Navier-Stokes equations in $\mathbb R^n\setminus\{0\}$ with $(-3)$-homogeneous, locally Lipschitz forces. Previous work [2] established the existence of $(-1)$-homogeneous solutions without any smallness assumption in dimensions $4\leq n\leq16$. In this paper, we remove the dimension restriction and obtain the existence of self-similar solutions in all higher dimensions. The new ingredient is a dimension-independent a priori estimate for the total head pressure on the sphere, obtained by adapting the source-flux method and the weighted identity of the pressure of Wang and Yang [28] to the homogeneous setting. This combines with the structural relation between the radial velocity and the total head pressure used in [2] to close the a priori estimates for the solutions in all dimensions.

The luminosity quoted for proposed particle colliders is usually derived from the analytic geometric formula, which assumes head-on collisions of identical, rigid Gaussian bunches. For the new generation of asymmetric machines—in particular lepton–hadron colliders such as the EIC, LHeC and FCC-eh—this assumption can misestimate the luminosity, because it ignores a few coupled effects that act in the interaction region such as hourglass effect, crossing angle, and mutual electromagnetic (beam–beam) deformation of the colliding bunches. We present AloHEP (A luminosity optimizer for High Energy Physics), an open-source, cross-platform Java application that simulates the interaction region of both symmetric and asymmetric colliders. AloHEP represents each bunch by an ensemble of macroparticles deposited on the grid with a cloud-in-cell scheme, and slices the crossing longitudinally. On each transverse slice it solves the two-dimensional electrostatic problem by a direct Green's-function convolution, then obtains the beam–beam forces by finite differencing and continuous bicubic interpolation. The hourglass effect, finite crossing angle and beam–beam pinch/disruption can be enabled independently, and the two colliding beams may consist of entirely different species (leptons, protons, heavy ions). A JSON-backed parameter database and an interactive graphical interface make AloHEP a flexible tool for the rapid prototyping of realistic luminosity estimates. We verify that the code reproduces the analytic geometric luminosity in the appropriate limit and present scaling, grid-convergence and asymmetric-collider benchmarks.

We present a framework for building and interpreting minimal transformer models. By constraining a transformer's embedding dimension and head size to 2, we enable full two-dimensional visualization of its internal representations. Embeddings, query/key/value transforms, attention outputs, residual streams, and decision boundaries can all be seen directly. Our central claim is that the learned geometry implies an algorithm; the arrangement of points and boundaries in R^2 can be read as a step-by-step procedure. We train a transformer on a simple task where it must produce the most recently observed even number whenever the '+' operator appears in a sequence of digits. Once trained, we visually walk through every step of the transformer's computation. We show how the model embeds the tokens and their respective positions in the sequence, transforms them via the Q, K, and V matrices, uses the dot product between the Q and K representations to form the attention matrix, and uses the attention matrix to select values that move the representation of each input token to the region of the domain of the output layer that will correctly predict the next token. We introduce a suite of interpretability visualizations that make the algorithmic interpretation of this procedure explicit. Our framework offers a pedagogical and experimental testbed to explore how transformers use informational geometry to implement next-token prediction.

Universal machine learning force-field generalization to multicomponent environments generated by compositional design remains insufficiently assessed. We construct a benchmark of 7,599 multicomponent configurations inspired by high-entropy design, elemental substitution and anion mixing. Eleven pretrained models are evaluated against density functional theory for energies, forces and stresses, with assessment extended to elastic, vibrational and adsorption-related properties. Force errors are analysed through training-reference coverage, local geometric heterogeneity, distance directionality and elemental response. Distances to training-reference environments reveal a qualitative association between coverage differences and increasing errors, while substantial variation remains at similar distances. Higher-error groups show greater local geometric heterogeneity, although OMat24 provides broad coverage of these environments. Relative to training-reference pair medians, errors remain low near the median, rise steeply on the compression side and increase more weakly on the extension side. After matching element pairs and absolute distance deviations, compression-side force errors are 1.81-1.95 times extension-side errors. Model-predicted pairwise interaction curves show greater curvature under compression. Fitting difficulty in independent elemental systems correlates with electronic band-energy responses to atomic displacements and Fermi-level shifts, and a similar pattern is observed in multicomponent systems. In parameter-matched comparisons, spherical-harmonic representations with maximum degrees of 2 and 4 lower test force errors for 38 and 40 of 43 elements, respectively, while differences in elemental difficulty remain. These findings inform force-field selection for experimental compositional design and identify targets for training-data sampling and model representations.

We prove invariance of the geometric Arveson-Douglas conjecture under Veronese embeddings of projective varieties. This provides new examples of singular varieties satisfying the conjecture. Furthermore, it reduces the conjecture to projective varieties whose defining ideals admit quadratic Gröbner bases, by keeping the same Schatten regularity thresholds. Our results lead to canonical examples of subproduct-systems whose Toeplitz algebras are not $KK$-equivalent to the complex numbers. Finally, we show that Douglas' fundamental class conjecture, asserting that the associated Toeplitz extension implements $\mathbb{T}$-equivariant duality in $KK$-theory, is invariant under Veronese embeddings as well. While the latter result bootstraps the fundamental class conjecture, it also leads to infinitely many counterexamples.