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01.
arXiv (CS.AI) 2026-06-19

Execution-bound advisory automation for agentic AI: a reproducible AIBOM-driven CSAF-VEX framework

arXiv:2606.19390v1 Announce Type: cross Abstract: A protocol driven framework is presented that binds SBOM and AIBOM artefacts to deterministic environment capture and structured runtime telemetry. Exploitability is computed from declared artefacts, observed activation conditions, and enforced execution policies. CSAF VEX advisories are generated from combined static and runtime evidence, cryptographically signed, and validated through deterministic replay. Evaluation uses approximately 10000 component entries across synthetic Agentic AI workloads 50 to 5000 components, incorporating OSV, GitHub Advisory, KEV, and EPSS datasets.

02.
arXiv (math.PR) 2026-06-19

Finite-Sample Bounds for Expected Signature Estimation under Weak Dependence

arXiv:2605.20541v2 Announce Type: replace-cross Abstract: The expected signature uniquely determines the law of a random rough path under a moment-growth condition, yet finite-sample bounds for estimating its truncations from a single long dependent trajectory remain unavailable. We study a strictly stationary stochastic process equipped with a geometric rough-path lift, observed in non-overlapping blocks of equally-spaced samples, and prove a non-asymptotic mean-squared error (MSE) bound for the block-averaging estimator of its truncated expected signature. Under moment and stationarity assumptions together with a direct covariance-decay condition on block signatures – strictly weaker than $\alpha$-mixing and applicable to long-range-dependent processes – the error separates into a discretization term and a fluctuation term, with rates determined respectively by path regularity and dependence strength. A levelwise rough-factorial variance analysis keeps finite-truncation constants explicit and yields an optimal allocation rule under a fixed observation budget. We verify the assumptions for independent-coordinate fractional Ornstein–Uhlenbeck processes in three regimes: short-range (Hurst $1/41/2$. Monte Carlo experiments show empirical slopes steeper than the guaranteed upper-bound rates.

03.
arXiv (CS.CV) 2026-06-15

QualiaNet: An Experience-Before-Inference Network

作者:

Human 3D vision involves two distinct stages: an Experience Module, where stereo depth is extracted relative to fixation, and an Inference Module, where this experience is interpreted to estimate 3D scene properties. Paradoxically, although stereo vision does not provide us with absolute distance information, it nonetheless affects our inferences about distance. We propose the Inference Module exploits a natural scene statistic: near scenes produce vivid disparity gradients, while far scenes appear comparatively flat. QualiaNet implements this two-stage architecture computationally: disparity maps simulating human stereo experience are passed to a CNN trained to estimate distance. The network can recover distance from disparity gradients alone, validating this approach.

04.
arXiv (CS.CV) 2026-06-17

Heterogeneous SAR-optical fusion for near-real-time land use and land cover mapping under cloud contamination: A novel framework and global benchmark dataset

Optical remote sensing imagery is frequently degraded by cloud and cloud-shadow contamination, which limits its reliability for near-real-time land use and land cover (LULC) mapping. Although synthetic aperture radar (SAR) can provide cloud-penetrating structural information, existing SAR-optical fusion methods often assume reliable optical observations and insufficiently address the semantic uncertainty introduced by cloud contamination. To address this issue, we propose CloudLULC-Net, an end-to-end heterogeneous SAR-optical fusion framework that directly predicts LULC maps from cloud-contaminated Sentinel-2 imagery and temporally adjacent Sentinel-1 SAR observations. The proposed network incorporates optical reliability modulation to suppress unreliable optical responses, heterogeneous information adaptive aggregation to model high-order spatial-channel interactions between optical and SAR representations, and a unified semantic mapping transformer to organize fused features in a LULC-oriented latent space. A semantic anchor-guided optimization strategy is further introduced to improve the consistency of intermediate semantic representations. To support this task, we construct CloudLULC-Set, a large-scale benchmark dataset containing 40,223 curated SAR-optical-label triplets with pixel-level LULC annotations across diverse geographic regions and cloud conditions. Experimental results show that CloudLULC-Net achieves an OA of 86.60%, an F1-score of 83.29%, and an mIoU of 73.51%, outperforming representative heterogeneous reconstruction-first and end-to-end SAR-optical mapping methods. Comparisons with existing global LULC products and analyses under different cloud-cover levels further demonstrate the robustness and practical value of CloudLULC-Net for target-date LULC mapping in cloud-prone regions.The project is publicly available at: https://github.com/RSIIPAC/CloudLULC

05.
arXiv (CS.CV) 2026-06-12

SalArt-VQA: Diagnosing Whether VLMs Understand Salient Artifacts in Generated Images

Vision-language models (VLMs) are increasingly used to detect whether AI-generated images contain visible artifacts, yet their ability to analyze such artifacts remains poorly understood. A correct image-level decision can still hide important failures: a model may correctly flag an artifact while relying on the wrong visual cue, selecting the wrong region, or describing a defect that the image does not support. To evaluate these behaviors directly, we introduce SalArt-VQA, a diagnostic benchmark for fine-grained SALient ARTifact understanding in AI-generated images. SalArt-VQA contains 950 images and 3,681 human-authored multiple-choice questions spanning artifact images, matched real reference images, and paired generated reference images. Four aligned question types evaluate presence detection, semantic localization, spatial grounding, and evidence-grounded defect identification, while the reference splits test calibration and abstention when the annotated defect is absent. Across 20 VLMs, SalArt-VQA reveals failures that image-level detection accuracy hides: the strongest model reaches 99.37% detection recall on artifact images but answers all four artifact-side questions correctly on only 53.26% of images. Comparing artifact images with artifact-free references reveals a sensitivity-calibration tradeoff: sensitive models often make unsupported artifact claims, while conservative models avoid false alarms largely by missing real artifacts. These results show that high artifact detection accuracy alone does not imply grounded artifact understanding. SalArt-VQA exposes these hidden failure modes and provides a fine-grained evaluation of whether VLM artifact claims are supported by local visual evidence.

06.
arXiv (quant-ph) 2026-06-17

Quantum Chip Paradigm Framework

arXiv:2606.17899v1 Announce Type: new Abstract: Quantum Electronic Design Automation (Q-EDA) is emerging as quantum chips move from laboratory prototypes to scalable engineering systems. This paper argues that superconducting quantum chip design is approaching a "SPICE moment" similar to early classical EDA, where growing qubit scale, control complexity, frequency planning, packaging, process variation, and cryogenic measurement feedback require a shift from experience-based design to model-driven engineering. We propose a Quantum Chip Paradigm Framework that treats Q-EDA not only as software, but as part of the quantum chip development paradigm. Unlike classical HDL-first design, quantum chip design must begin with physical structures such as Josephson junctions, resonators, couplers, readout elements, control lines, and packaging environments. The framework emphasizes PCell-based modeling, SPICE-Q simulation, Quantum PDKs, and design-technology-measurement co-optimization. We further outline a hierarchical Q-EDA system spanning physical structures, qubit PCells, logical qubits, quantum arithmetic, functional quantum IP, and Quantum SoC systems. The key goal is to turn physical models, layout rules, simulation results, fabrication data, and measurement feedback into reusable and auditable engineering objects for large-scale quantum processors and fault-tolerant quantum computing.

07.
arXiv (CS.CL) 2026-06-19

What sentiment analysis can't see: Measuring whether customers were helped, and what went wrong, across 70,000 support conversations

Most companies read their customer support data at scale using sentiment analysis, which measures how customers sound rather than whether they were satisfied with the result. We tested a richer alternative on 70,450 support conversations from a leading online fundraising platform: alongside tone, we used GPT-5.4 to estimate each customer's satisfaction and to flag whether they reported a concrete problem, then validated all three readings against the 1-to-5 ratings customers left on the conversations they rated. The satisfaction estimate tracked those ratings far better than sentiment did, correlating at 0.47 against 0.36 and flagging unhappy customers with far fewer false alarms. The structured read also sees what sentiment cannot: tone and satisfaction disagree in 44% of conversations, a single "Neutral" label hides everything from quietly satisfied customers to ones who quietly gave up, and the largest group of all is "tolerated friction," customers who are satisfied but still reporting a fixable problem, a standing issue that no sentiment-based dashboard can surface. The broader finding is that LLM-based annotation can capture far more than the tonality of a customer's language, offering strong potential for new business metrics grounded instead in the customer's state (whether they were satisfied) and the cause of their problem extracted directly from the raw textual data of interactions and feedback.

08.
arXiv (quant-ph) 2026-06-24

Teleportation-based quantum state tomography

arXiv:2511.18621v2 Announce Type: replace Abstract: We explicitly show that the quantum teleportation protocol can be employed to completely reconstruct arbitrary two- and three-qubit density matrices. We also extend the present analysis to n-qubit density matrices. The only quantum resources needed to implement the teleportation-based quantum state tomography protocol are the ability to make Bell measurements and the ability to prepare a few different single qubit states to be teleported from Alice to Bob.

09.
arXiv (CS.LG) 2026-06-19

On the Oracle Complexity of Interpolation-Based Gradient Descent

arXiv:2606.19878v1 Announce Type: new Abstract: Recent work on first-order optimizers for empirical risk minimization (ERM) has suggested that smoothness of ERM loss functions in the training data, rather than in the optimization parameters, can be leveraged to improve the oracle complexity of gradient descent (GD) methods. In this paper, we propose an inexact gradient method, piecewise polynomial interpolation-based gradient descent (PPI-GD), which approximates the full gradient in each iteration by querying the first-order oracle at equidistant points in the data domain to construct polynomial interpolants of the resulting gradient samples over appropriately sized patches of the data domain. We analyze the oracle complexity of PPI-GD for strongly convex and non-convex loss functions when the data space dimension is bounded by a polylogarithmic function of the number of training samples, and find it to outperform several GD variants in key regimes when the loss function is sufficiently smooth. Furthermore, our analysis extends several techniques from the error analysis of bicubic spline interpolants to the setting of $d$-variate tensor product polynomial interpolants which may be of independent interest in interpolation analysis.

10.
arXiv (CS.LG) 2026-06-16

Closing the Approximation Gap in Simulation-free Latent SDEs

arXiv:2606.16138v1 Announce Type: cross Abstract: Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics. Latent stochastic differential equations (SDEs) address this by modeling the system as an unobserved state that evolves according to a learnable SDE and generates the observations. Variational inference (VI) provides a tractable objective for fitting latent SDEs. Traditional VI algorithms evaluate this objective by numerical simulation over a time discretization, trading fidelity for computational cost. A recent class of algorithms, simulation-free VI, sidesteps this tradeoff by parameterizing the posterior through its instantaneous marginals rather than its drift. In this work, we show that the efficiency of existing simulation-free VI algorithms comes at a price: their parameterizations restrict the approximate posterior to a subset of the SDEs available to simulation-based methods, degrading posterior inference and parameter learning. We propose Helmholtz-SDE, a simulation-free VI algorithm that closes this gap by optimizing over path laws compatible with a prescribed collection of marginals. Helmholtz-SDE recovers dynamics more faithfully than prior simulation-free methods, with the largest gains under high posterior uncertainty. It further matches the performance of simulation-based VI at a fraction of the runtime.

11.
arXiv (CS.AI) 2026-06-24

LLMs Prompted for Legal Context Object More: Overrefusal from Small On-Premises LLMs in Criminal Legal Context

arXiv:2606.24585v1 Announce Type: new Abstract: While the validity of LLMs' use in the legal context remains subject to ethical and legal debate, legal professionals are already experimenting with personal LLMs, if only for translation and reformulation. However, even such a seemingly innocuous use can introduce biases through case processing speed if LLM assistants selectively refuse assistance on certain topics. To better anticipate such biases, we investigate several modern small LLMs that are most likely to be used as on-device assistants, to assess the impact of overrefusal on legal prompts. Surprisingly, we find that authority-style prefixes (``you are acting as an assistant of the national supreme court'', ``[...] defense lawyer'') systematically increase refusal rates by 2–20x over the no-prefix baseline, while a known role-play jailbreak prefix shows mixed effects, sharply increasing refusals in some models and barely shifting them in others. The finding suggests that small on-prem deployable LLMs are unstable under contextual framings that a real institutional user might naturally introduce, and further investigation is essential to minimize opportunities for bias.

12.
arXiv (CS.CV) 2026-06-12

Diffusion Transformer World-Action Model for AV Scene Prediction

Action-conditioned world models let an autonomous vehicle predict future camera scenes from its own planned controls, enabling planning and simulation without real-world rollouts, but at compact, trainable scale the futures are ambiguous and the field's standard distortion metrics actively mislead: they reward a blurry regression mean over a realistic prediction. We confront this with a compact latent world model that, given the present front-camera latent and a sequence of ego-actions, predicts future scene latents a frozen decoder renders to $256 \times 256$ frames up to 8 seconds ahead, evaluated on 150 held-out nuScenes scenes. We first benchmark where to predict: across six frozen encoders spanning four representation families, V-JEPA2 with temporal context reduces steering RMSE by 40% over the best single-frame encoder. We then train a latent Diffusion Transformer (DiT) and, through a controlled diagnosis, identify the four ingredients it needs: spatial tokens, the $x_0$ objective, residual anchoring, and sampling matched to target uncertainty. In a Stable-Diffusion-VAE encode-predict-decode pipeline we expose the central tension: distortion metrics (cosine similarity, SSIM) favor the blurry mean, masking that the diffusion model is far closer to the real frame distribution. Inception-based FID and KID reveal a clean perception-distortion frontier: diffusion attains KID 0.078 versus 0.375 for regression ($4.8\times$ better), and a deployable train-derived calibration makes this practical without test-time ground truth. The model is genuinely action-controllable (steering drives scene displacement, Spearman $\rho = 0.81$, vs $-0.18$ for regression). We trace limited single-pass motion to a shared-present anchor and engineer a compact 1.7M-parameter "jump" model that recovers full ground-truth motion magnitude ($1.02\times$ GT), where single-pass models capture less than half.

13.
arXiv (CS.CV) 2026-06-15

Trimodal Glioma Representation Alignment via Volumetric Contrastive Learning

Glioma grading and survival prediction require the integration of heterogeneous information collected at different spatial and biological scales. Histopathology describes tissue morphology, mRNA expression captures molecular activity, and magnetic resonance imaging provides a non-invasive view of tumor extent and radiological heterogeneity. Existing glioma prognosis models often combine only two of these sources, while their alignment objectives remain mostly pairwise. This paper introduces GLORIA, a novel trimodal framework for GLioma Omics - Radiology - hIstopathology Alignment. GLORIA processes whole-slide image regions, gene-expression profiles, and 3D MRI volumes through modality-specific encoders, projects them into a shared latent space, and aligns them with a Gramian contrastive loss that measures the volume spanned by the three modality embeddings. The aligned representations are fused through a cross-modal gating module and optimized jointly for three-class glioma grading and overall survival prediction. We evaluate GLORIA on a matched TCGA-GBM/LGG and BraTS21 cohort, comprising 132 patients with all three modalities. On the shared trimodal test set, GLORIA improves over the bimodal WSI-mRNA baseline in all the metrics considered.

14.
arXiv (CS.LG) 2026-06-12

Distribution-Agnostic Robust Trajectory Optimization via Chance-Constrained Reinforcement Learning

arXiv:2606.13605v1 Announce Type: cross Abstract: This paper presents a distribution-agnostic robust trajectory-optimization framework based on chance-constrained reinforcement learning. The uncertainty is represented here through initial conditions and process noise, with the only requirement being that it can be sampled. A deterministic nominal trajectory is first computed offline, and reinforcement learning is then used only to robustify that baseline through a structured affine closed-loop correction law comprising a feedforward control adjustment and time-varying feedback gains. Probabilistic feasibility is enforced empirically through rollout-based upper-tail quantiles, while terminal dispersion is regulated through covariance-feasibility penalties. The framework is assessed on two materially different trajectory design problems. The flagship case study is a three-dimensional multi-impulse Earth-Mars transfer, where the learned policy is benchmarked against a recent robust trajectory-optimization reference under Gaussian uncertainty and then evaluated under bounded uniform uncertainty and under process disturbances not seen during training. The second case study is a stochastic atmospheric pinpoint rocket landing problem, used to assess portability to a short-horizon continuous-thrust setting with drag, mass depletion, and glide-slope constraints. The results show that the proposed framework can remain competitive in upper-tail fuel cost while preserving probabilistic feasibility, and that the same robustification scaffold can be carried across heterogeneous spacecraft trajectory planning problems without redesign of its core stochastic-control structure.

15.
arXiv (CS.CV) 2026-06-16

Text region detection in historical astronomical diagrams

Text detection is a crucial task in the analysis of historical documents. While datasets and benchmarks exist for text detection in manuscripts and maps, the study of text in mathematical diagrams has received little attention. To address this, we introduce a large-scale, diverse, open-access dataset of 948 historical astronomical diagrams containing 10,940 oriented polygonal text regions. Our dataset spans ten centuries (8th to 18th) and seven main linguistic traditions: Arabic and Persian (115), Chinese (332), Byzantine (233), Latin (185), Hebrew (48), and Sanskrit (35). It captures a wide range of diagram styles and textual content, from symbols to multi-line paragraphs. Each text instance is annotated with ordered polygons that precisely delineate text regions and encode the reading direction. In addition, we annotated the 2,293 regions in Latin diagrams with 20 class labels. We evaluated several strong baselines on our dataset, including TESTR, DeepSolo++, and Poly-DETR, a simple extension of DINO-DETR that we design to predict ordered polygon vertices. Poly-DETR achieves state-of-the-art performance on the MTHv2 and cBAD2019 benchmarks and provides a solid, simple baseline on our dataset. Code and dataset available online.

16.
arXiv (CS.CL) 2026-06-11

I Understand How You Feel: Enhancing Deeper Emotional Support Through Multilingual Emotional Validation in Dialogue System

Emotional validation - explicitly acknowledging that a user's feelings make sense - has proven therapeutic value but has received little computational attention. Emotional validation in dialogue systems can be decomposed into (i) validating response identification, (ii) validation timing detection, and (iii) validating response generation. To support research on all three subtasks, we release M-EDESConv, a 120k English-Japanese multilingual corpus created through hybrid manual and automatic annotation, and M-TESC, a multilingual spoken-dialogue test set. For timing detection, we propose MEGUMI, a Multilingual Emotion-aware Gated Unit for Mutual Integration, that fuses frozen XLM-RoBERTa semantics with language-specific emotion encoders via cross-modal attention and gated fusion. MEGUMI shows superior performance on both the M-EDESConv and M-TESC datasets, both objectively and subjectively. Finally, our EmoValidBench benchmarks of GPT-4.1 Nano and Llama-3.1 8B indicate that current LLMs generate contextually similar and diverse validating responses, but emotional understanding remains a major area for improvement. Project page: https://github.com/zihaurpang/Multilingual-Emotional-Validation

17.
arXiv (CS.LG) 2026-06-16

Amortized mean-shift interacting particles

arXiv:2606.15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals – posterior expectations, tail probabilities, and risks – across a stream of observations. The standard estimate averages the integrand over posterior samples, a Monte-Carlo average whose error decays only as the square root of the sample size, so accuracy demands many samples – prohibitive when each one calls a partial-differential-equation forward model. Mean-shift interacting particles need far fewer: they return a small set of signed-weight nodes – a deterministic quadrature whose weighted averages estimate those integrals. Finding the nodes, however, is a per-observation optimization that, in its most accurate form, reads the posterior score at every step – returning the cost it meant to save. We introduce amortized mean-shift interacting particles, a learned map that emits the weighted nodes from an observation and a few posterior samples in a single forward pass. Training asks only for joint parameter-observation samples and a posterior to draw from – a conditional normalizing flow, an empirical conditional, or any reference the user can sample – and the map learns to integrate that posterior from samples alone, evaluating neither its density nor its score. Once trained, it generalizes to unseen observations and integrands at any node budget and improves on independent samples in two ways: by reweighting them, provably no worse than the equal weights of Monte-Carlo; and by moving them, which empirically lowers it further. Across closed-form, sampled, learned, and physics-based posteriors – up to a thousand-coefficient groundwater field – it integrates more accurately than the same number of samples at every budget, and a posterior-whitened, dimension-aware kernel removes the high-dimensional wall. The result is a Pareto improvement on Monte-Carlo integration, not a competitor to drawing more samples.

18.
bioRxiv (Bioinfo) 2026-06-18

Calculation of sequence space coverage in a mutagenesis library

Directed evolution requires screening of large mutagenesis libraries, but accurate calculation of library sizes needed to discover functional variants remains challenging. Existing models provide baseline estimates, yet current computational approaches for finding the best variants scale poorly with library complexity. Here, we introduce a scalable algorithmic framework to compute exact discovery probabilities in saturation mutagenesis libraries with no requirement for explicit sequence enumeration. By aggregating variants into a composition log–sum distribution and applying log-space convolution across randomisation blocks, it is possible to extend this to massive sequence spaces and mixed codon schemes. By inverting these calculations, absolute mathematical ceilings for experimental design are established. Ultimately, this framework provides a rapid, quantitative tool to balance the statistical coverage-diversity trade-off within the limitations of laboratory screening. Finally, this is implemented as an open-source web application (SSCC) that allows researchers to construct heterogeneous library designs and compute required sampling depths, coverage probabilities, and absolute randomisation limits.

19.
arXiv (CS.CV) 2026-06-11

Higher order PCA-like rotation-invariant features for detailed shape descriptors modulo rotation

作者:

PCA can be used for rotation invariant features, describing a shape with its $p_{ab}=E[(x_i-E[x_a])(x_b-E[x_b])]$ covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real shapes are usually much more complicated, hence there is proposed its extension to e.g. $p_{abc}=E[(x_a-E[x_a])(x_b-E[x_b])(x_c-E[x_c])]$ order-3 or higher tensors describing central moments, or polynomial times Gaussian allowing decodable shape descriptors of arbitrarily high accuracy, and their analogous rotation invariants. Its practical applications could be rotation-invariant features to include shape modulo rotation e.g. for molecular shape descriptors, or for up to rotation object recognition in 2D images/3D scans maybe also for 3D scene understanding, or shape similarity metric allowing inexpensive comparison of objects modulo rotation avoiding costly optimization over rotations.

20.
arXiv (CS.LG) 2026-06-12

Generative Modeling of Bach-Style Symbolic Music: A Comparative Study of Autoregressive, Latent-Variable, and Adversarial Approaches

arXiv:2606.13626v1 Announce Type: cross Abstract: We study generative modeling of Bach-style symbolic piano music using a shared MIDI corpus and three model families: autoregressive LSTMs with attention, latent-variable models including recurrent VAEs and vector-quantized VAEs, and generative adversarial networks. We compare their ability to model polyphonic note sequences, learn useful latent representations, and generate stylistically coherent compositions. Our experiments show that the autoregressive LSTM with attention produces the most musically coherent samples, while vector quantization helps mitigate posterior collapse and yields more structured outputs than conventional recurrent VAEs. The adversarial approach captures local pitch patterns but remains difficult to train and generalizes less reliably to Bach's style. These results highlight the relative strengths and failure modes of autoregressive, latent-variable, and adversarial approaches for symbolic music generation.

21.
Nature (Science) 2026-06-24

An ECG biomarker for sudden cardiac death discovered with deep learning

Sudden cardiac death is, in theory, preventable with defibrillators. But every year, many patients die without defibrillators because doctors fail to predict their risk1. The only predictive biomarker in wide use, cardiac left ventricular ejection fraction (LVEF), misses most sudden cardiac deaths2, and flags many low-risk patients for futile defibrillators that never fire3,4. Here we apply deep learning to a dataset linking all electrocardiograms (ECGs) in a Swedish region to death certificates. The resulting model isolates a high-risk group (2.2% of the sample) with a 7.0% annual rate of sudden cardiac death, higher than those with reduced LVEF (1.9% of the sample; 4.6% annual rate). Notably, 86.1% of the model’s high-risk patients were not flagged by LVEF. High-risk ECG patients with defibrillators implanted were 54.4% less likely to die than expected, suggesting a mortality benefit. We externally validate the model in a US health system, in which it predicts ventricular arrhythmias that cause sudden death; and a Taiwanese hospital registry, in which it specifically predicts future arrhythmic cardiac arrests. To visualize the waveform morphology ‘discovered’ by the predictive model, we pair it with a generative model of the ECG waveform. Together, they reveal a biomarker that is easily visible and robustly predicts sudden cardiac death, but has not to our knowledge been previously described. Tying the biomarker’s shape to electrophysiological first principles, we form and preliminarily test a new hypothesis on the mechanism of sudden cardiac death. A deep-learning model trained on electrocardiogram (ECG) waveforms identifies an easily visible biomarker that predicts sudden cardiac death more accurately than the current clinical state of the art.

22.
arXiv (CS.AI) 2026-06-17

The Discrete-Log Clock: How a Transformer Learns Modular Multiplication

arXiv:2606.17399v1 Announce Type: cross Abstract: When small transformers grok modular multiplication, prior work reports that the learned embedding has a "dense" Fourier spectrum requiring all frequencies. This contrasts with modular addition, where only a sparse set of key frequencies suffices. We show this density is an artifact of analyzing in the wrong basis. The natural Fourier transform for multiplication is not the standard additive DFT but the multiplicative character transform, which decomposes functions on the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ into its irreducible representations. Applying this transform to a grokked transformer trained on $a \cdot b \bmod 113$, we find the embedding spectrum becomes highly sparse (Gini coefficient 0.58 vs. 0.07 in the additive basis) with only 4 key frequencies carrying significant energy. Furthermore, 96.9% of MLP neurons are cleanly tuned to a single multiplicative frequency, and neuron activation heatmaps reveal 2D-periodic structure when reordered by the discrete logarithm. These results demonstrate the transformer reduces multiplication to addition in discrete-log space, implementing a "Discrete-Log Clock" algorithm analogous to Nanda et al.'s Clock algorithm for addition. The methodology generalizes: matching the analysis basis to the algebraic structure of the task reveals interpretable structure where standard tools see noise.

23.
arXiv (CS.CV) 2026-06-18

Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm

This paper addresses low-rank tensor completion (LRTC) by proposing a novel nonconvex surrogate, namely the ratio of the tensor nuclear norm to the tensor Ky Fan p-k norm (TNPK), to accurately approximate the tensor tubal rank. The TNPK possesses appealing properties, including scale invariance, parameter flexibility, and the existence of closed-form solutions under specific choices of p and k. With specific parameter settings of p and k, it reduces to the ratio of the tensor nuclear norm to the tensor Ky Fan k norm (TNK) or the ratio of the tensor nuclear norm to the tensor Frobenius norm (TNF). We construct a LRTC model and, under the tensor null space property (NSP), prove that low-rank tensors are local minimizers of the proposed model. Moreover, we derive the proximal operator of the Ky Fan p-k inverse-norm and further develop an efficient alternating direction method of multipliers (ADMM) algorithm with guaranteed subsequential convergence under mild conditions. Extensive experiments on synthetic and real-world datasets validate the superior performance of our method against state-of-the-art competitors.

24.
arXiv (CS.CV) 2026-06-19

Shape of Thought: Progressive Object Assembly via Visual Chain-of-Thought

Multimodal models for text-to-image generation have achieved strong visual fidelity, yet they remain brittle under compositional structural constraints, notably generative numeracy, attribute binding, and part-level relations. To address these challenges, we propose Shape-of-Thought (SoT), a visual CoT framework for process-supervised progressive shape assembly in the rendered 2D domain, without external engines at inference time. SoT trains a unified multimodal autoregressive model to generate interleaved textual plans and rendered intermediate states, helping the model capture shape-assembly logic without producing explicit geometric representations. Unlike text-only CoT, each decision is grounded in a rendered state, making counts, attachments, topology, and intermediate part-addition errors inspectable across the trajectory. To support this paradigm, we introduce SoT-26K, a large-scale dataset of grounded assembly traces derived from part-based CAD hierarchies, and T2S-CompBench, a benchmark for evaluating structural integrity and trace faithfulness. Fine-tuning on SoT-26K achieves 88.4% on component numeracy and 84.8% on structural topology, outperforming direct generation by +24.2 points on component numeracy and +19.3 points on structural topology. SoT establishes a transparent testbed for rendered-domain structure-aware generation. The code is available at https://github.com/yuhuo03/Shape-of-Thought.

25.
arXiv (CS.AI) 2026-06-17

Structural Preservation and the Logical Expressiveness of Graph Neural Networks

arXiv:2606.17882v1 Announce Type: new Abstract: Bridges between graph neural networks (GNNs) and logical formalisms have been established by fixing architectural choices, such as the types of aggregation, combination, and activation functions. These choices define restricted classes of GNNs for which tight correspondences with logical formalisms can be obtained, by showing that logical formulae can be translated into equivalent GNNs and, conversely, that GNNs can be translated into equivalent formulae. In this paper we take a semantic perspective by establishing the logical expressiveness of classes of GNN classifiers that are preserved under structural properties: embeddings (extensions), injective homomorphisms, and homomorphisms. We show that, for each such property, there exists a fragment of graded modal logic characterising the class of GNNs. In particular, preservation under embeddings, injective homomorphisms, and homomorphisms corresponds to existential graded modal logic, its existential-positive fragment, and existential-positive modal logic, respectively. These results characterise the expressiveness of broad classes of GNNs independently of specific architectural choices, but we also show that each of these classes admits a GNN architecture of the same expressiveness. Technically, our approach uses a new well-quasi-order result for trees of bounded height, yielding finite representations of unravelling-invariant classes.