arXiv:2606.29634v1 Announce Type: new Abstract: Cardiac arrhythmias, particularly atrial fibrillation, represent a major cardiovascular health burden and underscore the need for efficient and integrated strategies for electrical mapping and targeted therapy. Cardiac electrophysiology procedures depend on accurate identification of arrhythmogenic substrates followed by timely catheter ablation, but conventional diagnostic and therapeutic devices remain separate, often requiring repeated catheter exchanges and multiple access routes. Here, we report an adaptable strategy for functionalizing hollow-core sheaths with EP mapping capabilities, integrating multielectrode recording and ablation catheter delivery within a single compact platform. The device leverages thermal drawing to enable complex geometric fabrication, miniaturization, rapid prototyping, and scalable manufacturing of ultrathin electrode splines arranged circumferentially at the distal end to form an adjustable basket. The mapping sheath exhibited mechanical and electrophysiological properties suitable for intracardiac navigation and electrogram recording in bench-top evaluations, an in vitro left atrial phantom study, and ex vivo Langendorff-perfused porcine heart testing. In vivo porcine studies further demonstrated translational feasibility through vascular introduction, fluoroscopic visualization, intracardiac deployment, tissue contact, electrogram acquisition, and reconstruction of voltage and activation maps. These results support the development of intracardiac platforms with an adapted manufacturing approach, potentially guiding advances in agile cardiac mapping and ablation.
Science Journals
arXiv:2606.05512v2 Announce Type: replace Abstract: A Boolean function in CNF format is of type Positive$\wedge$Negative} if each clause C is either positive (i.e. all literals of C are positive) or negative (i.e. all literals of C are negative). As is well known, deciding the satisfiability of such CNFs is NP-complete. We say that a CNF is of type DisjointPositive if its clauses are positive and mutually disjoint. Dually define DisjointNegative. It is shown that the satisfiability of CNFs of type DisjointPositive$\wedge$DisjointNegative can be decided in quadratic time. Moreover, the modelset can be output in polynomial total time. This is relevant since it affects not only the modelsets of CNFs of type Positive$\wedge$Negative, but more generally of type Horn$\wedge$AntiHorn. As to the latter CNFs, they e.g. occur in connection with the fixpoints of a Monotone Boolean Network. In another vein, the unsatisfiability of a Horn$\wedge$AntiHorn CNF can be demonstrated by means wholly different to the often used method of clausal proofs.
arXiv:2606.29602v1 Announce Type: new Abstract: Large Language Models (LLMs) have rapidly evolved, transforming industries by automating complex tasks and generating human-like content. However, as their adoption accelerates, prompt injection vulnerabilities have become increasingly apparent. Malicious actors exploit these weaknesses to generate phishing emails, deceptive websites, nd malware, posing serious security risks. This paper presents an empirical evaluation of six state-of-the-art LLMs (DeepSeek, GPT, Gemini, Grok, Llama, and Qwen) under diverse adversarial prompt scenarios, including direct and multi-stage obfuscated attacks across multiple languages and character encodings. The proposed framework measures how effectively current LLMs resist manipulation into performing harmful actions. Our findings reveal systematic vulnerabilities across all tested models. Even direct prompt injections frequently induce the generation of phishing content, websites, and malware, while elaborate prompts achieve even higher malicious compliance rates, particularly for phishing. Models such as DeepSeek, Gemini, and Grok show especially high susceptibility under complex instructions. Notably, non-English languages consistently exhibit higher compliance rates than English, exposing significant gaps in multilingual safety alignment. Although simple character encodings reduce malicious outputs, they do not eliminate them. These results highlight persistent challenges in LLM safety and underscore the urgent need for stronger defenses and improved security mechanisms to support the ethical and secure deployment of LLMs in cybersecurity sensitive contexts.
arXiv:2601.17146v2 Announce Type: replace-cross Abstract: Empirical investigations into unintended model behavior often show that the algorithm is predicting another outcome than what was intended. These expos\'es highlight the need to identify when algorithms predict unintended quantities - ideally before deploying them into consequential settings. We propose a falsification framework that provides a principled statistical test for discriminant validity: the requirement that an algorithm predict intended outcomes better than impermissible ones. Drawing on falsification practices from causal inference, econometrics, and psychometrics, our framework compares calibrated prediction losses across outcomes to assess whether the algorithm exhibits discriminant validity with respect to a specified impermissible proxy. In settings where the target outcome is difficult to observe, multiple permissible proxy outcomes may be available; our framework accommodates both this setting and the case with a single permissible proxy. Throughout we use nonparametric hypothesis testing methods that make minimal assumptions on the data-generating process. We illustrate the method in an admissions setting, where the framework establishes discriminant validity with respect to gender but fails to establish discriminant validity with respect to race. This demonstrates how falsification can serve as an early validity check. We also provide analysis in a criminal justice setting, where we highlight the limitations of our framework and emphasize the need for complementary approaches to assess other aspects of construct validity and external validity.
arXiv:2601.21077v2 Announce Type: replace-cross Abstract: Electrides are exotic compounds in which excess electrons occupy interstitial regions of the crystal lattice and serve as anions, exhibiting exceptional properties such as low work function, high electron mobility, and strong catalytic activity. Although they show promise for diverse applications, identifying new electrides remains challenging due to the difficulty of achieving energetically favorable electron localization in crystal cavities. Here, we present an accelerated materials discovery framework that combines physical principles, diffusion-based materials generation with hierarchical thermodynamic and electronic structure screening. Using this workflow, we systematically explored 1,510 binary and 6,654 ternary chemical compositions containing excess valence electrons from electropositive alkaline, alkaline-earth, and early transition metals, and then filtered them with a high throughput validation on both thermodynamical stability and electronic structure analysis. As a result, we have identified 264 new electron rich compounds within 0.05 eV/atom above the convex hull at the density functional theory (DFT) level, including 13 thermodynamically stable electrides. Our approach demonstrates a generalizable strategy for targeted materials discovery in a vast chemical space.
arXiv:2602.01882v3 Announce Type: replace-cross Abstract: We provide explicit and polynomial bounds for the Homogeneous Wall Lemma which occurred for the first time implicitly in the $13$th entry of Robertson and Seymour's Graph Minors Series [JCTB 1990] and has since become a cornerstone in the algorithmic theory of graph minors. A wall where each brick is assigned a set of colours is said to be homogeneous if each brick is assigned the same set of colours. The Homogeneous Wall Lemma says that there exists a function $h$ that, given non-negative integers $q$ and $k$ and an $h(q,k)$-wall $W$ where each brick is assigned a, possibly empty, subset of $\{ 1, \ldots , q \}$ contains a $k$-wall $W'$ as a subgraph such that, if one assigns to each brick $B$ of $W'$ the union of the sets assigned to the bricks of $W$ in its interior, then $W'$ is homogeneous. It is well-known that $h(q,k) \in k^{\mathcal{O}(q)}$. The Homogeneous Wall Lemma plays a key role in most applications of the Irrelevant Vertex Technique where an exponential dependency of $h$ on $q$ usually causes non-uniform dependencies on meta-parameters at best and additional exponential blow-ups at worst. By proving that $h(q,k) \in \mathcal{O}(q^4 \cdot k^6)$, we provide a positive answer to a problem raised by Sau, Stamoulis, and Thilikos [ICALP 2020].
arXiv:2602.21160v4 Announce Type: replace-cross Abstract: In safety-critical classification, the cost of failure is often asymmetric, yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), that cannot distinguish whether a model's ignorance involves a benign or safety-critical class. We decompose MI into a per-class vector $C_k(x)=\sigma_k^{2}/(2\mu_k)$, with $\mu_k{=}\mathbb{E}[p_k]$ and $\sigma_k^2{=}\mathrm{Var}[p_k]$ across posterior samples. The decomposition follows from a second-order Taylor expansion of the entropy; the $1/\mu_k$ weighting corrects boundary suppression and makes $C_k$ comparable across rare and common classes. By construction $\sum_k C_k \approx \mathrm{MI}$, and a companion skewness diagnostic flags inputs where the approximation degrades. After characterising the axiomatic properties of $C_k$, we validate it on three tasks: (i) selective prediction for diabetic retinopathy, where critical-class $C_k$ reduces selective risk by 34.7\% over MI and 56.2\% over variance baselines; (ii) out-of-distribution detection on clinical and image benchmarks, where $\sum_k C_k$ achieves the highest AUROC and the per-class view exposes asymmetric shifts invisible to MI; and (iii) a controlled label-noise study in which $\sum_k C_k$ shows less sensitivity to injected aleatoric noise than MI under end-to-end Bayesian training, while both metrics degrade under transfer learning. Across all tasks, the quality of the posterior approximation shapes uncertainty at least as strongly as the choice of metric, suggesting that how uncertainty is propagated through the network matters as much as how it is measured.
arXiv:2606.14752v2 Announce Type: replace Abstract: Modern Vision-Language-Action (VLA) models must bridge pretrained vision-language reasoning and precise continuous robot control. Existing action tokenizers discretize actions primarily for reconstruction, producing codes that preserve motion geometry but provide only weak semantic supervision to the backbone. We therefore formulate action tokenization not as mere compression, but as semantic interface learning between multimodal reasoning and executable control. To this end, we introduce X-Tokenizer, a lightweight encoder-Semantic Residual Quantization (SRQ)-decoder architecture that provides a shared action interface across diverse robotic arm embodiments. Its key component, SRQ, imposes an asymmetric structure on residual vector quantization: the first level is trained with Masked Action Modeling (MAM) to form a discrete action language that captures coarse motion intent, while deeper levels remain reconstruction-oriented residuals that preserve fine-grained details. To further align action tokens with multimodal semantics, X-Tokenizer is pretrained with contrastive alignment to the representation space of a pretrained foundation model and with next-frame vision-language feature prediction. Pretrained on 2.4M trajectories (2.0B action frames), a single frozen X-Tokenizer plugs into a mixed discrete-continuous VLA as a representation-shaping supervision signal. X-Tokenizer achieves top real-world aggregate and strong RoboTwin 2.0 simulation results. Outperforming FAST in multimodal grounding (+13.5%) and long-horizon tasks (+8.25), it shows that action tokenizers serve as semantic interfaces for VLA pretraining beyond mere action compression.
arXiv:2606.15032v2 Announce Type: replace Abstract: World models have become a central abstraction in modern AI. The term now refers to several different objects: action-conditioned environment models, latent imagination models, future-video predictors, interactive neural simulators, latent predictive representations, and synthetic-data engines. Evaluation has broadened along with the term. Recent papers measure video realism, perceptual similarity, instruction following, physical plausibility, policy ranking, executability, planning success, and downstream policy improvement. This produces both metric diversity and a recurring problem of claim/evidence mismatch: papers sometimes make a stronger claim about what their model is useful for than their evaluation can establish. This paper surveys the recent literature and argues that, for models presented as world models for embodied decision-making, the more decisive issue is not whether the model generates visually convincing videos, but whether it supports reliable interventional reasoning, policy evaluation, planning, and policy optimization under intervention, policy-induced distribution shift, and long-horizon rollout. We organize the survey using an L0--L7 ladder spanning visual plausibility to policy optimization utility, noting that the levels cut across several orthogonal axes and so form an evidential hierarchy rather than a single scalar. The framework foregrounds interventional action fidelity, closed-loop rollout validity, reward/value prediction, policy-ranking agreement, optimization lift, model exploitability, and uncertainty calibration, with a minimal feasible reporting set for real-robot settings.
arXiv:2606.15623v4 Announce Type: replace Abstract: Pairwise comparison is the gold standard for subjective ranking tasks; however, exhaustive annotation requires a massive number of human comparisons ($O(n^2)$). While sorting-based methods have reduced this burden to $O(n\log n)$, they still require expensive human judgment for every single comparison. To further improve annotation efficiency, we propose leveraging a Vision-Language Model (VLM) not as an annotator replacement, but as a \emph{question prioritizer} to identify which comparisons genuinely require human judgment. The proposed \textbf{Surprise-Guided MergeSort (SGS)} framework achieves this through three integrated components: (1) a bottom-up MergeSort scheduler that structures comparisons and exploits transitivity, (2) a composite Surprise Scorer -- combining position-bias-cancelled VLM confidence, Elo gap, and vote entropy -- to quantify comparison ambiguity, and (3) an adaptive budget allocator that routes high-surprise pairs to humans while automating low-surprise pairs via transitivity inference. Validation was conducted on six diverse benchmarks spanning text similarity (STS-B, BIOSSES, SICKR-STS) and image quality assessment (KonIQ-10k, TID2013, LIVE Challenge). SGS effectively identified and skipped up to 535 non-informative comparisons per session. Consequently, it achieved Kendall's $\tau{\times}100$ improvements of $+6$ to $+12$ over Active Elo under the same total budget. These results demonstrate that combining VLM-guided surprise metrics with algorithmic sorting provides a generally consistent accuracy-efficiency trade-off across diverse domains.
arXiv:2606.15708v3 Announce Type: replace Abstract: Welcome to the ninth edition of the AI Index report. As AI continues to advance rapidly, the question becomes whether the systems built around it can keep up. Governance frameworks, evaluation methods, education systems, and the data infrastructure needed to track AI's impact are struggling to match the pace of the technology itself. That gap between what AI can do and how prepared we are to manage it runs through every chapter of this year's report. New in this edition, the report tracks how AI is being tested more ambitiously across reasoning, safety, and real-world task execution, and why those measurements are increasingly difficult to rely on. It also features new estimates of generative AI's economic value alongside emerging evidence of its labor market effects, an analytical framework on AI sovereignty, and a science chapter developed in collaboration with Schmidt Sciences. For the first time, the report features standalone chapters on AI in science and AI in medicine, reflecting AI's growing impact across these two domains.
arXiv:2606.16578v2 Announce Type: replace Abstract: Monte Carlo methods have proven highly effective for elliptic partial differential equations through algorithms such as Walk on Spheres and Walk on Stars, which evaluate solutions at individual points without volumetric meshing or global linear solves. Extending these methods to the transient regime has remained an open challenge: parabolic equations couple space and time through an anisotropic scaling, requiring joint sampling of spatial displacements and backward time steps whose distribution was not previously available in a unified, exact form. We present Walk on Heat Stars, a grid-free Monte Carlo solver that closes this gap by extending the boundary integral framework of Walk on Stars to the parabolic setting. Our method introduces a non-cylindrical boundary integral formulation that accommodates the time-varying domains induced by heat-ball sampling. The heat ball geometry is parameterized by a logarithmic time coordinate and a spatial direction, revealing that the double-layer kernel factorizes into independent Gamma and uniform components. This parameterization enables exact directional importance sampling of the recursive next walk position, the Neumann flux contribution, and the volumetric source term, yielding unbiased Monte Carlo estimators for all three components. We additionally derive a preliminary gradient estimator that expresses spatial derivatives as weighted boundary integrals of the solution, requiring no recursion on the gradient, and adapt a heteroscedastic regression-based denoiser to the space-time domain for variance reduction. We validate our method on analytical solutions across a range of geometries and spatial frequencies, confirm convergence at the expected Monte Carlo rate, and demonstrate practical applicability on heat sink and cooling scenes with mixed or pure Neumann boundary conditions.
arXiv:2602.24007v3 Announce Type: replace-cross Abstract: Protein function relies on dynamic conformational ensembles, yet current generative models like AlphaFold3 often fail to produce ensembles that match experimental data. Recent experiment-guided generators attempt to address this by steering the reverse diffusion process. However, these methods are limited by fixed sampling horizons and sensitivity to initialization, often yielding thermodynamically implausible results. We introduce a general inference-time optimization framework to solve these challenges. First, we optimize over latent representations to maximize ensemble log-likelihood, rather than perturbing structures post hoc. This approach eliminates dependence on diffusion length, removes initialization bias, and easily incorporates external constraints. Second, we present novel sampling schemes for drawing Boltzmann-weighted ensembles. By combining structural priors from AlphaFold3 with force-field-based priors, we sample from their product distribution while balancing experimental likelihoods. Our results show that this framework consistently outperforms state-of-the-art guidance, improving diversity, physical energy, and agreement with data in X-ray crystallography and NMR, often fitting the experimental data better than deposited PDB structures. Finally, inference-time optimization experiments maximizing ipTM scores reveal that perturbing AlphaFold3 embeddings can artificially inflate model confidence. This exposes a vulnerability in current design metrics, whose mitigation could offer a pathway to reduce false discovery rates in binder engineering.
arXiv:2603.15055v3 Announce Type: replace-cross Abstract: We present a theory-guided generalized Bayesian methodology for spatio-temporal raster data, which we use to train an ensemble of stochastic feed-forward neural networks with Gaussian-distributed weights. The methodology incorporates the dependence and causal structure of a spatio-temporal Ornstein-Uhlenbeck process into training and inference by enforcing constraints on the design of the data embedding and the related optimization routine. In inference mode, the networks are employed to generate causal ensemble forecasts by applying different initial conditions at different horizons. We call this workflow MMAF-guided learning. Experiments conducted on both synthetic and real data demonstrate that our forecasts remain calibrated across multiple time horizons. Moreover, we show that on such data, shallow feed-forward architectures can achieve performance comparable to, and in some cases better than, convolutional or diffusion deep learning architectures used in probabilistic forecasting tasks.
arXiv:2603.25645v3 Announce Type: replace-cross Abstract: Early screening via colonoscopy is critical for colon cancer prevention, yet developing robust AI systems for this domain is hindered by the lack of densely annotated, long-sequence video datasets. Existing datasets predominantly focus on single-class polyp detection and lack the rich spatial, temporal, and linguistic annotations required to evaluate modern Multimodal Large Language Models (MLLMs). To address this critical gap, we introduce Colon-Bench, generated via a novel multi-stage agentic workflow. Our pipeline seamlessly integrates temporal proposals, bounding-box tracking, AI-driven visual confirmation, and human-in-the-loop review to scalably annotate full-procedure videos. The resulting verified benchmark is unprecedented in scope, encompassing 528 videos, 14 distinct lesion categories (including polyps, ulcers, and bleeding), over 300,000 bounding boxes, 213,000 segmentation masks, and 133,000 words of clinical descriptions. We utilize Colon-Bench to rigorously evaluate state-of-the-art MLLMs across lesion classification, Open-Vocabulary Video Object Segmentation (OV-VOS), and video Visual Question Answering (VQA). The MLLM results demonstrate surprisingly high localization performance in medical domains compared to SAM-3. Finally, we analyze common VQA errors from MLLMs to introduce a novel "colon-skill" prompting strategy, improving zero-shot MLLM performance by up to 9.7% across most MLLMs. The dataset and the code are available at https://abdullahamdi.com/colon-bench .
arXiv:2603.29629v5 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ is the minimum number of word-representable graphs whose union is $G$. We investigate $\mu(H)$ for graph products $H$ obtained from $G_1$ and $G_2$ via six fundamental products: lexicographic, Cartesian, rooted, corona, tensor, and strong. We prove $\mu(H) = \max\{\mu(G_1), \mu(G_2)\}$ for Cartesian and rooted products. For the corona product, we show $\max\{\mu(G_1), \mu(G_2)\} \le \mu(H) \le \max\{\mu(G_1), \mu(G_2)\} + 1$, and show that the lower bound is tight when $\mu(G_1) > \mu(G_2)$ or $G_2$ admits a covering by $\mu(G_2)$ word-representable graphs, one of which is a comparability graph. For the lexicographic product, we show $\max\{\mu(G_1), \mu(G_2)\} \le \mu(H) \le \mu(G_1) + \mu(G_2)$, and show that the lower bound is tight when $\mathrm{cov}_{\mathrm{comp}}(G_2) \le \max\{\mu(G_1), \mu(G_2)\}$. We provide logarithmic bounds for tensor and strong products. We prove $G^{[k]}$ is word-representable if and only if $G$ is a comparability graph. We establish bounds $\mu(G^{[k]}) \le \mathrm{cov}_{\mathrm{comp}}(G)$ and $\mu(G^{[k]}) \le k$ for non-comparability word-representable graphs. Using lexicographic powers, we obtain the sublinear bound $\tau(n) \le n^{\log_8 6+\epsilon}$ for the extremal function $\tau(n)$. Finally, we address the Word-representable Bipartition (WB) problem, proving a negative answer for $n \geq 2593$: showing that for every such $n$, there exists a graph of order $n$ that cannot be vertex-partitioned into two word-representable induced subgraphs.
arXiv:2606.17555v2 Announce Type: replace Abstract: Banks face two threat families with fundamentally different detection requirements: signature-based fraud (card-not-present attacks, account takeover, ATM cloning) and behavioural financial crime (structuring, layering, mule networks, business email compromise). Static rule engines catch high-velocity events but remain blind to BEC payment redirection, session hijacking, and laundering layering, which are engineered to resemble legitimate activity at the individual level. This paper presents an AI security agent for retail and corporate banking using a three-component fusion architecture across two parallel event streams: transactions (card fraud, ACH/wire fraud, AML) and sessions (account takeover, hijacking, SIM-swap, insider abuse). Each stream combines an LSTM sequence model of per-account behaviour, a statistical velocity/threshold monitor, and a graph module capturing account-counterparty patterns (fan-in, fan-out, pass-through ratio) for laundering detection. Experiments on a synthetic log of 237,669 transactions and 113,508 sessions across 13 threat categories and 3,470 accounts show overall F1 of 0.787 (transaction) and 0.867 (session), versus 0.562/0.733 for a rule-based baseline and 0.655/0.713 for an LSTM-only baseline. The agent also includes a customer-facing verification chatbot (96.6% identity accuracy, 86.8% mass-reset detection) and an analyst case-summary assistant (99.3% action recommendation F1), with Critical-tier response latency under 0.43 ms at the 95th percentile.
arXiv:2606.18016v2 Announce Type: replace Abstract: Metaheuristic optimization of hybrid fiber-IAB networks demonstrates that integrating user dynamics into topology design enables more adaptive and cost-efficient backhaul architectures, contributing to the development of scalable and flexible 6G network infrastructures.
arXiv:2606.03283v3 Announce Type: replace-cross Abstract: Modern speaker verification (SV) systems rely on speaker embeddings that are effective but difficult to interpret or query in natural language. Most existing speech-text corpora target controllable synthesis or utterance-level captioning, offering limited speaker-level supervision for in-the-wild speaker recognition. This paper introduces SpeakerCard-1M, a bilingual speaker resource for evidence-grounded SV, derived from VoxCeleb1/2 and CN-Celeb1/2, where the ``-1M'' suffix refers to the 1.78M utterance-level captions contained in the release. We adopt a tool-first, LLM-last approach in which ten acoustic probes produce field-level evidence, the evidence is aggregated into speaker profiles under a schema that separates relatively stable traits from utterance-level states, and bilingual Speaker Cards are rendered by a constrained LLM that sees only the structured fields. The release includes 56.7k Speaker Card records over 10.2k speakers, 1.78M utterance-level captions, and speaker-ID-disjoint hard-negative triplets. We further define two SV-oriented cross-modal protocols, bidirectional Speaker-Text Retrieval (T2S-R / S2T-R) and Attribute-Conditioned Verification (AC-Verify), and compare a dual-encoder baseline against recent audio language models under a zero-shot forced-choice setting. Joint audio-text training costs only 0.31% absolute EER on VoxCeleb1-O relative to the audio-only baseline. Under a style-symmetric LLM-generated counterfactual protocol, eight recent audio language models (7B-30B+ parameters, both open- and closed-source) score 49-77% on pitch-level AC-Verify in a 2-way forced-choice setting, compared with 88.66% for our dual encoder.
arXiv:2604.23004v3 Announce Type: replace-cross Abstract: Graph burning is a discrete-time process that models the spread of social contagion. Initially, all vertices are unburned. In each round, one unburned vertex is selected and burned, while any unburned vertex that has a burned neighbour from the previous round also becomes burned. The burning number of a graph is the minimum number of rounds needed to burn the entire graph. In this paper, we study the burning number of graph powers. First, we show that for a connected graph~$G$, its graph power~$G^k$ contains a~$(k+1)^+$-branching tree as a spanning tree. A~$(k+1)^+$-branching tree is one in which all internal vertices have degree at least~$k+1$. We then show that $(k+1)^+$-branching trees on~$n$ vertices have burning number at most $\left\lceil{\sqrt{\frac{4(k-1)n}{k^2}}}~\right\rceil$. As the burning number of a graph is at most the burning number of any of its spanning trees, this gives an upper bound on the burning number of graph powers. We also derive an alternative upper bound on the burning number of~$k^+$-branching trees using the strongest currently known general burning number bound [Bastide et al.]. We then identify the ranges of~$k$ and~$n$ for which our bound outperforms or matches this alternative bound. Finally, we show that~$b(G^k) \le (1+o(1))\sqrt{n/k}$ based on the asymptotic burning number bound of Norin and Turcotte.
arXiv:2604.23354v3 Announce Type: replace-cross Abstract: Neural networks can be trained to learn task-relevant representations from data. Understanding how these networks make decisions falls within the Explainable AI (XAI) domain. This paper proposes to study an XAI topic: analysing, visualising and understanding the unknown organisation of network representations, particularly those a speaker recognition network learns from utterances, for recognising speaker identity. Past studies have employed algorithms (e.g. K-means) to analyse the different ways in which network representations can be naturally grouped into clusters, i.e. to analyse different flat clustering phenomena within the space defined by those representations. In contrast, this work applies two algorithms -- Single-Linkage Clustering (SLINK) and Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) -- to analyse the different ways in which representations from the speaker recognition network can form clusters with hierarchical relationships, i.e., to analyse different hierarchical clustering phenomena within the representation space of the speaker recognition network. Furthermore, an algorithm called Hierarchical Cluster-Class Matching (HCCM) is designed to semantically interpret one of the above hierarchical clustering phenomena analysed using SLINK. Given the clusters representing this phenomenon, HCCM identifies which ones best match individual semantic classes related to gender and nationality (e.g.\ male, female, Ireland, UK) and and-logic conjunctions of these classes (e.g.\ female and Ireland). The Liebig score metric is also proposed within HCCM to quantify the matching quality of each cluster-class pair and diagnose the factor that limits each match.
arXiv:2604.24196v3 Announce Type: replace-cross Abstract: This paper studies the identifiability and stability of drifting fields in the framework of Generative Modeling via Drifting. The motivating question is whether a zero-drift equilibrium identifies the target distribution and whether an approximately vanishing drift implies weak distributional convergence. Since the original drifting model employs the Laplace kernel by default, we first analyze why Gaussian score-based arguments fail to apply. This analysis motivates the introduction of companion-elliptic kernel families, which are characterized by a companion potential satisfying an elliptic closure relation. We show that this class naturally contains the Laplace kernel and consists precisely of Gaussian and Mat\'ern kernels with smoothness parameter $\nu>0$. Within this class, we establish field identifiability for arbitrary Borel probability measures on $R^d$: if the drifting field between two such measures vanishes identically, then they must coincide. For stability, we demonstrate that convergence of the field alone does not guarantee weak convergence, since mass may escape to infinity while remaining invisible to the field. Although tightness directly removes this obstruction and restores weak stability, we prove that, even without tightness, every $C_0$-vague cluster point lies exactly on the defect ray $\{cp:0\le c\le1\}$. Consequently, a single scalar $C_0$ observable suffices to detect the missing mass and recover weak convergence.
arXiv:2605.01765v2 Announce Type: replace-cross Abstract: Mediation analysis has traditionally focused on outcome-level summary contrasts, such as mean effects, which may obscure substantial distributional changes induced by complex and nonlinear causal mechanisms. We propose Distributional Causal Mediation Analysis (DCMA), a generative learning framework for identifying and estimating treatment effects on entire outcome distributions transmitted through multiple mediators. DCMA learns conditional generative models for the mediators and the outcome, recovering the relevant conditional distributions from observational data. Leveraging the identification formulas, it reconstructs interventional outcome distributions via Monte Carlo forward simulation by noise resampling, enabling the capture of both classical summary effects and rich distributional contrasts such as energy distance and the Wasserstein distance. Analytical error bounds are derived to decompose how estimation errors in the learned conditional models propagate to the reconstructed interventional outcome distributions. The empirical effectiveness of DCMA is demonstrated through numerical experiments and real-world data applications.
arXiv:2606.18066v2 Announce Type: replace Abstract: We introduce the Noise-Tilted Reverse Kernel (NTRK), a reward-guided diffusion sampler that injects reward gradients through the noise term, leaving the pretrained reverse kernel unchanged and requiring only a single sample per step. Reward-guided sampling at inference time has greatly expanded the versatility of pretrained diffusion models. Yet existing methods face a trade-off. Gradient-based guidance shifts the reverse mean, steering generation but pushing intermediate states outside the region that the model was trained on and degrading quality. Search-based methods preserve quality but gain no gradient signal. No prior method achieves both. NTRK resolves this by keeping the reverse mean fixed and biasing the noise term toward high reward. This is enabled by a whitening operator, the central mechanism behind NTRK, which converts reward gradients into noise-compatible perturbations without losing their guiding signal. Across various reward alignment tasks, NTRK outperforms recent state-of-the-art baselines without losing sample quality. Remarkably, on aesthetic generation, NTRK surpasses the reward of the best baseline at 500 NFEs using only 25 NFEs, a 20 times reduction in compute.
arXiv:2605.03283v2 Announce Type: replace-cross Abstract: We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints. Our contributions span both algebraic structure and statistical guarantees. On the algebraic side, we characterize the rank of the multilabel between-class scatter matrix, showing that the effective discriminant dimensionality can strictly exceed the classical single-label bound of $C-1$; we establish a multilabel partition of variance and prove that all four Fisher objectives are equivalent under the $W^\top S_t^{ML} W = I_r$ constraint while characterizing their divergence under the Stiefel constraint; and we prove a two-sided label-distance preservation bound relating projected distances to Hamming distances in label space. On the statistical side, we establish a finite-sample $O(k_{\max}\sqrt{d\log d/n}/gap_r)$ bound on the subspace estimation error under sub-Gaussian noise with a matching $\Omega(\sigma^2 d/(n\,gap_r))$ minimax lower bound, establishing a near-minimax-optimal rate (matching up to logarithmic and $k_{\max}$ factors) for multilabel discriminant subspace estimation. We further provide high-probability distance concentration, robustness guarantees under label interactions, and a regularization analysis preserving the spectral structure when $d \gg n$. All results are verified numerically on synthetic data generated from the linear label-effect model, covering both the algebraic identities and the multilabel-specific quantities ($k_{\max}$, $\kappa(S_t^{ML})$, $\|\Gamma/n\|_2$, $\Delta_r$) that govern the statistical bounds. The numerical experiments are designed as a sanity check for the theorems rather than as an empirical benchmark; evaluation on real multilabel datasets is left to future work targeting application-oriented venues.