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01.
medRxiv (Medicine) 2026-06-22

Association of Digoxin Use at Norwood Discharge with Fontan Completion: A Study from the Pediatric Heart Network Public Dataset

Background: Digoxin use after the Norwood procedure has been associated with improved interstage survival in hypoplastic left heart syndrome and related conditions. Whether this benefit translates into improved longer-term outcomes through staged palliation remains unknown. We aimed to determine the association of digoxin use at Norwood discharge with transplant-free survival and Fontan completion. Methods: We conducted a retrospective cohort study using the Pediatric Heart Network (PHN) Single Ventricle Reconstruction trial public dataset, including 549 infants enrolled at 15 North American centers between 2005 and 2008. Competing risk analysis was used to evaluate Fontan completion and Cox regression to assess death or transplantation within 6 years after the Norwood procedure. Mixed-effects models compared pre-Fontan hemodynamic and echocardiographic right ventricular indices between patients treated with and without digoxin after accounting for center clustering and adjustment for sex, shunt type, heart failure medications at Norwood discharge, and census block poverty level. Results: The 6-year cumulative incidence of Fontan completion was higher among patients discharged on digoxin than among those not receiving digoxin (82% vs 71%; p = 0.013). Competing-risk analysis accounting for death and transplant demonstrated a greater likelihood of Fontan completion among digoxin users (aHR 1.31; 95%CI 1.09-1.58; p = 0.005), without significant difference in the hazard of death or transplant (aHR 0.78; 95%CI 0.53-1.15; p = 0.208). No significant differences in pre-Fontan hemodynamic or echocardiographic indices were observed between groups. Initiation of digoxin post Stage II procedure was not associated with improved survival or likelihood to complete Fontan. Conclusion: Digoxin use at the time of Norwood discharge was associated with a 30% greater likelihood of Fontan completion by 6 years, without accompanying improvement in transplant-free survival. These findings extend prior observations of improved interstage outcomes associated with digoxin use and suggest that treatment may facilitate progression through staged palliation.

02.
arXiv (CS.CL) 2026-06-11

Gumbel-BEARD: Automatic Layer Selection for Self-Supervised Adaptation of Whisper in Low-Resource Domains

Speech foundation models often struggle in low-resource domains due to domain mismatch and data scarcity. We propose Gumbel-BEARD, a domain adaptation framework that automates Whisper encoder layer selection via an end-to-end trainable hard Gumbel-Softmax selector. It enables self-supervised adaptation with a BEST-RQ objective that dynamically adapts to target acoustic characteristics without manual tuning. Experiments on the MyST child speech corpus demonstrate efficiency and scalability: with 10 h of labeled data for fine-tuning, our method matches a fully supervised baseline trained on the complete 133 h labeled set. We establish new state-of-the-art word error rates (WERs) of 8.21% using Whisper-medium on MyST and 11.06% using Whisper-small on the OGI Spontaneous dataset. Evaluation on CORAAL further confirms robustness to adult dialectal domain shifts, with up to 6% relative WER reduction, highlighting the generalizability of our approach to diverse low-resource conditions.

03.
arXiv (CS.CL) 2026-06-11

Improving Cross-Format Robustness in Language Models with Multi-Format Training

Large language models often remain sensitive to answer format: a question solved correctly in one form may fail in another semantically equivalent form. To study this gap, we define cross-format robustness as the extent to which a model answers the same underlying question consistently across formats. We then compare full-format training with FormatMix, which expands only a subset of training items into multiple equivalent formats using either random or targeted selection. Across GLM4 and Llama-3.1, multi-format supervision consistently improves both task performance and cross-format robustness, whereas Multiple-choice question (MCQ)-only supervision alone brings little benefit and can even reduce robustness. We further find that expanding only about 30% of the training set into multiple formats often recovers most of the gain from full-format training, and this effect appears across the model families and sizes we study. These results suggest that format diversity, rather than additional supervision alone, is the key driver of robustness. That lightweight multi-format augmentation is a practical way to make LLMs less sensitive to answer format without changing the base model.

04.
arXiv (quant-ph) 2026-06-16

Ultrastrongly coupled open systems and fine grained time

arXiv:2606.16634v1 Announce Type: new Abstract: We study the dynamics of a d-level quantum system coupled to a bosonic reservoir when the coupling constant is large. It is known that in the limit of infinite coupling strength, the system undergoes an instantaneous nonselective measurement, resulting in the immediate decoherence in the measurement basis, followed by a unitary Zeno dynamics. Here we resolve this dynamical process by introducing a fine grained scaling regime of short times proportional to the inverse coupling. We provide a rigorous derivation of the open system dynamics in this regime of ultrastrong coupling and demonstrate how decoherence unfolds continuously in the new time scale. We show that Markovian dynamics which are not given by semigroups arise naturally, in contrast to what happens in the weak coupling theory.

05.
arXiv (CS.AI) 2026-06-19

FM-Agent: Scaling Formal Methods to Large Systems via LLM-Based Hoare-Style Reasoning

arXiv:2604.11556v2 Announce Type: replace-cross Abstract: LLM-assisted software development has become increasingly prevalent, and can generate large-scale systems, such as compilers. It becomes crucial to strengthen the correctness of the generated code. However, automated reasoning for large-scale systems remains challenging due to code complexity. Hoare logic offers an approach to decomposing a large system into smaller components and reasoning about them separately (i.e., compositional reasoning). However, existing works still struggle to scale, because Hoare logic requires writing formal specifications for each function, imposing a heavy human burden. The problem is exacerbated when code is generated by LLMs, as developers lack a deep understanding of each function's expected behavior. This paper presents FM-Agent, the first framework that realizes automated compositional reasoning for large-scale systems. Leveraging LLMs, FM-Agent introduces a top-down paradigm to automatically generate function-level specifications. Specifically, FM-Agent derives the specification of a function from how its callers expect the function to behave, so the generated specifications can reflect the developer's intent of a function even if the implementation is buggy. Developers' intent is usually expressed in natural language, while existing verifiers only support formulas. Therefore, FM-Agent generalizes Hoare-style inference to reason about functions against natural-language specifications. Finally, to confirm bug existence and explain bug causes, FM-Agent automatically generates test cases to trigger potential bugs. In our evaluation, FM-Agent successfully reasons about large-scale systems within 2 days, each of which has up to 143k LoC. These systems have already been tested by their developers, but FM-Agent still finds 522 newly discovered bugs. These bugs can cause serious consequences, including system crashes and incorrect execution results.

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

Pseudo-Formalization for Automatic Proof Verification

arXiv:2605.20531v2 Announce Type: replace-cross Abstract: Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most proofs, particularly those written by AI systems, have neither property, and translating them into formal languages remains challenging in many frontier math settings. We propose Pseudo-Formalization (PF), a proof format that captures the modularity and precision of formal proofs while retaining the flexibility of natural language. A Pseudo-Formal proof is decomposed into self-contained modules, each stating its premises, conclusion, and proof in natural language. To verify the correctness of a regular natural language proof, an LLM translates it to Pseudo-Formal and then verifies each module independently, an algorithm we call Block Verification (BV). We evaluate PF+BV on two benchmarks spanning olympiad and research-level mathematics, where it pareto-dominates LLM-as-judge baselines on error-finding precision and recall. To support future work, we release our research-level proof verification benchmark ArxivMathGradingBench.

07.
medRxiv (Medicine) 2026-06-16

Doctors, Wellness Influencers, and Probiotic Gummies: A Cross-Sectional Analysis of Gut Health Claims and Financial Conflicts on TikTok

TikTok has emerged as a major source of health information, yet concerns persist regarding the accuracy of content and influence of financial conflicts. Gut health content is particularly vulnerable to misinformation. This study examined the relationship between creator profession ("medical" versus "non-medical") and the quality of gut health claims and the presence of financial conflicts on TikTok. We conducted a cross-sectional study of 412 TikTok creator accounts identified using the search terms "guthealth," "gutcleansing," and "digestion." One video per creator was analyzed. Creator profession was categorized as medical or non-medical. Health claim quality was coded as high, moderate, or poor. Financial conflicts (Showcase, Subscription, external links) were assessed. Modified Poisson regression was used to estimate prevalence ratios (PRs) of health claim quality (high versus poor- or moderate-quality) and financial conflicts between medical and non-medical creators, and negative binomial regression was used to evaluate associations between claim quality and number of video likes. Non-medical creators were more likely than medical creators to present poor- or moderate-quality health claims (adjusted PR: 2.33; 95% CI: 1.50-3.62). Most creators (92%) exhibited at least one financial conflict, and Showcase use was greater among non-medical creators (adjusted PR: 1.57; 95% CI: 1.02-2.42). Videos containing moderate- and poor-quality health claims received three times as many likes as videos containing high-quality claims. Non-medical creators disproportionately produced lower-quality gut health content on TikTok, and misleading claims received greater engagement. These findings highlight a misalignment between information quality and visibility, emphasizing the need for interventions promoting evidence-based health communication.

08.
arXiv (quant-ph) 2026-06-17

A Lindbladian for holographic Brownian motion

arXiv:2606.17909v1 Announce Type: cross Abstract: We derive a Lindbladian description of holographic Brownian motion in the high-temperature regime. Starting from the influence functional for a trailing string endpoint, we identify the corresponding quantum master equation and prove that it is completely positive and trace-preserving. We determine the coefficients of the Lindbladian explicitly for two holographic backgrounds: the BTZ black hole and the AdS$_5$ black brane, restricting in the latter case to the endpoint fluctuation along the $x^1$-direction. We then analyze the time evolution of phase-space moments, energy relaxation, and steady states.

09.
arXiv (math.PR) 2026-06-18

A simple approach to the L{\o}kka-Zervos dichotomy for absolutely continuous dividend strategies

arXiv:2604.13302v3 Announce Type: replace-cross Abstract: We revisit the optimization problem solved in L{\o}kka & Zervos (2008), i.e., the maximization of dividends, in a Brownian risk model, with the possibility (not the obligation) of making capital injections. Following the approach introduced in Alvarez & Shepp (1998), Renaud & Simard (2021), Renaud et al. (2023), we consider instead absolutely continuous (AC) dividend strategies with an affine bound on the payment rates, while singular capital injections are still allowed. In addition, we incorporate a parameter for the cost of ruin or, said differently, a penalty at ruin in the performance function. We show that the solution is a so-called L{\o}kka-Zervos dichotomy: the surplus is never ruined by making bail-out payments, or no capital is injected and bankruptcy can occur; in either case, dividends are paid at full rate when the surplus is above a threshold. Our framework allows us to provide explicit conditions to express the dichotomy, either using the cost of capital injections or the cost of ruin as a criterion, which also exposes the underlying structure of the solution. In particular, for some values of the parameters, we show that it is optimal to liquidate. Moreover, we perform a numerical analysis highlighting the range of values generated under this AC affine-bound structure.

10.
arXiv (quant-ph) 2026-06-16

Achieving double-logarithmic precision dependence in optimization-based quantum unstructured search

arXiv:2603.26039v3 Announce Type: replace Abstract: Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size $N$. Recent studies have reformulated this task as a maximization problem on the unitary manifold and solved it via linearly convergent Riemannian gradient ascent (RGA) methods, resulting in a complexity of $O(\sqrt{N/M}\log (1/\varepsilon))$, where $M$ denotes the number of target items and $\varepsilon$ denotes the success probability error. In this work, we adopt the Riemannian modified Newton (RMN) method to solve the quantum search problem, under the assumption that the ratio $ M/N$ is known. We show that, in this setting, the Riemannian Newton direction is collinear with the Riemannian gradient in the sense that the Riemannian gradient is always an eigenvector of the corresponding Riemannian Hessian. This structure removes the overhead of Hessian inversion and allows the proposed RMN method to retain the local quadratic convergence in terms of the error $\varepsilon$. More precisely, we rigorously prove an overall complexity of $O(\sqrt{N/M}+\log\log(1/\varepsilon))$. Furthermore, our approach remains Grover-compatible, namely, it relies exclusively on the standard Grover diffusion and oracle operators to ensure algorithmic implementability, and its parameter update process can be efficiently precomputed on classical computers.

11.
arXiv (quant-ph) 2026-06-12

Quasi-local Edge Mode in XXX Spin Chain/Circuit with Interaction Boundary Defect

arXiv:2603.17835v2 Announce Type: replace-cross Abstract: We study the Heisenberg spin-1/2 model on a semi-infinite chain - or, equivalently, a trotterized unitary SU(2) symmetric six-vertex quantum circuit - with a boundary defect where the interaction between the two spins nearest the edge differs from that in the bulk. For sufficiently strong boundary interaction we explicitly construct a conserved operator quasi-localized near the boundary using a matrix-product ansatz. This quasi-local edge mode leads to non-decaying boundary correlation functions, corresponding to a nonzero boundary Drude weight. The correlation length of the edge mode diverges at a finite critical value of the boundary interaction, signaling a transition to ergodic boundary dynamics for subcritical interactions.

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

Unraveling Syntax: Language Modeling and the Substructure of Grammars

While language models achieve impressive results, their learning dynamics are far from understood. Many domains of interest – such as natural language syntax, coding languages, arithmetic – are captured by context-free grammars (CFGs). In this work, we extend prior work on neural language modeling of CFGs in a novel direction: how language modeling behaves with respect to CFG substructure, namely subgrammars. We define subgrammars, and prove a set of fundamental theorems connecting language modeling and subgrammars. We show that language modeling loss recurses linearly over its top-level subgrammars; applied recursively, the loss decomposes into losses for "irreducible" subgrammars. Under additional assumptions, and empirically, parametrized models learn subgrammars in parallel, unlike children who first master simple substructures. We find that subgrammar pretraining can improve final performance, but only for tiny models relative to the grammar, while alignment analyses show that pretraining consistently leads to internal representations that better reflect the grammar's substructure.

13.
arXiv (CS.AI) 2026-06-11

EKF-Based Depth Camera and Deep Learning Fusion for UAV-Person Distance Estimation and Following in SAR Operations

arXiv:2602.20958v2 Announce Type: replace-cross Abstract: Vision-based Unmanned Aerial Vehicles (UAVs) frameworks aid human search tasks by detecting and recognizing specific individuals, then tracking and following them while maintaining a safe distance. A key safety requirement for UAV following is the accurate estimation of the distance between camera and target object under real-world conditions, achieved by fusing multiple image modalities. As part of the system for automatic people detection and face recognition using deep learning, in this paper we present the fusion of depth camera measurements and monocular camera-to-body distance estimation for robust tracking and following. Deep learning based filtering of depth camera data and estimation of camera-to-body distance from a monocular camera are achieved with YOLO-pose, enabling real-time fusion of depth information using the Extended Kalman Filter (EKF) algorithm. The proposed subsystem, designed for use in drones, estimates and measures the distance between the depth camera and the human body keypoints, to maintain the safe distance between the drone and the human target. Our system provides an accurate estimated distance, which has been validated against motion capture ground truth data. The system has been tested in real time indoors, where it reduces the average errors, RMSE and standard deviations of distance estimation up to 15,3% in three tested scenarios. Based on the test results, the EKF fusion-based approach increases the depth detection range by reducing the errors outside the optimal depth camera working range. It also shows improved robustness and precision in challenging conditions, such as reflections and poor visibility, making it suitable for SAR.

14.
arXiv (CS.CL) 2026-06-16

Benchmarking LLM Agents on Meta-Analysis Articles from Nature Portfolio

Meta-analysis is a demanding form of evidence synthesis that combines literature retrieval, PI/ECO-guided study selection, and statistical aggregation. Its structured, verifiable workflow makes it an ideal substrate for evaluating systematic scientific reasoning, yet existing benchmarks lack ground truth across the full retrieval-screening-synthesis pipeline. We introduce MetaSyn, a dataset of 442 expert-curated meta-analyses from Nature Portfolio journals. Each entry pairs a research question with PI/ECO criteria, a retrieval corpus of 140k PubMed articles, verified positive studies, hard negatives that are topically similar but PI/ECO-ineligible, and complete search strategies and date bounds. Benchmarking twelve pipeline configurations (nine RAG variants and a protocol-driven agent) reveals a critical screening bottleneck: despite a retrieval ceiling of 90.9% recall at K=200, no system recovers more than 52.7% of ground-truth included literature. Current LLMs fail to reliably separate eligible studies from PI/ECO-failing distractors in pools of comparable topical relevance. Stage-attributed metrics capture where systems succeed and fail; a single end-to-end score does not.

15.
arXiv (CS.LG) 2026-06-12

Simultaneous Latent Budget Trees for Stratified Classification

arXiv:2606.13295v1 Announce Type: cross Abstract: In the era of Explainable Artificial Intelligence, there is a renewed focus on single trees for their ease of interpretation. This paper introduces Simultaneous Latent Budget Trees, a probabilistic machine learning framework for classification trees in the presence of a stratification factor such as a temporal, spatial, or demographic variable, acting as a control variable or potential confounder. Standard tree growth procedures are not designed to optimize a conditional split rule. A model-based split rule is proposed in which child nodes are interpreted as latent components of a simultaneous mixture model, such as the Simultaneous Latent Budget Model and its constrained versions, fitted to the parent node. Mixing parameters drive the observations, differently for each group, to the child nodes whereas latent budgets parameters update the response classes profile of each level of the control variable. Parameters are estimated by least squares considering a neural network perspective of the model. An informative tree structure can be interactively visualized with interpretation aids on the node and the paths, including visual pruning and decision tree selection procedure. Suitable measures are proposed to handle an unbalanced response class distribution. The proposed methodology is applied to investigate gender-related differences in disease progression of Amyotrophic Lateral Sclerosis. The SLBT library with the various tree-based algorithms is available in the linked GitHub repository.

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

AmchiBias: Measuring Stereotypical Bias in Goan Identity Groups with a Minimal Pair Dataset in English and Konkani

Socio-cultural stereotypical bias is an important consideration in the development and deployment of NLP systems. It is however often considered only at the national level, despite rich subnational socio-cultural structures. We present AmchiBias, the first benchmark for measuring socio-cultural stereotypical bias for the Indian state of Goa with its unique historically multicultural setting. It covers various Goan identity groups and comprises 313 minimal pairs across eight sociodemographic dimensions in both English and Devanagari Konkani. We then evaluate stereotypical bias in five multilingual encoder models on this benchmark. We find near-chance scores in Konkani, reflecting language incompetence for general multilingual models and a lack of Goan cultural competence for Indian language models. Queried in English, models with a stronger Indian language coverage show higher bias for pan-Indian groups than hyperlocal Goan groups. This suggests the English signal reflects pan-Indian pretraining associations rather than genuine Goan cultural knowledge. Our findings highlight a critical gap in low-resource multilingual NLP evaluation for hyperlocal community identities.

17.
arXiv (CS.LG) 2026-06-19

Capturing Intransitive Dominance in Tennis Forecasting: A Graph Neural Network Approach

arXiv:2510.20454v2 Announce Type: replace Abstract: Intransitive player dominance, where player A beats B, B beats C, but C beats A, is common in competitive tennis. Yet, there are few known attempts to incorporate it within forecasting methods. We address this problem with a graph neural network approach that explicitly models these intransitive relationships through temporal directed graphs, with players as nodes and their historical match outcomes as directed edges. Our model (65.7% accuracy, 0.214 Brier score) forecasts competitively with established rating systems such as Weighted Elo. Although it does not improve on the baseline in unconditional accuracy, a forecast-encompassing test shows that it carries complementary information. A combined forecast significantly outperforms Weighted Elo, and there is some indication that the gain grows more strongly on the intransitive matchups our model targets. A graph-based representation of player interactions thus captures a forecasting signal that transitive rating systems discard, even between players who share no common opponents.

18.
arXiv (CS.CV) 2026-06-16

PermaVid: Consistent Video Generation Across Edits via Disentangled Context Memory

Consistent video generation under editing operations requires persistence: when edits modify scene appearance or layout, subsequent generations should remain coherent across time and viewpoints. However, existing memory designs struggle to maintain long-term consistency after such modifications, as stored contexts may become outdated or invalid. To address this, we propose PermaVid, a novel framework built upon a multi-modal context memory that disentangles spatial context into semantic appearance and geometric structure, together with an edit-aware memory update and retrieval strategy that keeps memory evolution aligned with subsequent observations. Specifically, we develop two complementary memory banks: an RGB context memory that captures appearance-aware observations while implicitly encoding geometry, and a depth context memory that preserves geometry-only structure disentangled from semantics. Building on this design, we introduce a memory-guided video generation model that performs multi-modal feature fusion under reference conditions drawn from mixed-modality memory contexts. Experiments demonstrate that our method maintains strong long-term semantic and structural consistency after edits, significantly outperforming state-of-the-art methods.

19.
arXiv (CS.AI) 2026-06-12

Structured vs. Unstructured Pruning: An Exponential Gap

arXiv:2603.02234v3 Announce Type: replace-cross Abstract: The Strong Lottery Ticket Hypothesis (SLTH) states that large, randomly initialized neural networks contain sparse subnetworks capable of approximating a target function at initialization without training, suggesting that pruning alone is sufficient. Pruning methods are typically classified as unstructured, where individual weights can be removed from the network, and structured, where parameters are removed according to specific patterns, as in neuron pruning. Existing theoretical results supporting the SLTH rely almost exclusively on unstructured pruning, showing that logarithmic overparameterization suffices to approximate simple target networks. In contrast, neuron pruning has received limited theoretical attention, despite its practical appeal for direct hardware speedups. In this work, we consider the problem of approximating a single bias-free ReLU neuron by pruning hidden units of a randomly initialized two-layer ReLU network, effectively isolating the intrinsic limitations of neuron pruning. We show that achieving an $\varepsilon$-approximation requires a starting network size of $\Omega(1/\varepsilon)$ for neuron pruning, whereas weight pruning succeeds with only $O(\log(1/\varepsilon))$ hidden units, revealing an exponential separation between the two approaches.

20.
arXiv (quant-ph) 2026-06-11

The quantum harmonic oscillator and the real Hilbert space

arXiv:2606.12060v1 Announce Type: new Abstract: The harmonic oscillator is considered within generalized frameworks using complex and quaternionic numbers. The classical oscillator is considered in terms of a complex position function, and quantum oscillators are examined in terms of complex wave functions, and in terms of quaternionic wave functions as well. Both of the quantum solutions are obtained within the real Hilbert space formalism. The results reveal the complex and quaternionic descriptions as suitable frameworks for non-stationary processes, including damped oscillations, forced oscillations, and additionally self-interacting processes that cannot be appropriately described otherwise.

21.
Nature (Science) 2026-06-19

Daily briefing: Human detritus remakes geology

作者:

What, exactly, is a rock? Plus, a stem-cell success for a severe autoimmune disease and evidence that ‘AI deskilling’ is real. Researchers have tracked the electrical activity of individual brain cells during conversation in real time. Plus, the history of GPS and a cross-species transplant that could reveal clues about the origin of animals.

22.
arXiv (CS.CV) 2026-06-15

What Drives Test-Time Adaptation for CLIP? A Controlled Empirical Study from an Update Perspective

Vision-Language Models (VLMs) such as CLIP have become a standard backbone for open-vocabulary recognition, yet their zero-shot predictions remain vulnerable to distribution shifts encountered at deployment. Test-Time Adaptation (TTA) has recently been extended to CLIP as a lightweight solution, leading to a rapidly growing body of TTA4CLIP methods. However, empirical progress in this area has largely outpaced our understanding of what truly drives adaptation, where their gains originate, and under which shifts they remain reliable. In this paper, we take a step back from the pursuit of state-of-the-art accuracy and conduct a systematic controlled study of TTA4CLIP. We first organize existing methods into three unified paradigms according to what is updated at test time. We then introduce TTABC, an open-source TTA Benchmark for CLIP, which standardizes evaluation protocols and integrates more than 20 representative methods. Our controlled empirical analysis focuses on three key areas. First, we determine the driving factors in parameter-based methods, revealing that adaptation gains are primarily driven by test-time evidence and reliable proxies rather than heavy optimization. Second, we explore evidence utilization beyond heavy parameter tuning, showing that competitive and efficient performance can be achieved through cross- or current-sample evidence and lightweight prototype updates. Finally, we demonstrate that there is no silver bullet for TTA: no single adaptation paradigm is universally optimal, and the preferred paradigm depends on the nature of shift. We hope our benchmark and study provide a clearer understanding of the current TTA4CLIP landscape and establish a foundation for further research.

23.
arXiv (CS.LG) 2026-06-16

Rethinking Structural Anomaly Detection: From Decision Boundaries to Projection Operators

arXiv:2606.15280v1 Announce Type: new Abstract: Most existing anomaly detection methods rely on estimating a probability density or learning an enclosing decision boundary, implicitly assuming that normal data occupies a region of non-zero volume in the ambient space. In contrast, structural anomaly detection considers data that lies near a low-dimensional manifold, creating a mismatch between the inductive bias of existing methods and the structure of the data, often resulting in degraded performance. To address this mismatch, we introduce a geometric perspective. Specifically, we learn a projection operator onto the manifold of normal samples and define a sample as anomalous if it is altered by this projection. This formulation naturally integrates the inductive bias of manifold-supported data and reframes anomaly detection in terms of a projection residual, thereby resolving issues arising from modeling degenerate distributions. Notably, it provides a unifying interpretation of reconstruction-based methods by explaining their success and failure in terms of projection quality. In particular, it explains the strong generalization ability of projection-aligned models as a consequence of contraction behavior toward the manifold. Moreover, by decoupling anomaly detection from probabilistic modeling, it reduces the tendency to misclassify rare but normal samples, a widely recognized limitation of existing approaches. Empirically, we demonstrate that projection-aligned methods achieve strong performance, outperforming boundary-based methods while improving upon existing reconstruction-based approaches.

24.
arXiv (quant-ph) 2026-06-12

Geometric Algebra Quantum Gate Decomposition

arXiv:2606.12480v1 Announce Type: new Abstract: Quantum gates are usually described through matrix and tensor-product formalisms that often obscure their geometric structure. In this work, we formulate the Pauli and Clifford groups within the complex Geometric Algebra (GA) framework. We show that the Pauli group is naturally identified with the group of blades up to a global phase, thereby providing a geometric interpretation of Pauli operators and their commutation relations in terms of oriented subspaces. We further prove that Clifford operators are generated by products of {\pi}/4-Pauli rotors and introduce a greedy Pauli rotor decomposition algorithm whose empirical behavior suggests unexpectedly compact decompositions for Clifford operators. Finally, we show that Clifford+T universality admits a natural geometric interpretation through {\pi}/8-rotors within this framework.

25.
arXiv (CS.LG) 2026-06-12

Adaptive Weighted Averaging

arXiv:2606.12763v1 Announce Type: new Abstract: We study the problem of selecting the largest among $n$ unknown values $x_1,\dots,x_n$ given only a single unbiased estimate $y_i$ for each $x_i$. We design strategies that are simultaneously admissible (not uniformly dominated by any other strategy) and also never worse than a given baseline such as uniform random selection. We provide an application to stochastic optimization, where we obtain online-to-batch conversion bounds with a desirable "no-compromise" guarantee: they are never worse than standard random iterate selection, and yet can be significantly better in benign settings.