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01.
arXiv (CS.AI) 2026-06-24

MedPCFM: Improving Medical Point Cloud Completion by Integrating Point Transformers and Flow Matching

arXiv:2606.24433v1 Announce Type: cross Abstract: Medical point cloud completion is important for anatomical reconstruction and downstream clinical workflows, yet generative modeling in this setting remains insufficiently studied. We investigate completion through continuous-time generative modeling and introduce PCFM, a PTv3-backed flow matching approach for medical point cloud completion. We evaluate on SkullFix and SkullBreak, and additionally on the more recent Mandibular Defect dataset. We build strong baselines by adapting PTv3 to a deterministic encoder-decoder completion model and by instantiating diffusion completion (PCDiff) with both PVCNN and PTv3 denoisers. PCFM with PTv3 is competitive with the deterministic PTv3 baseline and achieves state-of-the-art generative performance across datasets, while requiring substantially fewer sampling steps than diffusion. At the best operating points, PTv3 also yields clear throughput gains, providing up to a 7$\times$ speed-up for PCFM compared to a PVCNN backbone. Finally, we study empirical scaling trends by varying model size and point cardinality, showing consistent gains with higher point resolution and informative trade-offs across model scales.

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

Visualizing LLM Latent Space Geometry Through Dimensionality Reduction

arXiv:2511.21594v3 Announce Type: replace Abstract: Large language models (LLMs) achieve state-of-the-art results across many natural language tasks, but their internal mechanisms remain difficult to interpret. In this work, we extract, process, and visualize latent state geometries in Transformer-based language models through dimensionality reduction. We capture layerwise activations at multiple points within Transformer blocks and enable systematic analysis through Principal Component Analysis (PCA) and Uniform Manifold Approximation and Projection (UMAP). We demonstrate experiments on GPT-2 and LLaMa models, where we uncover interesting geometric patterns in latent space. Notably, we identify a clear separation between attention and MLP component outputs across intermediate layers, a pattern not documented in prior work to our knowledge. We also characterize the high norm of latent states at the initial sequence position and visualize the layerwise evolution of latent states. Additionally, we demonstrate the high-dimensional helical structure of GPT-2's positional embeddings and the sequence-wise geometric patterns in LLaMa. We make our code available at https://github.com/Vainateya/Feature_Geometry_Visualization. A better formatted blog-post with identical content is available at https://iclr-blogposts.github.io/2026/blog/2026/vis-llm-latent-geometry/.

03.
arXiv (quant-ph) 2026-06-17

Many-body spectral transitions through the lens of the variable-range SYK2 model

arXiv:2412.14280v2 Announce Type: replace-cross Abstract: The Sachdev-Ye-Kitaev (SYK) model is a cornerstone in the study of quantum chaos and holographic quantum matter. Real-world implementations, however, deviate from the idealized all-to-all connectivity, raising questions about the robustness of its chaotic properties. In this work, we investigate a quadratic SYK model with distance-dependent interactions governed by a power-law decay. By analytically and numerically studying the spectral form factor (SFF), we uncover how transitions present in the single-particle limit carry over to the many-body system. Non-trivial cancellations in the one-loop contributions lead to a robustness of the SFF under a considerable reduction of the interaction range. Further suppression leads to a breakdown of perturbation theory around the infinite-range path-integral saddle and the appearance of new spectral regimes, marked by a higher dip and the emergence of a secondary plateau. Our results highlight the interplay between single-particle criticality and many-body dynamics, offering new insights into the quantum chaos-to-localization transition and its reflection in spectral statistics.

04.
arXiv (quant-ph) 2026-06-11

Raw-Curve Quantum Fingerprints: A Mahalanobis Authentication Framework with Drift Early Warning and Adversarial Detection

arXiv:2606.11644v1 Announce Type: new Abstract: Quantum cloud platforms are poised to deliver powerful computing capabilities, but users have no direct means to verify which physical device executes their workload. This lack of transparency enables hardware substitution attacks, where a malicious adversary could redirect a job to a substituted or inferior processor. We present a general authentication framework that addresses this problem by constructing multi-dimensional quantum fingerprints from raw measurement data. Without any curve fitting, we directly concatenate the raw statistics of complementary experiments into a high-dimensional feature vector that preserves subtle device-specific information. A Mahalanobis nearest-neighbor classifier achieves 100\% benign authentication accuracy on three superconducting processors over a three-week chronological split. The classifier naturally yields an authentication confidence $C_{\mathrm{claimed}}$ which reveals device-specific safety margins and motivates per-device alert thresholds. We assess the framework's robustness under two distinct scenarios. Under additive isotropic Gaussian noise, $C_{\mathrm{claimed}}$ decays predictably at a rate explained by inverse covariance traces, enabling an early warning mechanism. Against white-box adversarial perturbations, the same confidence threshold detects $L_2$ targeted attacks with near-perfect success and reveals device-dependent empirical thresholds for $L_\infty$ attacks, while untargeted and sparse attacks are ineffective. The proposed framework thus unifies fingerprint extraction, drift-resilient authentication, proactive health monitoring, and adversarial defense, offering a practical step toward trustworthy quantum cloud computing.

05.
arXiv (CS.AI) 2026-06-24

Exploring Dualistic Meta-Learning to Enhance Domain Generalization in Open Set Scenarios

arXiv:2606.23758v1 Announce Type: cross Abstract: Domain generalization learns from multiple source domains to generalize to unseen target domains. However, it often neglects the realistic case of label mismatch between source and target. Open set domain generalization is then proposed to recognize unseen classes in unseen domains. A simple approach trains one-vs-all classifiers to separate each class and detect outliers as unknown. Yet, the imbalance between few positive samples and many negative samples skews the decision boundary towards the positive ones, leading the model to over-reject out-of-distribution data, even from known classes in unseen domains. In this paper, we propose a novel meta-learning stategy called dualistic MEta-learning with joint DomaIn-Class matching (MEDIC), which considers implicit gradient matching towards inter-domain and inter-class task splits simultaneously to find optimal boundaries balanced for both domains and classes. Experimental results show that MEDIC not only outperforms prior methods in open set scenarios, but also maintains competitive close set generalization ability.

06.
PLOS Computational Biology 2026-06-11

MicroRNA target gene prediction model based on input-feature dependency and sample data expansion technique

Authors:

by Yan Shao, Yazhou Li, Hexin Zhai, Shimin Dong Predicting microRNA target genes is essential for understanding their biological functions. This study developed a miRNA target gene prediction model based on input-feature dependency. Features were treated as multiple random variables, with marginal densities estimated using Gaussian mixture models (GMM) and dependencies captured by regular vine (R-vine) copula to derive joint probability density functions. We constructed class-conditional joint densities for positive and negative samples separately using GMM and R-vine copula, then combined these with prior probabilities using Bayes’ rule to obtain posterior probabilities of positive interactions, using a standard 0.5 probability threshold for deterministic prediction. To address insufficient data and class imbalance, hybrid distribution mega-trend diffusion was used to generate virtual samples for data augmentation. Computational validation showed high predictive performance even when only 30% of the training data were used. As proof-of-concept, we experimentally validated one predicted interaction (miR-8485 targeting JAK2) using dual-luciferase, cellular, and animal experiments, confirming the biological relevance of this specific model-generated prediction. These findings provide a valuable tool for understanding miRNA functions and disease mechanisms.

07.
arXiv (CS.AI) 2026-06-16

Trust Between AI Agents: Measuring Formation, Breakage, and Recovery, with Implications for Governing Multi-Agent Systems

Authors:

arXiv:2606.14923v1 Announce Type: new Abstract: As language-model agents increasingly work in teams, each agent must decide how much to trust its teammates. Yet we lack a standard way to measure trust between AI agents. We propose a behavioral measure based on costly verification. In a cooperative survival game, checking a teammate's work consumes resources, while trusting a wrong answer can be fatal. Relative to a memoryless version of the same model, reduced verification provides an observable measure of trust. Using this framework, we study trust formation, breakage, and recovery across six frontier model snapshots. When paired with a consistently reliable teammate, four snapshots (Claude Opus 4.6, Claude Sonnet 4.6, GPT-5.1, and Gemini 3.1 Pro) reduce verification by roughly 60-85%, whereas two smaller snapshots show little or no such adjustment. Failures reverse this discount, but models differ in how they respond. Some concentrate renewed scrutiny on the culprit, while others become more cautious toward the entire team. Recovery is slower than formation, and clustered failures sustain suspicion far longer than the same number of failures spread apart. These differences have practical consequences. Models that form trust verify less, decide more quickly, and achieve higher payoffs in our environment. By contrast, persistent over-verification is associated with indecision rather than safety. Our results show that trust dispositions can be measured before deployment and suggest that calibration, rather than maximal suspicion, should be the central concern in the governance of multi-agent AI systems.

08.
arXiv (quant-ph) 2026-06-16

Forbidden transitions in superconducting artificial atoms

arXiv:2606.06069v2 Announce Type: replace Abstract: Artificial atoms built from Josephson junctions have become a powerful tool to explore the limits of quantum optics due to their strong coupling to electromagnetic fields and their sensitivity to changes at the single-photon level. This sensitivity to quantum fluctuations complements their metrological and computational use, which are based on the precise oscillating frequency of the underlying supercurrents. We present here a theory for Josephson junctions immersed in electromagnetic fields where focus is shifted from temporal correlations and towards spatial ones. Unlike the commonly used circuit and black-box descriptions, our work is based on a microscopic model that enables systematically accounting for the effect of the spatial and vectorial profile of an electromagnetic field over a junction. As an example of the interactions that emerge in such a setup, we investigate the possibility of driving a junction via a quadrupole transition, using typical experimental parameters in existing devices. With the transition being dependent on the gradient of the electric field – rather than its intensity – the junction can be excited in a region where the electric field vanishes.

09.
arXiv (CS.LG) 2026-06-24

XConv: Low-memory stochastic backpropagation for convolutional layers

arXiv:2106.06998v5 Announce Type: replace Abstract: Training convolutional neural networks at scale demands substantial memory, largely because intermediate activations must be stored for backpropagation. Existing remedies (checkpointing, invertible architectures, or gradient-approximation methods such as randomized automatic differentiation) either add significant computation, impose architectural constraints, or require non-trivial code changes. We propose XConv, a near-drop-in replacement for standard 2D and 3D convolutional layers that addresses all three: it preserves standard backpropagation, imposes no architectural constraints, and integrates into existing codebases with minimal changes. XConv exploits the algebraic structure of convolutional weight gradients, storing highly compressed projections of the activations rather than the full tensors and approximating the gradients via multi-channel randomized trace estimation. The number of probing vectors sets a memory-accuracy tradeoff and recovers the exact gradient in the limit. We establish convergence guarantees and error bounds for the estimator, showing that its gradient-error variance is comparable to that of stochastic gradient descent. Empirically, XConv matches exact-gradient methods across classification, generative modeling, super-resolution, inpainting, and segmentation, with gaps that narrow as the number of probing vectors grows, while reducing activation memory by a factor of two or more when convolutional activations dominate, and remaining computationally competitive with optimized convolution kernels at larger batch sizes. At half precision the gradient-approximation error falls to the rounding floor, so XConv adds essentially no error beyond that of low-precision arithmetic. The savings matter most where activation memory rather than compute is the binding constraint, such as high-resolution and volumetric training and on-device finetuning.

10.
arXiv (CS.CV) 2026-06-17

Looped World Models

Current world models face a fundamental tension: faithful long-horizon simulation demands deep computation, but deeper models are expensive to deploy and prone to compounding errors. We resolve this by introducing Looped World Models (LoopWM), which are the first looped architectures for world modelling. Our method iteratively refines latent environment states through a parameter-shared transformer block. This yield up to 100x parameter efficiency over conventional approaches with adaptive computation that automatically scales depth to match the complexity of each prediction step. Orthogonal to scaling model size and training data, LoopWM establishes iterative latent depth as a new scaling axis for world simulation, which might significantly push the community forward.

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

VibeThinker-3B: Exploring the Frontier of Verifiable Reasoning in Small Language Models

This technical report introduces VibeThinker-3B, a compact dense model with 3B parameters developed to investigate how far verifiable reasoning can be pushed within a strictly small-model regime. Building upon the Spectrum-to-Signal post-training paradigm, we systematically enhance the model through an optimized pipeline that includes curriculum-based supervised fine-tuning, multi-domain reinforcement learning, and offline self-distillation. Experimental evaluations demonstrate that VibeThinker-3B achieves frontier-level performance on highly demanding verifiable tasks. Specifically, it attains a score of 94.3 on AIME26 (improving to 97.1 with claim-level test-time scaling), an 80.2 Pass@1 on LiveCodeBench v6, and exhibits strong out-of-distribution generalization with a 96.1\% acceptance rate on recent unseen LeetCode contests. This effectively places it in the performance band of first-tier reasoning systems, matching or exceeding flagship models that are orders of magnitude larger, such as DeepSeek V3.2, GLM-5, and Gemini 3 Pro. Furthermore, a score of 93.4 on IFEval confirms that this extreme reasoning enhancement does not compromise strict instruction controllability. Extending our previous 1.5B work, these findings motivate the Parametric Compression-Coverage Hypothesis, which views verifiable reasoning as compressible into compact reasoning cores, while open-domain knowledge and general-purpose competence require broad parameter coverage over facts, concepts, and long-tail scenarios. This perspective suggests that compact models are not merely deployment-efficient substitutes, but a complementary path toward frontier-level performance in parameter-dense capability regimes.

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

RAMAC: Multimodal Risk-Aware Offline Reinforcement Learning and the Role of Behavior Regularization

arXiv:2510.02695v3 Announce Type: replace-cross Abstract: In safety-critical domains where online data collection is infeasible, offline reinforcement learning (RL) is attractive only if policies achieve high returns without catastrophic lower-tail risk. Prior work on risk-averse offline RL achieves safety at the cost of either (i) value/model-based pessimism or (ii) restricted policy classes that limit expressiveness, whereas diffusion/flow-based expressive generative policies have largely been used in risk-neutral settings. We introduce Risk-Aware Multimodal Actor-Critic (RAMAC), a simple, modular, model-free framework that couples an expressive generative actor (e.g., diffusion/flow) with a distributional critic and optimizes a composite objective that combines Conditional Value-at-Risk (CVaR) with behavioral cloning (BC), enabling risk-sensitive learning in complex multimodal scenarios. Since out-of-distribution (OOD) actions are a major driver of catastrophic failures in offline RL, we further provide an objective-level analysis showing that controlling behavior divergence via BC suppresses OOD actions and stabilizes CVaR. Instantiating RAMAC with a diffusion actor, we illustrate these insights on a 2-D risky bandit and evaluate on Stochastic-D4RL, observing consistent gains in $\mathrm{CVaR}_{0.1}$ while maintaining strong returns. The code and experimental results are available on the \href{https://kaifukazawa.github.io/ramac-project/} {project website}

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

Revisiting Outage for Edge Inference Systems

arXiv:2504.03686v3 Announce Type: replace-cross Abstract: One of the key missions of sixth-generation (6G) mobile networks is to deploy large-scale artificial intelligence (AI) models at the network edge to provide remote-inference services for edge devices. The resultant platform, known as edge inference, will support a wide range of Internet-of-Things applications, such as autonomous driving, industrial automation, and augmented reality. Given the mission-critical and time-sensitive nature of these tasks, it is essential to design edge inference systems that are both reliable and capable of meeting stringent end-to-end (E2E) latency constraints. Existing studies, which primarily focus on communication reliability as characterized by channel outage probability, may fail to guarantee E2E performance, specifically in terms of E2E inference accuracy and latency. To address this limitation, we propose a theoretical framework that introduces and mathematically characterizes the inference outage (InfOut) probability, which quantifies the likelihood that the E2E inference accuracy falls below a target threshold. Under an E2E latency constraint, this framework establishes a fundamental tradeoff between communication overhead (i.e., uploading more sensor observations) and inference reliability as quantified by the InfOut probability. To find a tractable way to optimize this tradeoff, we derive accurate surrogate functions for InfOut probability by applying a Gaussian approximation to the distribution of the received discriminant gain. Experimental results demonstrate the superiority of the proposed design over conventional communication-centric approaches in terms of E2E inference reliability.

14.
arXiv (CS.LG) 2026-06-25

$DT^2$: Decision-Targeted Digital Twins

arXiv:2606.25923v1 Announce Type: new Abstract: A digital twin (DT) is a virtual model of a real-world system that can assist decision-making by simulating scenarios induced by different policies. However, typical machine learning-based DTs do not optimise for this use case. We prove that, when model capacity is limited, training DTs to minimise one-step transition errors can produce suboptimal models for ranking sets of policies according to a reward function. We further show that this holds empirically, even with expressive model classes. To address this, we introduce $DT^2$, a decision-targeted DT training paradigm. Firstly, $DT^2$ uses fitted Q-evaluation to estimate values of candidate policies from offline data. A DT is then trained to generate rollouts that preserve pairwise policy rankings derived from these proxy ground-truth values with an architecture-agnostic loss function. We empirically demonstrate the efficacy of our method across a range of settings and architectures. $DT^2$ consistently improves policy ranking and reduces decision regret during policy selection relative to conventional DT training, both for policies used during training and for unseen policies, while maintaining a good level of raw simulation fidelity.

15.
arXiv (CS.AI) 2026-06-19

Reinforcement-aware Knowledge Distillation for LLM Reasoning

arXiv:2602.22495v3 Announce Type: replace-cross Abstract: Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL – guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher–old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

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

Mordal: Automated Pretrained Model Selection for Vision Language Models

Incorporating multiple modalities into large language models (LLMs) is a powerful way to enhance their understanding of non-textual data, enabling them to perform multimodal tasks. Vision language models (VLMs) form the fastest growing category of multimodal models because of their many practical use cases, including in healthcare, robotics, and accessibility. Unfortunately, even though different VLMs in the literature demonstrate impressive visual capabilities in different benchmarks, they are handcrafted by human experts; there is no automated framework to create task-specific multimodal models. We introduce Mordal, an automated multimodal model search framework that efficiently finds the best VLM for a user-defined task without manual intervention. Mordal achieves this both by reducing the number of candidates to consider during the search process and by minimizing the time required to evaluate each remaining candidate. Our evaluation shows that Mordal can find the best VLM for a given problem using $8.9\times$–$11.6\times$ lower GPU hours than grid search. We have also discovered that Mordal achieves about 69\% higher weighted Kendall's $\tau$ on average than the state-of-the-art model selection method across diverse tasks.

17.
arXiv (CS.LG) 2026-06-15

A General Framework for Decision Trees via Bregman Divergences

arXiv:2606.13984v1 Announce Type: cross Abstract: Decision trees are one of the fundamental tools in statistical learning due to their interpretability, flexibility, and their ability to adapt to nonlinear structures. Among them, the Classification and Regression Trees, introduced by Breiman, Friedman, Olshen, and Stone in 1984, became one of the most influential algorithms and remains one of the most widely used methods for classification and regression problems. On the other hand, Bregman divergences, introduced by Lev Bregman in 1967 in the context of convex optimization, provide a broad family of loss functions that naturally generalize the squared Euclidean distance. This family includes, among others, the Kullback-Leibler divergence, the Poisson divergence, and the Itakura-Saito divergence, as well as several losses associated with distributions belonging to the exponential family. Moreover, Bregman divergences possess a rich geometric structure and deep connections with convex analysis and information geometry. In this work, we propose a generalization of the CART paradigm based on Bregman divergences, thereby obtaining a broader family of decision trees adapted to different statistical models and underlying geometries. Although algorithms such as CART or classical implementations such as rpart incorporate different impurity criteria, these are usually introduced in an ad hoc manner for each specific model. In contrast, the Bregman divergence approach provides a unified framework that allows these criteria to be derived and interpreted from common convex and geometric principles. Beyond the algorithmic construction, we also investigate theoretical properties of these trees. In particular, we study how properties of the generating convex function – such as strong convexity or smoothness – influence impurity gains between parent and child nodes, as well as stability and consistency properties of the estimator.

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

Is Your Trajectory Displacement Safe in Long-tail?

arXiv:2606.16313v1 Announce Type: cross Abstract: Long-tail scenarios remain a major bottleneck for autonomous driving evaluation, even as datasets grow by orders of magnitude. Existing evaluation pipelines are rarely human-aligned, safety-aware, verifiable, and explainable at the same time: closed-loop metrics often saturate among strong planners, while unstructured human ratings can be noisy without a carefully designed protocol. We formulate planning evaluation as additional-threat detection: given a planner trajectory and an expert reference, does the planner's displacement introduce new unsafe driving behavior? We propose FluidTest, an evaluation pipeline with three components: a pairwise WebUI protocol for reliable human annotation; a taxonomy of 32 semantic threats with evidence-grounded decision graphs; and a three-agent verification system with reflection for precision and auditability. Experiments on the WOD-E2E dataset show that FluidTest produces consistent labels among trained annotators and identifies additional threats in 65% of Poutine trajectories and 51% of RAP trajectories. These results show that state-of-the-art planners can still exhibit substantial safety-relevant failures despite high Rater Feedback Scores (RFS) and low Average Displacement Error (ADE). Additional details, guidance, and code are available at https://fluidtest.web.app.

19.
arXiv (quant-ph) 2026-06-25

Quantum magic of strongly correlated fermions $-$ the Hubbard dimer

arXiv:2605.18494v2 Announce Type: replace Abstract: We study the non-stabilizerness (quantum magic) content of the Hubbard dimer, an analytically solvable, yet completely non-trivial, model of strongly correlated fermions. We consider zero- and finite-temperature properties as well as the time evolution after a quantum quench drives the system out of equilibrium. We evaluate local and nonlocal non-stabilizerness using both the robustness of magic and the stabilizer Renyi entropy, demonstrating how the latter often fails in detecting the mixed stabilizer states that are typically found in this kind of systems. Finally, we compare the non-stabilizerness with other genuine resources of quantum-state complexity, i.e., the fermionic non-Gaussianity and the superselected two-site entanglement. Our findings corroborate the role of non-stabilizerness as a fundamental quantum resource, capturing aspects of quantum complexity that elude traditional information-theoretic measures and providing a novel perspective on fermionic systems with tunable interactions.

20.
arXiv (CS.LG) 2026-06-11

Impact of Connectivity on Laplacian Representations in Reinforcement Learning

arXiv:2603.08558v3 Announce Type: replace Abstract: Learning compact state representations in Markov Decision Processes (MDPs) has proven crucial for addressing the curse of dimensionality in large-scale reinforcement learning (RL) problems. Existing principled approaches leverage structural priors on the MDP by constructing state representations as linear combinations of the state-graph Laplacian eigenvectors. When the transition graph is unknown or the state space is prohibitively large, the graph spectral features can be estimated directly via sample trajectories. In this work, we prove an upper bound on the approximation error of linear value function approximation under the learned spectral features. We show how this error scales with the algebraic connectivity of the state-graph, grounding the approximation quality in the topological structure of the MDP. We further bound the error introduced by the eigenvector estimation itself, leading to an end-to-end error decomposition across the representation learning pipeline. Additionally, our expression of the Laplacian operator for the RL setting, although equivalent to existing ones, prevents some common misunderstandings, of which we show some examples from the literature. Our results hold for general (non-uniform) policies without any assumptions on the symmetry of the induced transition kernel. We validate our theoretical findings with numerical simulations on gridworld environments.

21.
arXiv (math.PR) 2026-06-16

Hua-Chen New Theory of Economic Optimization

arXiv:2504.19134v4 Announce Type: replace-cross Abstract: Between 1957-1985, Chinese mathematician Loo-Keng Hua pioneered economic optimization theory through three key contributions: establishing economic stability's fundamental theorem, proving the uniqueness of equilibrium solutions in economic systems, and developing a consumption-integrated model 50 days before his death. Since 1988, Mu-Fa Chen has been working on Hua's theory. He introduced stochastics, namely Markov chains, to economic optimization theory. He updated and developed Hua's model and came up with a new model (Chen's model) which has become the starting point of a new economic optimization theory. Chen's theory can be applied to economic stability test, bankruptcy prediction, product ranking and classification, economic prediction and adjustment, economic structure optimization. Chen's theory can also provide efficient algorithms that are programmable and intelligent. {Stochastics} is the cornerstone of Chen's theory. There is no overlap between Chen's theory, and the existing mathematical economy theory and the economics developments that were awarded Nobel Prizes in Economics between 1969 and 2024. The distinguished features of Chen's theory from the existing theories are quantitative, calculable, predictable, optimizable, programmable and can be intelligent. This survey provides a theoretical overview of the newly published monograph [5rw24]. Specifically, the invariant of the economic structure matrix, also known as the Chen's invariant, was first published in this survey.

22.
arXiv (CS.CV) 2026-06-25

FunPiQ: A New Benchmark for Pixel-Level Quality Assessment in Fundus Images

Color fundus photography (CFP) is the most common ophthalmic imaging modality for large-scale screening. However, it is highly susceptible to degradations, making robust fundus image quality assessment (FIQA) crucial. The criteria for what constitutes high-quality at the image level vary across clinical tasks, making FIQA dependent on expert knowledge. This motivated the development of automated methods and datasets. While existing datasets aim to standardize image-level quality, their criteria often differ. Furthermore, image-level labels preclude the quantitative evaluation of localized degradations, which is essential for trustworthy FIQA. We argue that pixel-level FIQA based on anatomical visibility represents a more task-agnostic, explainable approach. In this work, we introduce FunPiQ, the first FIQA benchmark to provide pixel-level quality annotations. In addition, we propose EFIQA-CP, an explainable-by-design (EBD) method that uses quality pseudo-labels based on anatomical visibility to train a CNN via Non-Negative Positive-Unlabeled learning. Extensive evaluations of classification methods with post-hoc explanations, anomaly detection methods, and EBD methods demonstrate the superior performance of the last and, particularly, of EFIQA-CP.

23.
arXiv (math.PR) 2026-06-19

Towards practical PDMP sampling: Metropolis adjustments, locally adaptive step-sizes, and NUTS-based time lengths

arXiv:2503.11479v2 Announce Type: replace-cross Abstract: Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely, while Hamiltonian Monte Carlo (HMC) offers a generally efficient approach to sampling, its inability to adaptively tune step sizes impedes its performance when sampling complex distributions like funnels. To address these limitations, we introduce three innovative concepts: (a) a Metropolis-adjusted approximation for PDMP simulation that eliminates the need for explicit bounds without compromising the invariant measure, (b) an adaptive step size mechanism compatible with the Metropolis correction, and (c) a No U-Turn Sampler (NUTS)-inspired scheme for dynamically selecting path lengths in PDMPs. These three ideas can be seamlessly integrated into a single, `doubly-adaptive' PDMP sampler with favourable robustness and efficiency properties.

24.
arXiv (math.PR) 2026-06-12

Fourier Dimensions of Mandelbrot Cascades under Minimal Integrability

Authors:

arXiv:2606.08703v2 Announce Type: replace Abstract: This note announces exact Fourier dimension formulas for canonical Mandelbrot cascade measures under the minimal Kahane Peyriere integrability condition and records the canonical b adic extension on cubes. In the dyadic interval setting, the theorem is proved in a balanced vector weight model allowing dependence between sibling weights. Almost surely on non extinction, the Fourier, energy, and L2 dimensions all equal the energy exponent. The scalar specialization gives the canonical Mandelbrot Kahane Fourier dimension formula under the minimal integrability condition. On the circle, the endpoint formula is given by the endpoint lower local dimension exponent. For the b adic Mandelbrot cascade on cubes, the Fourier dimension is the minimum of 2 and the energy exponent, with the universal Fourier barrier at dimension two providing the high dimensional obstruction.

25.
arXiv (CS.LG) 2026-06-11

Online Shift Detection and Conformal Adaptation for Deployed Safety Classifiers

Authors:

arXiv:2606.11949v1 Announce Type: new Abstract: We present an online monitoring system for distributional shift in deployed safety classifiers, using calibrated sequential statistics to detect when a classifier has moved out of distribution. Upon detection, a conformal abstention layer adapts decision thresholds to recover a target error rate epsilon=0.1. In a pre-registered factorial evaluation (4 classifiers x 5 shift conditions x 20 seeds x 2 window sizes, 800 cells), the system achieves 86.6% valid detection (693/800, 95% CI [84.1%, 88.8%]) with mean latency of 39.5 steps. Detection holds across three ground-truth regimes: synthetic onset (86.6%), real temporal jailbreaks (85%, 17/20), and GCG adversarial attacks. Weighted conformal prediction recovers up to 39 pp of lost coverage for DeBERTa (ESS=46/300) but collapses for all other classifiers (ESS~300): logistic density ratio estimation achieves perfect source/target separability in high-dimensional embedding spaces, clipping all importance weights to the floor. DeBERTa shows a gradient from effective correction (paraphrase, ESS=46) to near-total collapse (adversarial suffix, ESS=206). PCA to 32 dimensions breaks the collapse, recovering 33 pp for Llama Guard and 21 pp for ShieldGemma. Variance decomposition reveals classifier (eta^2=0.243), shift type (eta^2=0.237), and their interaction (eta^2=0.185) all contribute substantially to detection latency variance (all p