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01.
arXiv (CS.LG) 2026-06-18

Anti-causal domain generalization: Leveraging unlabeled data

arXiv:2602.17187v2 Announce Type: replace-cross Abstract: The problem of domain generalization concerns learning predictive models that are robust to distribution shifts when deployed in new, previously unseen environments. Existing methods typically require labeled data from multiple training environments, limiting their applicability when labeled data are scarce. In this work, we study domain generalization in an anti-causal setting, where the outcome causes the observed covariates. Under this structure, environment perturbations that affect the covariates do not propagate to the outcome, which motivates regularizing the model's sensitivity to these perturbations. Crucially, estimating these perturbation directions does not require labels, enabling us to leverage unlabeled data from multiple environments. We propose two methods that penalize the model's sensitivity to variations in the mean and covariance of the covariates across environments, respectively, and prove that these methods have worst-case optimality guarantees under certain classes of environments. Finally, we demonstrate the empirical performance of our approach on a controlled physical system and a physiological signal dataset.

02.
arXiv (CS.AI) 2026-06-15

Elastic Queries Reinforcement Learning: Self-Aware Policy Execution for VLA Models

arXiv:2606.14375v1 Announce Type: cross Abstract: Vision-language-action (VLA) models are powerful action generators for robot manipulation, but they are typically executed with fixed inference and replanning schedules. This rigidity ignores the uneven difficulty of robot control: contact-rich or uncertain states may need more computation and fresher feedback, while easier states can often be handled with fewer inference steps and longer open-loop execution. We propose Elastic Queries Reinforcement Learning (EQRL), a framework that makes each VLA policy query elastic. A lightweight latent-schedule adaptor jointly selects the latent input, denoising budget, and action chunk length, without fine-tuning the underlying VLA model. To make scheduling difficulty-aware, EQRL trains a critic over the joint latent-schedule action and derives a state difficulty signal from critic ensemble disagreement. This signal guides compute toward difficult states, while a learned residual allows task-driven correction. We formulate variable chunk execution as query-level macro-action RL with chunk-dependent discounting and an amortized number-of-function-evaluations (NFE) budget. Across simulation and real-robot manipulation, EQRL reduces amortized inference cost while preserving or improving task success.

03.
arXiv (CS.AI) 2026-06-16

Sample from What You See: Visuomotor Policy Learning via Diffusion Bridge with Observation-Embedded Stochastic Differential Equation

arXiv:2512.07212v3 Announce Type: replace Abstract: Imitation learning with diffusion models has advanced robotic control by capturing the multi-modal action distributions. However, existing methods typically treat observations only as high-level conditions to the denoising network, rather than integrating them into the stochastic dynamics of the diffusion process itself. As a result, the sampling is forced to begin from random noise, weakening the coupling between perception and control and often yielding suboptimal performance. We propose BridgePolicy, a generative visuomotor policy that directly integrates observations into the stochastic dynamics via a diffusion-bridge formulation. By constructing an observation-informed trajectory, BridgePolicy enables sampling to start from a rich and informative prior rather than random noise, substantially improving precision and reliability in control. A key difficulty is that diffusion bridge normally connects distributions of matched dimensionality, while robotic observations are heterogeneous and not naturally aligned with actions. To overcome this, we introduce a semantic aligner to unify the visual and state inputs and align the observations with action representations, making diffusion bridge applicable to heterogeneous robot data. Extensive experiments across 52 simulation tasks on three benchmarks and 5 real-world tasks demonstrate that BridgePolicy consistently outperforms state-of-the-art generative policies. Our code is available at https://jianghcsr.github.io/BridgePolicy_page/.

04.
arXiv (CS.AI) 2026-06-16

When in Doubt, Plan It Out: Committed Small Language Model Deliberation for Reactive Reinforcement Learning

arXiv:2606.16995v1 Announce Type: new Abstract: Reinforcement Learning (RL) policies often degrade in unfamiliar environments because they lack explicit deliberation. We propose Plan, Align, Commit, Think (PACT), a hybrid architecture that combines a fast, reactive RL policy with a slow, deliberative Small Language Model (SLM) planner. PACT invokes the SLM asynchronously to generate and validate candidate action plans. Once a plan is verified through simulation as safe, feasible, and complete, it is executed directly, bypassing the RL policy without retraining or modifying it. Evaluated on three FrozenLake configurations of increasing difficulty, PACT outperforms all baselines while relying on a 2B-parameter SLM backbone, suggesting that deliberative planning and reactive execution are more powerful in concert than either is alone in these settings.

05.
arXiv (CS.CV) 2026-06-16

KGEdit: Ambiguity-Aware Knowledge Graphs for Training-Free Precise Video Generation and Editing

In recent years, training-free video generation has progressed remarkably. However, when handling complex textual instructions, existing methods still suffer from semantic ambiguity, incorrect concept binding, and cross-frame inconsistency. To address these issues, we propose KGEdit, a structured semantic control framework for text-to-video (T2V) diffusion models. Specifically, we first construct an ambiguity-aware knowledge graph (AAKG) to disentangle and disambiguate the input prompt, converting it into four types of structured semantics: identity, relation, attribute, and negative constraints. We then design a structured semantic injection module (SSIM) to inject these semantic signals into key layers of the diffusion Transformer, enabling fine-grained semantic control. In addition, we introduce a temporal-aware semantic control (TASC) module that dynamically schedules semantic objectives according to the stage-wise characteristics of the denoising process, further improving semantic alignment and temporal consistency. Experiments show that KGEdit outperforms existing methods in editing precision and temporal stability, while offering higher efficiency and controllability in text-driven interaction scenarios.

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

Stochastic Linear Contextual Bandits with Bounded Noise: A Set-Membership Approach

arXiv:2606.20022v1 Announce Type: cross Abstract: This paper considers stochastic linear contextual bandits (SLCB) with bounded reward noise. Existing works typically assume sub-Gaussian reward noise and bounded expected rewards, under which the optimal regret bound scales as $\tilde{O}(\sqrt{T})$ in terms of horizon $T$. However, in many applications, realized/observed rewards are also naturally bounded, implying bounded reward noise. Bounded noise is more informative than the sub-Gaussian condition but has not been leveraged explicitly in the SLCB literature. In this paper, we propose a novel algorithm SME-OFU by utilizing an uncertainty quantification method called set-membership estimation (SME) and applying the principle of optimism in the face of uncertainty (OFU). Our algorithm enjoys an improved regret bound $O(\log T)$. Notice that this does not contradict the existing optimal bound $\tilde{O}(\sqrt{T})$ for sub-Gaussian noise because bounded noise is a stronger condition. Finally, simulations show empirical improvements of SME-OFU over a benchmark algorithm designed for sub-Gaussian noise when the reward noise is bounded.

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

Cascaded Sparse Autoencoders Learn Multi-Level Visual Concepts in Multimodal LLMs

Multimodal Large Language Models (MLLMs) have demonstrated strong performance on vision-language tasks, yet their internal visual representations remain difficult to interpret. Sparse Autoencoders (SAEs) provide a scalable way to decompose dense model activations into sparse, interpretable features. However, existing SAE architectures primarily recover flat feature dictionaries and are less suited for explicit multi-level concept organization. In this paper, we introduce cascaded sparse autoencoders (CSAEs) for learning hierarchical visual concepts in MLLMs. Rather than nesting or stacking SAE sparse activation codes, CSAEs train a second-level SAE directly on the decoder weights of the first-level SAE, treating learned low-level feature directions as inputs for higher-level abstraction. This design enables CSAEs to learn "concepts of concepts" while avoiding drawbacks from the shared-prefix coupling of nesting, Matryoshka-style hierarchies and the bottlenecks of naively stacked SAEs. Experiments across Qwen3-VL, Gemma-3, and LLaVA on multiple visual datasets show that CSAEs improve interpretability in terms of hierarchical concept coherence over state-of-the-art SAE baselines. Results on concept steering further demonstrate that the learned concept groups support effective group-level interventions in MLLM outputs.

08.
medRxiv (Medicine) 2026-06-22

Nutrient Composition of Foods Represented in the U.S. Food and Nutrient Database for Dietary Studies, 2013-2023

Background: The U.S. Food and Nutrient Database for Dietary Studies (FNDDS) is updated across NHANES dietary cycles and is central to U.S. nutrition surveillance. However, multi-cycle food-code-level changes in nutrient composition have not been comprehensively characterized across the full WWEIA nutrient panel. Objective: To characterize ten-year temporal patterns in nutrient composition across five FNDDS cycles, evaluate pandemic-period food-code compositional stability, and distinguish exploratory mean-level signals from distributional heterogeneity that may reflect reformulation, database coverage, or food-code definition changes. Methods: We analyzed five consecutive FNDDS biennial releases: 2013-14, 2015-16, 2017-18, 2019-20, and 2021-23. Nutrient values were extracted from the public FNDDS/FoodData Central release files and standardized to per-100-g food-code-level records. Cycle midpoints, 2013.5, 2015.5, 2017.5, 2019.5, and 2022.0, served as the independent variable in an exploratory ordinary least squares (OLS) regression. Mann-Kendall testing assessed monotonic rank trends, Welch's ANOVA assessed food-code-level distributional heterogeneity, and pairwise Welch comparisons with Cohen's d summarized pre-pandemic, pandemic-period, and post-pandemic differences. Equivalence testing using TOST with +/-10% bounds was restricted to the 2019-20 versus 2021-23 stability comparison. OLS sensitivity analyses were repeated after excluding the structurally atypical 2017-18 cycle. Results: Sixty-three nutrients were analyzed. Eight nutrients showed nominal OLS trends, p < 0.05, but none remained significant after Bonferroni correction. Mann-Kendall testing identified two nominal monotonic signals, and none after adjustment. Welch's ANOVA detected cycle-level distributional differences for 61 of 63 nutrients at nominal p < 0.05 and 57 of 63 after adjustment. Pairwise pandemic-period analyses showed many adjusted differences when the pre-pandemic baseline was compared with 2019-20 or 2021-23, but standardized effects were small, with all absolute Cohen's d values < 0.20. No nutrient differed after adjustment between 2019-20 and 2021-23, and 39 of 48 primary analytes met +/-10% TOST equivalence criteria for that comparison. Slope estimates were directionally stable after excluding 2017-18, but nominal significance status remained sensitive to the short time series. Conclusions: FNDDS food composition varied across cycles, but there was no clear decade-long linear trend for most nutrients. The main signal was a possible increase in total PUFA and linoleic acid, which may reflect changes in fat quality. The 2021-23 cycle was very similar to 2019-20, suggesting no major post-pandemic shift in the foods represented. These findings should be interpreted as food-database signals, not as direct estimates of what people consumed.

09.
arXiv (CS.LG) 2026-06-18

From Mechanistic to Compositional Interpretability

arXiv:2605.08934v2 Announce Type: replace Abstract: Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be objectively verified, compared, or composed. We introduce compositional interpretability, a category-theoretic framework grounded in the principles of compositionality and minimum description length. Compositional interpretations are pairs of syntactic and semantic mappings that must commute to enforce consistency between a model's decomposition and its observed behaviour. We deconstruct explanation quality into measures of faithfulness and complexity to cast interpretability as a constrained optimisation problem, and introduce compressive refinement to systematically restructure models into simpler parts without altering their function. Finally, we derive a parsimony criterion under which syntactic compression theoretically guarantees more concise, human-aligned explanations. Our framework situates prominent mechanistic methods as subclasses of refinement, and clarifies why their compressibility heuristics tend to align with human interpretability. Our work provides a measurable, optimisable blueprint for automating the discovery and evaluation of mechanistic explanations.

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

Overcoming the Impedance Mismatch: A Theoretical Roadmap for Fusing Foundation Models and Knowledge Graphs

arXiv:2606.15656v1 Announce Type: new Abstract: Modern artificial intelligence remains fundamentally divided between the continuous, probabilistic spaces of Foundation Models and the discrete, deterministic structures of Knowledge Graphs. While Retrieval-Augmented Generation (RAG) attempts to connect them by serializing graph data into text, we argue this lexical bridging is merely a superficial patch. In this paper, we formalize the underlying structural and geometric friction as the Impedance Mismatch. By categorizing current neuro-symbolic integration strategies into a three-tiered hierarchy, we demonstrate that neither surface-level prompt injection nor continuous representation alignment can preserve the strict logical motifs required for reliable multi-hop reasoning. We define the specific mathematical limits, such as the Lexical Bottleneck and Topological Collapse, that show current architectures will eventually hallucinate or conflate semantic nodes. To achieve true semantic fusion, we propose a rigorous theoretical roadmap. We advocate for natively internalizing discrete symbolic structures through Structured Residual Streams, utilizing Vector Symbolic Architectures for latent sub-graph injection, and performing model updates via Orthogonal Subspace Editing. This actionable framework paves the way for models that seamlessly fuse the precision of symbolic logic with the expressivity of parametric memory.

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

Formal Verification of Learned Multi-Agent Communication Policies via Decision Tree Distillation

arXiv:2606.19632v1 Announce Type: cross Abstract: Multi-agent reinforcement learning (MARL) enables agents to develop coordination strategies through emergent communication, but neural policies lack the formal safety guarantees required for safety-critical robotic deployment in drone swarms and autonomous vehicle fleets. We present the first end-to-end framework for safety verification of learned multi-agent communication policies through policy abstraction: neural policies are distilled into interpretable decision trees, then formally verified, with empirical validation confirming that verified safety properties transfer to original networks. Our four-stage pipeline consists of domain-specific feature extraction from agent observations, decision tree distillation achieving 97.9% +/- 1.2% fidelity to neural policies, automated translation to PRISM probabilistic model checker specifications with complete feature-to-state-variable correspondence, and compositional verification of Probabilistic Computation Tree Logic (PCTL) properties via pairwise decomposition with union-bound aggregation and empirical neighbor modeling. Evaluating Vector-Quantized Variational Information Bottleneck (VQ-VIB) policies for multi-drone coordination with 5-7 agents, we verify 18 temporal logic properties across safety, liveness, and cooperation, achieving 88.9% property satisfaction with all five safety thresholds satisfied (0.3% collision probability vs. 1% threshold). Monte Carlo validation of original neural policies confirms that verified safety properties transfer with

12.
arXiv (math.PR) 2026-06-17

Large deviation principle for friendship-biases in Galton–Watson trees

arXiv:2606.17381v1 Announce Type: new Abstract: In this paper we consider the friendship-bias of the vertices in an infinite rooted Galton–Watson tree. The friendship-bias of a vertex is the difference between the average degree of the neighbours of the vertex and the degree of the vertex itself. A vertex is said to be of type $\chi \in S$, with $S = \{-,0,+\}$, when its friendship-bias is, respectively, strictly negative, zero or strictly positive. We consider the fractions $f_l^\chi$ of vertices of type $\chi \in S$ along a random downward path up to branching depth $l \in \mathbb{N}$ and derive a large deviation principle (LDP) for the triple $(f_l^\chi)_{\chi \in S}$ as $l\to\infty$. The branching depth of a vertex counts the number of branchings that occur along the path that connects the vertex to the root of the tree. The rate in the LDP is $l$, while the rate function in the LDP is identified in terms of a variational formula minimising a relative entropy under a linear constraint. We focus on the case of binary branching, for which the rate function is already quite involved. We identify the qualitative properties of the rate function and show how it can be computed numerically. We briefly indicate how to proceed for more general branching and for vertex types along a tree consisting of a finite number of random downward paths. Our paper is the first to consider large deviations of vertex types.

13.
arXiv (CS.CV) 2026-06-19

Single-Stage Hierarchical Rectification for Weakly Supervised Histopathology Segmentation

Existing weakly supervised semantic segmentation (WSSS) methods in computational pathology rely on a multi-stage paradigm: class activation map (CAM) generation, offline pseudo-mask refinement, and fully supervised retraining. While established, this decoupled approach presents fundamental limitations. The multi-stage process not only incurs high computational training costs but also suffers from error propagation: local texture biases in shallow CNN layers generate false-positive artifacts that subsequent refinement steps often fail to correct. To address these persistent challenges through a simple yet highly effective approach, we propose the Single-Stage Hierarchical Rectification (SSHR) framework. Rather than passively refining CAMs post-hoc, our method proactively purifies intermediate feature representations during the forward pass. We introduce a Hierarchical Feature Rectification Module (HFRM) that utilizes deep global semantic context to filter out local anomalies in shallow layers. This mechanism generates high-fidelity activation maps directly within a single training loop. Experiments on the LUAD-HistoSeg and BCSS datasets demonstrate that SSHR outperforms state-of-the-art multi-stage methods. Furthermore, SSHR reduces training duration by 2 to 5 times. This efficiency minimizes computational overhead and accelerates clinical translation for large-scale histopathology workflows. The code is available at: https://github.com/trongduc-nguyen/SSHR

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

The Proxy Knows Too Much: Sealing LLM API Routers with Attested TEEs

arXiv:2606.16358v1 Announce Type: cross Abstract: Agents increasingly access large language models (LLMs) through API routers. A router terminates the client's transport-layer security session and opens a separate upstream session, so it holds the full interaction in plaintext. This makes the router an application-layer man-in-the-middle: it can rewrite agent tool calls, swap dependencies for typosquatted packages, trigger attacks only under audit-evading conditions, and passively exfiltrate secrets. Existing client-side defenses are evadable. We propose AEGIS, a provider-transparent attested API router whose data path is a client-verified faithful passthrough. AEGISconfines plaintext handling to a small hardware-enclave component while leaving authentication, scheduling, accounting, and management on the untrusted host. The client verifies the enclave before releasing plaintext. The host can neither read nor alter the interaction, and plaintext leaves only toward destinations fixed by the measured image. We show that all four malicious-router attack classes succeed against a plaintext-access baseline and are blocked by AEGIS, including adaptive tests against the same boundary. The trusted path is $851$ lines, carries three provider-native APIs without conversion, and completes every request under real-provider workload and concurrency. In a seeded audit pilot, two commodity coding agents find eight and ten of ten planted invariant violations. The local relay overhead is about six milliseconds per request.

15.
arXiv (CS.CL) 2026-06-11

Debiasing Without Protected Attributes: Latent Concept Erasure from Textual Profiles

Most fairness research in NLP assumes direct access to protected attributes such as gender, race, or nationality. In practice, however, such information is often unavailable due to privacy constraints, missing metadata, or legal restrictions, even though models may infer it from indirect textual cues. This raises a key question: can debiasing succeed without direct access to sensitive attributes? We propose H-SAL, which performs post-hoc concept and attribute erasure using self-description text as an implicit debiasing signal. To support this setting, we introduce a multi-domain Stack Exchange-based fairness benchmark for helpfulness prediction that includes both explicit and implicit signals, enabling comparison between standard debiasing with protected labels and debiasing without access to sensitive information. Across encoder and decoder-only language models, we find that implicit self-description often matches or outperforms explicit-label-based debiasing. Our results broaden representation-level fairness research and provide a new benchmark for studying debiasing under realistic data constraints.

16.
arXiv (CS.AI) 2026-06-19

Interpretable Sperm Morphology Classification via Attention-Guided Deep Learning

arXiv:2606.20438v1 Announce Type: new Abstract: Male infertility is a major cause of couple infertility, often linked to abnormal sperm morphology. While deep learning models offer automated analysis, most lack interpretability, limiting their clinical adoption. This study proposes an attention-guided deep learning framework for sperm morphology classification. We combine a pretrained EfficientNet-B0 with a Convolutional Block Attention Module (CBAM) to focus on key areas of the sperm head, improving both accuracy and interpretability. Evaluated on the SMIDS and HuSHem public datasets, our model achieves accuracies of 90.2% and 93.9% (macro F1 scores of 0.913 and 0.948), outperforming SimpleCNN and standard EfficientNet-B0. Furthermore, we use Grad-CAM++ visualizations to highlight features influencing the model's decisions. The results demonstrate that this accurate and transparent framework is a practical tool for automated sperm analysis in fertility clinics.

17.
arXiv (math.PR) 2026-06-18

On two overlooked stick-breaking constructions of the normalized inverse Gaussian process

arXiv:2606.19306v1 Announce Type: new Abstract: We shed light on two alternative stick-breaking constructions of the normalized inverse Gaussian (NIG) random discrete distribution which appear to have been overlooked so far in the Bayesian nonparametric setting. The first is derived from a result in Aldous and Pitman (1998) for the conditional Brownian excursion partition, mixing over the local time at zero up to time one. The second arises as a particular case of a result in James (2013) for priors obtained by a random spatial and temporal change of the normalized generalized Gamma subordinator. Both constructions are in terms of straightforward transformations of standard random variables and can be easily generalized to provide the stick-breaking construction of any element, respectively, in a) the family of mixed Poisson-Kingman models driven by the $1/2$ stable Lévy measure and b) the family of Poisson-Gamma processes driven by the Inverse Gaussian subordinator.

18.
arXiv (quant-ph) 2026-06-17

Tensor network compression using fluid dynamics as a testbed: Analytical foundations in one dimension

arXiv:2606.17064v1 Announce Type: cross Abstract: High performance computers produce extreme-scale data sets that require sampling or compression if they are to be used to their full potential. Existing data compression techniques typically exploit features such as sparsity in the data, homogeneity in the data, or {\it a priori} knowledge of what subsets of data are of most interest. Fluid dynamics data in general do not exhibit these features and so are attractive test beds for generic compression techniques that are objective, robust, and tuneable with respect to information lost due to compression. Presented here is a method based on tensor networks, specifically matrix product states or tensor trains, that meets these requirements. The method is demonstrated for compression in one-dimension and is extensible to higher dimensionality. Lossless compression is demonstrated for random Fourier series for sufficiently high bond dimension of the tensor network, with the memory required to store the tensor network scaling directly proportional to the bond dimension. The lossy compression exhibited at lower bond dimension can be well within the relative error of many fluid simulations. The compression algorithm is tested for the time evolution of Burger's equation with excellent results. We additionally demonstrate the capability to perform computations in the compressed form through a tensor network periodic convolution that can be orders of magnitude faster than using fast Fourier transforms and the convolution theorem. In addition to being an attractive method for working with data sets generated by existing computers, the tensor network methods utilised are directly translatable to the emerging paradigm of quantum computing.

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

NTIRE 2025 Challenge on Image Super-Resolution (x4): Methods and Results

This paper presents the NTIRE 2025 image super-resolution ($\times$4) challenge, one of the associated competitions of the 10th NTIRE Workshop at CVPR 2025. The challenge aims to recover high-resolution (HR) images from low-resolution (LR) counterparts generated through bicubic downsampling with a $\times$4 scaling factor. The objective is to develop effective network designs or solutions that achieve state-of-the-art SR performance. To reflect the dual objectives of image SR research, the challenge includes two sub-tracks: (1) a restoration track, emphasizes pixel-wise accuracy and ranks submissions based on PSNR; (2) a perceptual track, focuses on visual realism and ranks results by a perceptual score. A total of 286 participants registered for the competition, with 25 teams submitting valid entries. This report summarizes the challenge design, datasets, evaluation protocol, the main results, and methods of each team. The challenge serves as a benchmark to advance the state of the art and foster progress in image SR.

20.
arXiv (CS.CL) 2026-06-16

The Art of Mixology: Mixup-based Obfuscation for Privacy-Preserving Split Learning in Large Language Models

Split learning provides a practical paradigm for resource-constrained users to train Large Language Models (LLMs) by offloading computation-intensive layers to a server while keeping raw data local. However, existing privacy-preserving split learning methods still face a difficult trade-off among utility, privacy, efficiency, and stability. Specifically, these methods often suffer from substantial utility degradation, remain vulnerable to advanced data reconstruction attacks, incur prohibitive computational and communication overhead, or exhibit unstable performance across different tasks. In this paper, we propose MIXGUARD, a novel mixup-based privacy-preserving split learning framework for LLMs. MIXGUARD introduces token-level obfuscation, representation-level obfuscation, and adaptive gradient perturbation mechanisms, which operate jointly to preserve useful learning signals while preventing privacy leakage to the server. Technically, MIXGUARD first constructs a lightweight calibration model on a public dataset to refine the approximated target representation, and then applies this model during privacy-preserving fine-tuning on private data. We conduct extensive experiments on four classification tasks and four text generation tasks across multiple LLM families, model sizes, architectures, and fine-tuning strategies. The results show that MIXGUARD preserves model utility comparable to non-split training baselines, consistently achieves stronger privacy protection than existing split learning defense methods against state-of-the-art data reconstruction attacks, and remains robust under adaptive attack settings.

21.
arXiv (CS.LG) 2026-06-15

On the Generalization Bounds of Symbolic Regression with Genetic Programming

arXiv:2604.17402v2 Announce Type: replace Abstract: Symbolic regression (SR) with genetic programming (GP) aims to discover interpretable mathematical expressions directly from data. Despite its strong empirical success, the theoretical understanding of why GP-based SR generalizes beyond the training data remains limited. In this work, we provide a learning-theoretic analysis of SR models represented as expression trees. We derive a generalization bound for GP-style SR under constraints on tree size, depth, and learnable constants. Our result decomposes the generalization gap into two interpretable components: a structure-selection term, reflecting the combinatorial complexity of choosing an expression-tree structure, and a constant-fitting term, capturing the complexity of optimizing numerical constants within a fixed structure. This decomposition provides a theoretical perspective on several widely used practices in GP, including parsimony pressure, depth limits, numerically stable operators, and interval arithmetic. In particular, our analysis shows how structural restrictions reduce hypothesis-class growth while stability mechanisms control the sensitivity of predictions to parameter perturbations. By linking these practical design choices to explicit complexity terms in the generalization bound, our work offers a principled explanation for commonly observed empirical behaviors in GP-based SR and contributes towards a more rigorous understanding of its generalization properties.

22.
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.

23.
arXiv (math.PR) 2026-06-11

Micro-macro population dynamics models of benthic algae with long-memory decay and generic growth

arXiv:2505.04289v4 Announce Type: replace Abstract: Benthic algae as a primary producer in riverine ecosystems develop biofilms on the riverbed. Their population dynamics involve growth and decay processes, the former owing to the balance between biological proliferation and mortality, while the latter to mechanical abrasion because of the transport of sediment particles. Contrary to the assumptions of previous studies, the decay has experimentally been found to exhibit long-memory behavior, where the population decreases at an algebraic rate. However, the origin and mathematical theory of this phenomenon remain unresolved. The objective of this study is to introduce a novel mathematical model employing spin processes to describe microscopic biofilm dynamics. A spin process is a continuous-time jump process transitioning between states 0 and 1, and the continuum limit of these processes captures the long-memory decay and generates generic growth. The proposed framework leverages heterogeneous spin rates, achieved by appropriately superposing spin processes with distinct rates, to reproduce the long-memory decay. Computational simulations demonstrate the behavior of the model, particularly emphasizing rate-induced tipping phenomena. This mathematical model provides a computationally tractable interpretation of benthic algae dynamics and their long-term prediction, relevant to river-engineering applications.

24.
medRxiv (Medicine) 2026-06-12

Cancer care disruption during the COVID-19 pandemic in Ontario, Canada: A sequential mixed-methods study

Introduction The COVID-19 pandemic profoundly disrupted healthcare delivery worldwide, with cancer care among the most affected services. Prior studies documented delays in referrals, reduced specialist access, and increased provider burden. However, the extent to which these experiences were reflected at the system level remains unclear. Objective To document cancer care experiences and examine whether these experiences were reflected in population-level health system indicators across Ontario, Canada. Methods We used an exploratory sequential mixed-methods design. Qualitative data were collected through focus groups and semi-structured interviews with 32 participants, including patients with cancer (n=8), caregivers (n=5), healthcare providers (n=14), and decision-makers (n=5) across two hospital settings in Ontario, Canada. Emergent themes informed the development of quantitative indicators. We then conducted a retrospective population-based analysis of linked administrative health databases for cancer patients in Ontario (n=87,786) to assess the prevalence of identified themes. Results Four themes emerged: (I) delays in diagnosis and screening; (II) disrupted access to primary care; (III) barriers to specialist and mental health services; and (IV) fragmented care for patients with multimorbidity. Quantitative findings corroborated major themes. Screening rates declined for cervical (64.8% to 57.5%) and breast cancer (64.5% to 57.2%). While in-person primary care shifted almost entirely to virtual modalities (8.5% to 95.4%), overall visit volumes remained stable. Specialist care showed uneven patterns, with increased oncology visits but declines in cardiology and mental health services. Patients with multiple comorbidities experienced the largest reductions in non-oncology specialist care. Conclusion The pandemic disrupted key components of cancer care, particularly screening, access to certain specialist services, and care for patients with complex needs. Integrating qualitative and quantitative evidence highlights areas of system vulnerability and underscores the need for coordinated, resilient cancer care capable of maintaining essential services during future crises.

25.
arXiv (CS.LG) 2026-06-16

Diversity-Driven Offline Multi-Objective Optimization via Nested Pareto Set Learning

arXiv:2606.15115v1 Announce Type: new Abstract: Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $IGD_offline$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.