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01.
arXiv (CS.CV) 2026-06-11

Active Sampling for Ultra-Low-Bit-Rate Video Compression via Conditional Controlled Diffusion

Diffusion models provide a powerful generative prior for perceptual reconstruction at ultra-low bitrates, but effective video compression requires controlling the generative process using highly compact conditioning signals. In this work, we present ActDiff-VC, a diffusion-based video compression framework for the ultra-low-bitrate regime. Our method partitions videos into variable-length segments, transmits keyframes only when needed, and summarizes temporal dynamics using a compact set of tracked point trajectories. Conditioned on these sparse signals, a conditional diffusion decoder synthesizes the remaining frames, enabling perceptually realistic reconstruction under severe rate constraints. To support this design, we introduce two mechanisms: content-adaptive keyframe selection and budget-aware sparse trajectory selection, which together enable compact yet effective conditioning for generative reconstruction. Experiments on the UVG and MCL-JCV benchmarks show that ActDiff-VC achieves up to 64.6\% bitrate reduction at matched NIQE, improves KID by up to 64.6\% and FID by up to 37.7\% at comparable bitrates against strong learned codecs, and delivers favorable perceptual rate–distortion trade-offs relative to learned and diffusion-based baselines in the ultra-low-bitrate regime.

02.
arXiv (quant-ph) 2026-06-19

Stalls and Spequlation: Pipelined Execution for Fault Tolerant Quantum Computation

arXiv:2606.19593v1 Announce Type: new Abstract: Fault-tolerant quantum computation requires the coordinated action of three distinct systems: classical control logic, quantum hardware, and classical error decoders. Current scheduling models treat logical operations as atomic, hiding the fact that these subsystems operate sequentially and spend significant time idle. We present a pipelined execution framework that decomposes each logical operation into its component stages i.e. Control, Execute, and Decode. Building on this, we discuss some speculation strategies that allow successor operations to begin processing before their predecessors have completed decoding. We evaluate our framework on several common benchmarks and show that pipelining with speculation reduces total pipeline steps by 20-40% compared to a no-speculation baseline. The most aggressive strategy consistently outperforms conservative alternatives, even though partial rollback is needed at times, because the per-rollback penalty is small relative to the parallelism gained. We further show that speculation facilitates load balancing by distributing work more evenly across the heterogeneous subsystems of a fault-tolerant quantum computer, converting idle time into useful computation while also saving on execution time.

04.
arXiv (CS.CV) 2026-06-12

LatentLens: Revealing Highly Interpretable Visual Tokens in LLMs

Transforming a large language model (LLM) into a vision-language model (VLM) can be achieved by mapping the visual tokens from a vision encoder into the embedding space of an LLM. Intriguingly, this mapping can be as simple as a shallow MLP transformation. To understand why LLMs can so readily process visual tokens, we need interpretability methods that reveal what is encoded in the visual token representations at every layer of LLM processing. In this work, we introduce LatentLens, a novel approach for mapping latent representations to descriptions in natural language. LatentLens encodes a large text corpus and stores contextualized token representations for each token in that corpus. Visual token representations are then compared to these contextualized representations and the top-nearest neighbor representations serve as descriptions of the visual token. We evaluate this method on 15 different VLMs, showing that commonly used methods, such as LogitLens, substantially underestimate the interpretability of visual tokens. With LatentLens instead, the majority of visual tokens are interpretable across all studied models and all layers. Qualitatively, we show that the descriptions produced by LatentLens are semantically meaningful and provide more fine-grained interpretations for humans compared to individual tokens. More broadly, our findings contribute new evidence on the alignment between vision and language representations and open up new directions for analyzing the latent representations of LLMs.

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

Variational Learning for Insertion-based Generation

arXiv:2606.02133v3 Announce Type: replace-cross Abstract: Non-monotonic sequence generation methods, such as masked diffusion models, provide a flexible alternative to left-to-right autoregressive modeling by allowing tokens to be generated in non-fixed and prescribed orders. Despite their practical advantages, most existing non-monotonic models are order-agnostic and rely on a fixed-length grid, limiting their ability to support variable-length generation and adaptive insertion order. In this work, we introduce a probabilistic framework for learning insertion order in variable-length insertion models. We formalize a bijective correspondence between insertion trajectories and permutations, which enables an exact reparameterization of the data likelihood as a sum over permutations. Building on this result, we propose the Insertion Process (IP), a stochastic generative model that jointly learns where to insert, what to insert, and when to terminate, trained via permutation-based variational inference. Unlike prior fixed-canvas approaches, IP natively supports variable-length generation and learns data-driven preferences over insertion orders. Experiments on goal-conditioned planning and molecular string generation demonstrate that learning insertion order improves both modeling quality and generalization in domains without a canonical left-to-right structure.

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

Latent Action Pretraining Through World Modeling

Vision-Language-Action (VLA) models have gained popularity for learning robotic manipulation tasks that follow language instructions. State-of-the-art VLAs, such as OpenVLA and $\pi_{0}$, were trained on large-scale, manually labeled action datasets collected through teleoperation. More recent approaches, including LAPA and villa-X, introduce latent action representations that enable unsupervised pretraining on unlabeled datasets by modeling abstract visual changes between frames. Although these methods have shown strong results, their large model sizes make deployment in real-world settings challenging. In this work, we propose LAWM, a model-agnostic framework to pretrain imitation learning models in a self-supervised way, by learning latent action representations from unlabeled video data through world modeling. These videos can be sourced from robot recordings or videos of humans performing actions with everyday objects. Our framework is able to transfer learned knowledge across tasks, environments, and embodiments. It outperforms models pretrained with ground-truth robot actions and other similar pretraining methods on the LIBERO benchmark and real-world setup, while being efficient and practical for real-world settings.

07.
bioRxiv (Bioinfo) 2026-06-18

Benchmarking attention-based methods for vision transformers' interpretability in retinal fundus imaging

Deep learning models based on Vision Transformers (ViTs) have shown strong performance in retinal fundus imaging, but their interpretability remains poorly understood. In particular, attention-based attribution methods are widely used to explain ViT predictions, despite limited evaluation of their faithfulness and biological relevance in medical imaging. Here, we systematically benchmark four attention-based interpretability methods for RETFound, a retinal ViT-based foundation model, that we previously fine-tuned to predict 17 retinal vascular phenotypes from UK Biobank fundus images1. We compare raw attention, attention rollout, gradient-weighted attention rollout, and Chefer's hybrid relevance-based method using both qualitative visualisation and quantitative evaluation frameworks. To assess attribution faithfulness, we perform perturbation-based deletion and insertion experiments, quantifying changes in model predictions as highly attended image regions are progressively removed or restored. To evaluate biological specificity, we run structure-aware analyses combining attribution maps with vessel segmentation and artery-vein labels through the Relative ratio of Attention Intensity (RAI) metric. Across models, attribution maps differed substantially depending on the selected interpretability method, highlighting the need for rigorous quantitative evaluation. Among the evaluated approaches, gradient-weighted attention rollout consistently achieved the strongest perturbation performance and produced attribution maps most closely aligned with the anatomical definition of the predicted retinal traits. Furthermore, vessel-type specific models systematically concentrate attention on the corresponding vascular structures despite being trained using only a single scalar value per image as supervision. These findings demonstrate that attention-based attribution methods capture biologically meaningful vascular representations, while also revealing method-dependent variability in attribution behaviour. This work provides a quantitative framework for evaluating interpretability methods in medical imaging with annotated segmentation and contributes toward more transparent and biologically grounded medical AI systems.

08.
arXiv (quant-ph) 2026-06-11

Additivity and chain rules for quantum entropies via multi-index Schatten norms

arXiv:2502.01611v3 Announce Type: replace Abstract: The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched Rényi entropy of quantum channels. For that, we generalize the results of [Devetak, Junge, King, Ruskai, CMP 2006] to multi-index Schatten norms. As an application, we strengthen the additivity statement of [Van Himbeeck and Brown, 2025] thus allowing the analysis of time-adaptive quantum cryptographic protocols. In addition, we establish chain rules for Rényi conditional entropies that are similar to the ones used for the generalized entropy accumulation theorem of [Metger, Fawzi, Sutter, Renner, CMP 2024].

09.
arXiv (CS.LG) 2026-06-11

HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

arXiv:2606.11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space. However, many existing architectures still struggle to represent nonlinear time-dependent systems that involve multi-scale structures, long-range interactions, and stable long-time evolution. In this work, we introduce the Hierarchical Adaptive Multi-scale Neural Operator (HAMNO), a neural-operator architecture that combines local convolutional representations, global spectral operators, and hierarchical encoder-decoder processing. The central component of HAMNO is a data-dependent gating mechanism that adaptively balances local and global information at each spatial location, allowing the model to resolve fine-scale features while preserving long-range dependencies. We further develop a physics-informed extension, PI-HAMNO, based on a multi-objective loss strategy that combines data fitting with strong- and weak-form physics constraints. The strong-form term penalizes the domain-integrated squared PDE residual in physical coordinates, while the weak-form term is constructed by multiplying the governing residual by finite-element test functions and evaluating the resulting element integrals using centroid-based tetrahedral quadrature. The framework is evaluated on non-periodic Allen-Cahn (AC), Cahn-Hilliard (CH), and Swift-Hohenberg (SH) equations defined on cubic domains. Across long-horizon rollout, data-limited training, out-of-distribution initial-condition shifts, and random-seed variations, HAMNO improves predictive accuracy over standard neural-operator baselines, while PI-HAMNO further enhances stability, physical consistency, and data efficiency. The implementation is publicly available at https://github.com/MBamdad/HAMNO .

10.
arXiv (CS.CL) 2026-06-15

Token-Level LLM Collaboration via FusionRoute

Large language models (LLMs) exhibit strengths across diverse domains. However, achieving strong performance across these domains with a single general-purpose model typically requires scaling to sizes that are prohibitively expensive to train and deploy. On the other hand, while smaller domain-specialized models are much more efficient, they struggle to generalize beyond their training distributions. To address this dilemma, we propose FusionRoute, a robust and effective token-level multi-LLM collaboration framework in which a lightweight router simultaneously (i) selects the most suitable expert at each decoding step and (ii) contributes a complementary logit that refines or corrects the selected expert's next-token distribution via logit addition. Unlike existing token-level collaboration methods that rely solely on fixed expert outputs, we provide a theoretical analysis showing that pure expert-only routing is fundamentally limited: unless strong global coverage assumptions hold, it cannot in general realize the optimal decoding policy. By augmenting expert selection with a trainable complementary generator, FusionRoute expands the effective policy class and enables recovery of optimal value functions under mild conditions. Empirically, across both Llama-3 and Gemma-2 families and diverse benchmarks spanning mathematical reasoning, code generation, and instruction following, FusionRoute outperforms both sequence- and token-level collaboration, model merging, and direct fine-tuning, while remaining competitive with domain experts on their respective tasks.

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

Auditing Machine Unlearning: A Systematic Research on Whether Models Truly Forget

arXiv:2606.16110v1 Announce Type: new Abstract: Machine unlearning has been extensively studied in response to growing privacy concerns and regulatory requirements. However, auditing whether unlearning algorithms have truly erased the influence of specific data remains an open challenge. The lack of reliable and practical auditing mechanisms can lead to critical privacy risks, such as residual information leakage. This paper initiates a systematic investigation into whether existing unlearning algorithms can truly forget the designated data. We propose the first practical and general-purpose auditing framework for machine unlearning, inspired by the concept of proof of ignorance. Our framework addresses the key practicality limitations of existing methods by eliminating the need for retraining-from-scratch baselines, avoiding the training of large numbers of shadow models, and requiring no intrusive intervention in the original training process. To evaluate the effectiveness of our framework, we first conduct validation experiments to verify its soundness and completeness. We then perform comprehensive experiments across six datasets and ten representative unlearning methods. The results demonstrate that our framework reliably distinguishes between successful and failed unlearning. In particular, we observe that retraining-based and fine-tuning-based methods can achieve effective unlearning, even when the target data remain in the original dataset. In contrast, de-optimization-based methods fail to achieve true unlearning and instead degrade the model's performance. Fisher/Hessian-based methods also fail to unlearn requested data, even formal certification is provided. Moreover, we show that our framework is robust against fake unlearning attempts and generalizes well to large language models.

12.
arXiv (CS.CL) 2026-06-17

LegalHalluLens: Typed Hallucination Auditing and Calibrated Multi-Agent Debate for Trustworthy Legal AI

AI systems deployed in legal workflows hallucinate at rates that aggregate metrics report at ~52%, but this average conceals where errors concentrate and in which direction they run, leaving compliance officers without an actionable signal for trustworthy deployment. We present LegalHalluLens, an auditing framework with three components: typed hallucination profiles across four legally-motivated claim categories (numeric, temporal, obligation/entitlement, factual) over CUAD (Hendrycks et al., 2021); a Risk Direction Index (RDI) that reduces omission-versus-invention bias to a single deployment-comparable scalar; and a typed debate pipeline calibrated to both magnitudes and directions. Across 510 contracts and 249,252 clause-level instances we measure a within-model gap of approximately 38-40 pp between obligation/numeric and temporal claims that aggregate reporting hides, and show that two systems with matched 52% rates can carry opposite RDIs. The debate pipeline reduces fabricated detections by 45% with per-category gains tracking the diagnosis, matching commercial APIs with a substantially smaller backbone (4B active parameters). Typed profiles and RDI surface failure modes that aggregate metrics hide; we further show these diagnostics serve as calibration inputs for multi-agent debate pipelines, where Skeptic challenges and asymmetric gates targeted at measured failure modes outperform generically-tuned debate. The framework supports direction-aware procurement, accountability, and agent design for legal AI deployed in the wild.

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

Counterexample Guided Learning in the Large using Reasoning Agents

arXiv:2606.11521v1 Announce Type: new Abstract: LLMs and LLM agents should improve when given feedback, but identifying when they are able to do so is difficult: feedback is heterogeneous, domain-specific, and difficult to control. We approach this challenge by asking LLMs to perform regular-expression induction, a classical symbolic learning problem where precise mechanisms for feedback exist in the form of counterexamples. In counterexample-guided learning, a learner (LLM) proposes candidate regular expressions from positive/negative-labeled strings, and the teacher (verifier) returns counterexamples showcasing the difference between the candidate and target languages. We identify novel counterexample-guided refinement strategies that enable effective regex learning, such as regularization and symbolic counterexample clusters. We also explore agentic strategies such as reflection and repair loops. Empirically, we find that verifier feedback substantially improves sample efficiency on challenging regex-induction tasks, reducing the number of labeled examples required and enabling learning of complex target expressions where standard prompting fails. For example, on the hardest task groups, our counterexample-guided framework improves success from 3.2% to 38.1% and from 38.9% to 74.1% on two different regex domains. These results suggest that LLMs can benefit from rich feedback beyond treating it as additional data, opening the door for robust verifier-guided methods for LLM-based program synthesis and formal reasoning.

14.
medRxiv (Medicine) 2026-06-22

Building accessible resources to empower communities: the case of the Lupus Mexican Registry

Motivation: Although SLE data in Latin America is increasing, clinical datasets remain difficult to access and interpret, highlighting the need for accessible tools that support data-driven precision medicine, citizen science, and public health initiatives. Results: We developed a user-friendly platform that enables us to explore LupusRGMX data through interactive queries, report generation, statistical modeling, and comprehensive insights. This resource supports community-oriented research, improves the visibility of underrepresented populations in lupus research, and provides a useful tool to enhance data accessibility. Availability and implementation: Developed in R using Shiny and bslib for interactive visualization and interface design. Available at https://github.com/NeuroGenomicsMX/Lupus_App_2.0 and https://lupusrgmx.liigh.unam.mx/shiny/lupus/

15.
arXiv (math.PR) 2026-06-18

Power Partitions and Hayman Functions

arXiv:2602.18575v3 Announce Type: replace Abstract: We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy–Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{\alpha_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(\beta_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $\alpha_k$ and~$\beta_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

16.
arXiv (CS.LG) 2026-06-12

Deep Learning-based Algebraic Reynolds Stress Closures for RANS Simulations of Turbulent Flows

arXiv:2605.26358v2 Announce Type: replace-cross Abstract: Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the closure problem). Offline-trained machine-learning (ML) closures suffer distribution shift in predictive simulations, while ML methods that bypass the governing equations struggle to generalise from scarce high-fidelity data. We develop a physics-derived deep learning closure model for RANS, the Deep Algebraic Reynolds Stress Model (DARSM), which can be trained on small datasets and accurately generalise across Reynolds numbers, to unseen geometries, and to different flow regimes. A neural network maps flow invariants to empirical parameters in an implicit algebraic Reynolds stress equation, derived from the Reynolds stress transport equations under the weak-equilibrium assumption, imposing physics-based structure on the ML closure. End-to-end optimisation through the governing PDEs and the coupled implicit closure eliminates distribution shift, but both unrolled and implicit automatic differentiation fail on the stiff coupled solver. We derive adjoint equations that exploit the solver's implicit-explicit structure for efficient optimisation. On canonical square-duct and periodic-hill benchmarks, DARSM reduces average test velocity error over baseline RANS by $2$-$4\times$ across Reynolds number, geometries, and flow regimes, with peak case-level reductions of $12\times$. The model trained on attached, anisotropy-dominated flows (square duct) accurately generalises without retraining to separated flows (periodic hills), a regime change in the underlying physics. DARSM also outperforms five established ML methods: offline training, tensor-basis neural networks, field-inversion machine learning, DeepONets, and physics-informed neural networks.

17.
arXiv (quant-ph) 2026-06-11

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data

arXiv:2601.13467v2 Announce Type: replace Abstract: Using the spinless Haldane model, we study the witness-filtered Berry curvature, quantum geometric tensor, and quantum Fisher information on the gapped strata of the parameter space and evaluate them through the Fukui-Hatsugai-Suzuki discretization. The filtered quantities isolate the part of the geometric response carried by sublattice coherence: they suppress contributions from regions where the occupied Bloch state is locally A/B-separable and emphasize regions where curvature and coherence coexist. We derive exact lattice identities, reconstruction formulas for the curvature-weighted coherence, and bounds relating the filtered quantum geometric tensor and quantum Fisher information to single-particle mode entanglement. Across the gap-closing stratum, the quantized response changes admit a natural description in terms of Hecke modifications. We elicit a corresponding Langlands viewpoint – not as a full correspondence, but as an organizational principle and as the mathematical shadow of these physical geometric constructions.

18.
arXiv (CS.CV) 2026-06-11

PIGEON: VLM-Driven Object Navigation via Points of Interest Selection

Object navigation in unseen indoor environments requires agents to perform semantic search under partial observability. Vision-language models (VLMs) provide strong semantic-spatial priors for this task, but how to interface them with robot navigation remains challenging: dense VLM inference is expensive, while abstracting environments into symbolic memories often separates high-level reasoning from the raw visual evidence that supports it. We propose we propose PIGEON (Point of Interest Guided Exploration for Object Navigation), a VLM-driven framework that formulates object navigation as raw-observation-grounded sparse decision problem. PIGEON introduces Points of Interest (PoIs) as sparse visual decision units that couple geometrically executable waypoints with raw egocentric observations. Rather than using VLMs as dense controllers or restricting them to frontier ranking, PIGEON enables VLMs to select among task-critical PoIs, including exploration frontiers, suspected target objects, traversable stairs, and floor-level summaries, while low-level planners execute continuous motion between them. This PoI interface further makes high-level navigation decisions verifiable, allowing us to develop an RLVR pipeline that improves local VLMs without manual Chain-of-Thought annotations. Extensive experiments on Habitat ObjectNav benchmarks show that PIGEON achieves state-of-the-art zero-shot performance, scales consistently with foundation model capacity, and transfers to Active Embodied Question Answering with only prompt modifications. Real-world deployments on physical robots further demonstrate its robustness and efficiency.

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

LEAP: Layer-skipping Efficiency via Adaptive Progression for Vision Transformer Distillation

Vision Foundation Models (VFMs) with Vision Transformer (ViT) backbones, such as DINOv2, have become essential for downstream tasks like object recognition and semantic segmentation. The immense computational requirements of backbones often necessitate distillation into smaller architectures for edge deployment. Feature-based knowledge distillation (KD) often suffers from the teacher-student gap; the student struggles to imitate teacher's complex feature map due to its limited capacity. To mitigate this bottleneck, we propose LEAP: Layer-skipping Efficiency via Adaptive Progression, a training curriculum for ViT feature-based knowledge distillation. By utilizing the teacher's intermediate feature maps as a sequence of progressively more difficult targets, our curriculum allows the student to build a foundational representation before tackling higher-level abstractions. Our results demonstrate that this paradigm significantly accelerates convergence through adaptive difficulty selection across various student model sizes and dataset scales. With our curriculum, the LEAP-distilled ViT-S achieves 90.1% accuracy on ImageNet-100, a +12.24% improvement compared with baseline. On ImageNet-1K, LEAP achieves +3.84% and +7.75% improvement for the instance retrieval task on the Oxford and Paris datasets, respectively. Furthermore, the curriculum enables 25.1% savings in training FLOPs and 21% savings in training time on ImageNet-100 by implementing early-stopping for teacher inference during the initial stages of training. Code is available at https://github.com/KevinZ0217/LEAP

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

Simplex-Constrained Sparse Bagging: Transitioning from Uniform Priors to Sparse Posteriors in Ensemble Learning

arXiv:2606.13589v1 Announce Type: new Abstract: We present Simplex-Constrained Sparse Bagging (SCSB), a mathematically rigorous framework for post-training compression and probability calibration of bootstrap-based bagging ensembles. Standard bagging ensembles (such as Random Forests, Bagged SVMs, and Bagged Neural Networks) assign uniform voting power to all constituent estimators. However, this naive uniform prior ignores the varying local competence of base estimators and contributes to model overconfidence. We formulate ensemble pruning and calibration as a joint optimization problem over the probability simplex by minimizing the Out-Of-Bag (OOB) loss. To induce sparsity, we address the theoretical "L1-simplex paradox" – the mathematical reality that the L1 norm is constant on the simplex and fails to prune – by introducing a concave quadratic penalty. SCSB is model-agnostic and achieves up to 96% ensemble compression, yielding linear inference speedups and superior probability calibration (lowered Expected Calibration Error) while preserving or enhancing generalization accuracy.

21.
arXiv (CS.LG) 2026-06-12

Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiability

arXiv:2606.12658v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue – which determines tumour kill and off-target toxicity – is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth – a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.

22.
arXiv (CS.LG) 2026-06-16

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

arXiv:2606.16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy, measured in the $W^{1,\infty}$-norm, by a fixed-size neural network using the Elementary Universal Activation Function ($\mathrm{EUAF}$). To extend this result to $W^{s,\infty}((a,b)^d)$ for $s\in\mathbb{N}$, we introduce a smooth activation $\mathrm{DUAF}_{\infty}$ from the family of Differentiable Universal Activation Functions ($\mathrm{DUAF}_n$). We prove that any function in $W^{s,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy in the $W^{s-1,\infty}$-norm by a fixed-size $\mathrm{DUAF}_{\infty}$-activated network. We further construct sigmoidal variants $\widetilde{\mathrm{DUAF}}_n$ and show that, for every $1\leq s\leq n$, fixed-size $\widetilde{\mathrm{DUAF}}_n$-activated networks still approximate any $f\in W^{s,\infty}((a,b)^d)$ with arbitrary accuracy in the $W^{s-1,\infty}$-norm. In all these results, the width and depth bounds are computed explicitly, and the proposed activations are elementary.

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

Spatial Priors via Space Filling Curves for Small and Limited Data Vision Transformers

Though Vision Transformers (ViTs) have become the dominant backbone in many computer vision tasks, due to permutation equivariance, their attention mechanism lacks explicit spatial inductive biases. This become particularly important in two settings: when model capacity is small or training data is limited. Inspired by the attention masking strategies in Linear Transformers and the scanning patterns of Vision SSMs, we introduce VIOLIN, a lightweight masked attention mechanism that encodes spatial structure within attention via Space Filling Curves (SFCs) with less than 0.0015% extra parameters and negligible computational overhead. VIOLIN scans the image using multiple SFCs to construct curve-specific decay masks, which are then combined and multiplied with the attention matrix. Across a wide range of evaluations, VIOLIN consistently improves performance. In limited data regimes such as fine-tuning on VTAB-1K, it boosts accuracy across all task groups and by up to 8.7% on the tasks where spatial information is essential. It can be combined with parameter-efficient fine-tuning methods such as LoRA to further increase the performance. Beyond fine-tuning, VIOLIN improves various small scale ViT architectures (e.g., DeiT, DINO) during pretraining on ImageNet-1K. Additionally, on pixel-level CIFAR-100 training, a task that is highly dependent on location information, VIOLIN increases accuracy by up to 7.2%. Overall, VIOLIN provides a computationally efficient yet effective way to inject spatial inductive bias into ViTs, especially benefiting small models and limited data settings.

24.
arXiv (CS.CV) 2026-06-18

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

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

25.
arXiv (CS.LG) 2026-06-18

SCOPE-FL: A Strategy-proof Chain-based Optimal pareto efficient Federated Learning System

arXiv:2606.18384v1 Announce Type: new Abstract: Hierarchical Federated Learning (HFL) enables scalable collaborative model training across distributed devices while preserving data privacy. However, existing HFL client selection mechanisms suffer from a fundamental strategic inefficiency. By prioritizing stability over Pareto efficiency (PE), they produce suboptimal resource allocations, and without strategy proofness (SP), participants are incentivized to misrepresent their true preferences, both failures degrading system overall welfare in the Pareto sense in practice. To address it, we propose SCOPE-FL (Strategy-proof Chain-based Optimal pareto efficient Federated Learning), a synchronous HFL framework that formulates client selection as a two-sided school choice problem solved through the Top Trading Cycle (TTC) algorithm that simultaneously guarantees PE and SP. For reward distribution, SCOPE-FL employs a scalable Shapley value approximation based on One-Round Reconstruction (OR), ensuring compensation proportional to each client's contribution. The entire mechanism executes via blockchain smart contracts, providing the tamper-proof environment required for the SP guarantees to hold in practice. A comprehensive evaluation on MNIST, Fashion-MNIST, and CIFAR-10 demonstrates that SCOPE-FL outperforms state-of-the-art approaches, including DA, IAS, and other methods across model accuracy, convergence rate, and reward efficiency, while achieving communication latency comparable to DA and blockchain overhead significantly lower than DA at scale.