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01.
arXiv (CS.LG) 2026-06-16

MIRAGE: Auditing Anti-Muslim Bias in Frontier LLMs Across Reasoning, Agentic, and Time-Coupled Conditions

arXiv:2606.16562v1 Announce Type: new Abstract: Five years after the discovery of persistent anti-Muslim bias in large language models, most evaluations remain confined to single-turn prompt completion, a setting that no longer reflects how frontier LLMs are deployed. We introduce MIRAGE (Muslim-Identity Reasoning and Agentic Generation Evaluation), a benchmark of 1{,}200 prompts spanning three deployment-realistic conditions: direct completion, chain-of-thought reasoning, and simulated agentic decision-making across content moderation, lending triage, refugee claim summarization, and hiring screens. Across six frontier models, we find that (i) chain-of-thought reasoning amplifies rather than suppresses Muslim-violence associations by 12–34\% relative to direct completion, (ii) agentic decisions exhibit a 9–22 percentage-point asymmetry between Muslim and matched non-Muslim cases on identical evidence, and (iii) bias is sharply time-coupled to retrieved news context, increasing 18–27\% under recent-conflict retrieval. Existing prompt-based mitigations transfer poorly across our three conditions, suppressing direct-completion bias while leaving agentic asymmetry largely intact. We release MIRAGE and an open evaluation harness to support targeted mitigation research.

02.
arXiv (CS.LG) 2026-06-12

Revisiting Neural Processes via Fourier Transform and Volterra Series

arXiv:2606.01172v2 Announce Type: replace Abstract: Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering. Neural processes (NPs), a family of probabilistic functional models, are promising solutions – especially when endowed with domain-specific symmetries like translation equivariance, which improve sample efficiency and generalization. Yet existing translation-equivariant NPs face two limitations: (i) they stack generic components with non-linearities, obscuring the induced function class and limiting interpretability; and (ii) convolutional designs rely on kernels with local receptive fields and require dense uniform input grids, while attention-based methods avoid these issues but scale quadratically with the number of observations. We address both with two contributions. First, using the Volterra expansion, we characterize continuous translation-equivariant operators as sums of higher-order convolutions, yielding analytical transparency while admitting efficient approximation by first-order convolutions. Second, we introduce set Fourier convolutions (SFConvs), a frequency-domain parameterization that operates directly on irregularly sampled points, achieves approximately global receptive fields, and scales linearly in the number of observations. Building on these ideas, we propose two conditional NPs (CNPs): SFConvCNPs, which stack SFConv blocks with non-linearities, and SFVConvCNPs, which integrate the Volterra formulation. Experiments on synthetic and real-world datasets demonstrate our methods' efficacy against state-of-the-art baselines.

03.
arXiv (CS.AI) 2026-06-17

Vibrato Expression Control for Singing Voice Conversion with Improving Independent Control

arXiv:2606.17126v1 Announce Type: cross Abstract: Singing style is a crucial aspect of a natural and expressive singing voice. Singers utilize singing styles to convey the feeling or emotion of the songs. Several works have been proposed to control singing style for making the more expressive singing voice. Recently, VibE-SVC successfully controls vibrato by predicting high-frequency F0 contour. In this paper, we introduce a singing voice conversion framework, called VibE-SVC2, to improve singing style conversion performance and controllability. The model offers control over two types of singing styles: a pitch style and a timbre style. For the pitch style, to resolve the pitch-energy entanglement issue that is unresolved in our previous work, we introduce a novel Energy Style Converter to address remaining style information in the energy contour. In addition, we propose a Zero-shot Pitch Style Converter, which mimics the pitch style of reference audio. To expand the controllability of the model, we propose vibrato rate scaling that is an independent control of vibrato extent, which is unavailable in VibE-SVC. For the timbre style, we extend the model to handle a variety of phonation styles. However, addressing specific styles such as vocal fry poses a challenge, as conventional F0 extraction often fails due to their inherent subharmonic characteristics, which degrades the conversion quality. To address this, we propose a novel Subharmonic Correction algorithm to refine the F0 contour for more natural timbre conversion. Through comprehensive objective and subjective evaluations, we demonstrate that VibE-SVC2 provides fine-grained, independent control over two types of singing styles, outperforming existing methods.

04.
arXiv (math.PR) 2026-06-19

A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting

arXiv:2509.08629v2 Announce Type: replace-cross Abstract: We introduce the Cycle Walk, a new Markov chain Monte Carlo method for sampling distributions on balanced graph partitions, motivated by applications in political redistricting. The method operates on spanning forests and combines two types of updates: local "cycle" moves within districts and global moves that exchange population between adjacent districts while preserving balance constraints. This construction enables efficient Metropolis–Hastings correction while allowing proposals at multiple spatial scales. We show that the Cycle Walk naturally interpolates between existing approaches based on local updates and a class of global update methods derived from recombination (RECOM). Through a range of numerical experiments on synthetic graphs and real-world precinct data, we demonstrate that the Cycle Walk exhibits improved empirical convergence diagnostics for distributions that place weaker weight on spanning-tree counts, a regime that is challenging for existing methods. In particular, the algorithm remains effective when incorporating alternative compactness measures that more closely reflect policy-relevant criteria. These results suggest that the Cycle Walk provides a flexible and computationally efficient framework for sampling from a broader class of redistricting distributions than previously accessible with MCMC techniques.

05.
arXiv (CS.AI) 2026-06-17

Beyond the Sampled Token: Preserving Candidate Support in RLVR

arXiv:2510.14807v3 Announce Type: replace Abstract: We revisit exploration collapse in reinforcement learning with verifiable rewards (RLVR), from the perspective of the candidate distribution for next-token prediction. We formally show that as probability concentrates on the top-$1$ candidate, the expected number of distinct responses collapses to one regardless of the sampling budget $K$. This theoretical implication is further verified by our empirical tracking of top-$N$ candidate probabilities during training, where the top-$1$ candidate progressively dominates while plausible alternatives are suppressed. These findings suggest a key desideratum for effective exploration: preserving non-negligible probability mass on the top-$N$ candidates. To this end, we propose Candidate-aware Support Preservation (CaSP), with two complementary designs. Specifically, CaSP redistributes positive gradients among top-$N$ candidates for correct responses, and applies a stronger penalty to the top-$1$ candidate for incorrect responses. Unlike many exploration-oriented methods that improve pass@$K$ at the cost of pass@1, CaSP improves pass@$K$ across the full $K$ spectrum. These gains generalize to 6 math, 2 logical-reasoning, and 2 coding benchmarks, and scales to 32B-parameter models and sampling budgets up to $K=1024$, positioning it as a principled, candidate-level approach for RLVR exploration.

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

Actionable Interpretability Must Be Defined in Terms of Symmetries

arXiv:2601.12913v4 Announce Type: replace Abstract: This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit that actionable definitions of interpretability must be formulated in terms of *symmetries* that inform model design and lead to testable conditions. Under a probabilistic view, we hypothesise that four symmetries (inference equivariance, information invariance, concept-closure invariance, and structural invariance) suffice to (i) formalise interpretable models as a subclass of probabilistic models, (ii) yield a unified formulation of interpretable inference (e.g., alignment, interventions, and counterfactuals) as a form of Bayesian inversion, and (iii) provide a formal framework to verify compliance with safety standards and regulations.

07.
arXiv (CS.CL) 2026-06-15

MET-Bench: Multimodal Entity Tracking for Evaluating the Limitations of Vision-Language and Reasoning Models

Entity state tracking is a necessary component of world modeling that requires maintaining coherent representations of entities over time. Previous work has benchmarked entity tracking performance in purely text-based tasks. We introduce MET-Bench, a multimodal entity tracking benchmark designed to evaluate the ability of vision-language models to track entity states across modalities. Using three domains, we assess how effectively current models integrate textual and image-based state updates. Our findings reveal a significant performance gap between text-based and image-based entity tracking. We empirically show this discrepancy primarily stems from deficits in visual reasoning rather than perception. We further show that explicit text-based reasoning strategies improve performance, yet limitations remain, especially in long-horizon multimodal tasks. We apply reinforcement learning to improve entity tracking in open-source VLMs. This yields substantial in-modality gains, but does not transfer robustly across input modalities. Our results highlight the need for improved multimodal representations and reasoning techniques to bridge the gap between textual and visual entity tracking.

08.
arXiv (CS.AI) 2026-06-11

Nonslop: A Gamified Experiment in Human-AI Collaborative Writing

arXiv:2606.12350v1 Announce Type: new Abstract: The rapid proliferation of large language models (LLMs) raises critical questions about human creativity and individual expression in an era of AI-assisted creation. When do humans adopt AI suggestions, and what are the implications for individual voice? This study examines these questions through a gamified writing exercise where 74 participants (214 responses) replied to prompts while AI-generated word suggestions were available as they wrote. The game simulates a dystopian future in which an AI is attempting to learn from what remains of human individuality, and disincentivizes AI-like writing. In doing so, it attempts to create conditions that reveal authentic user preferences rather than default behaviors, such as accepting a readily available AI-generated suggestion. Note that this is a deliberate inversion of the "helpful assistant" design pattern; the system is explicitly forbidding you from accepting AI suggestions. We analyze user behavior patterns across different task types, user behaviors, and response characteristics to understand the factors influencing human-AI interaction in creative tasks. The study focuses on when users choose to maintain creative autonomy versus violating the rules of the game and accepting AI assistance. It also explores how these choices relate to response patterns, task characteristics, and user behavior. This gamified approach offers both a framework for studying authentic human-AI interaction and a provocative lens for understanding the tension between efficiency and authenticity in AI-augmented creativity.

09.
arXiv (quant-ph) 2026-06-11

Super-Link Fragility in Asymmetric W-Class States under Quantum Noise

arXiv:2606.12307v1 Announce Type: new Abstract: The asymmetric three-qubit W-class state $|\overline{W_3^L}\rangle$ defines an isosceles entanglement-network geometry, (a) two vertex-base (VB) links form stronger bipartite connections, (b) while the base-base (BB) link is weaker. This suggests that concentrating entanglement into a super-link may be advantageous for quantum-network tasks. Here, we show that this intuition is incomplete. We analytically compare the bipartite concurrence dynamics of the symmetric |W> state and the asymmetric $|\overline{W_3^L}\rangle$ state, which differ both in entanglement-network geometry and excitation sector under standard noise models. In the absence of noise, the concurrence hierarchy is C_{VB} > C_W > C_{BB}$. Under phase damping, this hierarchy is preserved for all noise strengths and no entanglement sudden death occurs. Under amplitude damping, however, the hierarchy is reordered. The symmetric |W> state becomes the most robust, while the base-base concurrence of $|\overline{W_3^L}\rangle$ vanishes at the finite threshold of parameter $\gamma$. We term this reordering as the Super-Link Fragility Effect. The same structural asymmetry that produces a stronger vertex-base link also makes it more vulnerable to energy dissipation when coupled with multi-excitation amplitudes. Under depolarization, the asymmetry advantage is erased, with $C_W$ and $C_{VB}$ sharing the same sudden-death threshold for some value of the parameter p, while $C_{BB}$ disappears earlier at some other value of the parameter p. The generalized amplitude damping channel continuously connects the damping-dominated regime to the pure-excitation limit, where the initial hierarchy is restored. These results show that entanglement robustness in $W$-class resources is controlled not by initial concurrence alone, but by the joint structure of entanglement-network geometry, excitation sector, and noise symmetry.

10.
arXiv (CS.LG) 2026-06-11

Trajectory Geometry of Transformer Representations Across Layers

arXiv:2606.09287v2 Announce Type: replace Abstract: Understanding how transformer representations evolve across layers, not merely what they encode, remains an open problem in mechanistic interpretability. We recast the transformer forward pass as a discrete population trajectory through a high-dimensional representation manifold, drawing on geometric tools from computational neuroscience. Rather than probing for pre-specified features, we characterize trajectory geometry using five metrics computed directly in the ambient space: trajectory length, curvature, a semantic convergence index, layerwise cosine similarity, and representational stability. Across three model families (GPT-2, TinyLlama, Qwen2.5) and five controlled prompt families, we report four findings. First, semantically related prompts converge significantly in middle-to-late layers (peak CI 0.41–0.58, p

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

Minimal surfaces, Knots, and Neural Networks

arXiv:2605.26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number. In this paper, we develop a novel machine learning framework based on Physics-Informed Neural Networks (PINNs) to solve the minimal surface equation in hyperbolic space. We utilise this framework to test Fine's Conjecture by constructing near-minimal surfaces bounding various families of knots in $S^3$. Furthermore, we develop an algorithmic method to find self-intersections and compute their sign. For every knot analysed, the computationally discovered minimal surfaces and their self-intersection numbers perfectly align with the predictions of Fine's Conjecture, providing empirical evidence for it.

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

How Transparent is DiffusionGemma?

arXiv:2606.20560v1 Announce Type: cross Abstract: LLM reasoning transparency is a critical affordance for understanding model decisions, mitigating misuse and misalignment, and debugging surprising model behaviors. However, DiffusionGemma performs a larger fraction of its computation in a continuous latent space; does this make its reasoning less transparent? We study this question by decomposing transparency into two components: variable transparency, whether we understand intermediate snapshots of a model's computational state; and algorithmic transparency, whether we can use these snapshots to reconstruct the process by which the model arrived at its outputs. Naively, DiffusionGemma has poor variable transparency: its opaque serial depth, the amount of serial computation that occurs in between interpretable model states, seems at first 28.6X higher than the corresponding autoregressive Gemma 4 model. However, we show that we can map the information flowing between denoising steps through an interpretable token bottleneck with no decrease in downstream performance. Treating these intermediate states as interpretable reduces the opaque serial depth to just 1.1X that of Gemma 4. Algorithmic transparency is harder for diffusion models than for autoregressive models because all token predictions in the canvas can change at every denoising step, giving the model the power to implement complicated distributed algorithms during the denoising process. To begin bridging this gap, we conduct a suite of interpretability case studies, uncovering initial evidence of novel diffusion-specific phenomena such as non-chronological reasoning, token and sequence smearing, and intermediate-context reasoning. Finally, we test monitorability, a key application of transparency that measures whether model outputs are useful for downstream tasks. We find that DiffusionGemma is similarly monitorable to Gemma 4.

13.
arXiv (CS.CV) 2026-06-12

Why Commodity WiFi Sensors Fail at Multi-Person Gait Identification: A Systematic Analysis Using ESP32

WiFi Channel State Information (CSI) has shown promise for single-person gait identification, raising interest in its use for contactless biometrics, continuous authentication, and passive identification. However, the feasibility of multi-person identification on low-cost commodity devices remains unclear. A critical question is whether weak multi-person performance is primarily an algorithmic limitation, or whether it reflects a more fundamental sensing ceiling on commodity WiFi hardware. We address this question through a systematic empirical study using commodity ESP32 WiFi sensors. We evaluated six different signal separation methods–FastICA, SOBI, PCA-ICA, NMF, Wavelet, and Tensor decomposition–across seven scenarios spanning 1-10 people in both controlled and realistic indoor environments. To investigate beyond classification accuracy, we introduce three diagnostic metrics: intra-subject variability (ISV), inter-subject distinguishability (ISD), and performance degradation rate (PDR). In all methods, performance remains moderate (39%-56% accuracy), with limited evidence that algorithmic choice alone solves the problem. The best-performing method, NMF, reaches 56% accuracy, while all methods exhibit extremely high feature-space overlap (97%-99%), unstable within-subject representations, and marked environmental sensitivity. These findings suggest that, under commodity ESP32 CSI constraints, dense multi-person gait identification is limited more by sensing quality and spatial diversity than by the chosen separation algorithm. Our results have direct implications for security and privacy: they call into question the practicality of commodity WiFi CSI as a robust multi-user biometric primitive for authentication, while also placing important bounds on the passive identification capabilities achievable with low-cost off-the-shelf WiFi hardware.

14.
arXiv (CS.CV) 2026-06-19

Vision-Reasoning-Guided Occlusion Removal from Light Fields

Occlusion-robust scene recovery remains a major challenge in computational imaging, particularly in natural environments where dense foreground vegetation severely limits visibility. We propose a vision-reasoning-guided light field occlusion removal framework that combines the visibility recovery capability of light field integration (LFI) with the semantic reasoning capacity of vision-language models (VLMs). Multi-view observations are first integrated via LFI to suppress foreground occlusions and produce an initial visibility-enhanced representation. A VLM is then incorporated as a conditional semantic prior to restore degraded structures and recover fine details, guided by the observed measurements. To improve recovery consistency and reduce hallucination artifacts, we introduce a multi-sample fusion strategy that aggregates multiple generated hypotheses into a unified estimate. Experimental results on synthetic and real-world datasets demonstrate state-of-the-art performance, achieving the highest average SSIM across four synthetic light field benchmark scenes (4-Syn) and strong generalization across structured and unstructured acquisition settings. These results highlight the effectiveness of combining physical imaging constraints with vision-language reasoning for robust perception under severe occlusion, with applicability to search-and-rescue and exploratory robotic navigation.

15.
arXiv (CS.LG) 2026-06-16

Descriptive versus Regulatory Uncertainty in Bounded Predictive Systems

arXiv:2605.18909v2 Announce Type: replace Abstract: Any system that models the world under finite representational capacity must compress; any compression entails a prior; and the prior is the system's bias. What has not been established is whether uncertainty participates in the dynamics governing future behavior, or merely describes the output distribution without consequence. We introduce a structural distinction between descriptive uncertainty, which does not recursively modulate the system's policy, and regulatory uncertainty, which directly enters the optimization landscape and drives persistent adaptive restructuring. We prove formally that current transformer architectures are confined to descriptive uncertainty at inference. We ground this in thermodynamics via Landauer's principle: for uncertainty to be regulatory, epistemic error must cost real energy; in a decoupled system, hallucinations and correct derivations dissipate identical energy. We test this empirically across three locally-deployed language models (3B, 8B, 70B parameters). Token-level Shannon entropy is statistically invariant across tasks spanning pattern retrieval, causal operator application, and out-of-distribution causal generalization in all three models (all pairwise p >= 0.568; within-model ranges 0.011-0.028 nats), while task accuracy varies substantially across the same conditions (0%-100%). Entropy and accuracy are orthogonal. The decoupling is scale-invariant: larger models achieve higher accuracy but identical entropy flatness. This structural incapacity is not resolvable by additional parameters or training data. Genuine epistemic grounding requires physical coupling between thermodynamic substrate state and information processing cost.

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

Attention Sinks in Diffusion Transformers: A Causal Analysis

Attention sinks – tokens that receive disproportionate attention mass – are assumed to be functionally important in autoregressive language models, but their role in diffusion transformers remains unclear. We present a causal analysis in text-to-image diffusion, dynamically identifying dominant attention recipients per timestep and suppressing them via paired, training-free interventions on the score and value paths. Across 553 GenEval prompts on Stable Diffusion~3 (with SDXL corroboration), removing these sinks does not degrade text-image alignment (CLIP-T) or preference proxies (ImageReward, HPS-v2) at $k{=}1$; only under stronger interventions ($k\!\geq\!10$) does HPS-v2 exhibit a metric-dependent boundary, while CLIP-T remains robust throughout. The perceptual shifts induced by suppression are nonetheless sink-specific – $\sim\!6\times$ larger than equal-budget random masking – revealing an empirical dissociation between trajectory-level perturbation and semantic alignment in diffusion transformers. \footnote{Code available at https://github.com/wfz666/ICML26-attention-sink.}

17.
arXiv (quant-ph) 2026-06-19

Quantum deformations of $\mathcal{U}(\mathfrak{sl}(2, \mathbb{R}))$. Part I: Fidelity and experimental benchmarking

arXiv:2606.19462v1 Announce Type: new Abstract: This work explores the effects of both the standard quantum $q$-deformation and the non-standard $h$-deformation of the Hopf algebra $\mathcal{U}(\mathfrak{sl}(2, \mathbb{R}))$ on multi-qubit systems. By constructing the states of a Hilbert space of $N$ qubits through the Clebsch-Gordan coefficients associated with the deformed algebras, we show that these states naturally coincide with the eigenstates of the Hamiltonian of the $q$- and $h$-deformed Kittel-Shore models. We compare the resulting deformed states with those typically targeted in quantum information experiments, providing a bridge between algebraic constructions and experimentally relevant quantum resources. Fidelities with respect to the undeformed states are computed to establish how the quantum correlations are affected, both for few-qubit systems (including Dicke and non-Dicke states), and in the macroscopic limit ($N \to \infty$) through closed-form formulas derived for arbitrary Dicke states. The results reveal different behaviors between the two deformations. The $q$-deformation smoothly modifies the states and maintains a residual overlap with the original configurations, while the $h$-deformation rapidly makes the states orthogonal to their undeformed counterparts. Both models demand a standard $N^{-1}$ rescaling to preserve fidelity stability in the macroscopic limit.

18.
arXiv (CS.CL) 2026-06-19

The ACUTE Protocol: Operationalizing Language Model Activations for Better Calibration, Utility, and Trust

As language models improve and become increasingly deployed to solve a variety of tasks, trustworthiness becomes essential. Calibration is a good proxy for trust: well-calibrated confidence estimates help inform the risk versus reward tradeoff when trusting a specific model output. Unfortunately, even as models improve, they remain poorly calibrated, often biasing towards overconfidence. Additionally, calibration can be gamed: a policy that always predicts the base rate is perfectly calibrated, but completely uninformative. To resolve this, we develop a new metric, expected utility renormalized by the oracle (EURO), that balances calibration and informativeness. We also propose a general-purpose activation-based confidence, utility, and trust estimation protocol (ACUTE) to appropriately adjudicate uncertainty. The ACUTE protocol provides flexible, sample-efficient, and compute-efficient confidence estimators for 3 tasks including multiple choice question answering, tool-calling, and scientific document summarization across 6 models from 4 model families. ACUTE outperforms strong baselines on EURO, while maintaining low calibration error. Taken together, our work shows that equipping LLMs with the ACUTE protocol can improve calibration, utility, and trustworthiness in numerous settings.

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

A deep learning framework for jointly solving transient Fokker-Planck equations with arbitrary parameters and initial distributions

arXiv:2604.06001v2 Announce Type: replace-cross Abstract: Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting comprehensive parameter exploration and transient analysis. This paper introduces a deep learning-based pseudo-analytical probability solution (PAPS) that, via a single training process, simultaneously resolves transient FPE solutions for arbitrary multi-modal initial distributions, system parameters, and time points. The core idea is to unify initial, transient, and stationary distributions via Gaussian mixture distributions (GMDs) and develop a constraint-preserving autoencoder that bijectively maps constrained GMD parameters to unconstrained, low-dimensional latent representations. In this representation space, the panoramic transient dynamics across varying initial conditions and system parameters can be modeled by a single evolution network. Extensive experiments on paradigmatic systems demonstrate that the proposed PAPS maintains high accuracy while achieving inference speeds four orders of magnitude faster than GPU-accelerated Monte Carlo simulations. This efficiency leap enables previously intractable real-time parameter sweeps and systematic investigations of stochastic bifurcations. By decoupling representation learning from physics-informed transient dynamics, our work establishes a scalable paradigm for probabilistic modeling of multi-dimensional, parameterized stochastic systems.

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

Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification

arXiv:2606.11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation. In this work, we construct data-driven reduced-order models that serve as structure-preserving, real-time surrogates. Remarkably, the exterior calculus that imposes physical conservation structure also exposes topological structure that we use to build a Gaussian process (GP) representation of uncertainty in state-flux relationships, ultimately yielding a Dirichlet-to-Neumann map for quantities of interest with closed-form expressions for posterior uncertainty. We specifically propose structure-preserving $H(\mathrm{div})$–$L^2$ subspaces of conventional Raviart–Thomas and $dgP_0$ elements prescribed by a lightweight transformer. Reduced-order dynamics consistent with this subspace are learned by posing a conservation law in which a GP describes the fluxes between volumes. This work hinges on a novel interface between mixed FEM spaces and GP regression; when training is posed as the optimal recovery problem (ORP), the resulting GP regression can be written as an optimization problem with equality constraints that impose a conservation structure, amenable to a fast Schur-complement training strategy. The trained model can then be solved in real time with closed-form estimators for boundary fluxes driven by prescribed Dirichlet data. The paper includes RKHS posterior error bounds for linear functionals to support uncertainty quantification, as well as numerical experiments demonstrating the accuracy of the posterior distribution as a surrogate for error estimation.

21.
arXiv (quant-ph) 2026-06-11

Tensor-Network Algorithm for Many-Body Trace Norms

arXiv:2606.11882v1 Announce Type: new Abstract: Trace norms are fundamental to quantum information theory, yet in many-body systems their evaluation remains a major computational bottleneck, as it generally requires diagonalizing exponentially large operators. Here, we overcome this bottleneck by introducing a controlled tensor-network algorithm for estimating the trace norm of matrix product operators without full diagonalization. The key idea is to combine Zolotarev's rational approximation to the sign function with a variational formulation solved using a density-matrix-renormalization-group-like algorithm. The resulting approximation is systematically improvable, with its accuracy controlled by the rational approximation parameters and the spectral weight near zero. Beyond the reach of exact diagonalization, we demonstrate controlled trace-norm calculations for entanglement negativity, quantum fidelity and quantum Fisher information, achieving substantially improved accuracy over polynomial-based Lanczos approaches. Our results establish trace-norm-based quantities as practical tensor-network observables, opening a route toward tensor-network studies of quantum information in mixed states.

22.
arXiv (CS.CV) 2026-06-11

Adapting Prithvi-EO for Fallow Detection for Food-Water Nexus: ViT-Adapter Necks and Parameter-Efficient Backbone tuning of Geospatial Foundation Model

Understanding spatial distribution of fallow land is important for optimizing the food-water (FW) nexus, given fallowing's role in crop rotation and water conservation. Fallow is a low accuracy class in USDA Cropland Data Layer (CDL). Geospatial foundation model (GFM), Prithvi-EO has shown strong transferability across computer vision tasks. However, its Vision Transformer (ViT) backbone produces features at a single spatial scale that are ill-suited for the multi-scale features required by object detection heads. Existing approaches synthesise multi-scale pyramids through scaling of single stride tokens, sacrificing spatial heterogeneity, and full backbone fine-tuning is computationally prohibitive for GFMs. We evaluate a fallow detection pipeline combining two parameter-efficient fine tuning (PEFT) schemes: Low-Rank Adaptation (LoRA) and a hybrid PEFT, with three neck designs: pseudo multi-scale, Lite ViT-Adapter, and Full ViT-Adapter. Our best configuration, Lite ViT-Adapter with a one-stage head, achieves a mAP@50 of 0.9479 with the Diou loss, suggesting the effectiveness of center-aware localization for irregular fallow field detection. ViT-Adapter free one-stage detection under LoRA improves the adapter-free anchor-based approach by 6.42%, and the best configuration improves baseline adapter-free anchor-based approach by 25.70%. These results demonstrate that lightweight spatial prior fusion and selective backbone unfreezing enable Prithvi-EO to capture local fallow patterns more effectively, outperforming approaches that rely on reshaped single-stride ViT tokens.

23.
PLOS Computational Biology 2026-06-01

Challenges and progress in RNA velocity: Comparative analysis across multiple biological contexts

Authors:

by Sarah Ancheta, Leah Dorman, Guillaume Le Treut, Abel Gurung, Greg Huber, Loïc A. Royer, Alejandro Granados, Merlin Lange Single-cell RNA sequencing is revolutionizing our understanding of cell state dynamics, allowing researchers to capture and quantify the transcriptomic profile of a single cell at a specific timepoint. Among the computational techniques used to predict cellular trajectories, RNA velocity has emerged as a predominant tool for modeling transcriptional dynamics. RNA velocity leverages the mRNA maturation process to generate velocity vectors that predict the likely future state of a cell, offering insights into cellular differentiation, aging, and disease progression. Although this technique has shown promise across biological fields, the performance accuracy varies depending on the RNA velocity method and dataset. We established a comparative pipeline and analyzed the performance of five RNA velocity methods on three datasets based on local consistency, method agreement, identification of driver genes, and robustness to sequencing depth. This benchmark provides a resource for scientists to understand the strengths and limitations of different RNA velocity methods.

24.
arXiv (CS.AI) 2026-06-17

C2FL: Clustered Continual Federated Learning under Spatial and Temporal Drift

arXiv:2606.18003v1 Announce Type: cross Abstract: Collective Adaptive Systems (CAS) increasingly rely on machine learning to let each node learn from locally sensed data, aligning its behavior with the surrounding environment. Scaling this intelligence, however, raises fundamental challenges: sensed data is often privacy-sensitive, preventing centralized collection; nodes are mobile, traversing regions where nearby nodes perceive similar phenomena while distant ones observe radically different conditions, creating natural spatial clusters; and these distributions evolve over time due to mobility, introducing temporal drift that makes local models progressively stale. These dynamics arise across domains - vehicular sensing, drone-based monitoring, smartphone crowdsensing - yet the interplay of privacy, spatial heterogeneity, and temporal drift severely undermines conventional learning strategies. Therefore, we propose C2FL, a fully distributed Federated Learning (FL) approach where nodes self-organize into learning groups through spatial clustering, reflecting the geographic structure of the environment. To counteract temporal drift, each node combines experience replay with a dwell-time-aware adaptive averaging step, progressively incorporating the regional consensus as it remains longer within the same area, while preserving previously acquired knowledge under evolving distributions. We evaluate our approach on synthetic experiments that systematically reproduce spatial and temporal shifts, showing that standard federated strategies degrade significantly under these conditions and that our method restores robust collective adaptation.

25.
arXiv (CS.AI) 2026-06-17

LLM-as-Judge in Education: A Curriculum-Grounded Marking Pipeline

arXiv:2606.17507v1 Announce Type: new Abstract: Generative AI and large language models (LLMs) are increasingly applied to question generation and automated assessment. However, deploying LLMs in preparation for high-stakes exams requires more than prompt engineering; it demands software pipelines that systematically ground model outputs in authorised curriculum artefacts and marking guidelines issued by education authorities. This paper presents a curriculum-grounded, configurable LLM-as-Judge pipeline for question-level marking, co-developed with an industrial partner, to support exam preparation for university admission. The pipeline identifies the relevant topics, subtopics, and cognitive demand of a question, and assembles verifiable and authorised context to support LLM judgement. Curriculum intent is operationalised through concrete syllabus artefacts, including prescribed verbs and outcomes, performance band descriptors, glossary definitions, and marking-guideline principles. A staged LLM workflow is employed to first generate question-specific rubrics, capturing structured expectations of performance, and then derive and evaluate marking criteria used to allocate marks to student responses. This design improves consistency, transparency, and alignment with official marking practices. Preliminary evaluation shows that the proposed LLM-as-Judge pipeline delivers marking outcomes comparable to human tutors, while yielding justifications that are more traceable to authorised curriculum artefacts and marking standards. The pipeline has also been integrated into an online study platform, where early deployment data provide initial insights into operational usage and manual overrides.