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

ttda704 at SemEval-2026 Task 4: Modeling Narrative Structures via Pseudonymization and Multi-View Sentence Alignment

We present our approach to SemEval 2026 Task 4: Narrative Story Similarity and Narrative Representation Learning. Our solution uses contrastive learning with fine-tuned sentence transformers to capture narrative similarity across abstract themes, course of action, and outcomes. We develop two pipelines: (Track A) a single-view method that encodes full narratives with smart layer freezing to reduce overfitting, and (Track B) a multi-view method that models theme, plot, and outcome with view-specific projection heads and self-supervised alignment. Both pipelines build on sentence-transformers models and are trained with contrastive loss on synthetic data. The code is available at the following GitHub repository: https://github.com/dinhthienan33/SemEval2026-Task4-ttda704.

02.
arXiv (CS.LG) 2026-06-24

SkillHone: A Harness for Continual Agent Skill Evolution Through Persistent Decision History

arXiv:2606.08671v2 Announce Type: replace Abstract: Agent skills extend language-model agents with task-specific procedures, scripts, and references, but the tasks and environments they target continually change. Existing methods improve skills in bounded runs and retain only the final artifact, discarding the decision history that later agents need to interpret prior revisions, evaluations, and rejected alternatives. We introduce SkillHone, a harness for continual agent skill evolution grounded in persistent decision history. SkillHone pairs skill revisions with evaluation-side evidence that supplies practice feedback, recording structured histories of diagnoses, revisions, evidence, and outcomes. Role-separated subagents run candidate skills on practice probes with redacted reporting and propose revisions informed by prior decisions, enabling cross-session refinement without rediscovering past rationale. On deep-research benchmarks, SkillHone runs without a pre-integrated search stack and outperforms the commercially backed deep-research agent by 15.8 points on GAIA and 3.2 points on WebWalkerQA-EN, while also exceeding prior skill-evolution methods. We further deploy SkillHone on internal tool-mediated analysis scenarios, where it improves accuracy by an average of 18.8 points across seven settings.

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

Offline Diffusion Policy for Multi-User Delay-Constrained Scheduling

arXiv:2501.12942v2 Announce Type: replace Abstract: Effective multi-user delay-constrained scheduling is crucial in various real-world applications, including embodied AI, instant messaging, live streaming, and data center management, where efficient resource allocation is required among users with diverse delay sensitivities. In these scenarios, schedulers must make real-time decisions to satisfy both delay and resource constraints without prior knowledge of system dynamics, which are often time-varying and challenging to estimate. {Current learning-based methods typically require online interactions with actual systems during the training stage. Therefore, these approaches are often difficult or impractical, as they can significantly degrade system performance and incur substantial service costs.} To address these challenges, we propose a novel offline reinforcement learning-based algorithm, named \underline{S}cheduling By \underline{O}ffline Learning with \underline{C}ritic Guidance and \underline{D}iffusion Model (SOCD), to learn efficient scheduling policies purely from pre-collected offline data. SOCD innovatively employs a diffusion policy, complemented by a sampling-free critic network for policy guidance. By integrating the Lagrangian multiplier optimization into the offline reinforcement learning, SOCD efficiently trains high-quality constraint-aware policies exclusively from available datasets, eliminating the need for online interactions with the system. Experimental results demonstrate that SOCD is resilient to various system dynamics, including partially observable and large-scale environments, and delivers superior performance compared to existing methods.

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

High-performance gates on trapped ion qubits using counterpropagating pulse-shaped laser beams

arXiv:2606.15672v1 Announce Type: new Abstract: Highly-localized light-matter interactions are necessary for scaling trapped-ion architectures. In hyperfine qubits, counterpropagating beams generate entangling gates by coupling with motion, but this effect is undesirable during single-qubit operations. For that reason, single-qubit gates are traditionally implemented with copropagating beams, and the coexistence of two beam geometries adds hardware and computational overhead. In an effort towards collective performance improvement with minimal overhead, we design and implement pulse-amplitude and dephasing robust dynamically corrected gates using Space Curve Quantum Control (SCQC) and compare them against the constant-amplitude gate implementation. We perform gate set tomography on a four-qubit trapped-ion register, and we discover more than 50% error reduction when robust pulses are used. We find that counterpropagating robust gates often outperform their copropagating counterparts and reach error rates as low as $(3.59 \pm 1.25)\cdot 10^{-3}$, using diamond distance as a metric. This value establishes a laser-driven-gate error reference and is merely an order of magnitude higher than the best reported $microwave$ gate on a $single$ ion. Additional experiments reveal that robust pulses can effectively suppress non-Markovian errors that grow during runtime. Our work challenges the widely accepted belief that copropagating gates should be preferred for their weak motional coupling and invites the adoption of high-performance robust pulses that suppress multiple noise sources of the trapped-ion error budget.

05.
arXiv (CS.LG) 2026-06-18

Self-attention-based non-linear basis transformations for compact latent space modelling of dynamic optical fibre transmission matrices

arXiv:2406.07775v2 Announce Type: replace Abstract: Multimode optical fibres are hair-thin strands of glass that efficiently transport light. They promise next-generation medical endoscopes that provide unprecedented sub-cellular image resolution deep inside the body. However, confining light to such fibres means that images are inherently scrambled in transit. Conventionally, this scrambling has been compensated by pre-calibrating how a specific fibre scrambles light and solving a stationary linear matrix equation that represents a physical model of the fibre. However, as the technology develops towards real-world deployment, the unscrambling process must account for dynamic changes in the matrix representing the fibre's effect on light, due to factors such as movement and temperature shifts, and non-linearities resulting from the inaccessibility of the fibre tip when inside the body. Such complex, dynamic and nonlinear behaviour is well-suited to approximation by neural networks, but most leading image reconstruction networks rely on convolutional layers, which assume strong correlations between adjacent pixels, a strong inductive bias that is inappropriate for fibre matrices which may be expressed in a range of arbitrary coordinate representations with long-range correlations. We introduce a new concept that uses self-attention layers to dynamically transform the coordinate representations of varying fibre matrices to a basis that admits compact, low-dimensional representations suitable for further processing. We demonstrate the effectiveness of this approach on diverse fibre matrix datasets. We show our models significantly improve the sparsity of fibre bases in their transformed bases with a participation ratio, p, as a measure of sparsity, of between 0.01 and 0.11. Further, we show that these transformed representations admit reconstruction of the original matrices with < 10% reconstruction error, demonstrating the invertibility.

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

Stochastic epidemic model with varying infectivity and waning immunity: the law of large numbers with unbounded infectivity

arXiv:2606.11845v1 Announce Type: new Abstract: We revisit the large population limit of our epidemic model with infection age dependent infectivity and progressive immunity waning, under the assumption that the supremum in $t$ of the random infectivity function has a finite expectation, while the previous proofs assumed that this supremum admits a deterministic upper bound.

07.
medRxiv (Medicine) 2026-06-17

Perceptions of aging well among older adults with heart failure: insights from a qualitative study

Background: Heart failure (HF) is a prevalent and often debilitating cardiovascular condition among older adults, frequently accompanied by multimorbidity, functional limitations, and the need to age in place. Traditional models of successful aging emphasize disease absence and preserved function, yet most individuals with HF live with ongoing symptoms and chronic health challenges. How older adults with HF define aging well, particularly across different socioeconomic contexts, remains underexplored. Objectives: To explore how older adults with HF conceptualize aging well and to identify perceived facilitators and barriers across more and less resourced New York City neighborhoods. Methods: We conducted semi-structured interviews with 20 adults diagnosed with HF residing in Manhattan and Brooklyn neighborhoods classified by 2019 United States Census data. Interviews were guided by Rowe and Kahn's model. Transcripts were analyzed using an inductive-deductive thematic approach and interpreted in alignment with the Healthy People 2030 framework. Results: Participants had a mean age of 69 years; 50% identified as Black and 50% were women. Despite functional limitations, 65% reported aging well. Five themes emerged: maintaining physical function, maintaining cognitive function, sustaining social relationships, avoiding pain, and promoting overall well-being. Avoiding pain and promoting well-being extended beyond traditional models. Neighborhood context shaped priorities, with financial stability emphasized in more affluent areas and social cohesion prioritized in less affluent communities. Conclusions: Older adults with HF frequently perceive themselves as aging well despite chronic illness, reframing successful aging beyond disease avoidance. These findings support a patient-centered, place-informed model of aging well with implications for healthcare delivery and policy.

08.
arXiv (quant-ph) 2026-06-24

Spectator-transition crosstalk in a spin-3/2 silicon vacancy qudit in silicon carbide revealed by broadband Ramsey interferometry

arXiv:2601.15559v3 Announce Type: replace Abstract: Color center spins in 4H-SiC offer a rare combination of wafer-scale materials maturity with long spin coherence and chip-level photonics, making them promising building blocks for scalable quantum technologies. In particular, the silicon vacancy hosts an S=3/2 ground state, a native qudit that enables compact encodings and subspace-selective control, but also introduces spectator transitions: short, detuned pulses can coherently drive non-addressed level pairs and create crosstalk. Here we use broadband Ramsey interferometry to reveal and quantify such spectator-transition crosstalk. Experimentally, the Ramsey Fourier spectra display multiple lines beyond the addressed single-quantum transition. Analytically, we map each line to a pairwise energy difference between qudit levels of the rotating-frame Hamiltonian and assign its weight via compact amplitudes set by the prepared state and the microwave pulse parameters, predicting a deterministic six-branch structure. Numerical time-domain propagation with the experimental sampling reproduces the detuning map, and the measured peak positions coincide with the analytic branch lines without frequency fitting. Together these results provide a practical, spectator-aware framework for multilevel control in the silicon vacancy qudit. The approach offers clear guidance to suppress crosstalk or, conversely, to exploit spectator lines, for example as additional constraints for in situ pulse calibration and for phase-sensitive quantum state and process estimation.

09.
medRxiv (Medicine) 2026-06-16

The Target48 Neurodegeneration Panel: A Novel Tool for Profiling Protein Signatures in Neurodegenerative Disorders

Introduction: Novel tools for absolute quantification of established and emerging fluid neuro-biomarkers are required to advance diagnostic studies and improve biological insights. Methods: We conducted an extensive analytical and clinical validation of the Olink Target 48 Neurodegeneration panel (T48 Neuropanel) in 352 paired CSF and plasma samples from cognitively unimpaired controls (CU), Alzheimer dementia (AD), frontotemporal dementia (FTD), and dementia with Lewy bodies (DLB), n=44 per group. Comparisons with benchmark assays were performed. Results: Good detectability (CSF: 31 out of 42 assays; plasma: 38 out of 42 assays) and technical performance was observed. Benchmark assays showed good correlations, supporting method transformation formulas. Next to emerging biomarkers (MMP10, ITGB2), discriminative performance was excellent in AD: CSF pTau217: AUC=1; FTD: plasma NfL: AUC=0.952; and DLB: CSF DDC: AUC=0.901. Discussion: This analytical and clinical validation of the T48 Neuropanel highlights initial cut-offs and emerging biomarkers to aid clinical studies for the diagnosis, prognosis, and monitoring of neurodegenerative diseases. Highlights: The T48 Neuropanel shows robust analytical performance, with high detectability across both plasma and CSF matrices. The T48 Neuropanel validates established (i.e., pTau217, Abeta42, NfL, and GFAP) and emerging biomarkers (i.e., DDC, MMP10, ITGB2, ITGAM, NPTX2, NPTXR, SMOC1, sTREM1, and sTREM2) in CSF and plasma. CSF NfL, GFAP, ITGB2, and ITGAM and plasma GFAP were dysregulated across AD, FTD, and DLB dementias. -The multiplex design of the T48 Neuropanel enables rich biological interpretation by simultaneously quantifying established and emerging neurodegeneration biomarkers. Importantly, the inclusion of absolute quantification facilitates the establishment of cut-offs, supporting its potential for clinical translation.

10.
arXiv (math.PR) 2026-06-15

Longest weakly increasing subsequences of discrete random walks on the integers with heavy tailed distribution of increments

arXiv:2603.29047v2 Announce Type: replace-cross Abstract: We investigate the behavior of the length of the longest weakly increasing subsequences (weak LIS) of $n$-step random walks with nonzero integer increments $k = \pm 1, \pm 2, \dots$ given by a symmetric heavy tailed mass distribution proportional to $|k|^{-1-\alpha}$ for several values of the real parameter $\alpha > 0$ together with that of the simple random walk ($k=\pm 1$), to which the $n$-step heavy tailed walks reduce when $\alpha$ grows large enough that step jumps beyond $\pm 1$ become essentially absent on the scale of $n$. By means of exploratory fits, weighted nonlinear least squares, and nested-model comparisons, we found that the sample average length $\langle{L_{n}}\rangle$ scales like $\langle{L_{n}}\rangle \sim \sqrt{n}\log{n}$ when the distribution of increments has finite variance ($\alpha > 2$) and $\langle{L_{n}}\rangle \sim n^{\theta}$ with a varying exponent $\theta > 0.5$ when the variance is infinite ($\alpha \leq 2$). Distributional diagnostics indicate that the bulk of the $L_{n}$ distribution is very well-approximated by a lognormal model, though systematic deviations are observed in the tails. Our results corroborate and expand upon previous results for the LIS of other types of heavy-tailed random walks and raise a conjecture as to whether the distribution of $L_{n}$ is given, or can be effectively described, by a lognormal distribution.

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

ROVE: Unlocking Human Interventions for Humanoid Manipulation via Reinforcement Learning

arXiv:2606.17011v1 Announce Type: cross Abstract: Human interventions provide crucial corrective signals for post-training Vision-Language-Action (VLA) models. However, enabling seamless humanoid interventions is a formidable systems challenge due to complex whole-body kinematics and dexterous-hand control. Consequently, the collected intervention trajectories are often suboptimal, and methods that rely on human interventions as expert supervision can absorb hesitant, inefficient, or even erroneous behaviors. To address both the system and algorithmic challenges, we propose ROVE, a reinforcement learning framework for humanoid VLA post-training with imperfect human interventions. First, ROVE introduces a human-in-the-loop pipeline capable of collecting deployment and intervention data for humanoid manipulation. Second, it utilizes Optimistic Value Estimation (OVE) to prioritize high-value behaviors from mixed-quality trajectories. To further robustify value estimation, we incorporate cross-embodiment human experience videos to provide rich supervision for long-tailed failure and recovery modes. The resulting critic yields informative advantage signals, steering the VLA actor to focus on high-value behaviors rather than indiscriminately imitating all actions. On challenging real-world contact-rich and fine-grained humanoid manipulation tasks, ROVE outperforms experience-learning baselines and consistently improves across multiple rollout-intervention iterations.

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

A Risk Decomposition Framework for Pre-Hoc Fine-Tuning Prediction

arXiv:2606.17649v1 Announce Type: cross Abstract: The high cost of fine-tuning LLMs poses a significant economic barrier; pre-hoc performance prediction offers a critical solution to substantially reduce this expense. However, the theoretical limits of pre-hoc performance prediction remain unexplored. We formulate it as a stochastic estimation problem under information constraints, decomposing prediction risk into two components: an intrinsic limit (static data-model compatibility) and a reducible optimization variance. We prove that optimization variance admits a necessary lower bound on its decay rate, implying fundamental constraints on how quickly uncertainty dissipates, regardless of the predictor used. Based on these dynamics, we derive a budget-optimal probing principle and introduce a predictability phase diagram that organizes tasks into three distinct regimes: Static-Sufficient, Dynamic-Critical, and Noise-Dominant. Extensive experiments on synthetic and real-world benchmarks validate these theoretical regimes and demonstrate the efficiency of our probing strategy.

13.
arXiv (CS.LG) 2026-06-24

Grouped Query Experts: Mixture-of-Experts on GQA Self-Attention

arXiv:2606.20945v2 Announce Type: replace Abstract: Self-attention is central to Transformer performance and is often the most expensive part of the Transformer at long context lengths because its pairwise token interactions scale quadratically with sequence length. Standard dense attention also applies the same set of attention heads to every token regardless of token difficulty or information content. This uniform activation can waste compute, especially as sequences grow longer and attention cost increases rapidly. We propose Grouped Query Experts (GQE), a mixture-of-experts layer on top of grouped-query attention (GQA). Within each GQA group, a router selects k query-head experts per token while all key-value (KV) heads remain dense and unchanged. Thus, GQE keeps the KV cache benefits of GQA and reduces only the active query-head computation. On a fixed 30B token budget at the 250M parameter scale, GQE matches the all-active GQA baseline in downstream accuracy while activating half the query heads per token.

14.
arXiv (quant-ph) 2026-06-12

Explicit Quantum Circuit Simulation of Nonlinear 1-Dimensional Fluid with Carleman-linearized Boltzmann Method

arXiv:2606.12770v1 Announce Type: new Abstract: Quantum computation of fluid dynamics has attracted growing attention as a key application of fault-tolerant quantum computers anticipated in the coming decade, with lattice Boltzmann methods emerging as a particularly promising approach. Explicit and efficient elementary-gate-level circuit simulations, however, have so far been demonstrated only in the linear case. Here we include the leading nonlinearity through second-order Carleman linearization of the one-dimensional Boltzmann equation, and demonstrate, via explicit quantum-circuit simulation, the preparation of the final-time state using a Taylor-expansion-based ODE solver based on the quantum singular value transformation. With this construction, we analyze the gate and qubit complexities, which scale logarithmically with the grid size, the nonlinearity captured by the higher-order Carleman linearization, and the practical utility of higher-order expansions in the Taylor ODE solver. The construction provides a concrete baseline for computational cost reduction and further developments such as extensions to higher dimensions, complex geometries, and the extraction of physical quantities, towards industrially useful quantum CFD.

15.
arXiv (quant-ph) 2026-06-24

Connecting Quantum Tomography and Quantum Retrodiction

arXiv:2606.23777v1 Announce Type: new Abstract: Quantum tomography and quantum retrodiction are traditionally viewed as separate inference tasks: tomography reconstructs quantum states from measurement data, whereas retrodiction infers past quantum states from observed outcomes. We show that the two are manifestations of the same underlying principle. We prove that the Petz recovery map associated with a measurement channel is precisely the gradient update of the log-likelihood used in maximum-likelihood tomography. Consequently, repeated applications of the Petz map monotonically increase the likelihood. Extending beyond measurement channels, we derive a noncommutative generalization of the Petz map from the gradient of a generalized likelihood for arbitrary quantum channels. The resulting iterative procedure maximizes the likelihood and provides a general framework for quantum tomography, establishing a direct bridge between retrodiction, recovery maps, and statistical inference.

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

PaLMR: Towards Faithful Visual Reasoning via Multimodal Process Alignment

Reinforcement learning has recently improved the reasoning ability of Large Language Models and Multimodal LLMs, yet prevailing reward designs emphasise final-answer correctness and consequently tolerate process hallucinations–cases where models reach the right answer while misperceiving visual evidence. We address this process-level misalignment with PaLMR, a framework that aligns not only outcomes but also the reasoning process itself. PaLMR comprises two complementary components: a perception-aligned data layer that constructs process-aware reasoning data with structured pseudo-ground-truths and verifiable visual facts, and a process-aligned optimisation layer that constructs a hierarchical reward fusion scheme with a process-aware scoring function to encourage visually faithful chains-of-thought and improve training stability. Experiments on Qwen2.5-VL-7B show that our approach substantially reduces reasoning hallucinations and improves visual reasoning fidelity, achieving state-of-the-art results on HallusionBench while maintaining strong performance on MMMU, MathVista, and MathVerse. These findings indicate that PaLMR offers a principled and practical route to process-aligned multimodal reasoning, advancing the reliability and interpretability of MLLMs.

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

The FID Lottery: Quantifying Hidden Randomness in Generative-Model Evaluation

The Frechet Inception Distance (FID) is the de facto arbiter of image generation, yet most papers report just a single number from a single trained model using a single sampling seed. How reproducible is that number if we retrain the model, or merely resample from it? In this paper, we treat FID as a random variable on a two-axis panel of training and generation seeds, and measure its variance directly on several hundred SiT networks trained on class-conditional ImageNet 256x256. We report surprising findings: (a) Retraining the model using the same recipe with a different seed moves FID 3.2x more (in Inception feature space) than redrawing samples from a fixed network. (b) That gap is driven by three factors: random initialisation, data ordering, and the per-step Gaussian noise of the flow-matching loss. (c) Increasing compute or model size barely tightens the spread, holding the FID coefficient of variation (CoV) inside a 1-2% band. (d) Per-cell classifier-free-guidance tuning halves the spread but reshuffles which seeds work best, and a lucky training seed reaches the same FID with up to 2x less compute than an unlucky one. Based on these findings, we recommend a new FID evaluation protocol: evaluate under per-cell optimal guidance, treat any FID gap below the empirically measured ~1.3% CoV as inconclusive, and report an error bar over several training seeds rather than a single FID number.

18.
arXiv (CS.CL) 2026-06-17

Structural Role Injection in Handlebars-Templated LLM Prompts: Triple-Brace Interpolation, Delimiter Family, and the Limits of HTML Auto-Escaping

Large language model applications build prompts from templates, and Handlebars is a widely used templating engine and the default prompt-template format in Microsoft Semantic Kernel. Its double-brace {{x}} expression HTML-escapes the interpolated value and is documented as the safe default; its triple-brace {{{x}}} expression inserts the value raw. We show that this choice silently governs an application's exposure to structural role injection, where attacker-controlled data carries chat role delimiters that forge a higher-privilege turn. A model-free analysis establishes the mechanism: Handlebars escaping rewrites angle brackets but not square brackets, colons, or Markdown hashes, so it neutralises ChatML, Llama-3, and XML role delimiters (survival rate 0.00) while leaving Llama-2 [INST], legacy Human:/Assistant:, and Markdown ### delimiters intact (survival rate 1.00 for the last two). We then run 5760 trials across seven delimiter families, two attack objectives, and four models (GPT-3.5 Turbo, GPT-4o mini, GPT-4.1 mini, Claude Haiku 4.5) at a combined API cost of 1.63 USD. GPT-3.5 Turbo follows the task-hijack instruction in 97% of raw and 91% of escaped trials, with the escaping protection concentrated in the angle-bracket families and absent for the colon- and Markdown-based families; the harder secret-exfiltration objective, which does not saturate, exposes the same family interaction more cleanly. Claude Haiku 4.5 resists both objectives almost entirely. The escaped default protects only the delimiter schemes whose characters HTML escaping happens to cover, gives no protection for the rest, and cannot substitute for a structural separation of instruction and data.

19.
arXiv (CS.AI) 2026-06-24

On the Smallness of the Large Language Models Scaling Exponents

arXiv:2606.24504v1 Announce Type: new Abstract: We discuss reasons why the scaling exponents of current Large Language Models (LLMs) applications are indicating an unsustainable regime in terms of energy resources. We further show that attributing the smallness of such exponents to a numerical bias due to the neglect of a non-zero value of the loss function in the limit of infinite data (``pedestal effect") does not remove the unsustainability issue. Finally, the effects of the smoothness (roughness) of the data on the scaling exponents is commented upon based on an analogy with phenomenological models of fluid turbulence.

20.
arXiv (CS.AI) 2026-06-19

CRAX: Fast Safe Reinforcement Learning Benchmarking

arXiv:2606.20376v1 Announce Type: cross Abstract: Safety is a core concern for deploying reinforcement learning (RL) agents in real-world domains such as robotics and autonomous driving. While benchmarks have been central to progress in RL, existing safety benchmarks with high-fidelity 3D physics remain computationally slow, limiting large-scale experimentation and rapid prototyping. To address this gap, we propose CRAX (Constrained RL Accelerated with JAX). Built on top of the MuJoCo XLA (MJX) physics engine with realistic 3D dynamics, CRAX leverages vectorized operations and hardware acceleration, yielding up to ~100x speedups over comparable CPU-based safety benchmarks. The benchmark features six environment suites and three agent-specific tasks, each spanning three difficulty levels. Evaluating six popular safe RL methods shows that no single approach dominates across all tasks, and reveals the trade-offs between performance and safety. We find that curriculum learning across difficulty levels and safety transfer can improve performance over direct training in harder settings.

21.
arXiv (math.PR) 2026-06-15

Stability of the $k$-Plane Transform on Measures and Hölder-Type Comparisons of Wasserstein Metrics

arXiv:2605.00375v2 Announce Type: replace-cross Abstract: We establish stability estimates for the $k$-plane transform on finite positive Radon measures, with emphasis on Fourier and Wasserstein metrics. We first introduce a metric on $k$-plane transform data and prove a bi-Lipschitz stability estimate showing that this metric is equivalent to a generalized Fourier metric obtained by augmenting the Fourier distance between centered normalized measures with separate barycenter and total mass difference terms. Building on a Hölder-type comparison between Fourier and Wasserstein metrics due to Carrillo and Toscani, we extend this comparison to positive Radon measures under uniform bounds on centered moments of order slightly larger than $2$. This yields Hölder-type stability for the $k$-plane transform in a generalized $2$-Wasserstein metric and, in particular, a $W_2$-stability estimate for centered probability measures. We also compare the $2$-Wasserstein distance with its max-sliced analogue. For centered probability measures with uniformly bounded moments of order slightly larger than $2$, we prove a two-sided Hölder-type comparison between these distances. We then extend the result to positive Radon measures by applying it to centered normalized measures and adding separate barycenter and mass terms. Finally, for absolutely continuous compactly supported probability measures with bounded densities, we prove a strong equivalence between the $2$-Wasserstein distance of the measures and the $(k/2-1)$-order Sobolev norm of the $k$-plane transform data of the difference of their densities.

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

Uncertainty Estimation and Generalization Bounds for Modern Deep Learning

arXiv:2606.13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems. While neural networks achieve remarkable predictive performance, their ability to generalize and to quantify uncertainty remains only partly understood. This thesis approaches this challenge from both methodological and theoretical angles: unifying Bayesian inference, function-space modeling, and large-deviation theory under a common probabilistic perspective. On the methodological side, the thesis introduces the Deep Variational Implicit Process (DVIP), a scalable Bayesian framework that extends implicit processes to deep architectures. Complementing this, two post-hoc methods – the Variational Linearized Laplace Approximation (VaLLA) and the Fixed-Mean Gaussian Process (FMGP) – are proposed to equip pretrained deterministic networks with calibrated uncertainty estimates. The theoretical contributions focus on one of the central open questions in modern machine learning: why do large, over-parameterized neural networks generalize so well? To address this, the thesis develops a unified probabilistic framework that connects three key mechanisms – diversity, smoothness, and stochasticity – within the language of PAC-Bayesian and large-deviation theory.

23.
arXiv (CS.AI) 2026-06-11

Harness In-Context Operator Learning with Chain of Operators

arXiv:2606.12318v1 Announce Type: cross Abstract: Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining. In-Context Operator Networks (ICON) addresses this issue by prompting the model with numerical context so that the model learns specific operators from prompts and adapt to different operators without fine-tuning. However, ICON may still fail to generalize to out-of-distribution (OOD) operator tasks. Inpired by the success of harness engineering of Large Language models (LLMs), we introduce Chain of Operators (CHOP), a framework that harness a frozen ICON to OOD operator tasks without updating its parameters. Specifically, CHOP constructs a chain of operators consisting of explicit elementary transformations and the frozen ICON. Experiments on a scalar conservation law and a mean-field control problem show that CHOP reduces relative inference error over direct ICON evaluation, while each operator in the chain remains interpretable and in closed form. A chain constructed on one PDE family further generalizes to a different family, indicating shared mechanisms across harness systems.

24.
arXiv (CS.AI) 2026-06-16

LatentGym: A Testbed For Cross-Task Experiential Learning With Controllable Latent Structure

arXiv:2606.15306v1 Announce Type: cross Abstract: We envision continually learning agentic systems that become more useful over time: as they encounter sequences of related tasks, they should infer the hidden structure shared across those tasks and use it to improve future decisions. This cross-task experiential learning capability is pivotal in domains such as personalization and interactive assistance, but existing training/evaluation frameworks do not provide shared, controllable latent structures and cannot measure whether or why agents improve. We introduce LatentGym: a controllable suite in which each environment is organized around a ground-truth latent variable governing the structure across tasks. Our construction yields metrics that separate exploration (whether the agent's actions gather information about the latent) from exploitation (whether the agent uses what it has gathered). We demonstrate our suite on empirical studies addressing three questions: how and why frontier models fail to adapt across related tasks; whether post-training on related task sequences improves general cross-task adaptation, and where those gains come from; and how design choices such as inter-task feedback shape training dynamics and generalization. Together, these results establish a controlled foundation for studying how LLM agents learn from experience across tasks, and for designing agents that adapt more reliably in sequential, personalized, and interactive settings.

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

Multi-Token Residual Prediction

arXiv:2605.18817v2 Announce Type: replace Abstract: Diffusion Language Models (DLMs) generate text by iteratively denoising masked token sequences, offering a tradeoff between parallelism and quality compared to autoregressive models. In current practice, the number of tokens decoded per step is controlled by a confidence threshold, and quality degrades monotonically as more tokens are denoised per step. We introduce Multi-token Residual Prediction (MRP), a lightweight module that enables dependency-aware multi-token denoising within a single backbone forward pass. MRP exploits a key property of the denoising process: the logit distributions at adjacent denoising steps are remarkably similar. Rather than running the backbone a second time to obtain the next-step logits, MRP predicts the residual between steps from the backbone's hidden states, effectively denoising more tokens per backbone forward at a fraction of the cost. We apply MRP across the two operating regimes of DLM decoding. In the high-quality-low-throughput static denoising regime, MRP serves as a drafter for speculative decoding: its proposals are verified against the backbone, yielding lossless acceleration of up to 1.4x in SGLang. In the low-quality-high-throughput dynamic denoising regime, MRP instead drives a remasking scheme that revokes over-eager reveals, recovering most of the accuracy lost to aggressive low-threshold decoding and improving accuracy by up to 22.6 points on code generation task HumanEval and 17.7 points on reasoning task GSM8K.