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

Integrating Multi-Label Classification and Generative AI for Scalable Analysis of User Feedback

arXiv:2601.23018v1 Announce Type: cross Abstract: In highly competitive software markets, user experience (UX) evaluation is crucial for ensuring software quality and fostering long-term product success. Such UX evaluations typically combine quantitative metrics from standardized questionnaires with qualitative feedback collected through open-ended questions. While open-ended feedback offers valuable insights for improvement and helps explain quantitative results, analyzing large volumes of user comments is challenging and time-consuming. In this paper, we present techniques developed during a long-term UX measurement project at a major software company to efficiently process and interpret extensive volumes of user comments. To provide a high-level overview of the collected comments, we employ a supervised machine learning approach that assigns meaningful, pre-defined topic labels to each comment. Additionally, we demonstrate how generative AI (GenAI) can be leveraged to create concise and informative summaries of user feedback, facilitating effective communication of findings to the organization and especially upper management. Finally, we investigate whether the sentiment expressed in user comments can serve as an indicator for overall product satisfaction. Our results show that sentiment analysis alone does not reliably reflect user satisfaction. Instead, product satisfaction needs to be assessed explicitly in surveys to measure the user's perception of the product.

02.
arXiv (math.PR) 2026-06-15

Stability of Synthetic Ricci Curvature Lower Bounds for Inverse Limit Extended Metric Measure Spaces

arXiv:2606.14322v1 Announce Type: cross Abstract: We show that every Polish extended metric measure space arises as an inverse limit of metric measure spaces up to isomorphism. We then prove that synthetic Ricci curvature lower bounds and several functional inequalities, including the log-Sobolev, Talagrand, Poincaré, and dimension-free Harnack inequalities are stable under inverse limit. We discuss applications to infinite-dimensional spaces, including abstract Wiener spaces and their quotient spaces.

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

Differential Privacy of Gaussian Process Posterior Sampling

arXiv:2606.17995v1 Announce Type: cross Abstract: We study the privacy of releasing posterior sample paths from a Gaussian process (GP) when the entire training set including covariates and responses is private. Unlike standard differential-privacy (DP) mechanisms that add external noise, posterior sampling is random by construction. We show that this intrinsic randomness yields DP guarantees by deriving explicit Rényi-DP bounds for GP posterior sample-path release. The bounds separate posterior-mean leakage from data-dependent posterior-covariance leakage showing that meaningful privacy depends sharply on effective ridge regularisation. We apply membership-inference attacks to show that empirical leakage follows the predicted dependence on regularisation, posterior variance and the number of released posterior sample-paths. Utility experiments on downstream posterior-sampling tasks identify noisy-observation regimes where privacy-compatible regularisation preserves useful decisions with modest utility loss. When stronger privacy is needed, the intrinsic guarantee can be sharpened by adding calibrated GP noise, providing an explicit additional privacy knob.

04.
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.

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

SCALE: Self-uncertainty Conditioned Adaptive Looking and Execution for Vision-Language-Action Models

arXiv:2602.04208v2 Announce Type: replace-cross Abstract: Vision-Language-Action (VLA) models have emerged as a promising paradigm for general-purpose robotic control, with test-time scaling (TTS) gaining attention to enhance robustness beyond training. However, existing TTS methods for VLAs require additional training, verifiers, and multiple forward passes, making them impractical for deployment. Moreover, they intervene only at action decoding while keeping visual representations fixed-insufficient under perceptual ambiguity, where reconsidering how to perceive is as important as deciding what to do. To address these limitations, we propose SCALE, a simple inference strategy that jointly modulates visual perception and action based on 'self-uncertainty', inspired by uncertainty-driven exploration in Active Inference theory-requiring no additional training, no verifier, and only a single forward pass. SCALE broadens exploration in both perception and action under high uncertainty, while focusing on exploitation when confident-enabling adaptive execution across varying conditions. Experiments on simulated and real-world benchmarks demonstrate that SCALE improves state-of-the-art VLAs and outperforms existing TTS methods while maintaining single-pass efficiency.

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

Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models

arXiv:2606.12682v1 Announce Type: new Abstract: We demonstrate how supersymmetries of Hamiltonians for coupled Bose-Fermi systems can be used to place the Hamiltonians of the Jaynes-Cummings model and Dicke model under the rotating wave approximation in matrix form and provide explicit analytic solutions for their eigenvalues. We then use this supersymmetry to place the Liouvillians of the associated Markovian open systems in matrix form and provide explicit solutions for their eigenvalues. These results are a consequence of the fact that the Hamiltonian of the Jaynes-Cummings model commutes with the linear Casimir invariant of the superalgebra $u(1|1)$ and that the Hamiltonian of the Dicke model commutes both with the linear invariant of $\sum_{i} u_{i}(1|1)$ and with the invariant of an additional $su(2)$ algebra. Our methods apply to various coupled Bose-Fermi systems with $u(1|1)$ and more generally with $u(n|m)$ dynamical superalgebras, and may provide efficient tools for studying more complicated examples.

07.
arXiv (CS.CL) 2026-06-19

PASQA: Pitch-Accent-Focused Speech Quality Assessment Model Trained on Synthetic Speech with Accent Errors

Existing mean opinion score (MOS) prediction models typically predict utterance-level naturalness MOS and can be insensitive to localized pitch-accent errors. We propose Pitch-Accent-focused Speech Quality Assessment (PASQA), which explicitly targets pitch-accent correctness. To train our model, we construct a controlled Japanese accent-error dataset by changing accent patterns using an accent-controllable text-to-speech system, and compute a pseudo accent-quality score from the accent-error rate. PASQA builds on self-supervised representations and employs mora-conditioned fusion, ranking loss, an auxiliary accent-error localization task, and speaker-invariant training. Experiments show that conventional models fail to preserve the ordering by accent-error severity, whereas PASQA achieves high ordering accuracy on both seen and unseen speakers. Further, PASQA shows stronger agreement with human accent-correctness judgments. The code is available at https://github.com/lycorp-jp/PASQA.

08.
arXiv (CS.CL) 2026-06-16

The Dark Regulome: Disentangling Predictability from Regulation in Genomic Foundation Models

High-grade gliomas integrate into neural circuits through functional synapses with neurons, raising the question of which noncoding elements shape synaptogenic gene expression in tumor cells. The regulatory program written across the dark genome, what we call the $dark regulome$, is the natural substrate to probe, and sequence foundation models offer a zero-shot route through in-silico mutagenesis (ISM); yet likelihood-based scoring is tautologically coupled to local sequence predictability, leaving the regulatory interpretation underdetermined. Across three architecturally distinct foundation models (Caduceus-Ph, HyenaDNA, Enformer) and 30,448 dark genome elements at 92 glioma-relevant loci, we introduce a residualization-and-permutation diagnostic that separates predictability-driven from regulation-driven RIS variance. A sharp 10kb proximal-regulatory horizon survives every control we apply, but the LM-derived element-class hierarchy does not: a six-feature linear baseline matches Caduceus top-decile membership at AUC $= 0.985$. Cross-architecture decomposition cleanly separates a sequence-predictability layer (the two language models co-rank long well-predicted transposable elements) from a regulatory-output layer (Enformer alone retains residual cCRE-discriminative signal), with literally zero overlap between the two top-100 lists. Conservation, brain cis-eQTL, and STRING-PPI cross-checks then anchor what biology survives: top-100 elements across all three models are $3.3\times$ enriched per model for matching brain eQTLs ($p_\mathrm{emp} < 5\times 10^{-3}$), while a tempting transposable-element regulatory layer and a striking NRXN1+NLGN1 protein-pair convergence both fail proper permutation tests once those tests are constructed. We deliver the diagnostic as a general methodological tool for any ISM-based regulatory study.

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

Few shot chain-of-thought driven reasoning to prompt LLMs for open ended medical question answering

In this paper, we propose a modified version of the MedQA-USMLE dataset, named MEDQA-OPEN, which contains open-ended medical questions without options to mimic clinical scenarios, along with clinician-approved reasoned answers. Additionally, we implement a prompt driven by Chain of Thought (CoT) reasoning, CLINICR, to mirror the prospective process of incremental reasoning, reaching a correct response to medical questions. We empirically demonstrate how CLINICR outperforms the state-of-the-art 5-shot CoT-based prompt (Liévin et al., 2022). We also present an approach that mirrors real-life clinical practice by first exploring multiple differential diagnoses through MCQ-CLINICR and subsequently narrowing down to a final diagnosis using MCQ-ELIMINATIVE. Finally, emphasizing the importance of response verification in medical settings, we utilize a reward model mechanism, replacing the elimination process performed by MCQ-ELIMINATIVE.

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

Size Doesn't Matter: Cosine-Scored Sparse Autoencoders

arXiv:2606.15054v1 Announce Type: new Abstract: Sparse autoencoders (SAEs) detect features via inner product, so a feature's activation scales with both its directional alignment and the input's norm. Under BatchTopK, high-norm tokens inflate all pre-activations simultaneously, claiming dictionary slots regardless of content alignment. This matters because sublayer normalization has already discarded the magnitude the score measures, so the encoder detects a quantity the model does not read. We replace the score with a learned blend of cosine similarity and input magnitude, letting the optimizer choose how much norm to use; a per-feature extension lets each feature decide independently. In both regimes, training is free to recover inner product but never does, with no feature ever choosing more than half-magnitude dependence. At matched reconstruction, the cosine encoder learns features that align with human-recognizable concepts far more often than standard, filling dictionary slots that inner product wastes on norm detectors. Loss reweighting that equalizes gradients barely closes the gap, confirming forward-pass score geometry as the lever. The advantage is not universal across tasks or depths, but we believe cosine scoring should be the default for dictionary learning on normalized representations.

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

IBAD: Interpretable Behavioral Anomaly Detection on Human Mobility Data

arXiv:2606.16023v1 Announce Type: new Abstract: Human mobility appears highly diverse, yet much of a person's daily mobility can be explained by a small set of recurring behavioral templates, such as commuting, school-centered activities, caregiving, nightlife, or errand patterns. We present \texttt{IBAD} (\underline{I}nterpretable \underline{B}ehavioral \underline{A}nomaly \underline{D}etection), a framework that learns interpretable daily mobility templates and represents each individual as a distribution over mixtures of these templates. Rather than focusing on specific locations, IBAD characterizes activities that individuals perform across locations. This approach first discovers global behavioral templates using Latent Dirichlet Allocation (LDA), then employs a hierarchical self-supervised model to learn normal behavior of individuals from their soft behavioral templates. We also introduce a splicing benchmark that creates controlled behavioral mismatches between an individual's historical profile and injected mobility patterns. Experiments on real-world and synthetic datasets show that daily behavior can be effectively decomposed into a small number of interpretable templates. Crucially, we show that the learned behavioral archetypes transfer across distinct geographic and demographic contexts. Furthermore, IBAD maintains a robust competitive performance across all settings. For reproducibility purposes, the code is accessible at ~\href{https://github.com/USC-InfoLab/IBAD}{https://github.com/USC-InfoLab/IBAD}.

12.
arXiv (CS.AI) 2026-06-24

Ten Digits on a Train: AI-Assisted Verification of Two Eigenvalue Problems

arXiv:2606.23821v1 Announce Type: cross Abstract: Accurate numerical eigenvalues are often difficult to certify, especially in singular or non-normal settings. This article reports a human–AI collaboration on two such computations. For a singular self-adjoint Schrödinger operator, a verified zero count and Dirichlet–Neumann bracketing certify the complete negative spectrum to ten decimal places. For a delicate non-normal atom–molecule benchmark, a previously unresolved resonance pair is separated, with each member enclosed to ten digits. The second result is achieved not by increasing the precision of one-way shooting, but by reformulating the problem as a global matching system for projective solution lines. The infinite tail is encoded as uncertainty in the terminal projective data, and a componentwise, tail-robust Krawczyk–Brouwer inclusion supplies the certificate. This gives a reusable architecture for analytic boundary-value systems with ill-conditioned propagation and uncertain asymptotic data. The collaboration also exposes the strengths and limits of AI assistance. AI rapidly produced accurate candidates and plausible proof strategies, but several failed, including one apparently complete tail argument that omitted the componentwise check required by a nonuniform polydisc. Validated computation is a stringent test of AI-assisted mathematics: the output is not merely a number, but a number with a proof. These examples show why the proof object matters, and why human mathematical judgment remained decisive. More broadly, as AI makes code, exposition, and plausible numerical claims inexpensive, standards for verification, attribution, peer review, and training must adapt. The implications are unsettling; the opportunity is extraordinary.

13.
medRxiv (Medicine) 2026-06-24

Topical fresh Taraxacum mongolicum wet dressing as an adjunct to ceftriaxone for localized skin and soft tissue infections: A single-center assessor-blinded randomized controlled trial

Background: Localized skin and soft tissue infections may need systemic antibacterials, but local inflammation can delay symptom recovery. We evaluated whether topical fresh Taraxacum mongolicum wet dressing added to ceftriaxone was associated with short-term benefit in selected clinically stable adults. Methods: In this single-center, assessor-blinded, three-arm randomized trial, 180 adults aged 18-74 years were randomized 1:1:1 to topical T. mongolicum plus intravenous ceftriaxone, topical T. mongolicum alone, or ceftriaxone alone for 7 days. The primary outcome was day-7 clinical response assessed by blinded independent assessors using prespecified global clinical improvement criteria. Analyses followed the intention-to-treat principle; sensitivity analyses assessed robustness. Results: Day-7 clinical response rates were 91.67% (55/60), 76.67% (46/60), and 68.33% (41/60) in the combined, T. mongolicum, and ceftriaxone groups, respectively (overall P = 0.006). Compared with ceftriaxone alone, combined therapy had a higher response rate (risk difference, 23.3 percentage points; 95% CI, 9.6 to 37.0; risk ratio, 1.34; 95% CI, 1.11 to 1.62). Sensitivity analyses were directionally consistent. Secondary outcomes and bacterial clearance favored the combined group. No serious adverse events were reported. Conclusions: In selected clinically stable adults with localized skin and soft tissue infections, adjunctive topical fresh T. mongolicum plus ceftriaxone was associated with improved short-term outcomes compared with ceftriaxone alone. Findings require cautious interpretation because this was a single-center, partially blinded trial without a placebo dressing control. The dressing should not replace antibiotics, drainage, or urgent care when indicated. Trial registration: International Traditional Medicine Clinical Trial Registry, ITMCTR2026000549.

14.
arXiv (quant-ph) 2026-06-24

A no-go theorem for privacy in distributed sensing using Gaussian states

arXiv:2606.23796v1 Announce Type: new Abstract: In the discrete variable setting, entangled resource states allow a set of parties to learn a global function of a set of spatially separated systems, whilst keeping the local parameters of those systems completely private. In the continuous variable setting, distributed sensing has been carried out using Gaussian resource states, but without the same guarantees about privacy. Here, we show that perfect privacy is impossible to achieve for any distributed sensing protocol that uses Gaussian states as a resource. We also introduce a measure of relative privacy, bounding the degree to which any Gaussian distributed sensing protocol can keep local parameters hidden.

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

Fi-Gaussian: Frequency-Aware Implicit Gaussian Splatting for Single Image Dehazing

Single image dehazing continues to be hindered by the loss of high-frequency details and the difficulty of accurate physical scattering modeling. To address these issues, we propose Fi-Gaussian, a frequency-aware implicit Gaussian splatting network for single image dehazing. Unlike explicit rendering methods that rely on 3D point clouds, our method employs implicit Gaussian splatting to adaptively model the underlying distribution of clear images as a continuous representation in 2D feature space. The core of the network is a frequency-aware implicit Gaussian splatting module, which decouples low-frequency structural information and high-frequency texture information in the frequency domain and then performs adaptive Gaussian aggregation with complex-valued weights to recover fine details. In addition, a physics-driven scattering renormalization mechanism is introduced to estimate the transmission map and atmospheric light under the guidance of implicit Gaussian priors. Extensive experiments on multiple benchmark datasets demonstrate that Fi-Gaussian achieves state-of-the-art quantitative performance and produces visually superior dehazed results, validating the effectiveness of implicit Gaussian splatting for low-level vision tasks.

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

Resource-Aware LLM Reasoning for Mobile Edge General Intelligence

arXiv:2509.23248v3 Announce Type: replace Abstract: The rapid advancement of large language models (LLMs) has enabled an emergence of agentic artificial intelligence (AI) with powerful reasoning and autonomous decision-making capabilities. This integration with edge computing has led to the development of Mobile Edge General Intelligence (MEGI), which brings real-time, privacy-preserving reasoning to the network edge. However, deploying LLM-based agentic AI reasoning in MEGI environments poses significant challenges due to the high computational demands of reasoning and the limited resources of edge devices. To address these challenges, we propose a joint optimization framework for efficient LLM reasoning deployment in MEGI. First, we systematically review enhancement methods to identify mechanisms suitable for edge adaptation. Subsequently, we present a distributed framework that synergizes reasoning enhancement via adaptive CoT prompting with scalable deployment through a distributed MoE architecture. An important innovation of this approach involves modeling reasoning depth as a dynamic network resource variable, which is optimized jointly with expert activation and transmission power. This mechanism allows the system to dynamically regulate expert networks and reasoning complexity according to task requirements and device capabilities. Experimental evaluations in mobile edge environments demonstrate that the proposed framework effectively balances reasoning quality and resource efficiency. The results show that with less than one second of additional inference time, both accuracy and latency satisfaction rate can reach 90\%, validating the practical viability of deploying sophisticated LLM reasoning in resource-constrained MEGI systems.

17.
arXiv (math.PR) 2026-06-25

Mean-field games with rough common noise: the linear-quadratic case

arXiv:2602.19210v3 Announce Type: replace Abstract: Motivated by mean-field games (MFG) with common noise on the one hand and pathwise stochastic control theory on the other, we formulate here a linear-quadratic (LQ) MFG with rough common noise, along with a satisfactory well-posedness theory for the linear-quadratic case. A novel Volterra-type (or mild) formulation allows to keep technical (rough-stochastic) consideration to a minimum. We derive a characterization of the optimal state and optimal control through a rough forward-backward SDE (rough FBSDE), and provide an existence and uniqueness result under the usual assumptions. Our theory is accompanied by stability estimates with respect to initial data and common noise while we also establish continuity of what we call the Itô-Lions-Lyons map for rough mean-field games. Finally, we discuss randomization of the rough common noise under appropriate conditions on the coefficients. When the latter is given by the Stratonovich lift of a Brownian motion independent of the idiosyncratic noise, we show that solutions of the rough LQ MFG coincide with those obtained by conditioning on the common noise.

18.
arXiv (CS.CV) 2026-06-15

A Robust Point Cloud Analysis Framework Inspired By Primary Visual Cortex

Despite significant advancements in point cloud analysis, reducing energy consumption and improving robustness remain understudied, largely due to the inherent limitations of Convolutional Neural Networks (CNNs). To address this issue, we draw inspiration from the primary visual cortex and propose a Dendritic-Connected Continuous-Coupled Neural Network (DC-CCNN), a novel Brain-Inspired Neural Network (BINN) architecture for point cloud analysis. By combining discrete and continuous encoding, our design replaces traditional Multilayer Perceptrons (MLPs) with more efficient and robust BINNs. Building upon this framework, we further propose an extended model, DC-CCNN++, to improve robustness under complex corruption conditions. Specifically, we introduce a Neuro-Inspired Robust Modulation-and-Readout Module (NRMR) to enhance feature stability and decision robustness through global-context gain modulation and dual-code evidence integration. We also design a Cortically Inspired Progressive Variability Training (CPVT) strategy, which progressively exposes the model to structured environmental variability while preserving stable clean-sample anchors during training. Experimental results show that DC-CCNN++ improves the performance of brain-inspired networks on point cloud analysis while maintaining performance comparable to state-of-the-art methods. Compared with the original DC-CCNN, it achieves stronger results on both classification and part segmentation, and exhibits enhanced robustness against sparsity, occlusion, Gaussian noise, salt-and-pepper noise, and spatial transformations. With its efficiency, robustness, and biologically grounded design, DC-CCNN++ provides a promising alternative to traditional deep learning methods for point cloud analysis. Code is available at https://anonymous.4open.science/r/DC-CCNNpp-44E3.

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

BenchX: Benchmarking AI Models for Cancer Detection and Localization with Demographic and Protocol Biases

Artificial intelligence (AI) has achieved remarkable success in medical imaging, but it is widely recognized that these models often perform inconsistently across real-world clinical settings. Such inconsistencies occur when patient demographics and imaging protocols vary, for example, in detecting small tumors, analyzing scans from different contrast phases, or evaluating patients of different ages or sexes. To quantify these inconsistencies, we develop a large-scale, open benchmark of 85,355 CT scans that systematically evaluates 12 tumor-detection AI models across tumor size, location, patient subgroup, and imaging protocol. We leverage large language models (LLMs) to extract and organize subgroup information from clinical data, which makes the analysis both scalable and reproducible. Our benchmark reveals that current state-of-the-art AI models, optimized for average accuracy, perform poorly in rare or underrepresented subgroups, such as young, female African Americans. However, collecting sufficient annotated data for these rare cases is often impractical. The benchmark provides a foundation for building more reliable and robust AI models for tumor detection and highlighting the need for rigorous, subgroup-level evaluation in medical imaging and computer vision. Datasets, code

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

3D-CBM: A Framework for Concept-Based Interpretability in Generative 3D Modeling

This research introduces a framework for incorporating Concept Bottleneck Models (CBMs) into 3D generative architectures to address the inherent 'semantic gap' in deep geometric learning. As deep models become central to 3D content creation, explainability shifts from a peripheral feature to a fundamental requirement for trust and accountability in safety-critical domains such as healthcare and manufacturing. CBMs provide an intrinsic interpretability solution by constraining latent representations to align with human-defined concepts, yet their application to unstructured 3D data remains largely unexplored. We design, implement, and validate a formal 3D-CBM architecture that maps raw geometric inputs, including point clouds and meshes, into a multi-tiered taxonomy of interpretable primitives and functional attributes. The framework further identifies strategic datasets, such as PartNet and ShapeNet, specialized for concept-based supervision. Experimental results from a 3D part-manipulation proof-of-concept experiment demonstrate the framework's efficacy, achieving a concept prediction accuracy of 88.8\% and a Chamfer Distance of 0.0115. Critically, the model enables precise test-time intervention, allowing for the interactive correction of structural errors. This work establishes a foundation for semantically-steerable 3D generation and invites further exploration into collaborative human-in-the-loop design systems.

21.
arXiv (quant-ph) 2026-06-15

Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques

arXiv:2601.03035v2 Announce Type: replace Abstract: This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are presented as a way to deal with linear algebra on extremely (exponentially) large matrices and vectors, regardless of any particular application. The lectures include well-known algorithms to find eigenvectors of MPOs (the celebrated DMRG), solve linear problems, and recent learning algorithms that allow one to map a known function into an MPS (the Tensor Cross Interpolation, or TCI, algorithm). The lectures end with a discussion of how to represent functions and perform calculus with tensor networks using the "quantics" representation. They include the detailed analytical construction of important MPOs such as those for differentiation, indefinite integration, convolution, and the quantum Fourier transform. Three concrete applications are discussed in detail: the simulation of a quantum computer (either exactly or with compression), the simulation of a quantum annealer, and techniques to solve partial differential equations (e.g. Poisson, diffusion, or Gross-Pitaevskii) within the "quantics" representation. The lectures have been designed to be accessible to a first-year PhD student and include detailed proofs of all statements.

22.
arXiv (math.PR) 2026-06-16

The existence of invariant sublinear expectations for $G$-SDEs

arXiv:2606.15203v1 Announce Type: new Abstract: In this paper, we study the existence of invariant sublinear expectations of Markovian semigroups on sublinear expectation spaces. To achieve this, we establish a complete metric space of sublinear expectations, on which we extend Harris' method to the nonlinear setting on the convergence of sublinear semigroups. We then explore two cases of $G-$diffusions by studying the Lyapunov function and the local Doeblin condition. One is the $G-$Brownian motion on the unit circle which is the case studied in Feng and Zhao [Zhaonon], but with the new method. Another is the multidimensional $G-$SDEs on the whole space $\mathbb{R}^d$. We establish, for the first time in the literature, the existence of the invariant sublinear expectation for $G-$SDEs under the non-degenerate and weakly dissipative assumption. For this, we prove that for a class of $G-$SDEs, the $G-$expectation can be represented as the supremum of the semigroup of a family of SDEs, of which the regularity is obtained by considering the Bismut-Elworthy-Li formula and the Denis-Hu-Peng representation for the distribution of $G-$Brownian motions.

23.
arXiv (CS.LG) 2026-06-24

New Bounds for the Last Iterate of the Stochastic subGradient Method

arXiv:2606.24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives. For a fixed horizon $n$, we consider the standard fixed stepsizes $\eta =\Theta(1/\sqrt n)$. We prove that, for such stepsize policies, under additive i.i.d. subgradient noise with uniformly bounded variance, the last iterate features an optimization error of order $1/\sqrt n$, thereby removing the extra $(\log n)$ factor present in existing generic bounds. On the other hand, we show that without the i.i.d. assumption, the optimization error can be of order $(\log n)/\sqrt n$. Thus, under the uniformly bounded variance assumption alone, the last iterate of SsGM is suboptimal even in dimension one, resolving negatively an open problem posed in Koren and Segal, COLT, 2020.

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

Frontier: Towards Comprehensive and Accurate LLM Inference Simulation

arXiv:2605.21312v2 Announce Type: replace-cross Abstract: Modern LLM serving is no longer homogeneous or monolithic. Production systems now combine disaggregated execution, complex parallelism, runtime optimizations, and stateful workloads such as reasoning, agents, and RL rollouts. Simulation is attractive for exploring this growing design space, yet existing simulators lack the architectural completeness and decision-grade fidelity it demands. Their monolithic-replica abstractions are ill-suited to disaggregated serving, while average-case analytical proxies can distort SLA predictions and even reverse optimization conclusions. We present Frontier, a discrete-event simulator for modern LLM inference serving. Frontier features a disaggregated abstraction. It captures the structure and dynamics of modern serving systems by modeling co-location, Prefill-Decode Disaggregation (PDD), and Attention-FFN Disaggregation (AFD) with role-specific cluster workers, incorporating key runtime optimizations (e.g., CUDA Graphs, speculative decoding) within the scheduler-batch-engine loop, and supporting stateful requests for emerging workloads. It further provides accurate and generalizable predictions of computation, communication, and memory costs across diverse serving scenarios with complex workload compositions. On 16-H800 GPU testbed, Frontier achieves an average throughput error below 4%. Compared with state-of-the-art simulators, it reduces end-to-end latency error from 44.9% to 6.4% under co-location and from 51.7% to 2.6% under disaggregation. It scales to over 1K GPUs on commodity CPUs and enables new use cases such as SLA-dependent Pareto frontier exploration, heterogeneous disaggregated allocation, agentic reasoning scheduling validation, and RL post-training reconfiguration. We release Frontier at https://github.com/NetX-lab/Frontier.

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

Evaluating and Preserving Lexical Stress in English-to-Chinese Speech-to-Speech Translation

Speech-to-speech translation (S2ST) systems have achieved impressive progress in semantic accuracy and speech naturalness. However, the cross-lingual transfer of lexical stress, a vital cue for emphasis and speaker intent, remains heavily underexplored, compounded by a lack of reliable automatic evaluation metrics for tonal languages like Chinese. We investigate English-to-Chinese S2ST stress transfer by constructing a stress-annotated Chinese dataset and an XLS-R-based Mandarin stress detector. Integrating this with the English EmphAssess system, we propose a novel objective metric for cross-lingual stress evaluation. Furthermore, we fine-tune CosyVoice3 to build a stress-aware S2ST system. Experiments demonstrate that our proposed S2ST architecture significantly outperforms existing systems in stress translation capability while maintaining competitive translation quality. Furthermore, our evaluation metric exhibits a strong correlation with human subjective judgments.