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

MentisOculi: Revealing the Limits of Reasoning with Mental Imagery

Frontier models are transitioning from multimodal large language models (MLLMs) that merely ingest visual information to unified multimodal models (UMMs) capable of native interleaved generation. This shift has sparked interest in using intermediate visualizations as a reasoning aid, akin to human mental imagery. Central to this idea is the ability to form, maintain, and manipulate visual representations in a goal-oriented manner. To evaluate and probe this capability, we develop MentisOculi, a procedural, stratified suite of multi-step reasoning problems amenable to visual solution, tuned to challenge frontier models. Evaluating visual strategies ranging from latent tokens to explicit generated imagery, we find they generally fail to improve performance. Analysis of UMMs specifically exposes a critical limitation: While they possess the textual reasoning capacity to solve a task and can sometimes generate correct visuals, they suffer from compounding generation errors and fail to leverage even ground-truth visualizations. Our findings suggest that despite their inherent appeal, visual thoughts do not yet benefit model reasoning. MentisOculi establishes the necessary foundation to analyze and close this gap across diverse model families.

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

InterleaveThinker: Reinforcing Agentic Interleaved Generation

Recent image generators have demonstrated impressive photorealism and instruction-following capabilities in single-image generation and editing. However, constrained by their architectures, they cannot achieve interleaved generation (text-image sequence), which has crucial applications in visual narratives, guidance, and embodied manipulation. Even the latest open-source Unified Multimodal Models (UMMs) exhibit limited performance in this regard. In this paper, we introduce InterleaveThinker, the first multi-agent pipeline designed to endow any existing image generator with interleaved generation capabilities. Specifically, we employ a planner agent to organize the image-text input sequence, instructing the image generator on the required execution at each step. Subsequently, we introduce a critic agent to evaluate the generator's outputs, identify samples that deviate from the planned instructions, and refine the instructions for regeneration. To implement this pipeline, we construct the Interleave-Planner-SFT-80k and Interleave-Critic-SFT-112k to perform a format cold-start. Then we develop Interleave-Critic-RL-13k to reinforce the step-wise instruction correction capability within a generation trajectory using GRPO. Since a single interleaved generation trajectory may involve over 25 generator calls, optimizing the entire trajectory is computationally impractical. Therefore, we propose accuracy reward and step-wise reward, allowing single-step RL to effectively guide the entire generation trajectory. The results show that InterleaveThinker improves performance across various image generators. On interleaved generation benchmarks, it achieves performance comparable to Nano Banana and GPT-5. Surprisingly, it also significantly enhances the base model on reasoning-based benchmarks; for example, on 4-step FLUX.2-klein, we observe substantial gains on WISE and RISE.

03.
bioRxiv (Bioinfo) 2026-06-15

Inferring Cell Fate Trajectories in Time-Resolved Metabolic RNA Labeling data

Single-cell RNA sequencing provides high-resolution snapshots of cellular states but lacks direct information about transcriptional dynamics. Metabolic RNA labeling addresses this limitation by distinguishing newly synthesized RNA, offering insight into the direction of cell state changes, and providing valuable information when attempting to recover the underlying continuous dynamics from static snapshots of cell distributions. However, existing trajectory inference methods do not fully exploit this additional signal. Here, we propose FLOWSATATE, a framework for single-cell trajectory inference that leverages time-resolved RNA labeling within an Optimal Transport setting. We model cell dynamics as a gradient flow in an inferred potential landscape parameterized by a neural network, integrating both total and labeled RNA across time points. The learned potential enables identification of key genes and transcription factors driving cell fate decisions and supports prediction of future cellular states. We benchmark our approach on its ability to generalize unseen data and recover coherent trajectories. We also apply it to study colorectal cancer response to demethylation treatment as well as neuronal differentiation of embryonic stem cells.

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

CACR:Reinforcing Temporal Answer Grounding in Instructional Video via Candidate-Aware Causal Reasoning

The task of temporal answer grounding in instructional video (TAGV), which aims to locate precise video segments that respond to natural language queries, is increasingly important for direct video answer retrieval. This task remains challenging due to the need to comprehend semantically complex questions and to address the significant length mismatch between untrimmed videos and short target moments. Existing methods often suffer from sensitivity to irrelevant content or insufficient visual reasoning capabilities. To tackle these limitations, we propose a Candidate-Aware Causal Reasoning (CACR) framework. Our approach first employs a Visual-Language Pre-training based Candidate Selection (VBCS) algorithm to efficiently generate K candidate segments, then applies a temporal logic reasoning module enhanced by a rejection reward mechanism and optimized via Group Relative Policy Optimization (GRPO) for robust inference. Extensive experiments on six benchmarks demonstrate that our method achieves state-of-the-art performance in terms of mean Intersection-over-Union (mIoU), providing a new perspective for reasoning-based retrieval in long videos.

05.
arXiv (CS.CL) 2026-06-11

ICA Lens: Interpreting Language Models Without Training Another Dictionary

Finding interpretable directions in language-model representations is critical for understanding and controlling model behavior. Sparse autoencoders (SAEs) have become the standard tool for this purpose, but using them as the default first lens often requires training, storing, and evaluating large overcomplete dictionaries. This bottleneck limits rapid exploration and raises a fundamental question: how much interpretable structure is already visible from activation geometry before training another neural dictionary? Our intuition is simple: many interpretable directions are selective on tokens, and these directions should look less Gaussian than random directions. We therefore revisit independent component analysis (ICA), a classical method for finding non-Gaussian directions, as a compact lens for language-model interpretability. We find that ICA has been underestimated for LLM interpretability, because prior uses often relied on off-the-shelf ICA implementations that are brittle on LLM activations and lacked systematic tools for inspecting and evaluating the recovered directions. To bridge these gaps, we introduce ICALens, the first practical workflow for stable, efficient, and auditable ICA analysis of LLM representations. It combines an optimized GPU-parallel FastICA pipeline with LLM-specific stability recipes and better fitting diagnostics, enabling efficient and reliable layer-wise analysis. Across GPT-2 Small, Gemma 2 2B, and Qwen 3.5 2B Base, ICALens efficiently recovers compact, human-interpretable directions without per-layer gradient-based dictionary training. On SAEBench, ICA is competitive with public SAEs in sparse probing and outperforms them in targeted probe perturbation under small-to-medium budgets. These results suggest that ICA should not be viewed as a weak baseline, but as an efficient and complementary first lens for exploring language-model representations.

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

Equivariant Representation Learning via Class-Pose Decomposition

arXiv:2207.03116v4 Announce Type: replace Abstract: We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.

07.
arXiv (CS.AI) 2026-06-18

Where Did the Variability Go? From Vibe Coding to Product Lines by Regeneration

arXiv:2606.19042v1 Announce Type: cross Abstract: In vibe coding, an emerging AI-driven paradigm, an LLM generates an entire program from a natural language prompt, but what happens to the variability that traditional software engineering carefully builds into code? To answer this question, we conducted an exploratory analysis on 10 vibe coded C/C++ projects, which suggests that there is near-zero in-artifact variability, i.e., at compile and runtime. All variability decisions are resolved at a single new binding time, generation time, the moment the LLM produces the source code. Rather than treating this as a defect to fix, we propose Variability by Regeneration (VbR), to our knowledge the first product-line approach in which the LLM acts as the derivation engine, generating a purpose-built, free of dead code binary for each variant from a declarative specification, while a variant dispatcher transparently routes user requests to the matching binary. We formalise VbR, contrast it with classical SPL derivation, and demonstrate its full pipeline on a wc product family. For SPL engineering, variability in AI-generated software belongs in the specification, not in the code.

08.
arXiv (CS.LG) 2026-06-19

Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions

arXiv:2512.17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{m \times n}$ and a factorization rank $r \ll \min(m, n)$, NMD seeks matrices $W \in \mathbb{R}^{m \times r}$ and $H \in \mathbb{R}^{r \times n}$ such that $X \approx f(WH)$, where $f$ is an element-wise nonlinear function. We evaluate our method on several representative nonlinear models: the rectified linear unit activation $f(x) = \max(0, x)$, suitable for nonnegative sparse data approximation, the component-wise square $f(x) = x^2$, applicable to probabilistic circuit representation, and the MinMax transform $f(x) = \min(b, \max(a, x))$, relevant for recommender systems. The proposed framework flexibly supports diverse loss functions, including least squares, $\ell_1$ norm, and the Kullback-Leibler divergence, and can be readily extended to other nonlinearities and metrics. We illustrate the applicability, efficiency, and adaptability of the approach on real-world datasets, highlighting its potential for a broad range of applications.

09.
arXiv (math.PR) 2026-06-11

Sample Path Properties of the Fractional Wiener–Weierstrass Bridge II

arXiv:2606.11994v1 Announce Type: new Abstract: Fractional Wiener–Weierstrass bridges are a class of Gaussian processes obtained by replacing trigonometric functions in the construction of classical Weierstrass functions by fractional Brownian bridges. A number of their sample path properties were derived in Schied–Zhang (2024,2026). The analysis in these papers left several open questions, most of which are addressed here. Specifically, we prove that, in the regime in which the Weierstrass mechanism dominates the underlying fractional Brownian bridge, the limiting $b$-adic variation coefficient has an absolutely continuous distribution and is therefore genuinely random. At the critical point between the two roughness regimes, we establish the power-variation formula and the critical $\Phi$-variation limit conjectured in Schied–Zhang (2024). Finally, we derive the Hausdorff dimension for the graphs of the sample paths by proving a conjecture from Schied–Zhang (2026) for the missing high-Hurst case.

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

Aligning Quantum Operators with Large Language Models

arXiv:2606.13811v1 Announce Type: cross Abstract: Can Large Language Models (LLMs) understand and reason about quantum operators? Despite their remarkable capabilities in mathematics and symbolic reasoning, LLMs remain inherently blind to quantum representations such as unitary matrices. In this work, we take a step toward bridging this gap by introducing an approach that maps unitary operators into the latent space of an LLM, enabling unified modeling over quantum and linguistic inputs. We instantiate this idea on Clifford+T circuit synthesis over a Pauli rotation gate set, where our model achieves results competitive with state-of-the-art methods and scales consistently with training data, with no signs of saturation. Our approach further enables language-conditioned synthesis, allowing gate constraints unseen during training to be specified directly in natural language. This work suggests a path toward quantum–aware foundation models that can natively interpret and reason about quantum operations, which could have broader implications reaching across quantum compilation and algorithm discovery.

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

Q-Fold: Query-Aware Focus-Context Spatio-Temporal Folding for Long Video Understanding

Long-video understanding remains challenging for multimodal large language models, because temporally extended videos often contain thousands of frames and are therefore expensive to process exhaustively. Existing methods usually construct compact visual inputs from long videos under a limited visual budget. However, most of them still follow a frame-centric paradigm and apply similar representations to retained content regardless of its importance. This makes it difficult to preserve both high-fidelity visual evidence and broad temporal coverage. To address this issue, we propose Q-Fold, a training-free input construction framework for long-video understanding. Instead of treating isolated frames as the basic modeling unit, Q-Fold operates on contiguous temporal segments and constructs a heterogeneous Focus–Context representation under query guidance. Query-relevant segments are preserved as high-fidelity Focus Frames, while less relevant segments are folded into chronology-preserving contextual layouts. In this way, Q-Fold preserves critical visual evidence and broad temporal coverage, while better maintaining local temporal continuity within short segments. Experiments on four long-video benchmarks with multiple Video-MLLMs show that Q-Fold consistently improves performance without increasing the input budget. Notably, it achieves gains of up to 9.1 percentage points on an ultra-long video benchmark. Code will be made publicly available.

12.
arXiv (CS.CV) 2026-06-11

Towards Conditional Feature Alignment for Cross-Domain Counting

Object counting models often degrade under cross-domain deployment because density composition varies across domains and is itself task-relevant. Standard feature alignment methods tend to suppress such variation by encouraging global domain invariance, which can be harmful when source and target domains contain different proportions of background, sparse foreground, and dense foreground. We propose Conditional Feature Alignment (CFA), a cross-domain counting framework that aligns representations within label-induced conditions rather than across full marginal feature distributions. Given density annotations or pseudo-density predictions, CFA constructs foreground/background or density-level conditions and aligns only features belonging to matching conditions. We formalise this idea through a conditional divergence perspective, showing that conditional alignment removes within-condition discrepancy while preserving condition-marginal density shift. For unsupervised domain adaptation, CFA estimates source conditions from annotations and target conditions from detached pseudo-density maps, then performs condition-wise adversarial alignment with full-image consistency regularisation. For source-domain generalisation, we instantiate the same principle with MPCount by enforcing condition-wise memory-consistency between generated source-domain views. Experiments on crowd and cell counting benchmarks show competitive or improved performance across diverse UDA and DG settings. For example, on JHU-CROWD++ FH$\rightarrow$SN, CFA-DG reduces MAE/RMSE from MPCount's 216.3/421.4 to 90.5/169.9, indicating that condition-wise alignment is especially effective under large weather- and density-induced shifts. These results suggest that condition-wise alignment is a promising design principle for domain-adaptive counting.

13.
arXiv (CS.CV) 2026-06-16

Detect Before You Leap: Mirage Detection in Vision-Language Models

Vision-language models (VLMs) can produce confident visual answers even when the required visual evidence is missing, blank, or unrelated to the question. This failure mode, recently described as mirage (mirage2026), is especially concerning in medical and document VQA, where a plausible but visually ungrounded answer may be mistaken for image-based evidence. We study the complementary problem of pre-release mirage detection: given an image-question pair, determine whether the VLM should answer or abstain before generation. To that end, we propose a novel model-agnostic Text-Conditioned Layer-wise Internal Alignment (TC-LIA) method that probes patch-token representations across the layers of a CLIP ViT-H/14 vision encoder. The key idea is to project layer-wise image patch tokens into the final CLIP embedding space and measure their similarity with the question embedding, thereby tracking whether question-relevant visual evidence emerges across vision layers. TC-LIA summarizes this alignment trajectory using final image-text cosine similarity, late-layer top-k patch-text alignment, early-to-late gain, and layer-wise slope. These features are combined with pixel-statistic based blank/noise detection, zero-shot domain routing, and structured VLM self-assessment in an ensemble. Across five VQA domains with related, unrelated-real, and blank/noise inputs, and across twelve VLM backbones, Qwen2.5-VL-32B achieves the highest three-class detection accuracy of 94.7% with a 3.0% mirage rate, while Qwen2.5-VL-72B achieves 94.6% accuracy with a lower 2.8% mirage rate. Baseline mirage rates span 21.7-66.6%.

14.
arXiv (CS.AI) 2026-06-18

UPLOTS: A Unified Pretrained Language Model for Constrained Time-series Generation

arXiv:2606.10466v2 Announce Type: replace-cross Abstract: In time-series generation, existing approaches typically handcraft ortrain a separate model for each dataset, which hinders their scalability and fails to leverage shared temporal structures across domains. To address this fragmentation, we propose UPLOTS, a Unified, Prompt-guided Language model framework fOr constrained Time-Series Generation across diverse domains. Instead of building task-specific models, UPLOTS leverages a single pre-trained transformer backbone guided by learned constraint prompts, enabling on-demand generation with precise pattern control. One key innovation is our dynamic multi-dataset loss re-weighting and prompt-to-pattern mapping, which allows UPLOTS to internalize diverse temporal structures during training and conditionally generate them at inference. We evaluate UPLOTS on four real-world benchmarks and multiple constraint settings, including peak-period, calendar, load-level, and volatility patterns. Additional held-out constraint-combination and downstream forecasting experiments further demonstrate that UPLOTS generalizes beyond the original peak-pattern setting and improves data augmentation under scarce real-data regimes. Our code and baselines are available at anonymous github repo: https://anonymous.4open.science/r/UPLOTS-6C36.

15.
bioRxiv (Bioinfo) 2026-06-20

Ribosomes are covered by a coat of flexible protein fragments

Ribosomal proteins contain flexible terminal regions that are averaged out during electron density reconstructions, rendering them absent from experimental models derived by X-ray crystallography or cryogenic electron microscopy. These flexible protein fragments (FPFs) collectively form an invisible coat on the ribosome surface whose presence has been systematically overlooked. Here we analysed FPFs from 36 ribosomes spanning bacteria, eukaryotes, and mitochondria. We found that mitoribosomes harbour the most numerous and longest FPFs. Structural predictions confirmed that FPFs are predominantly disordered across all ribosome classes. Comparison of FPF amino acid composition against proteome-wide background frequencies revealed strong and domain-specific compositional biases. The balance between arginine and lysine content tracks the cardiolipin content of the membrane each ribosome class contacts. The arginine enrichment in mitoribosomal FPFs may additionally reflect selection arising from the RNA-rich environment of mitochondrial RNA granules, membraneless condensates where mitoribosomes are assembled. FPFs are uniformly depleted in aromatic residues, arguing against protein-driven liquid–liquid phase separation propensity. Our findings suggest that the flexibly tethered coat is a highly functional intrinsic part of all ribosomes.

16.
arXiv (CS.CV) 2026-06-18

Generalized Kullback-Leibler Divergence Loss

In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of (1) a weighted Mean Square Error (wMSE) loss and (2) a Cross-Entropy loss incorporating soft labels. Thanks to the decoupled structure of DKL loss, we have identified two areas for improvement. Firstly, we address the limitation of KL loss in scenarios like knowledge distillation by breaking its asymmetric optimization property along with a smoother weight function. This modification effectively alleviates convergence challenges in optimization, particularly for classes with high predicted scores in soft labels. Secondly, we introduce class-wise global information into KL/DKL to reduce bias arising from individual samples. With these two enhancements, we derive the Generalized Kullback-Leibler (GKL) Divergence loss and evaluate its effectiveness by conducting experiments on CIFAR-10/100, ImageNet, and vision-language datasets, focusing on adversarial training, and knowledge distillation tasks. Specifically, we achieve new state-of-the-art adversarial robustness on the public leaderboard – RobustBench and competitive knowledge distillation performance across CIFAR/ImageNet models and CLIP models, demonstrating the substantial practical merits. Our code is available at https://github.com/jiequancui/DKL.

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

Quest for quantum advantage: Monte Carlo wave-function simulations of the Coherent Ising Machine

arXiv:2501.02681v2 Announce Type: replace Abstract: The Coherent Ising Machine (CIM) is a quantum network of optical parametric oscillators (OPOs) intended to find ground states of the Ising model. This is an NP-hard problem, related to several important minimization problems, including the max-cut graph problem. In order to enhance its potential performance, we analyze the coherent coupling strategy for the CIM in a highly quantum regime. To explore this limit, without assuming gaussianity, we employ accurate numerical simulations. Due to the inherent complexity of the system, the maximum network size is limited. While master equation methods can be used, their scalability diminishes rapidly for larger systems. Instead, we use Monte Carlo wave-function methods, which scale as the wave-function dimension, and use large numbers of samples. These simulations involve Hilbert spaces exceeding $10^{7}$ dimensions. To evaluate success probabilities, we use quadrature probabilities. We demonstrate the potential for quantum computational advantage by reducing the time required to reach maximum success probability in a low-dissipation regime enabled by initial quantum superpositions and entanglement. Furthermore, we demonstrate that tailored time-dependent couplings can amplify these quantum effects. Comparisons with classical CIM models give evidence that quantum tunneling effects in this strong coupling limit can overcome trapping in false minima. This can greatly increase success rates, indicating a potential for quantum advantage. Finally, we perform a coherence analysis based on the state purity to examine the role of quantum coherence in CIM performance and to determine how state purity correlates with improved optimization outcomes.

18.
arXiv (quant-ph) 2026-06-15

Real-time pseudo entropy and modular-Hamiltonian correlations

arXiv:2606.14208v1 Announce Type: cross Abstract: Pseudo entropy is a complex-valued generalization of entanglement entropy defined from a reduced transition matrix. We study the pseudo entropy associated with a real-time transition matrix between an initial pure state and its unitary time evolution. For a subsystem $A$, we show that the short-time behavior of real-time pseudo entropy is governed by the correlation between the physical Hamiltonian $H$ and the modular Hamiltonian $K_A=-\log\rho_A$ of the initial reduced state, $ S_A(t,0)=S_A(0)-it \langle K_A(H-\langle H\rangle)\rangle + \mathcal{O}(t^2)$. For Hermitian dynamics, the initial imaginary response is controlled by the symmetrized covariance of $H$ and $K_A$ with an overall minus sign, while the initial real response is governed by their commutator. Thus the imaginary part of real-time pseudo entropy is not merely a branch artifact: it is a time-oriented modular response generated by the correlation between microscopic time evolution and subsystem coarse graining. We clarify the relation of this result to the known first law of pseudo entropy, derive an all-order expression in a Schmidt-diagonal model, recover thermal pseudo entropy as a special case, illustrate the covariance/commutator decomposition in a two-qubit model, and confirm the covariance response in transverse-field Ising-chain quenches, including a finite-size study of a modular susceptibility near the Ising critical region. We discuss how this amplitude-level oriented response can be related to ordinary entropy production, and also give a concrete $\mathcal{PT}$-symmetric toy-model illustration of the non-Hermitian extension.

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

ToolSense: A Diagnostic Framework for Auditing Parametric Tool Knowledge in LLMs

arXiv:2606.12451v1 Announce Type: new Abstract: Large language models deployed as agents over large tool catalogs face a critical tool-retrieval bottleneck. As embedding-based retrieval approaches rely on compact encoders that may under-capture specialized tool semantics, parametric tool retrieval addresses this by encoding each tool as a virtual token appended to the LLM vocabulary, fine-tuned in two stages (memorization then retrieval SFT) to use the LLM as a retriever, achieving strong performance on standard ToolBench retrieval benchmarks. Yet these benchmarks use verbose, fully-specified queries, and their evaluation applies constrained decoding that restricts outputs to valid token paths, neither reveals whether the model actually understands its tools. We introduce ToolSense, an open-source LLM-powered diagnostic framework that takes any tool catalog as input and automatically generates three benchmarks: a Realistic Retrieval Benchmark (RRB) with queries at three ambiguity tiers, an MCQ probing benchmark, and a QA probing benchmark. Applying ToolSense to ToolBench (~47k tools) and evaluating five parametric model training configurations reveals a knowledge-retrieval dissociation: on RRB queries, several configurations collapse by ~50-64 percentage points compared to fully-specified ToolBench benchmarks, falling below the embedding-model baseline. Additionally, despite strong retrieval performance, some models score near-random on factual probes, suggesting a knowledge-retrieval dissociation. We open-source the ToolSense framework and the ToolBench diagnostic benchmarks at https://github.com/SAP/toolsense.

20.
arXiv (quant-ph) 2026-06-15

Dissipation-induced superradiance in matter coupled to a self-interacting cavity

arXiv:2606.14526v1 Announce Type: new Abstract: Light-matter interactions are often modeled via the Dicke model, namely, by two-level systems coupled to a cavity mode. Alas, the threshold for superradiance is often experimentally inaccessible or hindered by light's diamagnetic term. Here, within the Dicke setting, we consider self-interacting light in a cavity, modeled by a photonic Kerr nonlinearity. We show that negative Kerr nonlinearity gives rise to a low-threshold superradiant phase with spin inversion. While unstable in a closed system, cavity dissipation stabilizes this lit phase, opening avenues for lasing and bath-engineered phases.

21.
arXiv (math.PR) 2026-06-18

Stable size-biasing and the positive scale-mixture order of generalized Gaussian laws

arXiv:2606.18458v1 Announce Type: new Abstract: Let $X_r\sim N_r(0,1)$ be the centered unit-scale generalized Gaussian random variable with density proportional to $\exp(-|x|^r/2)$. We prove that, for $p,q>0$, there exists a strictly positive random variable $V$, independent of $X_q$, such that $X_p\stackrel{d}{=}VX_q$ if and only if $p\le q$. Moreover, the law of $V$ is unique. For $pq$, the required Mellin quotient, viewed as the candidate characteristic function of $\log V$, is unbounded by Stirling's formula, and hence cannot be a characteristic function. The factor laws form a multiplicative cocycle, $V_{p,r}\stackrel{d}{=}V_{p,q}V_{q,r}$, for $p\le q\le r$, where the factors on the right-hand side are independent copies. Thus the Mellin quotient isolated by Dytso, Bustin, Poor and Shamai is realized constructively throughout the $p

22.
medRxiv (Medicine) 2026-06-18

Guiding the development of climate counterfactuals for health impact attribution studies

Climate change detection and attribution (D&A) methods have become vital for quantifying the influence of anthropogenic forcing on the Earth's systems, including human health. Health impact attribution (HIA) studies seek to disentangle climate-driven health effects from natural variability yet are often constrained by the availability of accessible counterfactual climate scenarios. This tutorial paper presents a flexible, reproducible framework for developing counterfactual climates without reliance on computationally intensive global circulation models. We provide practical, R-based methodologies for constructing both trend-based (temperature and non-temperature) and event-based counterfactual, using a variety of techniques including model residual detrending, data-driven decomposition (e.g., Singular Spectrum Analysis and Empirical Mode Decomposition) and stochastic weather generators. The tutorial also explores the incorporation of greenhouse gas concentrations as forcing variables, rather than global mean temperature anomalies. By operationalising these methods through worked examples and an open code repository, this paper aims to build capacity within the HIA community, enhance methodological transparency, and foster interdisciplinary collaboration between climate and health researchers.

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

Beyond Uniform Token-Level Trust Region in LLM Reinforcement Learning

arXiv:2606.10968v2 Announce Type: replace-cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has become standard for improving LLM reasoning. However, existing PPO-style trust-region mechanisms remain position-agnostic by enforcing uniform thresholds across all tokens independently. This pointwise treatment conflicts with autoregressive generation in two critical ways. First, uniform thresholds ignore autoregressive asymmetry. Early-stage deviations produce compounding sequence-level drift, causing static thresholds to under-regulate early divergence and excessively constrain late-stage exploration. Second, evaluating token-level divergence in isolation overlooks cumulative prefix drift, granting the same divergence allowance regardless of how far the conditioning history has already deviated from the rollout policy. To address this limitation, we propose CPPO (Cumulative Prefix-divergence Policy Optimization), a token-level masking rule that aligns updates with a finite-horizon policy-improvement bound via two coupled mechanisms. First, a position-weighted threshold imposes stricter limits at early positions whose effects persist longer, relaxing constraints for late-stage tokens. Second, a cumulative prefix budget tracks historical deviations, dynamically restricting further token-level deviation to prevent compounding errors along the prefix. Empirically, CPPO enhances training stability and significantly improves reasoning accuracy across various model scales.

24.
arXiv (math.PR) 2026-06-11

On the $d$-rigidity phase transition in random graphs

作者:

arXiv:2605.25711v2 Announce Type: replace-cross Abstract: We study generic $d$-dimensional rigidity in sparse random graphs. Our main result is that for every $d\ge 2$, the Erdős–Rényi random graph $G\sim G(n,c/n)$ undergoes a $d$-rigidity phase transition at the known, explicit, $d$-orientability threshold $c_d$: If $cc_d$, then $G$ is a.a.s. not independent in the generic $d$-rigidity matroid, and we give a sharp asymptotic estimate for its rank. In addition, the $d$-rigidity closure of $G$ has a giant clique of linear size, which contains all but at most $o(n)$ vertices of the $((d+1)+d)$-core of the graph. More generally, we compute, up to a $1+o(1)$ factor, the generic $d$-rigidity rank of random graphs with a given degree distribution. For example, we show that the uniform $n$-vertex $k$-regular graph a.a.s. has rank $\min(k/2,d)n+o(n).$ Our approach is to estimate the rigidity rank of a random graph from its Galton–Watson local weak limit, using a parameter that we call local flexibility.

25.
arXiv (CS.LG) 2026-06-11

PianoKontext: Expressive Performance Rendering from Deadpan Context

arXiv:2606.12282v1 Announce Type: cross Abstract: Expressive performance rendering (EPR) aims to generate realistic performances constrained on sequences of notes. However, flow matching audio editing models manipulate only synchronized music samples of the same duration, limiting their understanding of expressive timing. We introduce PianoKontext, a flow matching rendering model for classical piano music that generates variable-length performances in the latent space of a pretrained Music2Latent model. We synthesize MIDI scores into deadpan audio and employ Dynamic Time Warping (DTW) in the latent space to construct paired data for training. The aligned embeddings are concatenated in DiT blocks, allowing for a simple and effective learning of the dependencies between the score and performances. Audio samples are available at our demo page: https://realfolkcode.github.io/pianokontext_demo/.