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

InvDesMobility: a reliability-gated first-principles feedback framework for closed-loop materials discovery

arXiv:2606.16133v1 Announce Type: cross Abstract: Inverse materials design starts from target functionality and searches for structures that can realize it. Its value in closed-loop discovery depends not only on prediction performance, but also on whether expensive first-principles results are independently validated, provenance-recorded, and admitted as feedback only when evidence is sufficient. This is especially important for composite properties such as carrier mobility, where a final scalar value hides intermediate quantities, fit quality, convergence history, and workflow assumptions. Here we present InvDesMobility, a reliability-gated first-principles feedback framework that integrates multi-agent automated DFT, evidence stratification, generative structure proposal, acquisition ranking, and auditable release. Using 516 2DMatPedia-derived candidates, the workflow produced 280 QC-passed materials and 573 retained carrier-direction seed channels after channel-level reliability gating. These records were split into two feedback objects: relaxed structures updated the generative model, while retained mobility channels trained the acquisition model and set validation priority. Over multiple iterations, InvDesMobility screened 2.4 x 10^6 structures, submitted 102 candidates for DFT validation, and retained 86 reliability-gated generated channels across 41 formulas. Overall, the main contribution is not a fixed list of high-mobility materials, but a transferable feedback contract that makes closed-loop inverse design both useful and auditable when learning from expensive calculated properties. All source data, retained feedback records, and workflows are available at https://github.com/DreamLufei/invDesMobility, with an accompanying evidence website at https://dreamlufei.github.io/invDesMobility/.

02.
arXiv (CS.AI) 2026-06-19

Before the Pull Request: Mining Multi-Agent Coordination

arXiv:2606.19616v1 Announce Type: cross Abstract: Autonomous coding agents now open millions of pull requests, yet large-scale studies find their PRs are produced faster but accepted less often - a coordination and trust gap that pull-request-level telemetry cannot explain. We argue the missing signal lives before the PR, in how concurrent agents claim, divide, and collide over shared work. We study this process through grite, our open-source coordination substrate that needs no central server and stores its records inside git itself, so its append-only, signed event log captures the coordination process directly. We show that (i) this shared substrate reduces duplicate and conflicting work at bounded overhead - the share of work that merely re-does a teammate's task falls from 78% to 0% while useful throughput more than triples; (ii) every agent's copy of the log converges to the same state with no write silently dropped, where a file-based tracker loses concurrent writes; and (iii) the log is a mineable artefact from which concrete failure modes - conflicting edits, lock starvation, redundant rediscovery, race-to-close - are automatically recoverable with provenance, several invisible in pull-request history. We release the dataset, harness, and mining toolkit.

03.
Nature (Science) 2026-06-10

Mitochondria directly interact with the nuclear pore complex

Mitochondria regulate cellular processes through direct and indirect interactions with other organelles. A well-studied example has been contact with the endoplasmic reticulum at mitochondrial-associated endoplasmic reticulum membranes1, which control pathways including redox and calcium homeostasis2,3. Recent studies have also reported direct mitochondria–nuclear membrane contacts in cancer cells and yeast that promote pro-survival signalling4,5. Here we identify direct interactions between mitochondria and nuclear pores. Using two unbiased proteomic screens, GST pulldown and BioID, we found that VDAC1 was the top mitochondrial candidate that interacts with the filamentous nuclear pore protein RANBP2. In vitro RANBP2 CRISPR knockout, RANBP2 truncation or site-directed mutagenesis of RANBP2–VDAC1 interacting amino acids resulted in reduced mitochondria–nucleus proximity and decreased nuclear ATP and phosphocreatine levels. This was accompanied by a decline in the levels of the nuclear phosphoproteome and downregulation of pathways involved in histone modification, cellular differentiation and transcriptional regulation in vitro. Moreover, deletion of the RANBP2 C-terminal domain in vivo in mice resulted in embryonic lethality due to cardiac and neural crest differentiation defects. Collectively, these results describe a mechanism by which mitochondria directly interact with the nuclear pore complex, a phenomenon critical for regulation of nuclear energetics and cellular differentiation. Undoubtedly, additional roles of this interaction remain to be revealed. Mitochondria interact directly with the nuclear pore complex via VDAC1–RANBP2 binding to sustain nuclear ATP levels.

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

Robust State-Conditional Feature-Weighted Jump Models for Temporal Clustering

arXiv:2606.13146v1 Announce Type: cross Abstract: We propose a robust feature-weighted jump model for time-dependent clustering. A penalty is used to encourage smoothness of transitions over time, while robustness is achieved through the use of a Tukey's biweight loss function. An additional parameter controls the variability of feature weights across states, allowing the model to assign state-specific relevance to each feature. We illustrate in simulation how the method accurately recovers the true cluster sequence and reliably identifies relevant features, outperforming competing approaches, particularly in the presence of outliers. We conclude with two empirical applications, one on the number of conflict-related homicides in Kosovo in the period 1998-2000, and another on macroeconomic performance of twelve European countries in the period 1949-2024.

05.
arXiv (math.PR) 2026-06-11

Marked random graphs with given degree sequence: large deviations on the local topology

arXiv:2401.00351v2 Announce Type: replace Abstract: We investigate the behavior of the empirical neighborhood distribution of marked graphs in the framework of local weak convergence. Here we extend known results by considering uniform random graphs with given degree sequences and i.i.d. marks on half-edges and vertices. We establish a large deviation principle for such families of empirical measures. The proof builds on Bordenave and Caputo's seminal 2015 paper, and Delgosha and Anantharam's 2019 introduction of BC entropy, relying on combinatorial lemmas that allow one to construct suitable approximations of measures supported on marked trees. Possible applications of these results are in the study of interacting diffusions on top of random graphs.

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

4DP-QA: Scalable QA for 4D Perception in Vision Language Models

Despite recent advances, Vision Language Models (VLMs) still struggle to grasp the dynamics of the world. We note that the ability to reason about a 4D scene, challenging in itself, is further complicated by two factors. First, VLMs observe motion indirectly via its projection onto 2D images. Second, existing datasets fail to disentangle object and camera motion. To address these challenges, we present a QA generation pipeline that focuses on motion-related scene understanding. We take particular care of the entanglement of camera and object motion by casting tracking in both the traditional way and in a novel, fixed reference system, dubbed True-Motion Tracking, which provides an intuitive description of motion. From this pipeline, we generate a large-scale training dataset of 400K samples, 4DP-QA (4D Perception QA), and a 2.2K-sample benchmark, 4DP-QA-Bench. Training existing models on our dataset yields performance improvements on an external benchmark, validating the effectiveness of our method.

07.
arXiv (CS.LG) 2026-06-16

Continual Backdoor Training in IoT/CPS

arXiv:2606.14987v1 Announce Type: cross Abstract: Internet of Things (IoT) and Cyber-physical systems (CPS) increasingly rely on continual learning (CL) to adapt to evolving environments, device heterogeneity, and concept drift, thereby improving overall utility. While continual adaptation is essential for long-lived IoT deployments where data patterns evolve, it also introduces new security vulnerabilities. In particular, backdoor attacks can exploit incremental updates, replay buffers, and representation reuse to implant persistent malicious behaviors that remain dormant during normal operation but activate upon specific triggers. In this paper, we present a backdoor attack in continual learning used in IoT/CPS systems. To this end, we formalize an IoT/CPS-specific threat model, analyze why continual learning amplifies backdoor persistence in IoT pipelines, and evaluate our technique under varying conditions. Our analysis highlights critical open challenges in securing lifelong learning in IoT/CPS and industrial IoT (IIoT) environments, as well as the need for heightened security controls.

08.
arXiv (quant-ph) 2026-06-12

Reservoir-controlled electromagnetically induced gratings in a weakly driven two-level medium

arXiv:2606.13085v1 Announce Type: cross Abstract: We theoretically investigate the transmission and diffraction of a weak probe field from an electromagnetically induced grating formed in a weakly driven two-level medium coupled to engineered quantum reservoirs. Using a perturbative solution of the optical Bloch equations in the weak-driving regime, we analyze how normal-vacuum, thermal, and broadband squeezed-vacuum environments modify the probe susceptibility and consequently reshape both the spatial transmission function and the far-field diffraction patterns. We show that reservoir statistics have a pronounced impact on the diffraction response by altering the amplitude and phase of the induced grating. Thermal reservoirs enhance the transmission modulation and increase the intensity of the dominant diffraction orders, whereas squeezed-vacuum reservoirs generate strongly phase-sensitive modifications that selectively redistribute optical power among diffraction channels. We further demonstrate that the detuning between the squeezed reservoir and the driving field provides an efficient mechanism for controlling diffraction directionality, leading to substantial amplification of selected angular orders. In two-dimensional geometries, squeezed-vacuum correlations produce highly structured phase landscapes and strongly anisotropic diffraction patterns, enabling directional enhancement of specific diffraction channels while suppressing others. These results establish reservoir engineering as a versatile approach for controlling transmission, diffraction efficiency, and angular selectivity in minimal two-level systems, with potential applications in programmable photonic devices, beam steering, and quantum optical platforms.

09.
arXiv (CS.CV) 2026-06-12

LaME: Learning to Think in Latent Space for Multimodal Embedding via Information Bottleneck

Reasoning-driven universal multimodal embedding has advanced rapidly by introducing Chain-of-Thought (CoT) reasoning into the embedding pipeline. Despite the strong performance across both general and complex tasks, this paradigm suffers from two core limitations: (i) autoregressive CoT reasoning incurs high computational cost, making it impractical for low-latency retrieval; and (ii) embedding performance is heavily coupled with CoT annotation quality, making large-scale training unreliable. These raise fundamental questions: Is textual CoT the optimal form of reasoning for embedding, and can effective embedding reasoning be accomplished in latent space? To this end, we propose LaME (Latent Reasoning Multimodal Embedding), which formulates embedding-oriented latent reasoning as a weakly supervised information bottleneck. LaME employs K learnable reason tokens as a fixed-capacity bottleneck, completing all reasoning within a single forward pass. The two weak supervision signals structurally decouple contrastive from autoregressive objectives and eliminate dependence on CoT annotations, while a two-stage training pipeline ensures stable convergence. Experiments on MMEB-v2 and MRMR show that LaME achieves competitive performance, surpassing some explicit CoT-based models, while delivering 60x faster inference than explicit CoT methods and 2x faster than latent baselines with throughput comparable to discriminative embedding models. Code will be released.

10.
PLOS Computational Biology 2026-06-15

Environmental “knees” and “wiggles” as strong stabilizers of species’ range limits set by interspecific competition

by Farshad Shirani, Benjamin G. Freeman Whether interspecific competition is a major contributing factor to setting species’ range limits has been debated for a long time. Theoretical studies have proposed that the interactions between interspecific competition and disruptive gene flow along an environmental gradient can halt range expansion of ecologically similar species where they meet. However, the stability of such range limits has not been well addressed. We use a deterministic mathematical model of adaptive range evolution over a continuous habitat to show that the range limits set by interspecific competition are unlikely to be evolutionarily stable if the environmental optima for fitness-related traits vary (almost) linearly in space. That is, in a linear environment without a dispersal barrier or a third (or more) species, the range borders formed between two competing species constantly move towards the weaker species. We demonstrate that environmental nonlinearities such as “knees” and “wiggles”—wherein an isolated sharp change or a step-like change occurs in the steepness of a trait optimum—can strongly stabilize competitively formed range limits. The stabilization mechanism relies on the contrast that such nonlinearities create in the level of disruptive gene flow to the peripheral population of each species, and succeeds when an additional process, such as Allee effects, prevents the establishment of an infinitesimal population in the presence of an abundant competitor. We show that the stability of the range limits at these nonlinearities is robust against moderate environmental disturbances. Whether strong disturbances such as rapid high-amplitude climate changes can destabilize such range limits depends on how the competitive dominance of the species changes across the nonlinearity. Therefore, our findings underscore the importance of assessing species’ competitive ability when predicting responses to climate change, and identify geographic regions where established range limits are likely to persist as well as regions where shifting limits may eventually stabilize.

11.
arXiv (CS.LG) 2026-06-24

Learning the Koopman Operator using Attention Free Transformers

arXiv:2606.23957v1 Announce Type: new Abstract: Learning Koopman operators with autoencoders enables linear prediction in a latent space, but long-horizon rollouts often drift off the learned manifold, leading to phase and amplitude errors on systems with switching, continuous spectra, or strong transients. We introduce two complementary components that make Koopman predictors more robust. First, we add an attention-free latent memory (AFT) block that aggregates a short window of past latents to produce a corrected latent before each Koopman update. Unlike multi-head attention, AFT operates in linear time and adds only $\approx$30k parameters ($3d^2 + T^2$, fewer than matched multi-head attention), yet captures the local temporal context needed to suppress error divergence. Second, we propose dynamic re-encoding: lightweight, online change-point triggers (EWMA, CUSUM, and sequential two-sample tests) that detect latent drift and project predictions back onto the autoencoder manifold. Across three benchmark systems – Duffing oscillator, Repressilator, IRMA – our model consistently reduces error accumulation compared to a Koopman autoencoder and matched-capacity multi-head attention. We also compare against GRU and Transformer autoencoders, evaluated both from initial conditions and with a 50-step context, and find that Koopman+AFT (with optional re-encoding) attains markedly lower long-horizon error while maintaining lower inference latency. We report improvements over horizons up to 1000 steps, together with ablations over trigger policies. The result is a fast, compact predictor that stays on the learned manifold over long horizons.

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

Disentangling Hallucinations: Orthogonal Semantic Projection for Robust Interpretability

As Vision-Language Models are increasingly deployed in safety-critical applications, the trustworthiness of their explanations becomes crucial. Explainable AI (XAI) methods for Vision-Language Models often suffer from semantic hallucination, where attribution maps highlight prominent image regions even when prompted with incorrect text descriptions (e.g., highlighting a dog when prompted ``cat''). Although this problem is widespread, a formal mathematical analysis of XAI methods and CLIP embeddings is largely missing in the literature. We demonstrate that this phenomenon is not specific to a single architecture but is a fundamental consequence of Linear Semantic Leakage in high-dimensional embedding spaces. We propose a unified theoretical framework, Linear Semantic Attribution (LSA), which generalizes across discriminative methods. We introduce OSP, a geometric intervention that utilizes the residual property of OMP to disentangle unique semantic signals from shared concepts. We prove theoretically and demonstrate empirically that OSP minimizes hallucination by orthogonalizing the query vector against distractor concepts, rendering the attribution model blind to shared features while preserving fidelity for correct prompts. Our code is available at: https://github.com/emirhanbilgic/Orthogonal-Semantic-Projection

13.
PLOS Computational Biology 2026-06-22

TCRBinder: Unified pre-trained language model with paired-chain synergy for predicting T-cell receptor binding specificity

作者:

by Weihe Dong, Qiang Yang, Long Xu, Xiaokun Li, Kuanquan Wang, Suyu Dong, Gongning Luo, Xianyu Zhang, Tiansong Yang, Xin Gao, Guohua Wang Deciphering how human T cells recognise peptide-HLA (pHLA) complexes underpins next-generation vaccines and personalised immunotherapies, yet extreme sequence diversity and paired-chains interdependence still hamper reliable in silico prediction of T-cell receptor (TCR) specificity. To overcome these hurdles, we built TCRBinder, a paired-chain-aware deep model with a multi-branch encoder that routes each molecular component through dedicated transformer-based modules to capture contextual signals in both HLA pseudo-sequences and antigenic peptides while simultaneously processing the TCR α and β chains. This design captures the synergistic interaction between paired chains to emulate peptide-HLA-TCR (PHT) interactions and expose residue-level contact motifs. Across PHT and peptide-TCR (pTCR) benchmarks, the model delivered state-of-the-art performance (AUC-ROC = 0.911, AUPR = 0.791 for the PHT task) and remained superior on multiple independent datasets. We tracked the dynamics of clonal expansion and, in a large SARS-CoV-2 repertoire containing completely unseen peptides, improved the AUC-ROC by up to 16.3% over the leading alternatives. Moreover, TCRBinder provided mechanistic insights by pinpointing contact hotspots and quantifying residue contributions to binding probability. These capabilities position TCRBinder as a versatile tool for rational antigen discovery, immunotherapy stratification, and neoantigen vaccine design.

14.
arXiv (math.PR) 2026-06-15

Upper tails for irregular graphs beyond the mean-field regime

arXiv:2606.14564v1 Announce Type: new Abstract: Let $G_{n,p}$ be the binomial random graph of density $p$ and let $X_H$ be the number of copies of a fixed graph $H$ in $G_{n,p}$. We prove asymptotically tight bounds on the logarithmic upper-tail probability of $X_H$ whenever $H$ is a connected, irregular graph with maximum degree $\Delta \ge 2$ and $p \ge n^{-1/\Delta - \varepsilon_H} (\log n)^{\omega(1)}$ for an explicit $\varepsilon_H >0$. These bounds are expressed in terms of a new variational problem that generalises the combinatorial optimisation problem arising from the naïve mean-field approximation. This new variational problem includes an entropy term that corresponds to the large number of embeddings of certain highly structured graphs in $K_n$. For a certain class of irregular graphs $H$ that we call stable, we show that this description of the upper-tail probability is valid in a range of densities that is optimal up to a poly($\log\log n$) factor. For a further subclass of stable graphs, which includes all irregular complete bipartite graphs, we show that this range of densities is optimal up to a multiplicative constant.

15.
arXiv (CS.LG) 2026-06-11

Provable Recovery of Locally Important Signed Features and Interactions from Random Forest

arXiv:2512.11081v2 Announce Type: replace-cross Abstract: Feature and Interaction Importance (FII) methods are essential in supervised learning for assessing the relevance of input variables and their interactions in complex prediction models. In many domains, such as personalized medicine, local interpretations for individual predictions are often required, rather than global scores summarizing overall feature importance. Random Forests (RFs) are widely used in these settings, and existing interpretability methods typically exploit tree structures and split statistics to provide model-specific insights. However, theoretical understanding of local FII methods for RF remains limited, making it unclear how to interpret high importance scores for individual predictions. We propose a novel, local, model-specific FII method that identifies frequent co-occurrences of features along decision paths, combining global patterns with those observed on paths specific to a given test point. We prove that our method consistently recovers the true local signal features and their interactions under a Locally Spike Sparse (LSS) model and also identifies whether large or small feature values drive a prediction. We illustrate the usefulness of our method and theoretical results through simulation studies and a real-world data example.

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

Riviera model with egoistical settlers

arXiv:2606.16791v1 Announce Type: cross Abstract: The Riviera model mimics a densifying settlement along the coastline. In the lattice version, houses are built sequentially in empty sites with the constraint that every newly built house has at least one empty neighboring site. The distribution of clusters of adjacent houses does not obey a closed set of evolutionary equations, but the void-cluster-void distribution does. We compute the latter and extract the cluster distribution from it. In the jammed state, when all voids have length one and the evolution ceases, the cluster distribution has a neat form and exhibits a factorial decay with the length of the cluster. To investigate finite systems, we employ a static approach directly treating jammed states. If the coastline is a finite segment, we determine the statistics of the number of empty sites in the jammed state (the average, variance, and higher cumulants). We also study a continuum version in which houses are built along the line so that each newly built house is sufficiently separated from at least one neighboring house.

17.
medRxiv (Medicine) 2026-06-15

Nocturnal Respiratory Rate and Variability Predict Long-term Mortality in Stable Outpatients with Cardiovascular Disease

Background: Respiratory rate (RR) predicts short-term mortality in acute care settings, yet its prognostic significance in clinically stable outpatients remains poorly defined. Objectives: To determine whether the median and variability of nocturnal respiratory rate (NRR) are independently associated with long-term cardiovascular and all-cause mortality in outpatients with cardiovascular disease. Methods: We analyzed overnight chest belt waveforms from elective polysomnography in 5,679 older adults with cardiovascular disease enrolled in the Sleep Heart Health Study (SHHS). NRR was quantified at 30-second resolution, and per-subject median NRR and within-night variability (standard deviation) were derived. Kaplan-Meier survival analysis and Cox proportional hazards models were used to evaluate associations with cardiovascular and all-cause mortality over 3-year and 15-year follow-up periods, adjusting for demographic characteristics, cardiopulmonary comorbidities, and sleep apnea severity. Results: Higher median NRR and greater NRR variability were each associated with increased cardiovascular and all-cause mortality. Combining these metrics identified a high-risk group characterized by elevated median and high variability of NRR, with approximately five-fold higher 3-year all-cause mortality compared with a low-risk group; this association remained significant in Cox models (unadjusted HR: 2.61; 95% CI: 1.65, 4.14; p

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

Understanding Cross-Modal Contributions in Continual Vision-Language Models: A Theoretical Perspective

Continual vision-language models are commonly addressed through sequential fine-tuning; however, although this paradigm enables adaptation to new environments (tasks), it inherently emphasizes the contribution of previously learned environments (tasks) at the expense of the stability required to preserve previously acquired knowledge. While existing approaches have adequately studied continual learning and catastrophic forgetting in vision-language models (VLMs), the theoretical understanding of modality-specific contributions across a sequence of environments remains largely unexplored. In this paper, we present a new theoretical perspective to understand the cross-modal (vision-language) contributions to consecutive environments. We empirically evaluate our theoretical findings on large VLMs and demonstrate their effectiveness in capturing environment-level cross-modal contributions. Our analysis provides deeper insights into continual VLMs, highlighting their contribution robustness to varying task orders and inter-task similarities, and their improved generalization performance.

19.
arXiv (CS.LG) 2026-06-11

Multi-agent rendezvous in fluid flows via reinforcement learning

arXiv:2606.11274v1 Announce Type: cross Abstract: Rendezvous is a critical task for multi-agent systems, requiring agents to coordinate to meet at an unspecified location. However, achieving this in fluid environments presents a challenge, as it remains unclear how agents can exploit underlying fluid kinematics to facilitate convergence. In this study, we adopt a multi-agent reinforcement learning (MARL) approach to develop physics-informed rendezvous strategies in vortical flows. Compared to a naive strategy, where agents navigate toward their counterparts, MARL strategies significantly improve the rendezvous rate. MARL strategies also show transferability across varying vortex intensities, vortex scales, and swarm sizes. By breaking the symmetry of the state-action map, MARL strategy leverages a non-intuitive mechanism that prevents agents from becoming trapped in separate vortices, thereby enhancing rendezvous success. Additionally, a heuristic strategy is extracted from the learned strategy and also outperforms the naive strategy. Furthermore, a theoretical analysis demonstrates that fluid deformation impedes the rendezvous process. Large finite-time Lyapunov exponents identify where fluid effects separate adjacent agents, suggesting that targets should be planned in weak-deformation regions. Our findings reveal the important role that agent-fluid interactions play in multi-agent tasks and highlight the MARL capability to explore swarm intelligence in complex flow environments.

20.
arXiv (CS.AI) 2026-06-16

Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning

arXiv:2606.15576v1 Announce Type: cross Abstract: Reinforcement learning from verifiable rewards assigns a single scalar to each rollout, leaving token-level credit assignment underspecified in long reasoning traces. On-policy self-distillation addresses this by letting the same model act as a teacher conditioned on privileged information, producing a dense per-token signal. But the common choice of a ground-truth answer is only an endpoint cue: on terse-answer tasks, the teacher falls silent at the intermediate positions where path-level guidance matters most. We propose Hindsight Self-Distillation (HSD), which conditions the teacher on a successful peer rollout drawn from the current training group. Such a peer is an exact sample from the success-conditioned policy, requiring no additional sampled rollouts. By providing a full successful continuation rather than only the final answer, the resulting credit signal concentrates at the divergence position between a failed rollout and a successful peer. Across Qwen3-8B and Qwen3-32B on math and code benchmarks, HSD obtains the best result against GRPO variants and on-policy distillation baselines, with the largest gains on terse-answer tasks such as AIME.

21.
arXiv (math.PR) 2026-06-24

On domains of elliptic operators with distributional coefficients

arXiv:2509.24950v2 Announce Type: replace-cross Abstract: We show how one can use recently gained insights from the study of singular SPDEs, more particularly the study of singular operators via the theory of Paracontrolled Distributions, to construct domains for (singular) elliptic operators. Formally we consider \[ A (u) = (1 - \Delta) u + \nabla V \cdot \nabla u + \xi u + {{div} (\rho u)}, \] where $V \in \mathcal{C}^{\delta}$, $\xi \in \mathcal{C}^{- 2 + \delta}$, $\rho \in \mathcal{C}^{- 1 + \delta}, {div} \rho = 0$} and which satisfy a structural assumption that is notably satisfied when $\xi$ is a sub-critical noise, see {[MvZ22]}. We also show that under this assumption, one can construct a continuous change of variables $\Theta$ which satisfies \[ A \Theta - (1 - \Delta) \in \mathcal{L} (H^{2 - \delta''} ; H^{\delta'}) \] which allows us to define $A$ rigorously and parametrise a domain. Moreover, for suitably regularised operators \[ A_{\varepsilon} (u) := (1 - \Delta) u + \nabla V_{\varepsilon} \cdot \nabla u + (\xi_{\varepsilon} + c_{\varepsilon}) \cdot u + {{div} (\rho_{\varepsilon} \cdot u)}, \] we show that for a strongly converging regularised change of variables $\Theta_{\varepsilon} \rightarrow \Theta$ we have \[ A_{\varepsilon} \Theta_{\varepsilon} \rightarrow A \Theta in \mathcal{L} (H^2 ; L^2) \] which in particular implies norm resolvent convergence to a limiting closed operator. Finally, we give a class of examples and show how to apply these results to prove strong analytical local well-posedness for a singular Schrödinger equation formally given by \[ i \partial_t u + (1 - \Delta) u + \nabla V \cdot \nabla u + \xi \cdot u = - | u |^2 u \] for singular $V, \xi$ and that its solution is the limit of the solution of the classical solutions of a regularised equation

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

Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories

arXiv:2511.07368v3 Announce Type: replace-cross Abstract: Foundation models exhibit broad knowledge but limited task-specific reasoning, motivating post-training strategies such as RL with verifiable rewards (RLVR) and test-time scaling (TTS). While recent work highlights the role of exploration in improving pass@K, empirical evidence points to a paradox: RLVR and ORM/PRM typically reinforce existing paths rather than expanding the reasoning scope, raising the question of why exploration helps if no new patterns emerge. To reconcile this paradox, we adopt the perspective of Kim et al. (2025), viewing easy (e.g., simplifying a fraction) versus hard (e.g., discovering the some symmetry) reasoning steps as low versus high probability Markov transitions. In this tractable model, pretraining corresponds to tree-graph discovering, while post-training corresponds to CoT reweighting. We provably show that, both RLVR and ORM/PRM would favor heavily to several high-probability paths, and thereby forget rare-but-crucial CoTs. Building on this, we further prove that exploration strategies such as rejecting easy instances and KL regularization help preserve rare CoTs. Empirical simulations corroborate our theoretical results.

23.
arXiv (math.PR) 2026-06-11

Delta-Epsilon-Common Knowledge and Quantitative Agreement Theorems

arXiv:2606.11902v1 Announce Type: cross Abstract: Aumann defined common knowledge mathematically and established his now famous Agreement Theorem. We present a novel approach to quantifying how close individuals are to commonly knowing events, $(\delta,\epsilon)$-common knowledge, which is defined for any (and not just countable) probability spaces, and provide quantitative versions of the key results in this field. Specifically, we do this for Aumann's Agreement Theorem and Nielsen's extension thereof to random variables, as well as for the setting in which posteriors are communicated back and forth between individuals. Our results apply in particular to noisy communication settings.

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

HANCLIP: A Family of Hyperbolic Angular Negation Vision Language Models

Vision-Language Models (VLMs) are typically pre-trained on large-scale image-text datasets to capture semantic correspondences between visual content and natural language. However, they remain surprisingly brittle to negation: models often rely on shallow word co-occurrence and are easily distracted by misleading or irrelevant textual cues, even when their overall retrieval or classification performance is strong. Moreover, directly finetuning on negation data can interfere with previously acquired knowledge, causing noticeable degradation on standard vision-language benchmarks. To tackle these issues, this work introduces HANCLIP (Hyperbolic + Angular + Negation), a family of VLMs that explicitly restructures the embedding space to encode "what an image is not" alongside "what it is." HANCLIP is trained on a compact set of 20,000 image-text quadruplets and combines a hyperbolic formulation, which models hierarchical semantic relations and asymmetries, with an angular triplet objective that drives systematic separation between negated descriptions and their corresponding positives. This geometry-aware design strengthens negation sensitivity while preserving the global structure of pretrained representations, rather than overwriting them. Extensive experiments across multiple vision-language tasks show that HANCLIP delivers consistent gains on the negation-focused NegBench benchmark, while maintaining competitive or improved performance on standard classification and image-text retrieval benchmarks. The framework is model-agnostic and can be plugged into CLIP, LongCLIP, SmartCLIP, and HiMo-CLIP without large-scale retraining, demonstrating that a carefully designed geometric objective can substantially extend the reasoning capabilities of existing VLMs using only modest additional data.

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

FLiP: Towards understanding and interpreting multimodal multilingual sentence embeddings

This paper presents factorized linear projection (FLiP) models for understanding pretrained sentence embedding spaces. We train FLiP models to recover the lexical content from multilingual (LaBSE), multimodal (SONAR) and API-based (Gemini) sentence embedding spaces in several high- and mid-resource languages. We show that FLiP can recall more than 75% of lexical content from the embeddings, significantly outperforming existing non-factorized baselines. Using this as a diagnostic tool, we uncover the modality and language biases across the selected sentence encoders and provide practitioners with intrinsic insights about the encoders without relying on conventional downstream evaluation tasks. Our implementation is public https://github.com/BUTSpeechFIT/FLiP.