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01.
arXiv (CS.LG) 2026-06-18

Unlocking air traffic flow prediction through microscopic aircraft-state modeling

arXiv:2605.10083v2 Announce Type: replace Abstract: Short-term air traffic flow prediction in terminal airspace is essential for proactive air traffic management. Existing approaches predominantly model traffic flow as aggregated time series. However, traffic dynamics are governed by aircraft states and their interactions in continuous airspace. Such aggregation obscures fine-grained information, including aircraft kinematics, boundary interactions, and control intent. Here we present AeroSense, a state-to-flow modeling paradigm that predicts future traffic flow directly from instantaneous airspace situations represented as dynamic sets of aircraft states derived from ADS-B trajectories. By establishing an end-to-end mapping from microscopic aircraft states to future regional traffic flow, AeroSense preserves aircraft-level dynamics while naturally accommodating varying traffic density without relying on historical look-back windows. Experiments on a large-scale real-world dataset show that AeroSense exhibits admirable predictive accuracy and robustness over aggregation-based forecasting approaches, particularly during high-density traffic periods. These findings suggest that aircraft-state situation modeling provides a promising alternative to conventional time-series forecasting in air traffic flow management.

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

SkMTEB: Slovak Massive Text Embedding Benchmark and Model Adaptation

We introduce SkMTEB, the first comprehensive MTEB-style text embedding benchmark for Slovak, a low-resource West Slavic language, comprising 31 datasets across 7 task types – nearly 4$\times$ the depth of existing multilingual benchmark coverage for Slovak. Our evaluation of 31 embedding models reveals that large instruction-tuned multilingual models achieve the strongest performance, while existing Slovak-specific models trained for NLU tasks transfer poorly to embedding tasks. To address the need for efficient, locally-deployable Slovak embeddings, we develop \texttt{e5-sk-small} (45M parameters) and \texttt{e5-sk-large} (365M) by applying vocabulary trimming and fine-tuning to Multilingual E5 models. Despite size reductions of up to 62\%, our open-source models achieve competitive performance with proprietary APIs while remaining locally deployable for semantic search and retrieval-augmented generation (RAG). We release the benchmark, models, datasets, and code openly, hoping our approach offers a replicable path for other under-resourced languages.

03.
arXiv (math.PR) 2026-06-18

Denoising Distances in Metric Measure Spaces

arXiv:2606.18301v1 Announce Type: cross Abstract: Recent work studied the problem of finding clusters and denoising pairwise distances from noisy distances of points sampled on a manifold. We study the same problems in more general metric measure spaces under \lowerphiregularity{}. We give an algorithm that extracts large localized clusters around every sampled point and uses them to denoise distances to any fixed accuracy, with near-linear running time in the dense fixed-accuracy regime. We also show how to achieve much higher accuracy with a non-efficient algorithm. This suggests that unlike the Riemannian case, denoising to higher accuracy in more general metric spaces has a statistical-computational gap.

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

SpikeTAD: Spiking Neural Networks for End-to-End Temporal Action Detection

Video understanding is a crucial part of computer vision, with numerous application scenarios. With the increasing popularity of mobile devices, an increasing number of efforts are trying to deploy video understanding models on them. However, existing video understanding models are difficult to deploy due to their large size and prohibitive power consumption. Spiking Neural Networks (SNNs) have shown bioplausibility and low power advantages over Artificial Neural Networks (ANNs), especially on neuromorphic chips which are regarded as essential components of future mobile devices. However, excessively long conversion time-steps and severe performance degradation problems limit their application. To solve the problems above, we explore the application of SNNs on temporal action detection (TAD), which is an important task in video understanding, and propose the first SNN-based end-to-end TAD architecture coined as SpikeTAD. While maintaining extremely low power consumption, SpikeTAD achieves an average mAP of 67.2% in THUMOS14 and 37.42% in ActivityNet-1.3, demonstrating the feasibility of a low-power TAD model. Our code is available at https://github.com/MCG-NJU/SpikeTAD.

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

How LLMs Fail and Generalize in RTL Coding for Hardware Design?

Translating sequential programming priors into the parallel temporal logic of hardware design remains a crucial bottleneck for large language models(LLM). To investigate this, we introduce a new error taxonomy grounded in problem solvability, inspired by cognitive theory. Our taxonomy categorizes failures into syntactic, semantic, solvable functional, and unsolvable functional types. Evaluations reveal a strict empirical ceiling on the VerilogEval benchmark, as frontier models plateau at a 90.8% initial pass rate. These plateaus are defined by unsolvable functional errors, exposing persistent knowledge gaps immune to test time compute scaling. Furthermore, we expose a striking surface convergence gap: optimization readily eliminates syntax errors but concurrently exacerbates deeper functional failures. Our findings demonstrate that alignment techniques merely teach models to compile. While repeated sampling strategies can patch solvable errors, register-transfer level(RTL) coding capacity remains strictly bounded by pretraining knowledge. Addressing challenges in the current LLM based hardware generation pipeline requires more studies in model reasoning rather than alignment interventions.

07.
arXiv (CS.CL) 2026-06-11

Neural FOXP2 – Language Specific Neuron Steering for Targeted Language Improvement in LLMs

LLMs are multilingual by training, yet their lingua franca is often English, reflecting English language dominance in pretraining. Other languages remain in parametric memory but are systematically suppressed. We argue that language defaultness is governed by a sparse, low-rank control circuit, language neurons, that can be mechanistically isolated and safely steered. We introduce Neural FOXP2, that makes a chosen language (Hindi or Spanish) primary in a model by steering language-specific neurons. Neural FOXP2 proceeds in three stages: (i) Localize: We train per-layer SAEs so each activation decomposes into a small set of active feature components. For every feature, we quantify English vs. Hindi/Spanish selectivity overall logit-mass lift toward the target-language token set. Tracing the top-ranked features back to their strongest contributing units yields a compact language-neuron set. (ii) Steering directions: We localize controllable language-shift geometry via a spectral low-rank analysis. For each layer, we build English to target activation-difference matrices and perform layerwise SVD to extract the dominant singular directions governing language change. The eigengap and effective-rank spectra identify a compact steering subspace and an empirically chosen intervention window (where these directions are strongest and most stable). (iii) Steer: We apply a signed, sparse activation shift targeted to the language neurons. Concretely, within low to mid layers we add a positive steering along the target-language dominant directions and a compensating negative shift toward the null space for the English neurons, yielding controllable target-language defaultness.

08.
medRxiv (Medicine) 2026-06-17

High burden of subclinical TB in Africa revealed from a postmortem cohort.

Tuberculosis (TB) is increasingly recognised as a spectrum of infection and disease, yet the prevalence of viable, asymptomatic Mycobacterium tuberculosis (M.tb) infection remains uncertain. Subclinical Tuberculosis (scTB), defined as microbiologically confirmed M.tb infection in the absence of recognised symptoms, is under detected by symptom, sputum and imaging-based approaches. We conducted postmortem examinations of 94 adults who died from non-infectious causes, none of whom were clinically suspected of TB or reported TB related symptoms prior to death. Lung and extrapulmonary tissues were cultured for M.tb. Viable M.tb was confirmed in six individuals, corresponding to a prevalence of 6.4% (95% CI: 2.4 to 13.4%). These findings provide direct tissue-based evidence that viable, asymptomatic M.tb infection can persist beyond the reach of conventional clinical detection. Our data suggest that a biologically active reservoir of infection may exist undetected within high-burden settings, with implications for surveillance strategies aimed at TB elimination.

09.
arXiv (CS.LG) 2026-06-16

Circuit Tracing in Autoregressive Protein Language Models

arXiv:2606.16044v1 Announce Type: new Abstract: Protein language models (pLMs) can generate novel protein sequences with properties beyond those observed in nature, yet the mechanisms underlying protein generation remain poorly understood. Existing mechanistic interpretability methods based on sparse autoencoders and transcoders primarily focus on protein representation learning models and do not capture the computation required for autoregressive generation. Here, we introduce ProGenMech, a mechanistic interpretability framework for generative protein language models that extends cross-layer transcoders (CLTs) to ProGen3, a sparse Mixture-of-Experts model trained for both causal generation and span infilling. Unlike per-layer approaches, CLTs reconstruct each layer using sparse latent variables from all preceding layers, enabling faithful recovery of inter-layer generative computation. We further develop a zero-shot circuit discovery framework to identify sparse latent circuits responsible for protein generation and fitness prediction. In causal generation and zero-shot fitness estimation tasks, ProGenMech outperforms local transcoder baselines in recovering ProGen3's probability distribution and functional scoring behavior, while matching the original model's generative distribution in span infilling tasks. Moreover, the recovered circuits reveal biologically meaningful motifs and functional regions associated with conserved sequence patterns and protein fitness landscapes, establishing a foundation for interpretable and steerable protein generation.

10.
arXiv (math.PR) 2026-06-18

Evolution of Conditional Entropy for Diffusion Dynamics on Graphs

arXiv:2510.19441v2 Announce Type: replace-cross Abstract: The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their finite-time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs, and outline a mathematical framework that contextualizes diffusion and conditional entropy within the theories of continuous-time Markov chains and information theory. In particular, we highlight that this entropic measure satisfies an information-theoretical version of the second law of thermodynamics, thereby providing a parallelism between diffusion dynamics on networks and their physical counterparts. Furthermore, we obtain explicit results for its evolution on complete, path, and circulant graphs, as well as a mean-field approximation for Erdös-Rényi graphs. We also obtain asymptotic results for general networks and provide bounds for the evolution of conditional entropy. Finally, we experimentally demonstrate several properties of conditional entropy for diffusion over random graphs, such as the Watts-Strogatz model.

11.
medRxiv (Medicine) 2026-06-16

Language fMRI lateralization success and head motion in pediatric epilepsy patients with ADHD, and improvements based on fMRI task training

Introduction Language functional MRI (fMRI) is a valuable tool for presurgical planning in epilepsy. Functional MRI can be challenging in children, and head motion can compromise its utility. The candidacy of patients with ADHD for fMRI is sometimes queried regarding concerns about possible head motion. In 2020, we implemented an fMRI task training program, via telehealth and/or mock MRI. We aimed to determine whether training increased language lateralisation success and/or reduced head motion in all patients, and in those with ADHD. We also aimed to determine whether patients with ADHD exhibited more head motion during fMRI than those without ADHD. Methods We retrospectively identified 223 epilepsy (85%) and other neurosurgery patients, (241 scans including repeats) with language fMRI at Royal Children's Hospital, Melbourne, Australia, 2016-2024. There were 24 individuals with ADHD listed in the Electronic Medical Record, five of whom had diagnoses of both ADHD and autism; and nine with autism. Language lateralisation success was determined by clinician description recorded as left/right/bilateral in the medical record. 99 patients were provided the training including fMRI task practise. Head motion was quantified by maximum Framewise Displacement (FDmax; mm). Results ADHD was associated with lower language lateralisation success. Training was associated with greater language lateralisation success, across all patients, and in those with ADHD. Regarding ADHD and head motion, outliers in FDmax were seen in 5 young patients with ADHD. Data were trimmed to allow separate investigation of FDmax for the sample with and without extremes of head motion. In untrimmed data, FDmax was significantly higher in patients with ADHD than in those without. In trimmed data, FDmax was on average lower in patients with ADHD than those without, however this was not statistically supported. Regarding training and head motion, across all patients, FDmax was significantly lower for scans with training than without. In patients with ADHD, FDmax was on average lower for scans with training, however training was not associated with FDmax. Conclusions Language fMRI training was associated with higher language lateralization success, particularly in patients with ADHD. Training was associated with reduced head motion across all patients. Although some young patients with ADHD had substantial head motion, most in our sample did not move more than those without ADHD. We conclude that the training program increases success of language fMRI, and that an ADHD diagnosis should not be a contraindication to language fMRI.

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

Diffuse AI Control on Fuzzy Tasks

arXiv:2606.08892v2 Announce Type: replace Abstract: AI models deployed in critical domains, such as AI safety research, may subtly sabotage our efforts due to misalignment. Diffuse AI Control is a subfield of AI safety concerned with mitigating risks from AI sabotage distributed over long deployment horizons (diffuse threats). These risks are particularly pernicious on fuzzy tasks, i.e. tasks which are hard to grade or require intuition. To understand diffuse threats on fuzzy tasks, we introduce a framework that considers AI control as an adversarial game between a blue team and a red team. The blue team uses a weak trusted model to construct a weak score against which they would train a strong, potentially subversive model to remove the subversion propensity if it were present. The red team then tries to find model behaviors that are rated highly by the weak score, and thus might not be trained out, but actually correspond to poor performance. We test our framework on the task of writing experimental proposals for research questions from recent ML papers. We use a language model with access to the original paper as a proxy "ground-truth" scorer. Our red team discovers subversive behaviors using multi-objective evolutionary prompt optimization. We show that Opus~4.6 can write proposals that are worse according to the ground truth proxy than those of GPT-OSS-20B, while the weak scorer rates them as highly as the best proposals from Opus 4.6. We then propose an adversarial optimization algorithm for the blue team that discovers more robust prompts for the weak model. This algorithm produces a blue team prompt that our red team optimization fails to exploit.

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

How Much Memory Do We Need? Adaptive Memory Gate for Neural Operators

arXiv:2606.13443v1 Announce Type: new Abstract: Neural operators have emerged as a powerful data-driven approach for solving time-dependent PDEs. Among recent advances, memory-augmented neural operators explicitly incorporate past states and have achieved remarkable performance under low-resolution observation settings. However, existing approaches apply a fixed memory weight regardless of observation conditions, such as resolution or physical parameters, limiting their adaptability. Our preliminary experiments reveal that optimal memory weight varies with resolution and viscosity, implying that a fixed memory weight cannot simultaneously optimize performance across diverse settings. We propose AMGFNO, which dynamically modulates memory weight through a learnable gate. On the Kuramoto-Sivashinsky and Burgers' equations, AMGFNO achieves 55-79% nRMSE reduction over at low resolution, with the learned gate value automatically decreasing from $\bar{g} \approx 0.7$ to near-zero as resolution increases.

14.
arXiv (CS.CL) 2026-06-16

State-Grounded Multi-Agent Synthetic Data Generation for Tool-Augmented LLMs

Training tool-augmented LLM agents requires large corpora of multi-turn, tool-grounded conversational data that is expensive to annotate, privacy-constrained in production settings, and largely absent from public datasets. We present StateGen, a synthetic data generation platform that produces scored, reasoning-trace-rich training conversations by orchestrating a four-role LLM loop: a persona-conditioned user simulator, an agent under test, a state-grounded tool simulator, and a multi-axis LLM judge. The key architectural contribution is an authoritative state manager that maintains a structured world-state object across turns, enforcing a backend-is-truth invariant that eliminates the dominant class of tool-call hallucinations by construction. StateGen extends naturally to hierarchical multi-agent settings by declaring sub-agents as tools, all sharing a single state object. We report results on 64,698 evaluated conversations across three production corpora: tool-call hallucination scores reach 9.66/10, the system supports persona-driven variation via a 23-dimensional trait vector, and a cleanly separated train and golden evaluation set split confirms the data is not memorization bait (per-criterion gap analysis). Comparison with eight external systems shows that no single publicly available platform combines multi-turn generation, state-grounded tool simulation, hierarchical multi-agent support, and built-in judge scoring.

15.
bioRxiv (Bioinfo) 2026-06-19

Perturbation Curve models continuous transcriptional response trajectories and improves prediction of genetic modulations

Single-cell CRISPR screens, Perturb-seq, have revolutionized functional genomics by revealing biological causality. However, although perturbation assignments are typically represented as discrete labels, the cell-level effective strength of perturbations is often continuous and diverse. Current analytical frameworks struggle to decouple the variability in perturbation strength from the diversity of downstream responses. Here, we present Perturbation Curve (PertCurve), a nonlinear, curve-based computational framework that models the trajectories of transcriptomic responses by explicitly incorporating diverse perturbation magnitudes and strengths. By ordering cells by perturbation strength, we demonstrate that PertCurve accurately recapitulates the response magnitudes and reveals the distinct modularity and asynchrony patterns of downstream gene behaviors. These patterns are categorized into archetypes, including proportional, sensitive, and threshold responses. By applying this framework across CRISPRi/a modalities, we identify universal response patterns in viral infection, apoptosis, and proliferation genes, and reveal previously overlooked context-specific regulatory features in cell differentiation. Finally, incorporating PertCurve into perturbation prediction models and evaluation metrics enhances predictive performance, delivering actionable insights for refining established models.

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

From Uniform to Learned Graph Priors: Diffusion for Structure Discovery

arXiv:2606.11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges. However, these methods typically rely on oversimplified, factorized graph priors. Such priors, typically nearing uniform distributions, treat edges as independent entities. This systemic misalignment does not match the real-world systems and yields diffuse and indecisive edge posteriors limiting the reliability of structural discovery. To address this, we propose Diff-prior, a diffusion-parameterized adaptive prior used to calibrate latent graph distribution rather than generate graphs. Our core insight is to reframe prior integration as a learnable denoising-style calibration that organizes scattered, uncertain edge posteriors into a more reliable overall structure which can be trained by the diffusion model. Diff-prior learns an adaptive structure prior that performs structured calibration on the edge posteriors during inference, guiding it towards a distribution closer to the underlying structure. The diff-prior operates before structural sampling and acts as a denoising calibrator directly on the encoder edge distribution, which provides a generic training paradigm over structured variables. Experiments on standard benchmarks validated our framework, and the results indicate that Diff-prior improves the performance of structure inference and generates more decisive edge posteriors across multiple NRI-family architectures. The code is available on https://github.com/Hardy158118/Diffprior.

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

Connect the Dots: Training LLMs for Long-Lifecycle Agents with Cross-Domain Generalization Via Reinforcement Learning

This work presents a general framework for training large language models (LLMs) to "Connect the Dots" (CoD), a meta-capability required by long-lifecycle agents: as an LLM-based AI agent gets deployed in an environment, it solves a long sequence of tasks while continuously exploring the environment, learning from its own experiences, and iteratively self-updating its context about the environment, thereby achieving progressively better performance on future tasks conditioned on the updated context. Major components of the CoD framework include: (1) algorithm design and infrastructure for end-to-end reinforcement learning (RL) with long rollout sequences interleaving solve-task and update-context episodes; (2) tasks and environments for incentivizing and eliciting the targeted meta-capability in LLMs during training, as well as for faithfully measuring progress during evaluation. We present proof-of-concept implementations of the CoD framework, including a GRPO-style RL algorithm with fine-grained credit assignment, as well as tasks and environments tailored to the targeted meta-capability (rather than domain-specific LLM capabilities or standard task-by-task RL). Empirical results validate the efficacy of end-to-end RL training in the CoD setting, and demonstrate the potential for out-of-distribution generalization – within the training domains, across different domains, and from CoD to Ralph-loop settings – of the elicited meta-capability. Our investigation of CoD connects several lines of prior works, and opens up new opportunities for advancing LLMs and AI agents. To facilitate further research and applications, we release our implementations at \url{https://github.com/agentscope-ai/Trinity-RFT/tree/research/cod/examples/research_cod}.

18.
arXiv (CS.LG) 2026-06-12

To GAN or Not To GAN: Segmentation Analysis on Mars DEM

arXiv:2606.13252v1 Announce Type: new Abstract: To better understand Martian Surface, which is needed to enable Rovers navigate Mars with ease, it is necessary to be able to determine the location of mounds. Detecting and studying these morphologies can also help us find evidence of extraterrestrial life, in this case, more specifically, water or signs of life conducive environments. Detection of mounds was done by manually mapping morphological parameters onto Digital Elevation Models. This paper solves the problem by automatically detecting and or predicting mounds on Mars using Neural Network based Semantic Segmentation methodologies. This is done by using supervised semantic segmentation model and generative adversarial approach. A comparison of the approaches shows that adding extra artificially generated data did not improve the result.

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

Camera and LiDAR BEV Fusion for Cooperative 3D Object Detection on TUMTraf V2X

We describe a Camera and LiDAR fusion detector developed for the TUMTraf V2X cooperative 3D object detection track of the DriveX 2026 challenge. The detector fuses three roadside cameras with a fused infrastructure-plus-vehicle point cloud in a shared bird's-eye-view space and predicts boxes through a CenterPoint-style head with a generalized IoU regression loss and an IoU quality re-ranking head. Trained on the provided train and validation splits, the model reaches a 3D mAP of 0.85 on the public Codabench test split. While iterating on the system, we observed that 44 of the 50 test frames are also present in the released train (40) and validation (4) splits with their labels. We therefore conducted two additional studies to quantify how this overlap affects the final score: (1) a finetuning run that oversamples the 44 overlapping frames, reaching 0.89 mAP, and (2) a post-processing run that replaces predictions on those frames with the released ground truth, reaching 0.99 mAP (uploaded to our Codabench account for testing but not published on the leaderboard). All three configurations and their per-class results are reported.

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

Virtual Sensing to Enable Real-Time Monitoring of Inaccessible Locations & Unmeasurable Parameters

arXiv:2412.00107v2 Announce Type: replace-cross Abstract: Real-time monitoring of safety-critical interior states remains an open problem in energy systems where physical instrumentation is infeasible. Existing approaches rely on explicit governing equations, finite-dimensional state vectors, or per-instance retraining, which prevents mesh-independent, field-level inference at arbitrary interior coordinates under real-time constraints. We introduce operator-based virtual sensing for nuclear-grade thermal-fluid systems: we use the neural-operator framework to learn solution operators that map sparse boundary measurements to coupled internal fields in physically inaccessible regions, framing the problem class explicitly to distinguish it from classical state estimation and pointwise soft sensing. We instantiate this framework with MIMONet, a branch-trunk operator extended with three practical choices: multi-modal branch encoders for heterogeneous (scalar and function-valued) inputs; multiplicative branch fusion to preserve the bilinear PDE coupling structure; and shared-latent multi-field decoding with per-channel basis projections at the trunk's final layer. Evaluated across escalating complexity, from canonical lid-driven cavity flow to pressurized water reactor subchannels to fully coupled heat exchangers, MIMONet achieves below 5% relative errors and sub-millisecond inference on data-center accelerators (0.35 ms / 46 mJ per heat-exchanger inference on an NVIDIA H200, and sub-millisecond across the A40-H200-GH200 range), while remaining stable under 50% sensor noise. By staying accurate as geometric confinement and physics coupling intensify, MIMONet shows that operator-based virtual sensing can restore observability where physical instrumentation fails, establishing simulation-based feasibility within the evaluated operating envelopes as a step toward future experimental and cross-solver validation for safety-critical energy systems.

21.
arXiv (CS.AI) 2026-06-16

PO-PDDL: Learning Symbolic POMDPs from Visual Demonstrations for Robot Planning Under Uncertainty

arXiv:2606.15654v1 Announce Type: cross Abstract: Real-world robot task planning must operate under both stochastic action execution and partial observability, yet constructing Partially Observable Markov Decision Process (POMDP) models for real robotics domains remains difficult and labor-intensive. We introduce PO-PDDL, a symbolic formulation of POMDPs that preserves the relational structure and LLM-friendly syntax of the Planning Domain Definition Language (PDDL), while explicitly modeling partial observability, stochasticity, and beliefs. Building on this formulation, we propose a demonstration-driven pipeline for learning PO-PDDL models. The proposed method reconstructs latent symbolic state trajectories from real-robot execution videos, identifies partial observability via inconsistencies between inferred states and visual observations, and learns stochastic transition and observation models accordingly. The resulting PO-PDDL domains are reusable across tasks and enable online belief-space planning under both perception and execution uncertainty. Experiments on real-world long-horizon manipulation tasks show that our method consistently outperforms existing PDDL and POMDP model-learning approaches, achieving robust task planning under uncertainty with significantly lower planning cost.

22.
arXiv (quant-ph) 2026-06-11

Tensor-Network Algorithm for Many-Body Trace Norms

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

23.
arXiv (math.PR) 2026-06-19

The systole of random hyperbolic 3-manifolds

arXiv:2406.11783v2 Announce Type: replace-cross Abstract: We study the systole of a model of random hyperbolic 3-manifolds introduced by Petri and Raimbault, answering a question posed in that same article. These are compact manifolds with boundary constructed by randomly gluing truncated tetrahedra along their faces. We prove that the limit, as the volume tends to infinity, of the expected value of their systole exists and we give a closed formula of it. Moreover, we compute a numerical approximation of this value.

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

CountZES: Counting via Zero-Shot Exemplar Selection

Object counting in complex scenes is particularly challenging in the zero-shot (ZS) setting, where instances of unseen categories are counted using only a class name. Existing ZS counting methods that infer exemplars from text often rely on off-the-shelf open-vocabulary detectors (OVDs), which in dense scenes suffer from semantic noise, appearance variability, and multi-instance proposals. Alternatively, random image-patch sampling is employed, which fails to accurately delineate object instances. Since counting is sensitive to exemplar quality, such selection strategies often yield poorly representative exemplars, leading to inaccurate count estimation. To address these issues, we propose CountZES, an inference-only approach for object counting via ZS exemplar selection. CountZES discovers diverse exemplars through three synergistic stages: Detection-Anchored Exemplar (DAE), Density-Guided Exemplar (DGE), and Feature-Consensus Exemplar (FCE). DAE refines OVD detections to isolate precise single-instance exemplars. DGE introduces a density-driven, self-supervised paradigm to identify statistically consistent and semantically compact exemplars, while FCE reinforces visual coherence through feature-space clustering. Together, these stages yield a complementary exemplar set that balances textual grounding, count consistency, and feature representativeness. Experiments on diverse datasets demonstrate CountZES superior performance among ZOC methods while generalizing effectively across domains.

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

Learning from almost nothing: How neural networks survive heavy input corruption

arXiv:2606.11319v1 Announce Type: new Abstract: Learning from imperfect data is a central theme in machine learning, connecting practical questions of robustness to fundamental questions of learnability. Here we examine attribute noise: learning from corrupted inputs while keeping the labels intact, a setting that has received considerably less analytical attention than its label-noise counterpart. We consider two types of corruption models: additive noise and replacement noise. Through experiments with multi-layer perceptrons (MLPs) on corrupted classification datasets, we find that neural networks remain robust, maintaining well-above-chance accuracy even when inputs are >90% corrupted – far beyond human recognition. To understand this robustness, we analyze infinite-width networks in the heavy-corruption regime using a mean-field-inspired approach and derive a leading-order decision rule for the classification outcome: the network implements a prototype rule, the nearest-class-mean, assigning each test point to the class whose training-set average it most closely resembles. This leading-order decision rule is universal across a broad range of MLP architectures, holding for any depth, as well as a wide class of activation functions and noise distributions. The same centroid mechanism closely matches finite-width network behavior in our experiments and provides an interpretable and analytically tractable account of why learning can succeed even when individual training examples carry almost no signal.