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

Where Will They Go? Modelling Multimodal Pedestrian Manoeuvres from Ego-centric Videos

Pedestrian trajectory prediction from an ego-centric camera is challenging since it depends on complex interactions with vehicles and scene context, as well as the intention of the pedestrian. By modelling correlation and intent from the historical and future trajectories of the pedestrian, it will usually result in a multimodal (i.e. multiple modes) distribution. Existing stochastic predictors often sample multiple futures from a single unimodal distribution, which can yield sub-optimal 'mixed-mode' trajectories that lie between distinct motion patterns and become implausible in real scenes. In this paper, we propose MMPM, a mode-aware framework that separately models future trajectory distributions into semantically meaningful modes based on the pedestrian's crossing behavior. MMPM consists of two modules: behavior-aware Pedestrian Interaction Module (PIM) that jointly captures pedestrian-vehicle and pedestrian-environment interactions by introducing gaze, head and hand gesture, and a CVAE-based Mode-aware Trajectory Predictor (MTP) module to model the future trajectory distributions on two modes, crossing and non-crossing the road, separately. A query-based decoder further enforces mode consistency during decoding. Experiments on PIE and JAAD datasets show that our method surpasses state-of-the-art baselines. Our proposed MTP is model-agnostic, which can be integrated into existing frameworks such as BiTrap-NP and SGNet-ED to further improve future trajectory prediction performance. We additionally introduce a data-driven validation protocol that matches predictions to spatio-temporally consistent ground-truth trajectories, demonstrating improved frame-wise displacement errors over previous work.

02.
arXiv (CS.LG) 2026-06-16

GauS: Differentiable Scheduling Optimization via Gaussian Reparameterization

arXiv:2602.20427v2 Announce Type: replace Abstract: Efficient operator scheduling is a fundamental challenge in software compilation and hardware synthesis. While recent differentiable approaches have sought to replace traditional ones like exact solvers or heuristics with gradient-based search, they typically rely on categorical distributions that fail to capture the ordinal nature of time and suffer from a parameter space that scales poorly. In this paper, we propose a novel differentiable framework, GauS, that models operator scheduling as a stochastic relaxation using Gaussian distributions, which fully utilize modern parallel computing devices like GPUs. By representing schedules as continuous Gaussian variables, we successfully capture the ordinal nature of time and reduce the optimization space by orders of magnitude. Our method is highly flexible to represent various objectives and constraints, which provides the first differentiable formulation for the complex pipelined scheduling problem. We evaluate our method on a range of benchmarks, demonstrating that Gaus achieves Pareto-optimal results.

03.
arXiv (CS.CV) 2026-06-16

Double-Helix Vision (DH-V2): A Geometry-Based Visual Sampler for Bandwidth-Constrained Perception

Authors:

We present Double-Helix Vision (DH), a geometry-based visual sampler that compresses 2D images into compact 1D signals using paired golden-ratio-inspired spiral trajectories. Rather than processing every pixel uniformly, DH employs two phase-shifted helices (Alpha and Beta, offset by 180 degrees) to sample the image with biologically-inspired foveation: high density at the center, sparse coverage at the periphery. At 4K resolution, DH achieves a 1,433x compression ratio (99.93% reduction) while preserving the geometric structure of the scene. The full perception pipeline – including spatial mapping, temporal collision detection, and intra-frame structural disparity estimation – runs in 0.52 ms at 1080p on CPU-only hardware, with no neural network dependencies. On CIFAR-10 at extreme sampling budgets (K=128 points per helix), DH achieves a +6.03% accuracy gain over uniform random sampling. A JSON-serializable Robotics API is provided, delivering sub-millisecond spatial perception reports in 2.7 KB packets. Code and benchmarks are available under the MIT License.

04.
arXiv (CS.LG) 2026-06-17

Noise-Driven Escape from Metastable Phases explains Grokking in Deep Neural Networks

arXiv:2606.17120v1 Announce Type: new Abstract: Deep neural networks (DNNs) exhibit first order phase transitions under variations of the L2 regularization strength, with each transition marking the onset of a new learnable feature. Below a critical regularization strength, all features are in principle learnable, but coexisting metastable states, separated by energy barriers, can trap the network and impede convergence. A strength of DNNs is their ability to generalize. But many open questions remain, among them the origin of so called grokking: the abrupt, delayed onset of generalization after prolonged apparent overfitting. We show for linear DNNs that grokking is consistent with hysteresis in first-order L2 phase transitions: using L2 regularization to engineer deliberate trapping, we demonstrate that a model in a low-accuracy metastable state escapes only when SGD noise drives it across an energy barrier, with escape times following Arrhenius scaling. We reproduce grokking-like delayed convergence across two orders of magnitude in escape time by deliberately trapping models in metastable phases. Using sparse sub-sampling we also reproduce the canonical grokking curve where test error eventually approaches the final training error. Our work suggests that the number of metastable states equals the number of learnable features – one per singular value of the data covariance – the potential for hysteresis grows naturally with task complexity. We provide evidence that the same mechanism likely operates in general nonlinear DNNs. Our results provide routes toward more efficient learning schemes.

05.
arXiv (CS.CL) 2026-06-16

Simplifying the Modeling of Arbitrary Conditionals in Natural Language

Causal Transformers model sequences through an autoregressive factorization of the joint distribution, which enables efficient left-to-right decoding and conditional likelihood computation. However, they cannot tractably sample from or evaluate arbitrary conditionals – e.g., a block of text conditioned on past and future tokens. Recent work aims to solve this problem through novel architectures, but they often lead to sub-optimal modeling of such conditionals and degraded generations. We propose Arbitrary Conditionals GPT (AC-GPT) which introduces a simple modification to standard causal Transformers to enable evaluating and sampling from arbitrary conditionals – including past, future, and mixed contexts – within a single forward pass. Unlike prior approaches, our method preserves the standard left-to-right ordering and next-token prediction objective essential for both strong performance and efficient training on natural language. Crucially, this compatibility allows existing LLMs to be fine-tuned for arbitrary conditioning. Our empirical results indicate that our method outperforms baselines on modeling arbitrary conditionals, without degrading standard left-to-right performance.

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

Pretraining A Large Language Model using Distributed GPUs: A Memory-Efficient Decentralized Paradigm

Pretraining large language models (LLMs) typically requires centralized clusters with thousands of high-memory GPUs (e.g., H100/A100). Recent decentralized training methods reduce communication overhead by employing federated optimization; however, they still need to train the entire model on each node, remaining constrained by GPU memory limitations. In this work, we propose SParse Expert Synchronization (SPES), a memory-efficient decentralized framework for pretraining mixture-of-experts (MoE) LLMs. SPES trains only a subset of experts per node, substantially lowering the memory footprint. Each node updates its local experts and periodically synchronizes with other nodes, eliminating full-parameter transmission while ensuring efficient knowledge sharing. To mitigate limited per-expert data utilization under sparse expert updates, we introduce an expert-merging warm-up strategy, where experts exchange knowledge early in training, to rapidly establish foundational capabilities. With SPES, we train a 2B-parameter MoE LLM using 16 standalone 48GB GPUs over internet connections, which achieves competitive performance with centrally trained LLMs under similar computational budgets. We further demonstrate scalability by training a 7B model from scratch and a 9B model upcycled from a dense checkpoint, both of which match prior centralized baselines. Our code is available at https://github.com/zjr2000/SPES.

07.
arXiv (CS.LG) 2026-06-17

Data augmented bootstrap: Unifying confidence interval construction by approximate invariance

arXiv:2606.09049v2 Announce Type: replace-cross Abstract: We propose the data augmented bootstrap (DAB), a framework for constructing confidence intervals from approximately invariant transformations of the data. As special cases, DAB recovers popular methods that rely on exact group symmetries, such as conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics and the recently proposed SymmPI. Meanwhile, DAB also recovers the classical bootstrap method, which exploits the dataset's approximate invariance under uniform sampling of data indices as the dataset size grows. For all DAB methods, we establish theoretical coverage results that interpolate between finite-sample and asymptotic guarantees according to the strength of the invariance, and without assuming a group structure. The approximate invariance is measured in the Kolmogorov distance and, for statistics that satisfy Gaussian universality, reduces to conditional mean and variance matching. This allows us to incorporate data augmentation (DA), a widely used machine learning heuristic based on approximate invariances, into known statistical methods. We empirically test the performance of incorporating DA into bootstrap, wild bootstrap and conformal prediction for simulated settings as well as for image, language and scientific data.

08.
arXiv (CS.AI) 2026-06-18

Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation

Authors:

arXiv:2606.18828v1 Announce Type: cross Abstract: Traditional approaches place intelligence in the agent, whether as a learned policy or a search procedure. We instead place intelligence in the space itself: a scene induces a Riemannian metric on the configuration manifold, and action reduces to following the geodesics of that metric rather than invoking a separate planner or collision checker. A single Encoder-Router network realizes this idea through three complementary parameter groups – frame parameters that orient the generators, modulation parameters that govern their spatial propagation, and basic coefficients that determine their strength. These groups combine through a shared semigroup-superposition mechanism to produce a single Riemannian metric field, yielding a compact architecture whose geometry scales naturally with scene complexity. Trained on a single two-obstacle scene, the model demonstrates robust zero-shot generalization across unseen obstacle configurations, with orders-of-magnitude separation between collision-free and obstacle-penetrating path costs.

09.
bioRxiv (Bioinfo) 2026-06-11

OCOO-T : A SIMPLE AND SCALABLE VIRTUAL CELL MODEL FOR TRANSCRIPTIONAL PERTURBATION RESPONSE PREDICTION

Predicting single-cell transcriptional responses to genetic, chemical and cytokine perturbations is a fundamental challenge in computational biology and AI Virtual Cell (AIVC) modeling, with direct implications for drug discovery and the elucidation of gene regulatory networks. Existing approaches often rely on auxiliary cell-state encoders, hierarchical variational autoencoders, dedicated Transformer encoder-decoder modules, or gene-interaction priors to compress high-dimensional expression profiles into latent representations. While effective, these designs increase architectural complexity and may limit scalability and generalizability. This paper introduces OCOO-T, a minimalist flow-matching-based AIVC model for transcriptional perturbation response prediction. OCOO-T utilizes a vanilla Transformer stack that operates directly on continuous gene expression profiles and formulates perturbation response prediction as a continuous-time denoising process. Perturbation embeddings, dosage information, and cell-line/cell-type specificity are integrated through adaptive layer normalization and in-context tokens. Comprehensive evaluations on Tahoe100M, Replogle, and PBMC benchmarks demonstrate that OCOO-T achieves state-of-the-art performance across diverse perturbations and cell types while effectively scaling to long transcriptional profiles through patching and depatching of cellular contexts. By leveraging the simplicity of Transformer-based denoising for single-cell omics, OCOO-T provides an effective and scalable framework for in-silico cellular simulation.

10.
arXiv (CS.AI) 2026-06-11

FitText: Evolving Agent Tool Ecologies via Memetic Retrieval

arXiv:2605.02411v2 Announce Type: replace Abstract: A semantic gap separates how users describe tasks from how tools are documented. As API ecosystems scale to tens of thousands of endpoints, static retrieval from the initial query alone cannot bridge this gap: the agent's understanding of what it needs evolves during execution, but its tool set does not. We identify this retrieval interface, not planning, as the binding constraint on end-to-end agent performance, and introduce FitText, a training-free framework that makes retrieval dynamic by embedding it directly in the agent's reasoning loop. FitText treats retrieval as test-time evolution of hypotheses: the agent generates natural-language pseudo-tool descriptions (revisable beliefs about the tool it needs), refines them iteratively using retrieval feedback, and explores diverse alternatives through stochastic generation. Memetic Retrieval adds evolutionary selection pressure over candidate descriptions, guided by a tool memory that avoids redundant search. On ToolRet (three domains), FitText's reformulation strategies improve NDCG@5 by 2.7 to 10.6 points over static query retrieval across all base models; on StableToolBench (16,464 APIs) with GPT-5.4-mini, Memetic reaches an 84.3% pooled pass rate, a 26.7-point absolute gain over static query retrieval.

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

Redirecting the Flow: Image Customization through Attention Distribution Shift

Subject-driven image customization aims to generate images that not only follow textual instructions but also preserve the identity of a given reference subject. Existing approaches, including test-time fine-tuning, encoder-based methods, and token competition in shared attention spaces, suffer from limited efficiency, misalignment between extracted reference features and the generative process, and interference from irrelevant information. To address these limitations, we formulate the customization task as a distribution shift induced by incorporating reference images into text-to-image generation, and derive a Conditional Attention Distribution Shift formulation grounded in maximum entropy theory. Building on this formulation, we propose CustomShift, a dual-branch architecture based on Stable Diffusion 3. The Reference-Alignment Branch leverages self-attention between reference images and subject names to achieve layer-wise alignment with latent representations, while the Cross-Guidance Branch integrates textual and reference cues to guide generation. Experiments on the DreamBooth and Custom101 benchmarks demonstrate that our method consistently outperforms state-of-the-art approaches, achieving a better balance between semantic fidelity and subject consistency.

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

Token Factory: Efficiently Integrating Diverse Signals into Large Recommendation Models

arXiv:2606.19635v1 Announce Type: cross Abstract: Large Recommendation Models (LRMs) have demonstrated promising capabilities in industry-scale recommendation tasks. However, holistically integrating traditional signals into these transformer-based architectures effectively and efficiently remains a major challenge. Conventional approaches that "textualize" these signals directly or create discrete item representations often lead to excessively long prompts, substantial memory footprints, and high computational overhead. To overcome these limitations, we propose "Token Factory", a framework designed to transform traditional signals into "soft tokens" that can be directly processed by LRMs. This approach enables efficient integration and compression of heterogeneous input features, preventing prompt length explosion while enhancing model performance. We detail the architecture of Token Factory and present experimental results validating its effectiveness in a production-scale recommendation environment.

13.
Nature (Science) 2026-06-10

Human migration has surged since 2000 — these maps reveal where people are going

Authors:

Modelling with artificial-intelligence tools has filled gaps in migration data, revealing detailed global population movements from 1990 to 2023. Modelling with artificial-intelligence tools has filled gaps in migration data, revealing detailed global population movements from 1990 to 2023.

14.
arXiv (CS.AI) 2026-06-15

Korzhinskii-Net: Physics-Informed Neural Network for Sub-Surface Mineral Prospectivity Modelling

Authors:

arXiv:2606.13695v1 Announce Type: cross Abstract: Mineral prospectivity modelling (MPM) underpins exploration economics, yet most operational pipelines reduce to data-driven classifiers trained on shallow surface proxies. Such models are blind to the subsurface physics that actually localises ore: heat advection, fluid flow, and lithology-dependent precipitation. We present Korzhinskii-Net, a 2-D radial physics-informed neural network (PINN) that couples Darcy flow, advective-diffusive heat transport, and a softplus-saturated reaction rate into a single differentiable forward model, weakly supervised by surface and remote-sensing proxies. The network is named after Dmitri S. Korzhinskii (1899-1985), whose theory of infiltration metasomatism provides the physical scaffold. We evaluate Korzhinskii-Net on five ore provinces spanning four commodity classes – Norilsk (Ni-Cu-PGE), Pechenga (Ni-Cu sulphide), Udokan (sandstone-hosted Cu), Sukhoi Log (orogenic Au), and Mirny (kimberlitic diamond) – under a fair, leakage-controlled 5-fold cross-validation protocol with hard ring-shaped negatives. Korzhinskii-Net attains a mean PR-AUC of 0.885 versus 0.281 for the strongest classical baseline (gradient boosting), and a mean fractional rank of 0.019 versus 0.413. The improvement is consistent across all five provinces and four commodity systems, suggesting that physics-informed differentiable simulators, even when constrained only by global open-data proxies, can recover localisation patterns that pure feature-based learners systematically miss. We release the full pipeline and evaluation harness as open source.

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

You Don't Need Strong Assumptions: Visual Representation Learning via Temporal Differences

Progress in AI has largely been driven by methods that assume less. As compute and data increase, approaches with weaker inductive biases generally outperform those with stronger assumptions. This is particularly characteristic of the field of Visual Representation Learning, where approaches have gone from being dominated by Supervised Learning, to Weakly Supervised Learning, to the now widespread success of Self-Supervised Learning without human labels. Yet, even modern Self-Supervised Learning approaches still depend on strong inductive biases such as augmentations, masking, or cropping. If this trend holds, even these remaining biases should become bottlenecks at scale – and our experiments confirm this: the optimal strength of inductive biases decreases as data grows. This motivates the search for approaches that rely on fewer assumptions. To this end, we introduce Temporal Difference in Vision (TDV), a new paradigm for self-supervised learning from video that avoids existing inductive biases, relying instead on a causal assumption that the past causes the future. TDV functions by jointly training an image encoder and a motion encoder so that the current frame's representation plus the encoded motion equals the next frame's representation. Despite not leveraging any strong inductive biases, TDV matches state-of-the-art recipes on dense spatial tasks, laying the foundation for representation learning without strong assumptions.

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

Calibrated Triage, Not Autonomy: Confidence Estimation for Medical Vision-Language Models

A vision-language model can answer a question about a medical image fluently and confidently while barely using the image, leaning instead on language priors. In medicine this is the failure that matters most, because the answer looks trustworthy and is not, and the only protection is a confidence score reliable enough to tell the system when to abstain. We ask a deployment question rather than an accuracy one: how much imaging work a model can safely handle alone, and which confidence signal makes that possible. We evaluate seven confidence estimators across five open-weight LVLMs and three medical visual-question-answering datasets spanning broad clinical imaging, radiology, and pathology, with every probe trained only on natural images and applied without adaptation. Recast as bounded selective prediction (automate a case only when confidence clears a threshold, defer the rest), the comparison is cautionary. The standard metrics are poor guides: discrimination barely separates the methods, and the weak calibration of a cheap self-report is cheaply removed by off-domain temperature scaling without changing deployable yield. What distinguishes a usable estimator is the high-confidence region a clinician acts on: the weakest baselines are confidently wrong on 41 to 45 percent of their errors against 1 to 4 percent for the best probe, and no estimator is reliably best across domains or models. Safe handoff is governed at two levels: base-model competence sets a ceiling, so a well-calibrated score recovers roughly a third of radiology cases at a 20 percent error tolerance but almost none of pathology; the confidence layer then decides how much of that ceiling is reachable. The usable role today is calibrated triage, not autonomy: automate the cases a calibrated score marks safe, route the rest to a clinician. We release all outputs, correctness judgments, and confidence scores, with code.

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

MiniPIC: Flexible Position-Independent Caching in <100LOC

Retrieval-augmented and agentic workloads repeatedly prefill recurring predictable structured inputs (which we call "spans") such as documents and code files. Yet, prefix caching in engines such as vLLM cannot reuse their KV entries unless they share identical prefixes with another request, while Position-Independent Caching (PIC) implementations within production-grade inference servers typically either require substantial server code changes or keep KV state outside the server, incurring host-to-device transfer overhead. We present Minimalistic PIC (MiniPIC): a minimal, flexible and fast vLLM design built from two ingredients: positional-encoding-free KV cache and user-controlled cache-reuse primitives. MiniPIC stores unrotated K vectors in the KV cache, applies RoPE to K tiles inside attention using per-request logical positions, and exposes three user-facing and token-level primitives: block-aligned padding, span separator (SSep), and prompt depend (PDep), that modify hashing behavior and effective block-level causal attention structure. With fewer than 100 lines of core-engine changes plus a custom attention backend, these primitives are sufficient to realize multiple PIC methods, including Block-Attention, EPIC, and Prompt Cache, within the same running vLLM instance, while natively integrating with KV cache CPU offload implementations. On 2WikiMultihopQA, MiniPIC with interleaved scheduling improves prefill throughput by 49% over baseline vLLM, reduces cached-span time-to-first-token by up to two orders of magnitude, preserves the linear prefill scaling of uncached spans, and incurs only 5.7% worst-case overhead.

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

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

arXiv:2606.16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy, measured in the $W^{1,\infty}$-norm, by a fixed-size neural network using the Elementary Universal Activation Function ($\mathrm{EUAF}$). To extend this result to $W^{s,\infty}((a,b)^d)$ for $s\in\mathbb{N}$, we introduce a smooth activation $\mathrm{DUAF}_{\infty}$ from the family of Differentiable Universal Activation Functions ($\mathrm{DUAF}_n$). We prove that any function in $W^{s,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy in the $W^{s-1,\infty}$-norm by a fixed-size $\mathrm{DUAF}_{\infty}$-activated network. We further construct sigmoidal variants $\widetilde{\mathrm{DUAF}}_n$ and show that, for every $1\leq s\leq n$, fixed-size $\widetilde{\mathrm{DUAF}}_n$-activated networks still approximate any $f\in W^{s,\infty}((a,b)^d)$ with arbitrary accuracy in the $W^{s-1,\infty}$-norm. In all these results, the width and depth bounds are computed explicitly, and the proposed activations are elementary.

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

Certifiable Safe RLHF: Semantic Grounding and Fixed Penalty Constraint Optimization for Safer LLM Alignment

arXiv:2510.03520v2 Announce Type: replace-cross Abstract: Ensuring safety is a foundational requirement for large language models (LLMs). Achieving an appropriate balance between enhancing the utility of model outputs and mitigating their potential for harm is a complex and persistent challenge. Contemporary approaches frequently formalize this problem within the framework of Constrained Markov Decision Processes (CMDPs) and employ established CMDP optimization techniques. However, these methods exhibit two notable limitations. First, their reliance on reward and cost functions renders performance highly sensitive to the underlying scoring mechanism, which must capture semantic meaning rather than being triggered by superficial keywords. Second, CMDP-based training entails tuning dual-variable, a process that is both computationally expensive and does not provide any provable safety guarantee for a fixed dual variable that can be exploitable through adversarial jailbreaks. To overcome these limitations, we introduce Certifiable Safe-RLHF (CS-RLHF) that introduces a cost model trained on a large-scale corpus to assign semantically grounded safety scores. In contrast to the lagrangian-based approach, CS-RLHF adopts a rectified penalty-based formulation. This design draws on the theory of exact penalty functions in constrained optimization, wherein constraint satisfaction is enforced directly through a suitably chosen penalty term. With an appropriately scaled penalty, feasibility of the safety constraints can be guaranteed at the optimizer, eliminating the need for dual-variable updates. Empirical evaluation demonstrates that CS-RLHF outperforms state-of-the-art LLM model responses rendering at-least 5 times efficient against nominal and jail-breaking prompts

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

Seeing Roads Through Words: A Language-Guided Framework for RGB-T Driving Scene Segmentation

Robust semantic segmentation of road scenes under adverse illumination, lighting, and shadow conditions remain a core challenge for autonomous driving applications. RGB-Thermal fusion is a standard approach, yet existing methods apply static fusion strategies uniformly across all conditions, allowing modality-specific noise to propagate throughout the network. Hence, we propose CLARITY that dynamically adapts its fusion strategy to the detected scene condition. Guided by vision-language model (VLM) priors, the network learns to modulate each modality's contribution based on the illumination state while leveraging object embeddings for segmentation, rather than applying a fixed fusion policy. We further introduce two mechanisms - one which preserves valid dark-object semantics that prior noise-suppression methods incorrectly discard, and a hierarchical decoder that enforces structural consistency across scales to sharpen boundaries on thin objects. Experiments on the MFNet dataset demonstrate that CLARITY establishes a new state-of-the-art (SOTA), achieving 62.3% mIoU and 77.5% mAcc.

21.
arXiv (quant-ph) 2026-06-17

A polynomial-time approximation scheme for minimum-weight decoding of topological codes

arXiv:2606.18145v1 Announce Type: new Abstract: Two-dimensional topological translationally invariant (2D TTI) stabilizer codes lie at the heart of fault-tolerant quantum computation, but using them requires solving the decoding problem. Minimum-weight decoding of these codes was recently shown to be NP-hard, even in basic settings, such as the color code with Pauli $Z$ errors and the toric code with Pauli $X$, $Y$ and $Z$ errors. Here, we prove that minimum-weight decoding of 2D TTI codes nonetheless admits a polynomial-time approximation scheme (PTAS), i.e., for any constant $\varepsilon>0$, a recovery operator of weight within a multiplicative factor of $1+\varepsilon$ of the minimum can be found in polynomial time. Our approach builds on Arora's PTAS for Euclidean problems, such as the traveling salesman problem, and applies when decoding can be cast in terms of point-like excitations connected by string-like errors. It therefore extends beyond two dimensions, covering certain higher-dimensional topological codes and quantum memories, including the toric code with phenomenological or circuit-level noise.

22.
medRxiv (Medicine) 2026-06-15

Prevalence and Clinical Impact of Pathogenic Variants in Cardiomyopathy Genes Among Individuals with Cardiac Conduction Disorders

Importance: Cardiac conduction disorders have traditionally been regarded as a secondary manifestation of underlying structural heart diseases. However, isolated conduction disorders may precede the onset of heart failure (HF) suggesting shared mechanisms. Objective: To evaluate the prevalence and clinical significance of pathogenic/likely pathogenic (P/LP) rare variants in cardiomyopathy genes among individuals with conduction disorders. Design, Setting, and Participants: Biobank analysis of 192,834 participants with whole genome sequence data from Vanderbilt's BioVU and 353,092 participants from the All of Us Research Program (AoU). Participants with primary conduction disorder (left bundle branch block [LBBB], right bundle branch block [RBBB], high-grade atrioventricular block [AVB]) were identified after excluding secondary causes. Exposures: P/LP variants in cardiomyopathy genes. Main Outcomes and Measures: Primary outcome was P/LP carrier status by age and HF status. Secondary outcomes included incident HF and composite ventricular arrhythmias/sudden cardiac death/mortality (VA/SCD/mortality). Results: Among 16,959 participants with conduction disorders in BioVU and 13,442 in AoU, 432 (2.6%) and 206 (1.5%) were P/LP carriers, respectively. Conduction disorder was independently associated with carrier status (BioVU p

23.
arXiv (quant-ph) 2026-06-17

Unveiling Hierarchical Invariants in Multiphoton Linear Optics

arXiv:2506.12857v2 Announce Type: replace Abstract: Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.

24.
arXiv (math.PR) 2026-06-17

Cutoff for asymmetric shelf shuffle

arXiv:2606.18039v1 Announce Type: new Abstract: A mechanical shuffler consists of $m$ shelves. A deck of $n$ cards, arranged in increasing order, is dealt from the bottom sequentially. Each card is assigned a shelf uniformly at random and placed on the top (bottom) of the existing pile with probability $p$ ($1-p$) independently. We refer to this as asymmetric shelf-shuffle. We find the law $\nu_{n, m}^{(p)}$ of the permutation induced by the asymmetric shelf-shuffle and show that the pair consisting of the number of descents and the number of valleys is a sufficient statistic. This generalizes a result of Diaconis, Fulman, and Holmes (Ann. Appl. Prob., 2013) corresponding to the case $p=1/2$. For $p=1/2$, Chen and Ottolini (ECP, 2025) established the cutoff in the total variation distance near $\lfloor n^{5/4}\rfloor$. We establish the cutoff for the asymmetric shelf shuffle. Let $\nu_n$ be the uniform measure on the set of all permutations $S_n$ of $\{1, \ldots, n\}$. For a fixed $p\neq 1/2$ and $c>0$, we show that \[\operatorname{TV}\left(\nu_{n, \lfloor cn^{3/2}\rfloor }^{(p)}, \nu_n\right)=1-2\Phi\left(-\frac{|2p-1|}{4\sqrt{3}c}\right)+O_{c, p}(n^{-1/2})\;.\] We also establish the cutoff in the separation distance near $m\approx n^{2}$ and in the relative entropy near $m=n^{3/2}$. In both cases, we also obtain the cutoff profile explicitly.

25.
arXiv (math.PR) 2026-06-16

Universality in the target arrival statistics of non-conservative search processes

arXiv:2606.16025v1 Announce Type: cross Abstract: Stochastic search processes in which searchers are continuously introduced to and removed from a target search domain are fundamental to a wide class of physical and artificial systems. The theory of such non-conservative search processes is, however, much less developed than for search processes with a fixed number of particles. Here we exploit a natural mapping between non-conservative stochastic search and queueing theory to derive the full time-dependent distribution of target arrivals under minimal assumptions on the underlying search process. Remarkably, we find that the steady-state inter-arrival time distribution is exactly exponential, regardless of the details of the search process, showing a robust universality that emerges directly from the queueing framework. Thus, counterintuitively, the arrival statistics of a non-conservative search process are much simpler than sequential search-and-capture processes involving a fixed number of searchers. This has major implications for target resource accumulation, where the delivery of resources is counter-balanced by their downstream consumption.