In 1957, Steinhaus proved that a chain of regular tetrahedra, meeting face-to-face and forming a closed loop does not exist. Over the years, various modifications of this statement have been considered and analysed. Weakening the statement by only requiring the tetrahedra of a chain to be wild, i.e. having all faces congruent, results in various examples of such chains. In this paper, we elaborate on the construction of these chains of wild tetrahedra. We therefore introduce the notions of chains and clusters of wild tetrahedra and relate these structures to simplicial surfaces. We establish that clusters and chains of wild tetrahedra can be described by polyhedra in Euclidean 3-space. As a result, we present methods to construct toroidal polyhedra arising from chains and provide a census of such toroidal polyhedra consisting of up to 20 wild tetrahedra. Here, we classify toroidal polyhedra with respect to self-intersections and reflection symmetries. We further prove the existence of an infinite family of toroidal polyhedra emerging from chains of wild tetrahedra and present clusters of wild tetrahedra that yield polyhedra of higher genera.
In this paper, we provide explicit recursive constructions of infinitely many non-equivalent wild knots contained in the Menger sponge, in such a way that we can control their set of wild points that lies in a usual Cantor set contained in the Menger sponge. Furthermore, we show that wild knots of dynamically defined type arising from Kleinian group actions can be isotoped into the sponge. We want to emphasize that our approach is constructive and geometric.
We introduce the wild number of an edge-colored graph as a measure of how close an edge-colored graph is to having a spanning tree in every color. This combinatorial concept originates in the algebraic theory of generalized graph splines. After showing that determining the wild number of a graph is an NP-complete problem, we provide bounds on the wild number and find the exact wild number for trees, cycles, and families of graphs with restrictions on the edge-colorings. This article serves as an invitation to the topic of wild numbers and includes several open problems, many of which are suitable for undergraduate research projects.
We describe and analyze a computionally efficient refitting procedure for computing high-probability upper bounds on the instance-wise mean-squared prediction error of penalized nonparametric estimates based on least-squares minimization. Requiring only a single dataset and black box access to the prediction method, it consists of three steps: computing suitable residuals, symmetrizing and scaling them with a pre-factor $ρ$, and using them to define and solve a modified prediction problem recentered at the current estimate. We refer to it as wild refitting, since it uses Rademacher residual symmetrization as in a wild bootstrap variant. Under relatively mild conditions allowing for noise heterogeneity, we establish a high probability guarantee on its performance, showing that the wild refit with a suitably chosen wild noise scale $ρ$ gives an upper bound on prediction error. This theoretical analysis provides guidance into the design of such procedures, including how the residuals should be formed, the amount of noise rescaling in the wild sub-problem needed for upper bounds, and the local stability properties of the block-box procedure. We illustrate the applicability of this proc
Inspired by the model theory of difference fields in characteristic zero, a class of automorphisms of an algebraic variety, here called compound fundamental isotrivial, is introduced. These are algebraic dynamical systems that are built up via a finite sequence of equivariant fibrations from (possibly nonautonomous) algebraic dynamics which trivialise after base extension over themselves. Every wild automorphism of an abelian variety is compound fundamental isotrivial. Conversely, it is shown that the only irreducible projective varieties admitting a wild automorphism that is compound fundamental isotrivial are the abelian varieties. That is, the wild automorphism conjecture of Reichstein, Rogalski, and Zhang is here proven for compound fundamental isotrivial dynamics. Along the way, a counterexample to the naive generalisation of the conjecture to the nonautonomous setting of $σ$-varieties is provided.
Wild knots--knots with infinite knotting behavior--have resisted traditional methods of knot classification, making them more of a curiosity in topology than a subject of sustained investigation. In this paper, we present a new way to investigate these objects. We extend Lomonaco and Kauffman's knot mosaic theory to represent a substantial subclass of wild knots that have isolated wild points. Our mosaics consist of infinite rooted trees with mosaics assigned to vertices and embedding functions governing connections. In developing this framework, we also introduce a notion of mosaic tangles as well as mosaic rigid vertex spatial graphs of which mosaic singular knots are a special case.
Despite rapid advances in automatic speech recognition (ASR) and large audio-language models, robust recognition in real-world environments remains limited by an "acoustic robustness bottleneck": models often lose acoustic grounding and produce omissions or hallucinations under severe, compositional distortions. We propose Mega-ASR, a unified ASR-in-the-wild framework that combines scalable compound-data construction with progressive acoustic-to-semantic optimization. We introduce Voices-in-the-Wild-2M, covering 7 classic acoustic phenomena and 54 physically plausible compound scenarios, and train Mega-ASR with Acoustic-to-Semantic Progressive Supervised Fine-Tuning and Dual-Granularity WER-Gated Policy Optimization. Extensive experiments demonstrate that Mega-ASR achieves significant advantages over prior state-of-the-art systems on adverse-condition ASR benchmarks (45.69% vs. 54.01% on VOiCES R4-B-F, and 21.49% vs. 29.34% on NOIZEUS Sta-0). On complex compositional acoustic scenarios, Mega-ASR further delivers over 30% relative WER reduction against strong open- and closed-source baselines, establishing a scalable paradigm for robust ASR in-the-wild.
Robust detection of AI-generated images in the wild remains challenging due to the rapid evolution of generative models and varied real-world distortions. We argue that relying on a single training regime, resolution, or backbone is insufficient to handle all conditions, and that structured heterogeneity across these dimensions is essential for robust detection. To this end, we propose HEDGE, a Heterogeneous Ensemble for Detection of AI-GEnerated images, that introduces complementary detection routes along three axes: diverse training data with strong augmentation, multi-scale feature extraction, and backbone heterogeneity. Specifically, Route~A progressively constructs DINOv3-based detectors through staged data expansion and augmentation escalation, Route~B incorporates a higher-resolution branch for fine-grained forensic cues, and Route~C adds a MetaCLIP2-based branch for backbone diversity. All outputs are fused via logit-space weighted averaging, refined by a lightweight dual-gating mechanism that handles branch-level outliers and majority-dominated fusion errors. HEDGE achieves 4th place in the NTIRE 2026 Robust AI-Generated Image Detection in the Wild Challenge and attains st
NASA's Stardust mission returned rocky material from the coma of comet 81P/Wild 2 (pronounced "Vilt 2") to Earth for laboratory study on January 15, 2006. Comet Wild 2 contains volatile ices and likely accreted beyond the orbit of Neptune. It was expected that the Wild 2 samples would contain abundant primordial molecular cloud material--interstellar and circumstellar grains. Instead, the interstellar component of Wild 2 was found to be very minor, and nearly all of the returned particles formed in broad and diverse regions of the solar nebula. While some characteristics of the Wild 2 material are similar to primitive chondrites, its compositional diversity testifies to a very different origin and evolution history than asteroids. Comet Wild 2 does not exist on a continuum with known asteroids. Collisional debris from asteroids is mostly absent in Wild 2, and it likely accreted dust from the outer and inner Solar System (across the putative gap created by a forming Jupiter) before dispersal of the solar nebula. Comets are a diverse set of bodies, and Wild 2 may represent a type of comet that accreted a high fraction of dust processed in the young Solar System.
In this paper, we study wild character varieties on compact Riemann surfaces and construct Poisson maps from wild to tame character varieties by unfolding irregular singularities into regular ones. Furthermore, we show that these unfolding Poisson maps induce Poisson birational equivalences between wild and tame character varieties. This result provides an affirmative answer to a conjecture posed by Klimes, Paul, and Ramis.
We describe our entry to the ICIP 2026 Grand Challenge on Extreme In-the-Wild License Plate Super-Resolution (XLPSR), which scored 9.73 wECR on the public validation leaderboard. The system pairs a Hybrid Attention Transformer super-resolution (HAT) front-end with an ensemble of two scene-text recognisers (PARSeq-S and CLIP4STR-B) and a confidence-weighted character-voting scheme that abstains on uncertain positions. We treat XLPSR as a recognition task gated by image legibility: the SR step exists to lift characters out of sub-pixel territory, and the asymmetric scoring rule (+2 / -1 / 0) is exploited explicitly through abstention. Our pipeline runs in 1.7 s per sequence on RTX 3090 (max 2.7 s, p99 2.4 s), well under the 60 s/sequence Docker budget.
Achieving robust humanoid hiking in complex, unstructured environments requires transitioning from reactive proprioception to proactive perception. However, integrating exteroception remains a significant challenge: mapping-based methods suffer from state estimation drift; for instance, LiDAR-based methods do not handle torso jitter well. Existing end-to-end approaches often struggle with scalability and training complexity; specifically, some previous works using virtual obstacles are implemented case-by-case. In this work, we present \textit{Hiking in the Wild}, a scalable, end-to-end parkour perceptive framework designed for robust humanoid hiking. To ensure safety and training stability, we introduce two key mechanisms: a foothold safety mechanism combining scalable \textit{Terrain Edge Detection} with \textit{Foot Volume Points} to prevent catastrophic slippage on edges, and a \textit{Flat Patch Sampling} strategy that mitigates reward hacking by generating feasible navigation targets. Our approach utilizes a single-stage reinforcement learning scheme, mapping raw depth inputs and proprioception directly to joint actions, without relying on external state estimation. Extensive
While the field of 3D scene reconstruction is dominated by NeRFs due to their photorealistic quality, 3D Gaussian Splatting (3DGS) has recently emerged, offering similar quality with real-time rendering speeds. However, both methods primarily excel with well-controlled 3D scenes, while in-the-wild data - characterized by occlusions, dynamic objects, and varying illumination - remains challenging. NeRFs can adapt to such conditions easily through per-image embedding vectors, but 3DGS struggles due to its explicit representation and lack of shared parameters. To address this, we introduce WildGaussians, a novel approach to handle occlusions and appearance changes with 3DGS. By leveraging robust DINO features and integrating an appearance modeling module within 3DGS, our method achieves state-of-the-art results. We demonstrate that WildGaussians matches the real-time rendering speed of 3DGS while surpassing both 3DGS and NeRF baselines in handling in-the-wild data, all within a simple architectural framework.
We prove that all wild blocks of type $A$ Hecke algebras with quantum characteristic $e \geqslant 3$ -- i.e. blocks of weight at least $2$ -- are strictly wild, with the possible exception of the weight $2$ Rouquier block for $e = 3$. As a corollary, we show that for $e \geqslant 3$, all wild blocks of the $q$-Schur algebras are strictly wild, without exception.
We survey a few results on differentiable, symplectic, or analytic wild dynamics.
By relying on a new approach to Lefschetz type questions based on Beilinson's singular support and Saito's characteristic cycle, we prove an instance of the wild Lefschetz theorem envisioned by Deligne. Our main tool are new finiteness results for the characteristic cycles of perverse sheaves.
To enable egocentric contextual AI in always-on smart glasses, it is crucial to be able to keep a record of the user's interactions with the world, including during reading. In this paper, we introduce a new task of reading recognition to determine when the user is reading. We first introduce the first-of-its-kind large-scale multimodal Reading in the Wild dataset, containing 100 hours of reading and non-reading videos in diverse and realistic scenarios. We then identify three modalities (egocentric RGB, eye gaze, head pose) that can be used to solve the task, and present a flexible transformer model that performs the task using these modalities, either individually or combined. We show that these modalities are relevant and complementary to the task, and investigate how to efficiently and effectively encode each modality. Additionally, we show the usefulness of this dataset towards classifying types of reading, extending current reading understanding studies conducted in constrained settings to larger scale, diversity and realism.
Large language models (LLMs) for code generation are becoming integral to modern software development, but their real-world prevalence and security impact remain poorly understood. We present the first large-scale empirical study of AI-generated code (AIGCode) in the wild. We build a high-precision detection pipeline and a representative benchmark to distinguish AIGCode from human-written code, and apply them to (i) development commits from the top 1,000 GitHub repositories (2022-2025) and (ii) 7,000+ recent CVE-linked code changes. This lets us label commits, files, and functions along a human/AI axis and trace how AIGCode moves through projects and vulnerability life cycles. Our measurements show three ecological patterns. First, AIGCode is already a substantial fraction of new code, but adoption is structured: AI concentrates in glue code, tests, refactoring, documentation, and other boilerplate, while core logic and security-critical configurations remain mostly human-written. Second, adoption has security consequences: some CWE families are overrepresented in AI-tagged code, and near-identical insecure templates recur across unrelated projects, suggesting "AI-induced vulnerabi
Existence of wild attractors -- attractors whose basin has a positive Lebesgue measure but is not a residual set -- has been one of central themes in one-dimensional dynamics. It has been demonstrated by H. Bruin et al. that Fibonacci maps with a sufficiently flat critical point admit a wild attractor. We propose a constructive trichotomy that describes possible scenarios for the Lebesgue measure of the Fibonacci attractor based on a computable criterion. We use this criterion, together with a computer-assisted proof of existence of a Fibonacci renormalization $2$-cycle for non-integer critical degrees, to demonstrate that Fibonacci maps do not have a wild attractor when the degree of the critical point is $d=3.8$ (and, conjecturally, for $2< d \le 3.8$), and do admit it when $d=5.1$ (and, conjecturally, for $d \ge 5.1$).
Image geolocation is a critical task in various image-understanding applications. However, existing methods often fail when analyzing challenging, in-the-wild images. Inspired by the exceptional background knowledge of multimodal language models, we systematically evaluate their geolocation capabilities using a novel image dataset and a comprehensive evaluation framework. We first collect images from various countries via Google Street View. Then, we conduct training-free and training-based evaluations on closed-source and open-source multi-modal language models. we conduct both training-free and training-based evaluations on closed-source and open-source multimodal language models. Our findings indicate that closed-source models demonstrate superior geolocation abilities, while open-source models can achieve comparable performance through fine-tuning.