Daily Papers

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree tree where the weight of each node is the sum of the weights of its children. A treemap for tree is a hierarchical partition of a rectangle into simply connected regions, usually rectangles. Each region represents a node of tree and its area is proportional to the weight of the corresponding node. An important quality criterion for treemaps is the aspect ratio of its regions. One cannot bound the aspect ratio if the regions are restricted to be rectangles. In contrast, polygonal partitions, that use convex polygons, have bounded aspect ratio. We are the first to obtain convex partitions with optimal aspect ratio O(depth(tree)). However, depth(tree) still depends on the input tree. Hence we introduce a new type of treemaps, namely orthoconvex treemaps, where regions representing leaves are rectangles, L-, and S-shapes, and regions representing internal nodes are orthoconvex polygons. We prove that any input tree, irrespective of the weights of the nodes and the depth of the tree, admits an orthoconvex treemap of constant aspect ratio. We also obtain several specialized results for single-level treemaps, that is, treemaps where the input tree has depth~1.

Accurately quantifying tree cover is an important metric for ecosystem monitoring and for assessing progress in restored sites. Recent works have shown that deep learning-based segmentation algorithms are capable of accurately mapping trees at country and continental scales using high-resolution aerial and satellite imagery. Mapping at high (ideally sub-meter) resolution is necessary to identify individual trees, however there are few open-access datasets containing instance level annotations and those that exist are small or not geographically diverse. We present a novel open-access dataset for individual tree crown delineation (TCD) in high-resolution aerial imagery sourced from OpenAerialMap (OAM). Our dataset, OAM-TCD, comprises 5072 2048x2048 px images at 10 cm/px resolution with associated human-labeled instance masks for over 280k individual and 56k groups of trees. By sampling imagery from around the world, we are able to better capture the diversity and morphology of trees in different terrestrial biomes and in both urban and natural environments. Using our dataset, we train reference instance and semantic segmentation models that compare favorably to existing state-of-the-art models. We assess performance through k-fold cross-validation and comparison with existing datasets; additionally we demonstrate compelling results on independent aerial imagery captured over Switzerland and compare to municipal tree inventories and LIDAR-derived canopy maps in the city of Zurich. Our dataset, models and training/benchmark code are publicly released under permissive open-source licenses: Creative Commons (majority CC BY 4.0), and Apache 2.0 respectively.

The FOR-instance dataset (available at https://doi.org/10.5281/zenodo.8287792) addresses the challenge of accurate individual tree segmentation from laser scanning data, crucial for understanding forest ecosystems and sustainable management. Despite the growing need for detailed tree data, automating segmentation and tracking scientific progress remains difficult. Existing methodologies often overfit small datasets and lack comparability, limiting their applicability. Amid the progress triggered by the emergence of deep learning methodologies, standardized benchmarking assumes paramount importance in these research domains. This data paper introduces a benchmarking dataset for dense airborne laser scanning data, aimed at advancing instance and semantic segmentation techniques and promoting progress in 3D forest scene segmentation. The FOR-instance dataset comprises five curated and ML-ready UAV-based laser scanning data collections from diverse global locations, representing various forest types. The laser scanning data were manually annotated into individual trees (instances) and different semantic classes (e.g. stem, woody branches, live branches, terrain, low vegetation). The dataset is divided into development and test subsets, enabling method advancement and evaluation, with specific guidelines for utilization. It supports instance and semantic segmentation, offering adaptability to deep learning frameworks and diverse segmentation strategies, while the inclusion of diameter at breast height data expands its utility to the measurement of a classic tree variable. In conclusion, the FOR-instance dataset contributes to filling a gap in the 3D forest research, enhancing the development and benchmarking of segmentation algorithms for dense airborne laser scanning data.

High-fidelity 3D head generation plays a crucial role in the film, animation and video game industries. In industrial pipelines, studios typically enforce a fixed reference topology across all head assets, as such a clean and uniform topology is a prerequisite for production-level rigging, skinning and animation. In this paper, we present TOPOS, a framework tailored for single image conditioned 3D head generation that jointly recovers geometry and appearance under such an industry-standard topology. In contrast to general 3D generative models which produce triangle meshes with inconsistent topology and numerous vertices, hindering semantic correspondence and asset-level reuse, TOPOS generates head meshes with a fixed, studio-style topology, enabling consistent vertex-level correspondence across all generated heads. To model heads under this unified topology, we proposed a novel variational autoencoder structure, termed TOPOS-VAE. Inspired by multi-model large language models (MLLMs), our TOPOS-VAE leverages the Perceiver Resampler to convert input pointclouds sampled from head meshes of diverse topologies into the target reference topology. Building upon TOPOS-VAE's structured latent space, we train a rectified flow transformer, TOPOS-DiT, to efficiently generate high-fidelity head meshes from a single image. We further present TOPOS-Texture, an end-to-end module that produces relightable UV texture maps from the same portrait image via fine-tuning a multimodal image generative model. The generated textures are spatially aligned with the underlying mesh geometry and faithfully preserve high-frequency appearance details. Extensive experiments demonstrate that TOPOS achieves state-of-the-art performance on 3D head generation, surpassing both classical face reconstruction methods and general 3D object generative models, highlighting its effectiveness for digital human creation.

While the availability of large and diverse datasets has contributed to significant breakthroughs in autonomous driving and indoor applications, forestry applications are still lagging behind and new forest datasets would most certainly contribute to achieving significant progress in the development of data-driven methods for forest-like scenarios. This paper introduces a forest dataset called FinnWoodlands, which consists of RGB stereo images, point clouds, and sparse depth maps, as well as ground truth manual annotations for semantic, instance, and panoptic segmentation. FinnWoodlands comprises a total of 4226 objects manually annotated, out of which 2562 objects (60.6\%) correspond to tree trunks classified into three different instance categories, namely "Spruce Tree", "Birch Tree", and "Pine Tree". Besides tree trunks, we also annotated "Obstacles" objects as instances as well as the semantic stuff classes "Lake", "Ground", and "Track". Our dataset can be used in forestry applications where a holistic representation of the environment is relevant. We provide an initial benchmark using three models for instance segmentation, panoptic segmentation, and depth completion, and illustrate the challenges that such unstructured scenarios introduce.

We present TreeON, a novel neural-based framework for reconstructing detailed 3D tree point clouds from sparse top-down geodata, using only a single orthophoto and its corresponding Digital Surface Model (DSM). Our method introduces a new training supervision strategy that combines both geometric supervision and differentiable shadow and silhouette losses to learn point cloud representations of trees without requiring species labels, procedural rules, terrestrial reconstruction data, or ground laser scans. To address the lack of ground truth data, we generate a synthetic dataset of point clouds from procedurally modeled trees and train our network on it. Quantitative and qualitative experiments demonstrate better reconstruction quality and coverage compared to existing methods, as well as strong generalization to real-world data, producing visually appealing and structurally plausible tree point cloud representations suitable for integration into interactive digital 3D maps. The codebase, synthetic dataset, and pretrained model are publicly available at https://angelikigram.github.io/treeON/.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

Neurons in the brain are organized such that nearby cells tend to share similar functions. AI models lack this organization, and past efforts to introduce topography have often led to trade-offs between topography and task performance. In this work, we present TopoLoss, a new loss function that promotes spatially organized topographic representations in AI models without significantly sacrificing task performance. TopoLoss is highly adaptable and can be seamlessly integrated into the training of leading model architectures. We validate our method on both vision (ResNet-18, ResNet-50, ViT) and language models (GPT-Neo-125M, NanoGPT), collectively TopoNets. TopoNets are the highest-performing supervised topographic models to date, exhibiting brain-like properties such as localized feature processing, lower dimensionality, and increased efficiency. TopoNets also predict responses in the brain and replicate the key topographic signatures observed in the brain's visual and language cortices. Together, this work establishes a robust and generalizable framework for integrating topography into leading model architectures, advancing the development of high-performing models that more closely emulate the computational strategies of the human brain.

We introduce Tree D-fusion, featuring the first collection of 600,000 environmentally aware, 3D simulation-ready tree models generated through Diffusion priors. Each reconstructed 3D tree model corresponds to an image from Google's Auto Arborist Dataset, comprising street view images and associated genus labels of trees across North America. Our method distills the scores of two tree-adapted diffusion models by utilizing text prompts to specify a tree genus, thus facilitating shape reconstruction. This process involves reconstructing a 3D tree envelope filled with point markers, which are subsequently utilized to estimate the tree's branching structure using the space colonization algorithm conditioned on a specified genus.

Knowledge of tree species distribution is fundamental to managing forests. New deep learning approaches promise significant accuracy gains for forest mapping, and are becoming a critical tool for mapping multiple tree species at scale. To advance the field, deep learning researchers need large benchmark datasets with high-quality annotations. To this end, we present the PureForest dataset: a large-scale, open, multimodal dataset designed for tree species classification from both Aerial Lidar Scanning (ALS) point clouds and Very High Resolution (VHR) aerial images. Most current public Lidar datasets for tree species classification have low diversity as they only span a small area of a few dozen annotated hectares at most. In contrast, PureForest has 18 tree species grouped into 13 semantic classes, and spans 339 km^2 across 449 distinct monospecific forests, and is to date the largest and most comprehensive Lidar dataset for the identification of tree species. By making PureForest publicly available, we hope to provide a challenging benchmark dataset to support the development of deep learning approaches for tree species identification from Lidar and/or aerial imagery. In this data paper, we describe the annotation workflow, the dataset, the recommended evaluation methodology, and establish a baseline performance from both 3D and 2D modalities.

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an EL-labeling. By use of this EL-labeling, we show the lattice is supersolvable and compute the M\"obius function of an interval of the poset.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

A heuristic extending the Squarified Treemap technique for the representation of hierarchical information as treemaps is presented. The original technique gives high quality treemap views, since items are laid out with rectangles that approximate squares, allowing easy comparison and selection operations. New key steps, with a low computational impact, have been introduced to yield treemaps with even better aspect ratios and higher homogeneity among items.

Forests worldwide are increasingly threatened by climate change and disturbances such as fire, pests, and pathogens, creating an urgent need for scalable monitoring of tree cover and tree mortality. Aerial imagery from drones and aircraft is a key data source for detailed and large-scale mapping of tree crowns and mortality. However, related progress is limited by the lack of globally representative, harmonized datasets for joint segmentation of tree cover and mortality. We introduce two novel, open, machine-learning-ready datasets to enable joint segmentation of tree cover and tree mortality from centimeter-scale aerial imagery for the first time at global scales. With DTE-aerial-train, we provide a training dataset comprising 385K image patches of size 1024x1024 pixels, with resolutions ranging from 2.5 to 20 cm. It includes multi-class expert-annotated and -audited pseudo-labels for tree cover and mortality. With DTE-aerial-bench, we provide a geographically balanced benchmark test set of 25 globally distributed orthoimages totaling 525 patches with high-quality expert annotations for both tree cover and mortality. Both the training and benchmark datasets span tropical, temperate, boreal, and dryland biomes and cover a wide range of forest structures and mortality patterns. Using the benchmark test set for evaluation, we establish strong reference baselines that improve mortality segmentation across all biomes and scales with significant gains in challenging regions, such as boreal forests, where the F1 score increases from 0.40 to 0.58 with around 45% relative improvement. All data, models, and code will be publicly released under permissive open-source licenses. An interactive visualization of the benchmark dataset is available at deadtrees.earth/releases/dte-aerial-bench.

Mapping individual tree crowns is essential for tasks such as maintaining urban tree inventories and monitoring forest health, which help us understand and care for our environment. However, automatically separating the crowns from each other in aerial imagery is challenging due to factors such as the texture and partial tree crown overlaps. In this study, we present a method to train deep learning models that segment and separate individual trees from RGB and multispectral images, using pseudo-labels derived from aerial laser scanning (ALS) data. Our study shows that the ALS-derived pseudo-labels can be enhanced using a zero-shot instance segmentation model, Segment Anything Model 2 (SAM 2). Our method offers a way to obtain domain-specific training annotations for optical image-based models without any manual annotation cost, leading to segmentation models which outperform any available models which have been targeted for general domain deployment on the same task.

4D head capture aims to generate dynamic topological meshes and corresponding texture maps from videos, which is widely utilized in movies and games for its ability to simulate facial muscle movements and recover dynamic textures in pore-squeezing. The industry often adopts the method involving multi-view stereo and non-rigid alignment. However, this approach is prone to errors and heavily reliant on time-consuming manual processing by artists. To simplify this process, we propose Topo4D, a novel framework for automatic geometry and texture generation, which optimizes densely aligned 4D heads and 8K texture maps directly from calibrated multi-view time-series images. Specifically, we first represent the time-series faces as a set of dynamic 3D Gaussians with fixed topology in which the Gaussian centers are bound to the mesh vertices. Afterward, we perform alternative geometry and texture optimization frame-by-frame for high-quality geometry and texture learning while maintaining temporal topology stability. Finally, we can extract dynamic facial meshes in regular wiring arrangement and high-fidelity textures with pore-level details from the learned Gaussians. Extensive experiments show that our method achieves superior results than the current SOTA face reconstruction methods both in the quality of meshes and textures. Project page: https://xuanchenli.github.io/Topo4D/.

Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive (top-down) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structure and then repeatedly merge the communities using a linkage method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis.

Detailed forest inventories are critical for sustainable and flexible management of forest resources, to conserve various ecosystem services. Modern airborne laser scanners deliver high-density point clouds with great potential for fine-scale forest inventory and analysis, but automatically partitioning those point clouds into meaningful entities like individual trees or tree components remains a challenge. The present study aims to fill this gap and introduces a deep learning framework, termed ForAINet, that is able to perform such a segmentation across diverse forest types and geographic regions. From the segmented data, we then derive relevant biophysical parameters of individual trees as well as stands. The system has been tested on FOR-Instance, a dataset of point clouds that have been acquired in five different countries using surveying drones. The segmentation back-end achieves over 85% F-score for individual trees, respectively over 73% mean IoU across five semantic categories: ground, low vegetation, stems, live branches and dead branches. Building on the segmentation results our pipeline then densely calculates biophysical features of each individual tree (height, crown diameter, crown volume, DBH, and location) and properties per stand (digital terrain model and stand density). Especially crown-related features are in most cases retrieved with high accuracy, whereas the estimates for DBH and location are less reliable, due to the airborne scanning setup.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

We introduce TopoPrimer, a framework that makes the global topological structure of the series population an explicit input to any forecasting model. TopoPrimer improves accuracy across diverse domains, stabilizes forecasts under seasonal demand spikes, and closes the cold-start gap. Precomputed once per domain via persistent homology and spectral sheaf coordinates, TopoPrimer deploys per token for fully-trained models and as a lightweight adapter for pre-trained backbones. Of these two components, sheaf coordinates are the primary accuracy driver. Across four public benchmarks on Chronos and TimesFM, TopoPrimer consistently improves forecasting accuracy, with gains of up to 7.3% MSE on ECL. The topology advantage persists with near-identical magnitude across zero-shot and fine-tuned backbones, suggesting topology and per-series training capture complementary signals. The gains are most pronounced in difficult regimes. Under peak seasonal demand, classical and zero-shot models degrade by up to 50%, while TopoPrimer stays within 10%. At cold start with no item history, TopoPrimer reduces MAE by 27% over a topology-free baseline.

We present TopoMortar, a brick wall dataset that is the first dataset specifically designed to evaluate topology-focused image segmentation methods, such as topology loss functions. TopoMortar enables to investigate in two ways whether methods incorporate prior topological knowledge. First, by eliminating challenges seen in real-world data, such as small training set, noisy labels, and out-of-distribution test-set images, that, as we show, impact the effectiveness of topology losses. Second, by allowing to assess in the same dataset topology accuracy across dataset challenges, isolating dataset-related effects from the effect of incorporating prior topological knowledge. In these two experiments, it is deliberately difficult to improve topology accuracy without actually using topology information, thus, permitting to attribute an improvement in topology accuracy to the incorporation of prior topological knowledge. To this end, TopoMortar includes three types of labels (accurate, noisy, pseudo-labels), two fixed training sets (large and small), and in-distribution and out-of-distribution test-set images. We compared eight loss functions on TopoMortar, and we found that clDice achieved the most topologically accurate segmentations, Skeleton Recall loss performed best particularly with noisy labels, and the relative advantageousness of the other loss functions depended on the experimental setting. Additionally, we show that simple methods, such as data augmentation and self-distillation, can elevate Cross entropy Dice loss to surpass most topology loss functions, and that those simple methods can enhance topology loss functions as well. clDice and Skeleton Recall loss, both skeletonization-based loss functions, were also the fastest to train, making this type of loss function a promising research direction. TopoMortar and our code can be found at https://github.com/jmlipman/TopoMortar

An n-vertex tree T is said to be graceful if there exists a bijective labelling φ:V(T)to {1,ldots,n} such that the edge-differences {|φ(x)-φ(y)| : xyin E(T)} are pairwise distinct. The longstanding graceful tree conjecture, posed by Rósa in the 1960s, asserts that every tree is graceful. The gracesize of an n-vertex tree T, denoted gs(T), is the maximum possible number of distinct edge-differences over all bijective labellings φ:V(T)to {1,ldots,n}. The graceful tree conjecture is therefore equivalent to the statement that gs(T)=n-1 for all n-vertex trees. We prove an asymptotic version of this conjecture by showing that for every varepsilon>0, there exists n_0 such that every tree on n>n_0 vertices satisfies gs(T)geqslant (1-varepsilon)n. In other words, every sufficiently large tree admits an almost graceful labelling.

We propose HyperSteiner -- an efficient heuristic algorithm for computing Steiner minimal trees in the hyperbolic space. HyperSteiner extends the Euclidean Smith-Lee-Liebman algorithm, which is grounded in a divide-and-conquer approach involving the Delaunay triangulation. The central idea is rephrasing Steiner tree problems with three terminals as a system of equations in the Klein-Beltrami model. Motivated by the fact that hyperbolic geometry is well-suited for representing hierarchies, we explore applications to hierarchy discovery in data. Results show that HyperSteiner infers more realistic hierarchies than the Minimum Spanning Tree and is more scalable to large datasets than Neighbor Joining.

We present an algorithm that constructs Calabi-Yau threefold orientifolds and their F-theory uplifts to elliptically-fibered Calabi-Yau fourfolds, embedded in toric varieties at codimension one and two respectively. The resulting Calabi-Yau fourfolds arise from triangulations of 6d reflexive polytopes -- which our method constructs from orientifold data -- and are smooth away from isolated terminal singularities. For many of our fourfolds, the construction of the mirror manifold is immediate, enabling the computation of fourfold periods, and thus the seven-brane superpotential. We present multiple examples that demonstrate these capabilities. Our algorithms work with CYTools and are available through a GitHub repository.

We present PrediTree, the first comprehensive open-source dataset designed for training and evaluating tree height prediction models at sub-meter resolution. This dataset combines very high-resolution (0.5m) LiDAR-derived canopy height maps, spatially aligned with multi-temporal and multi-spectral imagery, across diverse forest ecosystems in France, totaling 3,141,568 images. PrediTree addresses a critical gap in forest monitoring capabilities by enabling the training of deep learning methods that can predict tree growth based on multiple past observations. %Initially focused on French forests, PrediTree is designed as an expanding resource with ongoing efforts to incorporate data from other countries. To make use of this PrediTree dataset, we propose an encoder-decoder framework that requires the multi-temporal multi-spectral imagery and the relative time differences in years between the canopy height map timestamp (target) and each image acquisition date for which this framework predicts the canopy height. The conducted experiments demonstrate that a U-Net architecture trained on the PrediTree dataset provides the highest masked mean squared error of 11.78%, outperforming the next-best architecture, ResNet-50, by around 12%, and cutting the error of the same experiments but on fewer bands (red, green, blue only), by around 30%. This dataset is publicly available on URL{HuggingFace}, and both processing and training codebases are available on URL{GitHub}.

We introduce Diagram of Thought (DoT), a framework that models iterative reasoning in large language models (LLMs) as the construction of a directed acyclic graph (DAG) within a single model. Unlike traditional approaches that represent reasoning as linear chains or trees, DoT organizes propositions, critiques, refinements, and verifications into a cohesive DAG structure, allowing the model to explore complex reasoning pathways while maintaining logical consistency. Each node in the diagram corresponds to a proposition that has been proposed, critiqued, refined, or verified, enabling the LLM to iteratively improve its reasoning through natural language feedback. By leveraging auto-regressive next-token prediction with role-specific tokens, DoT facilitates seamless transitions between proposing ideas and critically evaluating them, providing richer feedback than binary signals. Furthermore, we formalize the DoT framework using Topos Theory, providing a mathematical foundation that ensures logical consistency and soundness in the reasoning process. This approach enhances both the training and inference processes within a single LLM, eliminating the need for multiple models or external control mechanisms. DoT offers a conceptual framework for designing next-generation reasoning-specialized models, emphasizing training efficiency, robust reasoning capabilities, and theoretical grounding. The code is available at https://github.com/diagram-of-thought/diagram-of-thought.

Data collection for forestry, timber, and agriculture currently relies on manual techniques which are labor-intensive and time-consuming. We seek to demonstrate that robotics offers improvements over these techniques and accelerate agricultural research, beginning with semantic segmentation and diameter estimation of trees in forests and orchards. We present TreeScope v1.0, the first robotics dataset for precision agriculture and forestry addressing the counting and mapping of trees in forestry and orchards. TreeScope provides LiDAR data from agricultural environments collected with robotics platforms, such as UAV and mobile robot platforms carried by vehicles and human operators. In the first release of this dataset, we provide ground-truth data with over 1,800 manually annotated semantic labels for tree stems and field-measured tree diameters. We share benchmark scripts for these tasks that researchers may use to evaluate the accuracy of their algorithms. Finally, we run our open-source diameter estimation and off-the-shelf semantic segmentation algorithms and share our baseline results.

Accurate estimation of forest biomass, a major carbon sink, relies heavily on tree-level traits such as height and species. Unoccupied Aerial Vehicles (UAVs) capturing high-resolution imagery from a single RGB camera offer a cost-effective and scalable approach for mapping and measuring individual trees. We introduce BIRCH-Trees, the first benchmark for individual tree height and species estimation from tree-centered UAV images, spanning three datasets: temperate forests, tropical forests, and boreal plantations. We also present DINOvTree, a unified approach using a Vision Foundation Model (VFM) backbone with task-specific heads for simultaneous height and species prediction. Through extensive evaluations on BIRCH-Trees, we compare DINOvTree against commonly used vision methods, including VFMs, as well as biological allometric equations. We find that DINOvTree achieves top overall results with accurate height predictions and competitive classification accuracy while using only 54% to 58% of the parameters of the second-best approach.

Oil palm cultivation remains one of the leading causes of deforestation in Indonesia. To better track and address this challenge, detailed and reliable mapping is needed to support sustainability efforts and emerging regulatory frameworks. We present an open-access geospatial dataset of oil palm plantations and related land cover types in Indonesia, produced through expert labeling of high-resolution satellite imagery from 2020 to 2024. The dataset provides polygon-based, wall-to-wall annotations across a range of agro-ecological zones and includes a hierarchical typology that distinguishes oil palm planting stages as well as similar perennial crops. Quality was ensured through multi-interpreter consensus and field validation. The dataset was created using wall-to-wall digitization over large grids, making it suitable for training and benchmarking both conventional convolutional neural networks and newer geospatial foundation models. Released under a CC-BY license, it fills a key gap in training data for remote sensing and aims to improve the accuracy of land cover types mapping. By supporting transparent monitoring of oil palm expansion, the resource contributes to global deforestation reduction goals and follows FAIR data principles.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

The segmentation of forest LiDAR 3D point clouds, including both individual tree and semantic segmentation, is fundamental for advancing forest management and ecological research. However, current approaches often struggle with the complexity and variability of natural forest environments. We present ForestFormer3D, a new unified and end-to-end framework designed for precise individual tree and semantic segmentation. ForestFormer3D incorporates ISA-guided query point selection, a score-based block merging strategy during inference, and a one-to-many association mechanism for effective training. By combining these new components, our model achieves state-of-the-art performance for individual tree segmentation on the newly introduced FOR-instanceV2 dataset, which spans diverse forest types and regions. Additionally, ForestFormer3D generalizes well to unseen test sets (Wytham woods and LAUTx), showcasing its robustness across different forest conditions and sensor modalities. The FOR-instanceV2 dataset and the ForestFormer3D code are publicly available at https://bxiang233.github.io/FF3D/.

This paper introduces TopoDiffuser, a diffusion-based framework for multimodal trajectory prediction that incorporates topometric maps to generate accurate, diverse, and road-compliant future motion forecasts. By embedding structural cues from topometric maps into the denoising process of a conditional diffusion model, the proposed approach enables trajectory generation that naturally adheres to road geometry without relying on explicit constraints. A multimodal conditioning encoder fuses LiDAR observations, historical motion, and route information into a unified bird's-eye-view (BEV) representation. Extensive experiments on the KITTI benchmark demonstrate that TopoDiffuser outperforms state-of-the-art methods, while maintaining strong geometric consistency. Ablation studies further validate the contribution of each input modality, as well as the impact of denoising steps and the number of trajectory samples. To support future research, we publicly release our code at https://github.com/EI-Nav/TopoDiffuser.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Forests play a critical role in global ecosystems by supporting biodiversity and mitigating climate change via carbon sequestration. Accurate aboveground biomass (AGB) estimation is essential for assessing carbon storage and wildfire fuel loads, yet traditional methods rely on labor-intensive field measurements or remote sensing approaches with significant limitations in dense vegetation. In this work, we propose a novel learning-based method for estimating AGB from a single ground-based RGB image. We frame this as a dense prediction task, introducing AGB density maps, where each pixel represents tree biomass normalized by the plot area and each tree's image area. We leverage the recently introduced synthetic 3D SPREAD dataset, which provides realistic forest scenes with per-image tree attributes (height, trunk and canopy diameter) and instance segmentation masks. Using these assets, we compute AGB via allometric equations and train a model to predict AGB density maps, integrating them to recover the AGB estimate for the captured scene. Our approach achieves a median AGB estimation error of 1.22 kg/m^2 on held-out SPREAD data and 1.94 kg/m^2 on a real-image dataset. To our knowledge, this is the first method to estimate aboveground biomass directly from a single RGB image, opening up the possibility for a scalable, interpretable, and cost-effective solution for forest monitoring, while also enabling broader participation through citizen science initiatives.

In enterprise datasets, documents are rarely pure. They are not just text, nor just numbers; they are a complex amalgam of narrative and structure. Current Retrieval-Augmented Generation (RAG) systems have attempted to address this complexity with a blunt tool: linearization. We convert rich, multidimensional tables into simple Markdown-style text strings, hoping that an embedding model will capture the geometry of a spreadsheet in a single vector. But it has already been shown that this is mathematically insufficient. This work presents Topo-RAG, a framework that challenges the assumption that "everything is text". We propose a dual architecture that respects the topology of the data: we route fluid narrative through traditional dense retrievers, while tabular structures are processed by a Cell-Aware Late Interaction mechanism, preserving their spatial relationships. Evaluated on SEC-25, a synthetic enterprise corpus that mimics real-world complexity, Topo-RAG demonstrates an 18.4% improvement in nDCG@10 on hybrid queries compared to standard linearization approaches. It's not just about searching better; it's about understanding the shape of information.

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of n variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the problem of learning the best polytree is NP-hard, we study which restrictions make it more tractable by considering for example in-degree bounds, properties of score functions measuring the quality of a polytree, and approximation algorithms. We devise an algorithm that finds the optimal polytree in time O((2+ε)^n) for arbitrarily small ε> 0 and any constant in-degree bound k, improving over the fastest previously known algorithm of time complexity O(3^n). We further give polynomial-time algorithms for finding a polytree whose score is within a factor of k from the optimal one for arbitrary scores and a factor of 2 for additive ones. Many of the results are complemented by (nearly) tight lower bounds for either the time complexity or the approximation factors.

This research advances individual tree crown (ITC) segmentation in lidar data, using a deep learning model applicable to various laser scanning types: airborne (ULS), terrestrial (TLS), and mobile (MLS). It addresses the challenge of transferability across different data characteristics in 3D forest scene analysis. The study evaluates the model's performance based on platform (ULS, MLS) and data density, testing five scenarios with varying input data, including sparse versions, to gauge adaptability and canopy layer efficacy. The model, based on PointGroup architecture, is a 3D CNN with separate heads for semantic and instance segmentation, validated on diverse point cloud datasets. Results show point cloud sparsification enhances performance, aiding sparse data handling and improving detection in dense forests. The model performs well with >50 points per sq. m densities but less so at 10 points per sq. m due to higher omission rates. It outperforms existing methods (e.g., Point2Tree, TLS2trees) in detection, omission, commission rates, and F1 score, setting new benchmarks on LAUTx, Wytham Woods, and TreeLearn datasets. In conclusion, this study shows the feasibility of a sensor-agnostic model for diverse lidar data, surpassing sensor-specific approaches and setting new standards in tree segmentation, particularly in complex forests. This contributes to future ecological modeling and forest management advancements.

Automatic tree density estimation and counting using single aerial and satellite images is a challenging task in photogrammetry and remote sensing, yet has an important role in forest management. In this paper, we propose the first semisupervised transformer-based framework for tree counting which reduces the expensive tree annotations for remote sensing images. Our method, termed as TreeFormer, first develops a pyramid tree representation module based on transformer blocks to extract multi-scale features during the encoding stage. Contextual attention-based feature fusion and tree density regressor modules are further designed to utilize the robust features from the encoder to estimate tree density maps in the decoder. Moreover, we propose a pyramid learning strategy that includes local tree density consistency and local tree count ranking losses to utilize unlabeled images into the training process. Finally, the tree counter token is introduced to regulate the network by computing the global tree counts for both labeled and unlabeled images. Our model was evaluated on two benchmark tree counting datasets, Jiangsu, and Yosemite, as well as a new dataset, KCL-London, created by ourselves. Our TreeFormer outperforms the state of the art semi-supervised methods under the same setting and exceeds the fully-supervised methods using the same number of labeled images. The codes and datasets are available at https://github.com/HAAClassic/TreeFormer.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

This work introduces TopoBenchmarkX, a modular open-source library designed to standardize benchmarking and accelerate research in Topological Deep Learning (TDL). TopoBenchmarkX maps the TDL pipeline into a sequence of independent and modular components for data loading and processing, as well as model training, optimization, and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBenchmarkX is that it allows for the transformation and lifting between topological domains. This enables, for example, to obtain richer data representations and more fine-grained analyses by mapping the topology and features of a graph to higher-order topological domains such as simplicial and cell complexes. The range of applicability of TopoBenchmarkX is demonstrated by benchmarking several TDL architectures for various tasks and datasets.

Images of the natural world, collected by a variety of cameras, from drones to individual phones, are increasingly abundant sources of biological information. There is an explosion of computational methods and tools, particularly computer vision, for extracting biologically relevant information from images for science and conservation. Yet most of these are bespoke approaches designed for a specific task and are not easily adaptable or extendable to new questions, contexts, and datasets. A vision model for general organismal biology questions on images is of timely need. To approach this, we curate and release TreeOfLife-10M, the largest and most diverse ML-ready dataset of biology images. We then develop BioCLIP, a foundation model for the tree of life, leveraging the unique properties of biology captured by TreeOfLife-10M, namely the abundance and variety of images of plants, animals, and fungi, together with the availability of rich structured biological knowledge. We rigorously benchmark our approach on diverse fine-grained biology classification tasks, and find that BioCLIP consistently and substantially outperforms existing baselines (by 17% to 20% absolute). Intrinsic evaluation reveals that BioCLIP has learned a hierarchical representation conforming to the tree of life, shedding light on its strong generalizability. Our code, models and data will be made available at https://github.com/Imageomics/bioclip.

Foundation segmentation models achieve reasonable leaf instance extraction from top-view crop images without training (i.e., zero-shot). However, segmenting entire plant individuals with each consisting of multiple overlapping leaves remains challenging. This problem is referred to as a hierarchical segmentation task, typically requiring annotated training datasets, which are often species-specific and require notable human labor. To address this, we introduce ZeroPlantSeg, a zero-shot segmentation for rosette-shaped plant individuals from top-view images. We integrate a foundation segmentation model, extracting leaf instances, and a vision-language model, reasoning about plants' structures to extract plant individuals without additional training. Evaluations on datasets with multiple plant species, growth stages, and shooting environments demonstrate that our method surpasses existing zero-shot methods and achieves better cross-domain performance than supervised methods. Implementations are available at https://github.com/JunhaoXing/ZeroPlantSeg.

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere.

Forest monitoring and education are key to forest protection, education and management, which is an effective way to measure the progress of a country's forest and climate commitments. Due to the lack of a large-scale wild forest monitoring benchmark, the common practice is to train the model on a common outdoor benchmark (e.g., KITTI) and evaluate it on real forest datasets (e.g., CanaTree100). However, there is a large domain gap in this setting, which makes the evaluation and deployment difficult. In this paper, we propose a new photorealistic virtual forest dataset and a multimodal transformer-based algorithm for tree detection and instance segmentation. To the best of our knowledge, it is the first time that a multimodal detection and segmentation algorithm is applied to large-scale forest scenes. We believe that the proposed dataset and method will inspire the simulation, computer vision, education, and forestry communities towards a more comprehensive multi-modal understanding.

This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise dissimilarities between data points, but extensions to vector data are also discussed (2) the output is a "stepwise dendrogram", a data structure which is shared by all implementations in current standard software. We present algorithms (old and new) which perform clustering in this setting efficiently, both in an asymptotic worst-case analysis and from a practical point of view. The main contributions of this paper are: (1) We present a new algorithm which is suitable for any distance update scheme and performs significantly better than the existing algorithms. (2) We prove the correctness of two algorithms by Rohlf and Murtagh, which is necessary in each case for different reasons. (3) We give well-founded recommendations for the best current algorithms for the various agglomerative clustering schemes.

Vision-language models (VLMs) have made significant strides in reasoning, yet they often struggle with complex multimodal tasks and tend to generate overly verbose outputs. A key limitation is their reliance on chain-of-thought (CoT) reasoning, despite many tasks benefiting from alternative topologies like trees or graphs. To address this, we introduce STELAR-Vision, a training framework for topology-aware reasoning. At its core is TopoAug, a synthetic data pipeline that enriches training with diverse topological structures. Using supervised fine-tuning and reinforcement learning, we post-train Qwen2VL models with both accuracy and efficiency in mind. Additionally, we propose Frugal Learning, which reduces output length with minimal accuracy loss. On MATH-V and VLM-S2H, STELAR-Vision improves accuracy by 9.7% over its base model and surpasses the larger Qwen2VL-72B-Instruct by 7.3%. On five out-of-distribution benchmarks, it outperforms Phi-4-Multimodal-Instruct by up to 28.4% and LLaMA-3.2-11B-Vision-Instruct by up to 13.2%, demonstrating strong generalization. Compared to Chain-Only training, our approach achieves 4.3% higher overall accuracy on in-distribution datasets and consistently outperforms across all OOD benchmarks. We have released datasets, and code will be available.

Panoptic segmentation is the combination of semantic and instance segmentation: assign the points in a 3D point cloud to semantic categories and partition them into distinct object instances. It has many obvious applications for outdoor scene understanding, from city mapping to forest management. Existing methods struggle to segment nearby instances of the same semantic category, like adjacent pieces of street furniture or neighbouring trees, which limits their usability for inventory- or management-type applications that rely on object instances. This study explores the steps of the panoptic segmentation pipeline concerned with clustering points into object instances, with the goal to alleviate that bottleneck. We find that a carefully designed clustering strategy, which leverages multiple types of learned point embeddings, significantly improves instance segmentation. Experiments on the NPM3D urban mobile mapping dataset and the FOR-instance forest dataset demonstrate the effectiveness and versatility of the proposed strategy.

The increasing demand for commodities is leading to changes in land use worldwide. In the tropics, deforestation, which causes high carbon emissions and threatens biodiversity, is often linked to agricultural expansion. While the need for deforestation-free global supply chains is widely recognized, making progress in practice remains a challenge. Here, we propose an automated approach that aims to support conservation and sustainable land use planning decisions by mapping tropical landscapes at large scale and high spatial resolution following the High Carbon Stock (HCS) approach. A deep learning approach is developed that estimates canopy height for each 10 m Sentinel-2 pixel by learning from sparse GEDI LIDAR reference data, achieving an overall RMSE of 6.3 m. We show that these wall-to-wall maps of canopy top height are predictive for classifying HCS forests and degraded areas with an overall accuracy of 86 % and produce a first high carbon stock map for Indonesia, Malaysia, and the Philippines.

Leaf-lesion segmentation is topology-sensitive: small merges, splits, or false holes can be biologically meaningful descriptors of biochemical pathways, yet they are weakly penalized by standard pixel-wise losses in Euclidean latents. I explore HyperTopo-Adapters, a lightweight, parameter-efficient head trained on top of a frozen vision encoder, which embeds features on a product manifold -- hyperbolic + Euclidean + spherical (H + E + S) -- to encourage hierarchical separation (H), local linear detail (E), and global closure (S). A topology prior complements Dice/BCE in two forms: (i) persistent-homology (PH) distance for evaluation and selection, and (ii) a differentiable surrogate that combines a soft Euler-characteristic match with total variation regularization for stable training. I introduce warm-ups for both the hyperbolic contrastive term and the topology prior, per-sample evaluation of structure-aware metrics (Boundary-F1, Betti errors, PD distance), and a min-PD within top-K Dice rule for checkpoint selection. On a Kaggle leaf-lesion dataset (N=2,940), early results show consistent gains in boundary and topology metrics (reducing Delta beta_1 hole error by 9%) while Dice/IoU remain competitive. The study is diagnostic by design: I report controlled ablations (curvature learning, latent dimensions, contrastive temperature, surrogate settings), and ongoing tests varying encoder strength (ResNet-50, DeepLabV3, DINOv2/v3), input resolution, PH weight, and partial unfreezing of late blocks. The contribution is an open, reproducible train/eval suite (available at https://github.com/ChimdiWalter/HyperTopo-Adapters) that isolates geometric/topological priors and surfaces failure modes to guide stronger, topology-preserving architectures.

Adversarially perturbed images of text can cause sophisticated OCR systems to produce misleading or incorrect transcriptions from seemingly invisible changes to humans. Some of these perturbations even survive physical capture, posing security risks to high-stakes applications such as document processing, license plate recognition, and automated compliance systems. Existing defenses, such as adversarial training, input preprocessing, or post-recognition correction, are often model-specific, computationally expensive, and affect performance on unperturbed inputs while remaining vulnerable to unseen or adaptive attacks. To address these challenges, TopoReformer is introduced, a model-agnostic reformation pipeline that mitigates adversarial perturbations while preserving the structural integrity of text images. Topology studies properties of shapes and spaces that remain unchanged under continuous deformations, focusing on global structures such as connectivity, holes, and loops rather than exact distance. Leveraging these topological features, TopoReformer employs a topological autoencoder to enforce manifold-level consistency in latent space and improve robustness without explicit gradient regularization. The proposed method is benchmarked on EMNIST, MNIST, against standard adversarial attacks (FGSM, PGD, Carlini-Wagner), adaptive attacks (EOT, BDPA), and an OCR-specific watermark attack (FAWA).

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.