Trees

Gradient Boosting Decision Trees (GBDTs) dominate tabular machine learning, with modern implementations like XGBoost, LightGBM, and CatBoost being based on Newton boosting: a second-order descent step in the space of decision trees. Despite its empirical success, the global convergence of Newton boosting is poorly understood compared to first-order boosting. In this paper, we introduce Restricted Newton Descent, which studies convex optimization with Newton's method on Hilbert spaces with inexact iterates, based on the concepts of cosine angle and weak gradient edge. Within this framework, we recover Newton boosting with GBDTs and classical finite-dimensional theory as special cases. We first prove that vanilla Newton boosting achieves a linear rate of convergence for smooth, strongly convex losses that satisfy a Hessian-dominance condition. To handle general convex losses with Lipschitz Hessians, we extend a recent gradient regularized Newton scheme to the restricted weak learner setting. This scheme minimally modifies the classical algorithm by introducing an adaptive $\ell_2$-regularization term proportional to the square root of the gradient norm at each iteration. We establish a $\mathcal{O}(\frac{1}{k^2})$ rate for this scheme, thereby obtaining a globally convergent second-order GBDT algorithm with a rate matching that of first-order boosting with Nesterov momentum. In numerical experiments, we show that our scheme converges while vanilla Newton boosting may diverge.

Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical decision trees and diffusion processes in appropriate limiting regimes. Our unification reveals a shared optimization principle: \emph{Global Trajectory Score Matching (GTSM)}, for which gradient boosting (in an idealized version) is asymptotically optimal. We underscore the conceptual value of our work through two key practical instantiations: \treeflow, which achieves competitive generation quality on tabular data with higher fidelity and a 2\times computational speedup, and \dsmtree, a novel distillation method that transfers hierarchical decision logic into neural networks, matching teacher performance within 2% on many benchmarks.

Hedges and other linear woody features provide valuable ecosystem services, particularly within intensively managed agricultural landscapes. They are key elements for climate adaptation and biodiversity amongst others not only due to a largely varying flora, but also as a feeding-, resting-, and nesting place for many animals and insects including valuable pollinators. Therefore, they require dedicated management, preservation, and attention. Thus, systematic and large-scale mapping of these features from Earth observation data is of high importance. However, transferable and reusable workflows for linear woody feature mapping remain a key methodological challenge, given the diversity of sensor types, spatial resolutions, data acquisition conditions, and complex landscape variability encountered across study areas. We introduce a modular workflow built around two independently optimizable components. Firstly, a flexible input data interface that consolidates heterogeneous Earth observation data into a binary woody vegetation mask, and secondly, a deep neural network trained to separate linear from non-linear shapes within these masks. We demonstrate the workflow by deriving three national-scale linear woody feature maps for all of Germany from three input sources with 0.73 m, 1 m and 3 m spatial resolution, respectively, by using a single trained model without retraining. Evaluation against refined reference data from four federal state biotope mapping campaigns and comparison with two existing linear woody feature maps demonstrate that the workflow produces competitive results across all evaluation sites on a national level. The modular design and its demonstrated applicability at national scale provide a foundation for scalable and generalizable linear woody feature mapping beyond Germany.

Climate change and resource depletion demand a shift from the dominant linear "take-make-use-dispose" paradigm of construction toward circular, low-waste practices. Material reuse offers a promising pathway by reducing raw material extraction, mitigating waste, and extending the service lifespan of carbon-sequestering materials such as timber. Realizing this potential, however, requires addressing technical and logistical challenges across both design and construction for accommodating heterogeneous, reclaimed material inventories. This paper presents an integrated framework that couples data-driven computational design with feedback-driven adaptive human-robot collaborative (co-robotic) fabrication and assembly to enable the realization of nonstandard structures made from reclaimed timber of varying length and geometries, supplemented with new off-the-shelf timber when necessary. The framework is validated through Timbrelyn, a built case-study installation that demonstrates how timber reuse can inform and enhance architectural expression. This work contributes to the development of integrated design-to-fabrication workflows that advance adaptive, feedback-driven methods to handle inventory constraints and reclaimed material uncertainties, facilitating material reuse in the design and construction of new buildings and structures.

The shift from stand-level to individual-tree-level forest assessments supports improved species mapping and biodiversity monitoring, particularly in boreal ecosystems where tree species like aspen (Populus tremula L.) play a keystone role. Airborne laser scanning (ALS) is the standard for such inventories, but a major limitation for developing improved species classification methods is the small number of publicly available ALS datasets containing high-quality, field-validated reference data. Recently, multispectral ALS data has shown promise for tree species classification, but the progress is hindered by the lack of open multispectral ALS datasets with high-quality field reference data. This paper presents and details an open multispectral ALS dataset for tree species classification that was used before its public release for an international benchmarking study of machine learning and deep learning classification methods in a related publication by Taher et al.,(2026). The dataset comprises 6326 segment-level point clouds of individual trees representing nine species in southern Finland. The point cloud data has been acquired using two multispectral laser scanning systems each operating at three laser wavelengths: a helicopter-borne system (HeliALS) with a point density exceeding 1000 points\m2 and an Optech Titan system with approximately 35 points\m2. Furthermore, we present a crowdsourcing application that facilitates the collection of high-quality field reference data of tree species in an efficient and scalable manner. Our article showcases the versatility of the open dataset by presenting new analyses on species classification using multispectral data building upon the initial findings of Taher et al.,(2026).

Accurate classification of tropical tree species from unoccupied aerial vehicle (UAV) imagery remains challenging due to high species diversity and strong visual similarity among species at typical image resolutions (centimeters per pixel). In contrast, models trained on close-up citizen science photographs captured with smartphones achieve strong plant species classification performance. Recent advances in UAV data acquisition now enable the collection of close-up images that are spatially registered with top-view aerial imagery and approach the level of visual detail found in smartphone photographs, with the trade-off that such high-resolution photos cannot be acquired for many trees. In this work, we evaluate the performance of existing methods using paired top-view and close-up UAV imagery collected in a species-rich tropical forest. Through fine-tuning experiments, we quantify the performance gap between vision foundation models and in-domain generalist plant recognition models across both image types (high-resolution close-up versus coarser-resolution top-view imagery). We show that classification performance is consistently higher on close-up images than on top-view aerial imagery, and that this performance gap widens for rare species. Finally, we propose that self-supervised representation alignment across these two spatial scales offers a promising approach for integrating fine-grained visual information into canopy-level species classification models based on top-view UAV imagery. Leveraging high-resolution close-up UAV imagery to enhance canopy-level species classification could substantially improve large-scale monitoring of tropical forest biodiversity.

Summarizing deeply nested discussion threads requires handling interleaved replies, quotes, and overlapping topics, which standard LLM summarizers struggle to capture reliably. We introduce ThreadSumm, a multi-stage LLM framework that treats thread summarization as a hierarchical reasoning problem over explicit aspect and content unit representations. Our method first performs content planning via LLM-based extraction of discourse aspects and Atomic Content Units, then applies sentence ordering to construct thread-aware sequences that surface multiple viewpoints rather than a single linear strand. On top of these interpretable units, ThreadSumm employs a Tree of Thoughts search that generates and scores multiple paragraph candidates, jointly optimizing coherence and coverage within a unified search space. With this multi-proposal and iterative refinement design, we show improved performance in generating logically structured summaries compared to existing baselines, while achieving higher aspect retention and opinion coverage in nested discussions.

Continual learning aims to update models under distribution shift without forgetting, yet many high-stakes deployments, such as healthcare, also require interpretability. In practice, models that adapt well (e.g., deep networks) are often opaque, while models that are interpretable (e.g., decision trees) are brittle under shift, making it difficult to achieve both properties simultaneously. In response, we propose Tree of Concepts, an interpretable continual learning framework that uses a shallow decision tree to define a fixed, rule-based concept interface and trains a concept bottleneck model to predict these concepts from raw features. Continual updates act on the concept extractor and label head while keeping concept semantics stable over time, yielding explanations that do not drift across sequential updates. On multiple tabular healthcare benchmarks under continual learning protocols, our method achieves a stronger stability-plasticity trade-off than existing baselines, including replay-enhanced variants. Our results suggest that structured concept interfaces can support continual adaptation while preserving a consistent audit interface in non-stationary, high-stakes domains.

Hyperspectral tree species classification is challenging due to limited and imbalanced class labels, spectral mixing (overlapping light signatures from multiple species), and ecological heterogeneity (variability among ecological systems). Addressing these challenges requires methods that integrate biological and structural characteristics of vegetation, such as canopy architecture and interspecific interactions, rather than relying solely on spectral signatures. This paper presents a biologically informed, semi-supervised deep learning method that integrates multi-sensor Earth observation data, specifically hyperspectral imaging (HSI) and airborne laser scanning (ALS), with expert, ecological knowledge. The approach relies on biologically inspired pseudo-labelling over a precomputed canopy graph, yielding accurate classification at low training cost. In addition, ecological priors on species cohabitation are automatically derived from reliable sources using large language models (LLMs) and encoded as a cohabitation matrix with likelihoods of species occurring together. These priors are incorporated into the pseudo-labelling strategy, effectively introducing expert knowledge into the model. Experiments on a real-world forest dataset demonstrate 5.6% improvement over the best reference method. Expert evaluation of cohabitation priors reveals high accuracy with differences no larger than 15%.

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.

Zero-shot object-goal navigation (ZSON) requires navigating unknown environments to find a target object without task-specific training. Prior hierarchical solutions mainly focus on either scene understanding and representations (belief) or high-level decision-making and planning (policy), yet treat the option, i.e., the subgoal candidate that belief proposes and policy selects, as an interface inherited from adjacent modules rather than a design axis in its own right. In practice, options are predominantly single waypoints scored by destination utility: a lone destination hides the value gathered en route, and a flat list obscures the relationships among candidates. Our insight is that the option space should be a tree of paths. Full paths expose en-route information gain that destination-only scoring systematically neglects; a tree of shared segments enables coarse-to-fine LLM reasoning that dismisses or pursues entire branches before examining individual leaves, compressing the combinatorial path space into an efficient hierarchy. We instantiate this insight in REST (Receding Horizon Explorative Steiner Tree), a training-free framework that (1) builds an explicit open-vocabulary 3D map from online RGB-D streams; (2) grows an agent-centric tree of safe and informative paths as the option space via sampling-based planning; and (3) textualizes each branch into a spatial narrative and selects the next-best path through chain-of-thought LLM reasoning. Across the Gibson, HM3D, and HSSD benchmarks, REST consistently ranks among the top methods in success rate and path efficiency.

This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the Optimal Decision Tree and Set Cover. We study these two fundamental tasks under precedence constraints, that is, if a test (or set) $X$ is a predecessor of $Y$, then in any feasible decision tree $X$ needs to be an ancestor of $Y$ (or respectively, if $Y$ is added to set cover, then so must be $X$). For the Optimal Decision Tree we consider two optimization criteria: worst case identification time (height of the tree) or the average identification time. Similarly, for the Set Cover we study two cost measures: the size of the cover or the average cover time. Our approach is to develop a number of algorithmic reductions, where an approximation algorithm for one problem provides an approximation for another via a black-box usage of a procedure for the former. En route we introduce other optimization problems either to complete the `reduction landscape' or because they hold the essence of combinatorial structure of our problems. The latter is brought by a problem of finding a Maximum Density Precedence-Closed Subfamily, where the density is defined as the ratio of the number of items the family covers to its size. We provide $\mathcal{O}^*(\sqrt{m})$-approximation polynomial-time algorithms for all aforementioned problems. The picture is complemented by a number of hardness reductions that provide $\mathcal{O}(m^{1/12-ε})$-inapproximability results for the decision tree and covering problems. Besides giving a complete set of results for general precedence constraints, we also provide polylogarithmic approximation guarantees for two most typically studied and applicable graph types, outforests and inforests. By providing corresponding hardness results, we show most of these results to be tight.

We present Spanning Tree Autoregressive (STAR) modeling, which can incorporate prior knowledge of images, such as center bias and locality, to maintain sampling performance while also providing sufficiently flexible sequence orders to accommodate image editing at inference time. Approaches that expose conventional autoregressive (AR) models in visual generation to arbitrary sequence orders via random permutation suffer from degraded sampling performance or compromise the flexibility in sequence order choice at inference time. Instead, STAR utilizes traversal orders of uniform spanning trees in a lattice defined by the positions of image patches. Traversal orders are obtained via breadth-first search, allowing us to efficiently construct a spanning tree via rejection sampling whose traversal order ensures that the connected partial observation of the image appears as a prefix for native image inpainting support. Through the tailored yet structured sequence order randomization strategy, STAR preserves the capability of postfix completion while maintaining sampling performance, without any significant changes to the model architecture widely adopted in language AR modeling.

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear combinations of predictor variables in their leaf nodes to form predictions, which can help achieve higher accuracy and smaller trees. Typical algorithms for learning model trees from training data work in a greedy fashion, growing the tree in a top-down manner by recursively splitting the data into smaller and smaller subsets. Crucially, the selected splits are only locally optimal, potentially rendering the tree overly complex and less accurate than a tree whose structure is globally optimal for the training data. In this paper, we empirically investigate the effect of constructing globally optimal model trees for classification and regression with linear support vector machines at the leaf nodes. To this end, we present mixed-integer linear programming formulations to learn optimal trees, compute such trees for a large collection of benchmark data sets, and compare their performance against greedily grown model trees in terms of interpretability and accuracy. We also compare to classic optimal and greedily grown decision trees, random forests, and support vector machines. Our results show that optimal model trees can achieve competitive accuracy with very small trees. We also investigate the effect on the accuracy of replacing axis-parallel splits with multivariate ones, foregoing interpretability while potentially obtaining greater accuracy.