Decision trees are regarded for high interpretability arising from their hierarchical partitioning structure built on simple decision rules. However, in practice, this is not realized because axis-aligned partitioning of realistic data results in deep trees, and because ensemble methods are used to mitigate overfitting. Even then, model complexity and performance remain sensitive to transformation of the input, and extensive expert crafting of features from the raw data is common. We propose the first system to alternate sparse feature learning with differentiable decision tree construction to produce small, interpretable trees with good performance. It benchmarks favorably against conventional tree-based models and demonstrates several notions of interpretability of a model and its predictions.

Feature construction is of vital importance in reinforcement learning, as the quality of a value function or policy is largely determined by the corresponding features.

Points were sampled uniformly in the bands denoted by dashed lines. We posit that these barriers are due, at least in part, to the sensitivity of decision trees to transformations of the input resulting from greedy construction and simple decision rules. Of these, key limitation is the latter; even if we replace greedy construction with a perfect tree learner, simple distributions can nonetheless require an arbitrarily large axis-aligned tree to fit.

While this setup has enjoyed a lot of attention in the applied community, there hasn't be theoretical work that even formalizes the desired guarantees.

--The double coverage problem focuses on determining efficient, collision-free routes for multiple robots to simultaneously cover linear features (e.g., surface cracks or road routes) and survey areas (e.g., parking lots or local regions) in known environments. In these problems, each robot carries two functional roles: service (linear feature footprint coverage) and exploration (complete area coverage). Service has a smaller operational footprint but incurs higher costs (e.g., time) compared to exploration. T o reduce the complexity for optimal planning solutions, we analyze the manifold attachment process during graph traversal from a Morse theory perspective. We show that solutions satisfying minimum path length and collision-free constraints must belong to a Morse-bounded collection. T o identify this collection, we introduce the HCMR algorithm. In HCMR, cyclic merging search regulates traversal behavior, while edge sequence back propagation converts these regulations into graph edge traversal sequences. Incorporating balanced partitioning, the optimal sequence is selected to generate routes for each robot. We prove the optimality of the HCMR algorithm under a fixed sweep direction. The multi-robot simulation results demonstrate that the HCMR algorithm significantly improves planned path length by at least 10.0%, reduces task time by at least 16.9% in average, and ensures conflict-free operation compared to other state-of-the-art planning methods. Area coverage and line coverage have emerged as key challenges in a wide range of robotic applications. Area coverage focuses on surveying open spaces to ensure full visibility and detect various objects of interest [4], supporting tasks in environmental monitoring [13], infrastructure inspection [18], agricultural surveying [14], and search-and-rescue operations [8]. A practical example of combined area and line coverage requirements is a bridge deck inspection [11], as illustrated in Figure 1.

Millions of biological sample records collected in the last few centuries archived in natural history collections are un-georeferenced. Georeferencing complex locality descriptions associated with these collection samples is a highly labour-intensive task collection agencies struggle with. None of the existing automated methods exploit maps that are an essential tool for georeferencing complex relations. We present preliminary experiments and results of a novel method that exploits multi-modal capabilities of recent Large Multi-Modal Models (LMM). This method enables the model to visually contextualize spatial relations it reads in the locality description. We use a grid-based approach to adapt these auto-regressive models for this task in a zero-shot setting. Our experiments conducted on a small manually annotated dataset show impressive results for our approach ($\sim$1 km Average distance error) compared to uni-modal georeferencing with Large Language Models and existing georeferencing tools. The paper also discusses the findings of the experiments in light of an LMM's ability to comprehend fine-grained maps. Motivated by these results, a practical framework is proposed to integrate this method into a georeferencing workflow.

Federated learning has become a widely used paradigm for collaboratively training a common model among different participants with the help of a central server that coordinates the training. Although only the model parameters or other model updates are exchanged during the federated training instead of the participant's data, many attacks have shown that it is still possible to infer sensitive information such as membership, property, or outright reconstruction of participant data. Although differential privacy is considered an effective solution to protect against privacy attacks, it is also criticized for its negative effect on utility. Another possible defense is to use secure aggregation which allows the server to only access the aggregated update instead of each individual one, and it is often more appealing because it does not degrade model quality. However, combining only the aggregated updates, which are generated by a different composition of clients in every round, may still allow the inference of some client-specific information. In this paper, we show that simple linear models can effectively capture client-specific properties only from the aggregated model updates due to the linearity of aggregation. We formulate an optimization problem across different rounds in order to infer a tested property of every client from the output of the linear models, for example, whether they have a specific sample in their training data (membership inference) or whether they misbehave and attempt to degrade the performance of the common model by poisoning attacks. Our reconstruction technique is completely passive and undetectable. We demonstrate the efficacy of our approach on several scenarios which shows that secure aggregation provides very limited privacy guarantees in practice. The source code will be released upon publication.

In previous studies, quadratic modelling of natural images has resulted in cell models that react strongly to edges and bars. Here we apply quadratic Independent Component Analysis to natural image patches, and show that up to a small approximation error, the estimated components are computing conjunctions of two linear features. These conjunctive features appear to represent not only edges and bars, but also inherently two-dimensional stimuli, such as corners. In addition, we show that for many of the components, the underlying linear features have essentially V1 simple cell receptive field characteristics. Our results indicate that the development of the V2 cells preferring angles and corners may be partly explainable by the principle of unsupervised sparse coding of natural images.

This paper introduces the correlated arc orienteering problem (CAOP), where the task is to find routes for a team of robots to maximize the collection of rewards associated with features in the environment. These features can be one-dimensional or points in the environment, and can have spatial correlation, i.e., visiting a feature in the environment may provide a portion of the reward associated with a correlated feature. A robot incurs costs as it traverses the environment, and the total cost for its route is limited by a resource constraint such as battery life or operation time. As environments are often large, we permit multiple depots where the robots must start and end their routes. The CAOP generalizes the correlated orienteering problem (COP), where the rewards are only associated with point features, and the arc orienteering problem (AOP), where the rewards are not spatially correlated. We formulate a mixed integer quadratic program (MIQP) that formalizes the problem and gives optimal solutions. However, the problem is NP-hard, and therefore we develop an efficient greedy constructive algorithm. We illustrate the problem with two different applications: informative path planning for methane gas leak detection and coverage of road networks.

We present an algorithm to extract features from high-dimensional gene expression profiles, based on the knowledge of a graph which links together genes known to participate to successive reactions in metabolic pathways. Motivated by the intuition that biologically relevant features are likely to exhibit smoothness with respect to the graph topology, the algorithm involves encoding the graph and the set of expression profiles into kernel functions, and performing a generalized form of canonical correlation analysis in the corresponding reproducible kernel Hilbert spaces. Function prediction experiments for the genes of the yeast S. Cerevisiae validate this approach by showing a consistent increase in performance when a state-of-the-art classifier uses the vector of features instead of the original expression profile to predict the functional class of a gene.