-- Dormant tree pruning is labor-intensive but essential to maintaining modern highly-productive fruit orchards. In this work we present a closed-loop visuomotor controller for robotic pruning. The controller guides the cutter through a cluttered tree environment to reach a specified cut point and ensures the cutters are perpendicular to the branch. We train the controller using a novel orchard simulation that captures the geometric distribution of branches in a target apple orchard configuration. Unlike traditional methods requiring full 3D reconstruction, our controller uses just optical flow images from a wrist-mounted camera. We deploy our learned policy in simulation and the real-world for an example V-Trellis envy tree with zero-shot transfer, achieving a 30% success rate - approximately half the performance of an oracle planner . Modern farming techniques have adopted carefully designed tree structures that improve productivity and labor efficiency but must be maintained through detailed dormant tree pruning and training. We focus on one such structure -- Envy apple trees in a V -trellis setting -- where trees are grown in approximately planar rows. The main trunk grows 15 degrees off vertical, and the primary support branches are tied to horizontal wires between posts (see Figure 2).

Large language models (LLMs) have shown strong performance across natural language reasoning tasks, yet their reasoning processes remain brittle and difficult to interpret. Prompting techniques like Chain-of-Thought (CoT) enhance reliability by eliciting intermediate reasoning steps or aggregating multiple outputs. However, they lack mechanisms for enforcing logical structure and assessing internal coherence. We introduce Theorem-of-Thought (ToTh), a novel framework that models reasoning as collaboration among three parallel agents, each simulating a distinct mode of inference: abductive, deductive, and inductive. Each agent produces a reasoning trace, which is structured into a formal reasoning graph. To evaluate consistency, we apply Bayesian belief propagation guided by natural language inference (NLI), assigning confidence scores to each step. The most coherent graph is selected to derive the final answer. Experiments on symbolic (WebOfLies) and numerical (MultiArith) reasoning benchmarks show that ToTh consistently outperforms CoT, Self-Consistency, and CoT-Decoding across multiple LLMs, while producing interpretable and logically grounded reasoning chains. Our findings suggest a promising direction for building more robust and cognitively inspired LLM reasoning. The implementation is available at https://github.com/KurbanIntelligenceLab/theorem-of-thought.

Multi-Agent Reinforcement Learning is widely used for multi-robot coordination, where simple graphs typically model pairwise interactions. However, such representations fail to capture higher-order collaborations, limiting effectiveness in complex tasks. While hypergraph-based approaches enhance cooperation, existing methods often generate arbitrary hypergraph structures and lack adaptability to environmental uncertainties. To address these challenges, we propose the Skewness-Driven Hypergraph Network (SDHN), which employs stochastic Bernoulli hy-peredges to explicitly model higher-order multi-robot interactions. By introducing a skewness loss, SDHN promotes an efficient structure with Small-Hyperedge Dominant Hypergraph, allowing robots to prioritize localized synchronization while still adhering to the overall information, similar to human coordination.

The widespread availability of off-the-shelf machine learning models poses a challenge: which model, of the many available candidates, should be chosen for a given data analysis task? This question of model selection is traditionally answered by collecting and annotating a validation dataset -- a costly and time-intensive process. We propose a method for active model selection, using predictions from candidate models to prioritize the labeling of test data points that efficiently differentiate the best candidate. Our method, CODA, performs consensus-driven active model selection by modeling relationships between classifiers, categories, and data points within a probabilistic framework. The framework uses the consensus and disagreement between models in the candidate pool to guide the label acquisition process, and Bayesian inference to update beliefs about which model is best as more information is collected. We validate our approach by curating a collection of 26 benchmark tasks capturing a range of model selection scenarios. CODA outperforms existing methods for active model selection significantly, reducing the annotation effort required to discover the best model by upwards of 70% compared to the previous state-of-the-art. Code and data are available at https://github.com/justinkay/coda.

Developing controllers that generalize across diverse robot morphologies remains a significant challenge in legged locomotion. Traditional approaches either create specialized controllers for each morphology or compromise performance for generality. This paper introduces a two-stage teacher-student framework that bridges this gap through policy distillation. First, we train specialized teacher policies optimized for individual morphologies, capturing the unique optimal control strategies for each robot design. Then, we distill this specialized expertise into a single Transformer-based student policy capable of controlling robots with varying leg configurations. Our experiments across five distinct legged morphologies demonstrate that our approach preserves morphology-specific optimal behaviors, with the Transformer architecture achieving 94.47% of teacher performance on training morphologies and 72.64% on unseen robot designs. Comparative analysis reveals that Transformer-based architectures consistently outperform MLP baselines by leveraging attention mechanisms to effectively model joint relationships across different kinematic structures. We validate our approach through successful deployment on a physical quadruped robot, demonstrating the practical viability of our morphology-agnostic control framework. This work presents a scalable solution for developing universal legged robot controllers that maintain near-optimal performance while generalizing across diverse morphologies.

We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the input to a high-dimensional latent representation, enabling uncertainty-aware prediction of the solution. Specifically, the architecture consists of a confidence-aware encoder and a probabilistic decoder. The encoder implements a high-dimensional latent variable model based on a Gaussian process (LVM-GP), where the latent representation is constructed by interpolating between a learnable deterministic feature and a Gaussian process prior, with the interpolation strength adaptively controlled by a confidence function learned from data. The decoder defines a conditional Gaussian distribution over the solution field, where the mean is predicted by a neural operator applied to the latent representation, allowing the model to learn flexible function-to-function mapping. Moreover, physical laws are enforced as soft constraints in the loss function to ensure consistency with the underlying PDE structure. Compared to existing approaches such as Bayesian physics-informed neural networks (B-PINNs) and deep ensembles, the proposed framework can efficiently capture functional dependencies via merging a latent Gaussian process and neural operator, resulting in competitive predictive accuracy and robust uncertainty quantification. Numerical experiments demonstrate the effectiveness and reliability of the method.

We propose novel classical and quantum online algorithms for learning finite-horizon and infinite-horizon average-reward Markov Decision Processes (MDPs). Our algorithms are based on a hybrid exploration-generative reinforcement learning (RL) model wherein the agent can, from time to time, freely interact with the environment in a generative sampling fashion, i.e., by having access to a "simulator". By employing known classical and new quantum algorithms for approximating optimal policies under a generative model within our learning algorithms, we show that it is possible to avoid several paradigms from RL like "optimism in the face of uncertainty" and "posterior sampling" and instead compute and use optimal policies directly, which yields better regret bounds compared to previous works. For finite-horizon MDPs, our quantum algorithms obtain regret bounds which only depend logarithmically on the number of time steps $T$, thus breaking the $O(\sqrt{T})$ classical barrier. This matches the time dependence of the prior quantum works of Ganguly et al. (arXiv'23) and Zhong et al. (ICML'24), but with improved dependence on other parameters like state space size $S$ and action space size $A$. For infinite-horizon MDPs, our classical and quantum bounds still maintain the $O(\sqrt{T})$ dependence but with better $S$ and $A$ factors. Nonetheless, we propose a novel measure of regret for infinite-horizon MDPs with respect to which our quantum algorithms have $\operatorname{poly}\log{T}$ regret, exponentially better compared to classical algorithms. Finally, we generalise all of our results to compact state spaces.

The theoretical study of Bayesian neural networks was initiated by Neal [29] who proved that if a shallow Bayesian neural network is initialized with independent Gaussian parameters (i.e., biases and weights), then the output of the network converges in distribution to a Gaussian process, as the number of neurons grows large ( i.e., in the wide width limit). This result was extended to Bayesian deep neural networks two decades later (see [16, 22, 26]) and only recently it has been made quantitative by the use of the optimal transport theory (see [6] and [33]), by the Stein method for Gaussian approximation (see [3, 4, 8, 13]), and by alternative techniques ([7, 11]). Another promising approach to analyze Bayesian neural networks is through the lens of large deviations. First results in this direction are given in [23]. These findings have been successively generalized in [2, 34]. A different perspective is provided by the so-called mean field analysis of networks (see [27, 15]). The advantage of the Bayesian framework is that it allows to include in the model both prior knowledge and observed data through a prior distribution on network's parameters and a likelihood function, respectively. The emergence of Gaussian processes helped to understand how large neural networks work, how to make them more efficient, and motivated the use of Bayesian regression inference methods, see [22]. However, as noticed by [28] and [21], the connection with Gaussian processes also highlighted the limitations of wide width neural networks with independent and Gaussian distributed weights.

Transductive learning is a supervised machine learning task in which, unlike in traditional inductive learning, the unlabelled data that require labelling are a finite set and are available at training time. Similarly to inductive learning contexts, transductive learning contexts may be affected by dataset shift, i.e., may be such that the IID assumption does not hold. We here propose a method, tailored to transductive classification contexts, for performing model selection (i.e., hyperparameter optimisation) when the data exhibit prior probability shift, an important type of dataset shift typical of anti-causal learning problems. In our proposed method the hyperparameters can be optimised directly on the unlabelled data to which the trained classifier must be applied; this is unlike traditional model selection methods, that are based on performing cross-validation on the labelled training data. We provide experimental results that show the benefits brought about by our method.

Traffic congestion due to uncertainties, such as accidents, is a significant issue in urban areas, as the ripple effect of accidents causes longer delays, increased emissions, and safety concerns. To address this issue, we propose a robust framework for predicting the impact of accidents on congestion. We implement Automated Machine Learning (AutoML)-enhanced Deep Embedding Clustering (DEC) to assign congestion labels to accident data and predict congestion probability using a Bayesian Network (BN). The Simulation of Urban Mobility (SUMO) simulation is utilized to evaluate the correctness of BN predictions using evidence-based scenarios. Results demonstrate that the AutoML-enhanced DEC has outperformed traditional clustering approaches. The performance of the proposed BN model achieved an overall accuracy of 95.6%, indicating its ability to understand the complex relationship of accidents causing congestion. Validation in SUMO with evidence-based scenarios demonstrated that the BN model's prediction of congestion states closely matches those of SUMO, indicating the high reliability of the proposed BN model in ensuring smooth urban mobility.