Energy-based models (EBMs) offer a flexible framework for parameterizing probability distributions using neural networks. However, learning EBMs by exact maximum likelihood estimation (MLE) is generally intractable, due to the need to compute the partition function (normalization constant). In this paper, we propose a novel formulation for approximately learning probabilistic EBMs in combinatorially-large discrete spaces, such as sets or permutations. Our key idea is to jointly learn both an energy model and its log-partition, both parameterized as a neural network. Our approach not only provides a novel tractable objective criterion to learn EBMs by stochastic gradient descent (without relying on MCMC), but also a novel means to estimate the log-partition function on unseen data points. On the theoretical side, we show that our approach recovers the optimal MLE solution when optimizing in the space of continuous functions. Furthermore, we show that our approach naturally extends to the broader family of Fenchel-Young losses, allowing us to obtain the first tractable method for optimizing the sparsemax loss in combinatorially-large spaces. We demonstrate our approach on multilabel classification and label ranking.

We consider a teacher-student model of supervised learning with a fully-trained 2-layer neural network whose width $k$ and input dimension $d$ are large and proportional. We compute the Bayes-optimal generalisation error of the network for any activation function in the regime where the number of training data $n$ scales quadratically with the input dimension, i.e., around the interpolation threshold where the number of trainable parameters $kd+k$ and of data points $n$ are comparable. Our analysis tackles generic weight distributions. Focusing on binary weights, we uncover a discontinuous phase transition separating a "universal" phase from a "specialisation" phase. In the first, the generalisation error is independent of the weight distribution and decays slowly with the sampling rate $n/d^2$, with the student learning only some non-linear combinations of the teacher weights. In the latter, the error is weight distribution-dependent and decays faster due to the alignment of the student towards the teacher network. We thus unveil the existence of a highly predictive solution near interpolation, which is however potentially hard to find.

This paper considers the problem of estimating chirp parameters from a noisy mixture of chirps. While a rich body of work exists in this area, challenges remain when extending these techniques to chirps of higher order polynomials. We formulate this as a non-convex optimization problem and propose a modified Langevin Monte Carlo (LMC) sampler that exploits the average curvature of the objective function to reliably find the minimizer. Results show that our Curvature-guided LMC (CG-LMC) algorithm is robust and succeeds even in low SNR regimes, making it viable for practical applications.

Construction robotics increasingly relies on natural language processing for task execution, creating a need for robust methods to interpret commands in complex, dynamic environments. While existing research primarily focuses on what tasks robots should perform, less attention has been paid to how these tasks should be executed safely and efficiently. This paper presents a novel probabilistic framework that uses sentiment analysis from natural language commands to dynamically adjust robot navigation policies in construction environments. The framework leverages Building Information Modeling (BIM) data and natural language prompts to create adaptive navigation strategies that account for varying levels of environmental risk and uncertainty. We introduce an object-aware path planning approach that combines exponential potential fields with a grid-based representation of the environment, where the potential fields are dynamically adjusted based on the semantic analysis of user prompts. The framework employs Bayesian inference to consolidate multiple information sources: the static data from BIM, the semantic content of natural language commands, and the implied safety constraints from user prompts. We demonstrate our approach through experiments comparing three scenarios: baseline shortest-path planning, safety-oriented navigation, and risk-aware routing. Results show that our method successfully adapts path planning based on natural language sentiment, achieving a 50\% improvement in minimum distance to obstacles when safety is prioritized, while maintaining reasonable path lengths. Scenarios with contrasting prompts, such as "dangerous" and "safe", demonstrate the framework's ability to modify paths. This approach provides a flexible foundation for integrating human knowledge and safety considerations into construction robot navigation.

Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the super-exponential scaling of topologies. This scaling challenge limits the efficiency of Euclidean-based approximate inference methods. Motivated by the geometric connections between trees and hyperbolic space, we develop novel hyperbolic extensions of two sequential search algorithms: Combinatorial and Nested Combinatorial Sequential Monte Carlo (\textsc{Csmc} and \textsc{Ncsmc}). Our approach introduces consistent and unbiased estimators, along with variational inference methods (\textsc{H-Vcsmc} and \textsc{H-Vncsmc}), which outperform their Euclidean counterparts. Empirical results demonstrate improved speed, scalability and performance in high-dimensional phylogenetic inference tasks.

Safe reinforcement learning has traditionally relied on predefined constraint functions to ensure safety in complex real-world tasks, such as autonomous driving. However, defining these functions accurately for varied tasks is a persistent challenge. Recent research highlights the potential of leveraging pre-acquired task-agnostic knowledge to enhance both safety and sample efficiency in related tasks. Building on this insight, we propose a novel method to learn shared constraint distributions across multiple tasks. Our approach identifies the shared constraints through imitation learning and then adapts to new tasks by adjusting risk levels within these learned distributions. This adaptability addresses variations in risk sensitivity stemming from expert-specific biases, ensuring consistent adherence to general safety principles even with imperfect demonstrations. Our method can be applied to control and navigation domains, including multi-task and meta-task scenarios, accommodating constraints such as maintaining safe distances or adhering to speed limits. Experimental results validate the efficacy of our approach, demonstrating superior safety performance and success rates compared to baselines, all without requiring task-specific constraint definitions. These findings underscore the versatility and practicality of our method across a wide range of real-world tasks.

We provide new connections between two distinct federated learning approaches based on (i) ADMM and (ii) Variational Bayes (VB), and propose new variants by combining their complementary strengths. Specifically, we show that the dual variables in ADMM naturally emerge through the "site" parameters used in VB with isotropic Gaussian covariances. Using this, we derive two versions of ADMM from VB that use flexible covariances and functional regularisation, respectively. Through numerical experiments, we validate the improvements obtained in performance. The work shows connection between two fields that are believed to be fundamentally different and combines them to improve federated learning. The goal of federated learning is to train a global model in the central server by using the data distributed over many local clients (McMahan et al., 2016). Such distributed learning improves privacy, security, and robustness, but is challenging due to frequent communication needed to synchronise training among nodes. This is especially true when the data quality differs drastically from client to client and needs to be appropriately weighted. Designing new methods to deal with such challenges is an active area of research in federated learning. We focus on two distinct federated-learning approaches based on the Alternating Direction Method of Multipliers (ADMM) and Variational Bayes (VB), respectively. The ADMM approach synchronises the global and local models by using constrained optimisation and updates both primal and dual variables simultaneously.

Transformers have emerged as the dominant architecture in the field of deep learning, with a broad range of applications and remarkable in-context learning (ICL) capabilities. While not yet fully understood, ICL has already proved to be an intriguing phenomenon, allowing transformers to learn in context -- without requiring further training. In this paper, we further advance the understanding of ICL by demonstrating that transformers can perform full Bayesian inference for commonly used statistical models in context. More specifically, we introduce a general framework that builds on ideas from prior fitted networks and continuous normalizing flows which enables us to infer complex posterior distributions for methods such as generalized linear models and latent factor models. Extensive experiments on real-world datasets demonstrate that our ICL approach yields posterior samples that are similar in quality to state-of-the-art MCMC or variational inference methods not operating in context.

Learning curves are a concept from social sciences that has been adopted in the context of machine learning to assess the performance of a learning algorithm with respect to a certain resource, e.g., the number of training examples or the number of training iterations. Learning curves have important applications in several machine learning contexts, most notably in data acquisition, early stopping of model training, and model selection. For instance, learning curves can be used to model the performance of the combination of an algorithm and its hyperparameter configuration, providing insights into their potential suitability at an early stage and often expediting the algorithm selection process. Various learning curve models have been proposed to use learning curves for decision making. Some of these models answer the binary decision question of whether a given algorithm at a certain budget will outperform a certain reference performance, whereas more complex models predict the entire learning curve of an algorithm. We contribute a framework that categorises learning curve approaches using three criteria: the decision-making situation they address, the intrinsic learning curve question they answer and the type of resources they use. We survey papers from the literature and classify them into this framework.

Weaknesses: - Can we interpret the results as follows: If the TAR assumption is satisfied with positive limits, and we use MLE, then temporal interference does not cause bias. If this interpretation is correct, then it would be illuminating if the authors provide the intuitive connection between the TAR assumption and temporal interference. It is not clear if the estimations that the authors have required are feasible if the state space is large. The next natural question is how robust the results are if we use other methods for estimation. This could have been shown by providing some simulations, which is a part missing from the manuscript.