Liquid democracy with ranked delegations is a novel voting scheme that unites the practicability of representative democracy with the idealistic appeal of direct democracy: Every voter decides between casting their vote on a question at hand or delegating their voting weight to some other, trusted agent. Delegations are transitive, and since voters may end up in a delegation cycle, they are encouraged to indicate not only a single delegate, but a set of potential delegates and a ranking among them. Based on the delegation preferences of all voters, a delegation rule selects one representative per voter. Previous work has revealed a trade-off between two properties of delegation rules called anonymity and copy-robustness. To overcome this issue we study two fractional delegation rules: MIXEDBORDA BRANCHING, which generalizes a rule satisfying copy-robustness, and the RANDOMWALKRULE, which satisfies anonymity. Using the Markov chain tree theorem, we show that the two rules are in fact equivalent, and simultaneously satisfy generalized versions of the two properties. Combining the same theorem with Fulkerson's algorithm, we develop a polynomial-time algorithm for computing the outcome of the studied delegation rule. This algorithm is of independent interest, having applications in semi-supervised learning and graph theory.

Binary Balanced Tree Recursive Neural Networks (BBT-RvNNs) enforce sequence composition according to a preset balanced binary tree structure. Thus, their nonlinear recursion depth (which is the tree depth) is just log2 n(nbeing the sequence length). Such logarithmic scaling makes BBT-RvNNs efficient and scalable on long sequence tasks such as Long Range Arena (LRA). However, such computational efficiency comes at a cost because BBT-RvNNs cannot solve simple arithmetic tasks like ListOps. On the flip side, RvNN models (e.g., Beam Tree RvNN) that do succeed on ListOps (and other structure-sensitive tasks like formal logical inference) are generally several times more expensive (in time and space) than even Recurrent Neural Networks.

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES models the LES flow by treating each full-order trajectory as a random realization of the underlying dynamics, as such, the effect of small-scales is marginalized to obtain the deterministic evolution of the LES state. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and an encoder-decoder pair for transforming between the latent space and the desired ideal flow field. This stands in sharp contrast to other types of neural parameterization of closure models where each trajectory is treated as a deterministic realization of the dynamics. We show the effectiveness of our approach (niLES - neural ideal LES) on two challenging chaotic dynamical systems: Kolmogorov flow at a Reynolds number of 20,000 and flow past a cylinder at Reynolds number 500. Compared to competing methods, our method can handle non-uniform geometries using unstructured meshes seamlessly. In particular, niLES leads to trajectories with more accurate statistics and enhances stability, particularly for long-horizon rollouts.

Sharpness-aware minimization (SAM) was proposed to reduce sharpness of minima and has been shown to enhance generalization performance in various settings. In this work we show that perturbing only the affine normalization parameters (typically comprising 0.1% of the total parameters) in the adversarial step of SAM can outperform perturbing all of the parameters.

We propose a Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We first prove that the contrastive loss is a negative log-likelihood on the spherical space. We propose three methods that ensure a positive definite covariance matrix. Lastly, we present a novel decomposition of the Generalized Gauss-Newton approximation. Empirically, we show that our Laplacian Metric Learner (LAM) yields well-calibrated uncertainties, reliably detects out-of-distribution examples, and has state-of-the-art predictive performance.

This paper presents IB-POMCP, a novel algorithm for online planning under partial observability. Our approach enhances the decision-making process by using estimations of the world belief's entropy to guide a tree search process and surpass the limitations of planning in scenarios with sparse reward configurations. By performing what we denominate as an information-guided planning process, the algorithm, which incorporates a novel I-UCB function, shows significant improvements in reward and reasoning time compared to state-of-the-art baselines in several benchmark scenarios, along with theoretical convergence guarantees.

We study the problem of regret minimization in Multi-Agent Multi-Armed Bandits (MAMABs) where the rewards are defined through a factor graph. We derive an instance-specific regret lower bound and characterize the minimal expected number of times each global action should be explored. This bound and the corresponding optimal exploration process are obtained by solving a combinatorial optimization problem whose set of variables and constraints exponentially grow with the number of agents, and cannot be exploited in the design of efficient algorithms. Inspired by Mean Field approximation techniques used in graphical models, we provide simple upper bounds of the regret lower bound. The corresponding optimization problems have a reduced number of variables and constraints. By tuning the latter, we may explore the trade-off between the achievable regret and the complexity of computing the corresponding exploration process. We devise Efficient Sampling for MAMAB (ESM), an algorithm whose regret asymptotically matches the approximated lower bounds. The regret and computational complexity of ESM are assessed numerically, using both synthetic and real-world experiments in radio communications networks.