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Planning a public transit network is a challenging optimization problem, but essential in order to realize the benefits of autonomous buses. We propose a novel algorithm for planning networks of routes for autonomous buses. We first train a graph neural net model as a policy for constructing route networks, and then use the policy as one of several mutation operators in a evolutionary algorithm. We evaluate this algorithm on a standard set of benchmarks for transit network design, and find that it outperforms the learned policy alone by up to 20% and a plain evolutionary algorithm approach by up to 53% on realistic benchmark instances.

Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function at a set of collocation points within the domain. The quality of a PINNs solution depends upon numerous parameters, including the number and distribution of these collocation points. In this paper we consider a number of strategies for selecting these points and investigate their impact on the overall accuracy of the method. In particular, we suggest that no single approach is likely to be "optimal" but we show how a number of important metrics can have an impact in improving the quality of the results obtained when using a fixed number of residual evaluations. We illustrate these approaches through the use of two benchmark test problems: Burgers' equation and the Allen-Cahn equation.

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To select the sparsity and robustness of linear regressors, techniques like k-fold cross-validation are commonly used for hyperparameter tuning. However, cross-validation substantially increases the computational cost of sparse regression as it requires solving many mixed-integer optimization problems (MIOs). Additionally, validation metrics often serve as noisy estimators of test set errors, with different hyperparameter combinations leading to models with different noise levels. Therefore, optimizing over these metrics is vulnerable to out-of-sample disappointment, especially in underdetermined settings. To improve upon this state of affairs, we make two key contributions. First, motivated by the generalization theory literature, we propose selecting hyperparameters that minimize a weighted sum of a cross-validation metric and a model's output stability, thus reducing the risk of poor out-of-sample performance. Second, we leverage ideas from the mixed-integer optimization literature to obtain computationally tractable relaxations of k-fold cross-validation metrics and the output stability of regressors, facilitating hyperparameter selection after solving fewer MIOs. These relaxations result in an efficient cyclic coordinate descent scheme, achieving lower validation errors than via traditional methods such as grid search. On synthetic datasets, our confidence adjustment procedure improves out-of-sample performance by 2%-5% compared to minimizing the k-fold error alone. On 13 real-world datasets, our confidence adjustment procedure reduces test set error by 2%, on average.

Standard reinforcement learning from human feedback (RLHF) approaches relying on parametric models like the Bradley-Terry model fall short in capturing the intransitivity and irrationality in human preferences. Recent advancements suggest that directly working with preference probabilities can yield a more accurate reflection of human preferences, enabling more flexible and accurate language model alignment. In this paper, we propose a self-play-based method for language model alignment, which treats the problem as a constant-sum two-player game aimed at identifying the Nash equilibrium policy. Our approach, dubbed Self-Play Preference Optimization (SPPO), utilizes iterative policy updates to provably approximate the Nash equilibrium. Additionally, we propose a new SPPO objective which is both strongly motivated by theory and is simple and effective in practice. In our experiments, using only 60k prompts (without responses) from the UltraFeedback dataset and without any prompt augmentation, by leveraging a pre-trained preference model PairRM with only 0.4B parameters, SPPO can obtain a model from fine-tuning Mistral-7B-Instruct-v0.2 that achieves the state-of-the-art length-controlled win-rate of 28.53% against GPT-4-Turbo on AlpacaEval 2.0. It also outperforms the (iterative) DPO and IPO on MT-Bench, Arena-Hard, and the Open LLM Leaderboard. Starting from a stronger base model Llama-3-8B-Instruct, we are able to achieve a length-controlled win rate of 38.77%. Notably, the strong performance of SPPO is achieved without additional external supervision (e.g., responses, preferences, etc.) from GPT-4 or other stronger language models. Codes are available at //github.com/uclaml/SPPO.

Recent advancements in diffusion models have been effective in learning data priors for solving inverse problems. They leverage diffusion sampling steps for inducing a data prior while using a measurement guidance gradient at each step to impose data consistency. For general inverse problems, approximations are needed when an unconditionally trained diffusion model is used since the measurement likelihood is intractable, leading to inaccurate posterior sampling. In other words, due to their approximations, these methods fail to preserve the generation process on the data manifold defined by the diffusion prior, leading to artifacts in applications such as image restoration. To enhance the performance and robustness of diffusion models in solving inverse problems, we propose Diffusion State-Guided Projected Gradient (DiffStateGrad), which projects the measurement gradient onto a subspace that is a low-rank approximation of an intermediate state of the diffusion process. DiffStateGrad, as a module, can be added to a wide range of diffusion-based inverse solvers to improve the preservation of the diffusion process on the prior manifold and filter out artifact-inducing components. We highlight that DiffStateGrad improves the robustness of diffusion models in terms of the choice of measurement guidance step size and noise while improving the worst-case performance. Finally, we demonstrate that DiffStateGrad improves upon the state-of-the-art on linear and nonlinear image restoration inverse problems.

Integrated sensing and communication (ISAC) systems have the issue of secrecy leakage when using the ISAC waveforms for sensing, thus posing a potential risk for eavesdropping. To address this problem, we propose to employ movable antennas (MAs) and reconfigurable intelligent surface (RIS) to enhance the physical layer security (PLS) performance of ISAC systems, where an eavesdropping target potentially wiretaps the signals transmitted by the base station (BS). To evaluate the synergistic performance gain provided by MAs and RIS, we formulate an optimization problem for maximizing the sum-rate of the users by jointly optimizing the transmit/receive beamformers of the BS, the reflection coefficients of the RIS, and the positions of MAs at communication users, subject to a minimum communication rate requirement for each user, a minimum radar sensing requirement, and a maximum secrecy leakage to the eavesdropping target. To solve this non-convex problem with highly coupled variables, a two-layer penalty-based algorithm is developed by updating the penalty parameter in the outer-layer iterations to achieve a trade-off between the optimality and feasibility of the solution. In the inner-layer iterations, the auxiliary variables are first obtained with semi-closed-form solutions using Lagrange duality. Then, the receive beamformer filter at the BS is optimized by solving a Rayleigh-quotient subproblem. Subsequently, the transmit beamformer matrix is obtained by solving a convex subproblem. Finally, the majorization-minimization (MM) algorithm is employed to optimize the RIS reflection coefficients and the positions of MAs. Extensive simulation results validate the considerable benefits of the proposed MAs-aided RIS-ISAC systems in enhancing security performance compared to traditional fixed position antenna (FPA)-based systems.

The recent development of fact verification systems with natural logic has enhanced their explainability by aligning claims with evidence through set-theoretic operators, providing faithful justifications. Despite these advancements, such systems often rely on a large amount of training data annotated with natural logic. To address this issue, we propose a zero-shot method that utilizes the generalization capabilities of instruction-tuned large language models. To comprehensively assess the zero-shot capabilities of our method and other fact verification systems, we evaluate all models on both artificial and real-world claims, including multilingual datasets. We also compare our method against other fact verification systems in two setups. First, in the zero-shot generalization setup, we demonstrate that our approach outperforms other systems that were not specifically trained on natural logic data, achieving an average accuracy improvement of 8.96 points over the best-performing baseline. Second, in the zero-shot transfer setup, we show that current systems trained on natural logic data do not generalize well to other domains, and our method outperforms these systems across all datasets with real-world claims.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.