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Is intelligence realized by connectionist or classicist? While connectionist approaches have achieved superhuman performance, there has been growing evidence that such task-specific superiority is particularly fragile in systematic generalization. This observation lies in the central debate between connectionist and classicist, wherein the latter continually advocates an algebraic treatment in cognitive architectures. In this work, we follow the classicist’s call and propose a hybrid approach to improve systematic generalization in reasoning. Specifically, we showcase a prototype with algebraic representation for the abstract spatial-temporal reasoning task of Raven’s Progressive Matrices (RPM) and present the ALgebra-Aware Neuro-Semi-Symbolic (ALANS) learner. The ALANS learner is motivated by abstract algebra and the representation theory. It consists of a neural visual perception frontend and an algebraic abstract reasoning backend: the frontend summarizes the visual information from object-based representation, while the backend transforms it into an algebraic structure and induces the hidden operator on the fly. The induced operator is later executed to predict the answer’s representation, and the choice most similar to the prediction is selected as the solution. Extensive experiments show that by incorporating an algebraic treatment, the ALANS learner outperforms various pure connectionist models in domains requiring systematic generalization. We further show the generative nature of the learned algebraic representation; it can be decoded by isomorphism to generate an answer. 

Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built upon it have made interesting attempts aiming at the interpretability of text modeling. However, latent space EBMs also inherit some flaws from EBMs in data space; the degenerate MCMC sampling quality in practice can lead to poor generation quality and instability in training, especially on data with complex latent structures. Inspired by the recent efforts that leverage diffusion recovery likelihood learning as a cure for the sampling issue, we introduce a novel symbiosis between the diffusion models and latent space EBMs in a variational learning framework, coined as the latent diffusion energy-based model. We develop a geometric clustering-based regularization jointly with the information bottleneck to further improve the quality of the learned latent space. Experiments on several challenging tasks demonstrate the superior performance of our model on interpretable text modeling over strong counterparts. 

Ensembles of predictions are critical to modern weather forecasting. However, visualizing ensembles and their means in a useful way remains challenging. Existing methods of creating ensemble means do not recognize the physical structures that humans could identify within the ensemble members; therefore, visualizations for variables such as reflectivity lose important information and are difficult for human forecasters to interpret. In response, the authors create an improved ensemble mean that retains more structural information. The authors examine and expand upon the object-based Geometry-Sensitive Ensemble Mean (GEM) defined by Li and Zhang from a meteorological perspective. The authors apply low-intensity thresholding to WRF-simulated radar reflectivity images of lake-effect snowbands, tropical cyclones, and severe thunderstorms and then process them with the GEM system. Gaussian mixture model–based signatures retain the geometric structure of these phenomena and are used to compute a Wasserstein barycenter as the centroid for the ensemble; D2 clustering is employed to examine different scenarios among the ensemble members. Three types of ensemble mean image are created from the centroid of the ensemble or cluster, which each improve upon the traditional pixel-wise average in different ways, successfully capture aspects of the ensemble members’ structure, and have potential applications for future forecasting efforts. The adjusted best member is a better representative member, the Bayesian posterior mean is an improved structure-based weighted average, and the mixture density mean is an outline of the key structures in the ensemble. Each is shown to improve upon a simple arithmetic mean via quantitative comparison with observations.