Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL) divergence. In this paper, we focus on the following parametric family: mixtures of isotropic Gaussians (i.e., with diagonal covariance matrices proportional to the identity) and uniform weights. We develop a variational framework and provide efficient algorithms suited for this family. In contrast with mixtures of Gaussian with generic covariance matrices, this choice presents a balance between accurate approximations of multimodal Bayesian posteriors, while being memory and computationally efficient. Our algorithms implement gradient descent on the location of the mixture components (the modes of the Gaussians), and either (an entropic) Mirror or Bures descent on their variance parameters. We illustrate the performance of our algorithms on numerical experiments.

In the method section of our paper, we describe the general encoding-decoding paradigm. We provide a brief overview of our data preprocessing pipeline, which involves the following steps. We employ the method of Boussard et al. (2021) to estimate the location of Decentralized registration (Windolf et al., 2022) is applied to track and correct Figure 6: Motion drift in "good" and "bad" sorting recordings. "bad" sorting example, which is still affected by drift even after registration. To decode binary behaviors, such as the mouse's left or right choices, we utilize In this section, we provide visualizations to gain insights into the effectiveness of our proposed decoder.

Cross-domain recommender (CDR) systems aim to transfer knowledge from data-rich domains to data-sparse ones, alleviating sparsity and cold-start issues present in conventional single-domain recommenders. However, many CDR approaches rely on overlapping users or items to establish explicit cross-domain connections, which is unrealistic in practice. Moreover, most methods represent user preferences as fixed discrete vectors, limiting their ability to capture the fine-grained and multi-aspect nature of user interests. To address these limitations, we propose DUP-OT (Distributional User Preferences with Optimal Transport), a novel framework for non-overlapping CDR. DUP-OT consists of three stages: (1) a shared preprocessing module that extracts review-based embeddings using a unified sentence encoder and autoencoder; (2) a user preference modeling module that represents each user's interests as a Gaussian Mixture Model (GMM) over item embeddings; and (3) an optimal-transport-based alignment module that matches Gaussian components across domains, enabling effective preference transfer for target-domain rating prediction. Experiments on Amazon Review datasets demonstrate that DUP-OT mitigates domain discrepancy and significantly outperforms state-of-the-art baselines under strictly non-overlapping training settings, with user correspondence revealed only for inference-time evaluation.

Rehearsal-based Continual Learning (CL) maintains a limited memory buffer to store replay samples for knowledge retention, making these approaches heavily reliant on the quality of the stored samples. Current Rehearsal-based CL methods typically construct the memory buffer by selecting a representative subset (referred to as coresets), aiming to approximate the training efficacy of the full dataset with minimal storage overhead. However, mainstream Coreset Selection (CS) methods generally formulate the CS problem as a bi-level optimization problem that relies on numerous inner and outer iterations to solve, leading to substantial computational cost thus limiting their practical efficiency. In this paper, we aim to provide a more efficient selection logic and scheme for coreset construction. To this end, we first analyze the Mean Squared Error (MSE) between the buffer-trained model and the Bayes-optimal model through the perspective of localized error decomposition to investigate the contribution of samples from different regions to MSE suppression. Further theoretical and experimental analyses demonstrate that samples with high probability density play a dominant role in error suppression. Inspired by this, we propose the Probability Density-Aware Coreset (PDAC) method. PDAC leverages the Projected Gaussian Mixture (PGM) model to estimate each sample's joint density, enabling efficient density-prioritized buffer selection. Finally, we introduce the streaming Expectation Maximization (EM) algorithm to enhance the adaptability of PGM parameters to streaming data, yielding Streaming PDAC (SPDAC) for streaming scenarios. Extensive comparative experiments show that our methods outperforms other baselines across various CL settings while ensuring favorable efficiency.

Reviewer 6: We address the reviewer's points in the order they are stated:

Neural Information Processing Systems http://nips.cc/