We propose a novel randomized algorithm for constructing binary neural networks with tunable accuracy. This approach is motivated by hyperdimensional computing (HDC), which is a brain-inspired paradigm that leverages high-dimensional vector representations, offering efficient hardware implementation and robustness to model corruptions. Unlike traditional low-precision methods that use quantization, we consider binary embeddings of data as points in the hypercube equipped with the Hamming distance. We propose a novel family of floating-point neural networks, G-Nets, which are general enough to mimic standard network layers. Each floating-point G-Net has a randomized binary embedding, an embedded hyperdimensional (EHD) G-Net, that retains the accuracy of its floating-point counterparts, with theoretical guarantees, due to the concentration of measure. Empirically, our binary models match convolutional neural network accuracies and outperform prior HDC models by large margins, for example, we achieve almost 30% higher accuracy on CIFAR-10 compared to prior HDC models. G-Nets are a theoretically justified bridge between neural networks and randomized binary neural networks, opening a new direction for constructing robust binary/quantized deep learning models. Our implementation is available at https://github.com/GNet2025/GNet .

Predicting a patient's length of stay (LOS) in the intensive care unit (ICU) is a critical task for hospital resource management, yet remains challenging due to the heterogeneous and irregularly sampled nature of electronic health records (EHRs). In this work, we propose S$^2$G-Net, a novel neural architecture that unifies state-space sequence modeling with multi-view Graph Neural Networks (GNNs) for ICU LOS prediction. The temporal path employs Mamba state-space models (SSMs) to capture patient trajectories, while the graph path leverages an optimized GraphGPS backbone, designed to integrate heterogeneous patient similarity graphs derived from diagnostic, administrative, and semantic features. Experiments on the large-scale MIMIC-IV cohort dataset show that S$^2$G-Net consistently outperforms sequence models (BiLSTM, Mamba, Transformer), graph models (classic GNNs, GraphGPS), and hybrid approaches across all primary metrics. Extensive ablation studies and interpretability analyses highlight the complementary contributions of each component of our architecture and underscore the importance of principled graph construction. These results demonstrate that S$^2$G-Net provides an effective and scalable solution for ICU LOS prediction with multi-modal clinical data. The code can be found at https://github.com/ShuqiZi1/S2G-Net.

Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance of Euclidean convolution neural networks (CNNs). However, these two symmetries are fundamentally different: The translation equivariance of CNNs corresponds to symmetries of the fixed domain acting on the image signals (sometimes known as active symmetries), whereas in GNNs any permutation acts on both the graph signals and the graph domain (sometimes described as passive symmetries). In this work, we focus on the active symmetries of GNNs, by considering a learning setting where signals are supported on a fixed graph. In this case, the natural symmetries of GNNs are the automorphisms of the graph. Since real-world graphs tend to be asymmetric, we relax the notion of symmetries by formalizing approximate symmetries via graph coarsening. We present a bias-variance formula that quantifies the tradeoff between the loss in expressivity and the gain in the regularity of the learned estimator, depending on the chosen symmetry group. To illustrate our approach, we conduct extensive experiments on image inpainting, traffic flow prediction, and human pose estimation with different choices of symmetries. We show theoretically and empirically that the best generalization performance can be achieved by choosing a suitably larger group than the graph automorphism, but smaller than the permutation group.

Counterfactual prediction is a fundamental task in decision-making. G-computation is a method for estimating expected counterfactual outcomes under dynamic time-varying treatment strategies. Existing G-computation implementations have mostly employed classical regression models with limited capacity to capture complex temporal and nonlinear dependence structures. This paper introduces G-Net, a novel sequential deep learning framework for G-computation that can handle complex time series data while imposing minimal modeling assumptions and provide estimates of individual or population-level time varying treatment effects. We evaluate alternative G-Net implementations using realistically complex temporal simulated data obtained from CVSim, a mechanistic model of the cardiovascular system.