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Neural networks continue to struggle with compositional generalization, and this issue is exacerbated by a lack of massive pre-training. One successful approach for developing neural systems which exhibit human-like compositional generalization is \textit{hybrid} neurosymbolic techniques. However, these techniques run into the core issues that plague symbolic approaches to AI: scalability and flexibility. The reason for this failure is that at their core, hybrid neurosymbolic models perform symbolic computation and relegate the scalable and flexible neural computation to parameterizing a symbolic system. We investigate a \textit{unified} neurosymbolic system where transformations in the network can be interpreted simultaneously as both symbolic and neural computation. We extend a unified neurosymbolic architecture called the Differentiable Tree Machine in two central ways. First, we significantly increase the model's efficiency through the use of sparse vector representations of symbolic structures. Second, we enable its application beyond the restricted set of tree2tree problems to the more general class of seq2seq problems. The improved model retains its prior generalization capabilities and, since there is a fully neural path through the network, avoids the pitfalls of other neurosymbolic techniques that elevate symbolic computation over neural computation.

Biophysical modeling of brain tumors has emerged as a promising strategy for personalizing radiotherapy planning by estimating the otherwise hidden distribution of tumor cells within the brain. However, many existing state-of-the-art methods are computationally intensive, limiting their widespread translation into clinical practice. In this work, we propose an efficient and direct method that utilizes soft physical constraints to estimate the tumor cell concentration from preoperative MRI of brain tumor patients. Our approach optimizes a 3D tumor concentration field by simultaneously minimizing the difference between the observed MRI and a physically informed loss function. Compared to existing state-of-the-art techniques, our method significantly improves predicting tumor recurrence on two public datasets with a total of 192 patients while maintaining a clinically viable runtime of under one minute - a substantial reduction from the 30 minutes required by the current best approach. Furthermore, we showcase the generalizability of our framework by incorporating additional imaging information and physical constraints, highlighting its potential to translate to various medical diffusion phenomena with imperfect data.

Photoacoustic imaging (PAI) suffers from inherent limitations that can degrade the quality of reconstructed results, such as noise, artifacts and incomplete data acquisition caused by sparse sampling or partial array detection. In this study, we proposed a new optimization method for both two-dimensional (2D) and three-dimensional (3D) PAI reconstruction results, called the regularized iteration method with shape prior. The shape prior is a probability matrix derived from the reconstruction results of multiple sets of random partial array signals in a computational imaging system using any reconstruction algorithm, such as Delay-and-Sum (DAS) and Back-Projection (BP). In the probability matrix, high-probability locations indicate high consistency among multiple reconstruction results at those positions, suggesting a high likelihood of representing the true imaging results. In contrast, low-probability locations indicate higher randomness, leaning more towards noise or artifacts. As a shape prior, this probability matrix guides the iteration and regularization of the entire array signal reconstruction results using the original reconstruction algorithm (the same algorithm for processing random partial array signals). The method takes advantage of the property that the similarity of the object to be imitated is higher than that of noise or artifact in the results reconstructed by multiple sets of random partial array signals of the entire imaging system. The probability matrix is taken as a prerequisite for improving the original reconstruction results, and the optimizer is used to further iterate the imaging results to remove noise and artifacts and improve the imaging fidelity. Especially in the case involving sparse view which brings more artifacts, the effect is remarkable. Simulation and real experiments have both demonstrated the superiority of this method.

Astronomers often deal with data where the covariates and the dependent variable are measured with heteroscedastic non-Gaussian error. For instance, while TESS and Kepler datasets provide a wealth of information, addressing the challenges of measurement errors and systematic biases is critical for extracting reliable scientific insights and improving machine learning models' performance. Although techniques have been developed for estimating regression parameters for these data, few techniques exist to construct prediction intervals with finite sample coverage guarantees. To address this issue, we tailor the conformal prediction approach to our application. We empirically demonstrate that this method gives finite sample control over Type I error probabilities under a variety of assumptions on the measurement errors in the observed data. Further, we demonstrate how the conformal prediction method could be used for constructing prediction intervals for unobserved exoplanet masses using established broken power-law relationships between masses and radii found in the literature.

A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both image and data sizes are large and therefore the forward model is costly to evaluate. Since several years algorithms from stochastic optimization are used for tomographic image reconstruction with great success by subsampling the data. Here we propose a novel way how stochastic optimization can be used to speed up image reconstruction by means of image domain sketching such that at each iteration an image of different resolution is being used. Hence, we coin this algorithm ImaSk. By considering an associated saddle-point problem, we can formulate ImaSk as a gradient-based algorithm where the gradient is approximated in the same spirit as the stochastic average gradient am\'elior\'e (SAGA) and uses at each iteration one of these multiresolution operators at random. We prove that ImaSk is linearly converging for linear forward models with strongly convex regularization functions. Numerical simulations on CT show that ImaSk is effective and increasing the number of multiresolution operators reduces the computational time to reach the modeled solution.

Security concerns in large-scale networked environments are becoming increasingly critical. To further improve the algorithm security from the design perspective of decentralized optimization algorithms, we introduce a new measure: Privacy Leakage Frequency (PLF), which reveals the relationship between communication and privacy leakage of algorithms, showing that lower PLF corresponds to lower privacy budgets. Based on such assertion, a novel differentially private decentralized primal--dual algorithm named DP-RECAL is proposed to take advantage of operator splitting method and relay communication mechanism to experience less PLF so as to reduce the overall privacy budget. To the best of our knowledge, compared with existing differentially private algorithms, DP-RECAL presents superior privacy performance and communication complexity. In addition, with uncoordinated network-independent stepsizes, we prove the convergence of DP-RECAL for general convex problems and establish a linear convergence rate under the metric subregularity. Evaluation analysis on least squares problem and numerical experiments on real-world datasets verify our theoretical results and demonstrate that DP-RECAL can defend some classical gradient leakage attacks.

A key strategy in societal adaptation to climate change is using alert systems to prompt preventative action and reduce the adverse health impacts of extreme heat events. This paper implements and evaluates reinforcement learning (RL) as a tool to optimize the effectiveness of such systems. Our contributions are threefold. First, we introduce a new publicly available RL environment enabling the evaluation of the effectiveness of heat alert policies to reduce heat-related hospitalizations. The rewards model is trained from a comprehensive dataset of historical weather, Medicare health records, and socioeconomic/geographic features. We use scalable Bayesian techniques tailored to the low-signal effects and spatial heterogeneity present in the data. The transition model uses real historical weather patterns enriched by a data augmentation mechanism based on climate region similarity. Second, we use this environment to evaluate standard RL algorithms in the context of heat alert issuance. Our analysis shows that policy constraints are needed to improve RL's initially poor performance. Third, a post-hoc contrastive analysis provides insight into scenarios where our modified heat alert-RL policies yield significant gains/losses over the current National Weather Service alert policy in the United States.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

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.

Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.