Multimodal fusion is crucial in joint decision-making systems for rendering holistic judgments. Since multimodal data changes in open environments, dynamic fusion has emerged and achieved remarkable progress in numerous applications. However, most existing dynamic multimodal fusion methods lack theoretical guarantees and easily fall into suboptimal problems, yielding unreliability and instability. To address this issue, we propose a Predictive Dynamic Fusion (PDF) framework for multimodal learning. We proceed to reveal the multimodal fusion from a generalization perspective and theoretically derive the predictable Collaborative Belief (Co-Belief) with Mono- and Holo-Confidence, which provably reduces the upper bound of generalization error. Accordingly, we further propose a relative calibration strategy to calibrate the predicted Co-Belief for potential uncertainty. Extensive experiments on multiple benchmarks confirm our superiority. Our code is available at https://github.com/Yinan-Xia/PDF.

In this work, we propose a novel method for Bayesian Networks (BNs) structure elicitation that is based on the initialization of several LLMs with different experiences, independently querying them to create a structure of the BN, and further obtaining the final structure by majority voting. We compare the method with one alternative method on various widely and not widely known BNs of different sizes and study the scalability of both methods on them. We also propose an approach to check the contamination of BNs in LLM, which shows that some widely known BNs are inapplicable for testing the LLM usage for BNs structure elicitation. We also show that some BNs may be inapplicable for such experiments because their node names are indistinguishable. The experiments on the other BNs show that our method performs better than the existing method with one of the three studied LLMs; however, the performance of both methods significantly decreases with the increase in BN size.

ABSTRACT We present a flow-based generative approach to emulate grids of stellar evolutionary models. By interpreting the input parameters and output properties of these models as multi-dimensional probability distributions, we train conditional normalizing flows to learn and predict the complex relationships between grid inputs and outputs in the form of conditional joint distributions. Leveraging the expressive power and versatility of these flows, we showcase their ability to emulate a variety of evolutionary tracks and isochrones across a continuous range of input parameters. In addition, we describe a simple Bayesian approach for estimating stellar parameters using these flows and demonstrate its application to asteroseismic datasets of red giants observed by the Kepler mission. By applying this approach to red giants in open clusters NGC 6791 and NGC 6819, we illustrate how large age uncertainties can arise when fitting only to global asteroseismic and spectroscopic parameters without prior information on initial helium abundances and mixing length parameter values. We also conduct inference using the flow at a large scale by determining revised estimates of masses and radii for 15,388 field red giants. These estimates show improved agreement with results from existing grid-based modelling, reveal distinct population-level features in the red clump, and suggest that the masses of Kepler red giants previously determined using the corrected asteroseismic scaling relations have been overestimated by 5 10%.

Mergers of binary neutron stars (BNSs) emit signals in both the gravitational-wave (GW) and electromagnetic (EM) spectra. Famously, the 2017 multi-messenger observation of GW170817 led to scientific discoveries across cosmology, nuclear physics, and gravity. Central to these results were the sky localization and distance obtained from GW data, which, in the case of GW170817, helped to identify the associated EM transient, AT 2017gfo, 11 hours after the GW signal. Fast analysis of GW data is critical for directing time-sensitive EM observations; however, due to challenges arising from the length and complexity of signals, it is often necessary to make approximations that sacrifice accuracy. Here, we develop a machine learning approach that performs complete BNS inference in just one second without making any such approximations. This is enabled by a new method for explicit integration of physical domain knowledge into neural networks. Our approach enhances multi-messenger observations by providing (i) accurate localization even before the merger; (ii) improved localization precision by $\sim30\%$ compared to approximate low-latency methods; and (iii) detailed information on luminosity distance, inclination, and masses, which can be used to prioritize expensive telescope time. Additionally, the flexibility and reduced cost of our method open new opportunities for equation-of-state and waveform systematics studies. Finally, we demonstrate that our method scales to extremely long signals, up to an hour in length, thus serving as a blueprint for data analysis for next-generation ground- and space-based detectors.

The field of Neural-Symbolic (NeSy) systems is growing rapidly. Proposed approaches show great promise in achieving symbiotic unions of neural and symbolic methods. However, each NeSy system differs in fundamental ways. There is a pressing need for a unifying theory to illuminate the commonalities and differences in approaches and enable further progress. In this paper, we introduce Neural-Symbolic Energy-Based Models (NeSy-EBMs), a unifying mathematical framework for discriminative and generative modeling with probabilistic and non-probabilistic NeSy approaches. We utilize NeSy-EBMs to develop a taxonomy of modeling paradigms focusing on a system's neural-symbolic interface and reasoning capabilities. Additionally, we introduce a suite of learning techniques for NeSy-EBMs. Importantly, NeSy-EBMs allow the derivation of general expressions for gradients of prominent learning losses, and we provide four learning approaches that leverage methods from multiple domains, including bilevel and stochastic policy optimization. Finally, we present Neural Probabilistic Soft Logic (NeuPSL), an open-source NeSy-EBM library designed for scalability and expressivity, facilitating real-world application of NeSy systems. Through extensive empirical analysis across multiple datasets, we demonstrate the practical advantages of NeSy-EBMs in various tasks, including image classification, graph node labeling, autonomous vehicle situation awareness, and question answering.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Understanding causal relationships in dynamic systems is essential for numerous scientific fields, including epidemiology, economics, and biology. While causal inference methods have been extensively studied, they often rely on fully specified causal graphs, which may not always be available or practical in complex dynamic systems. Partially specified causal graphs, such as summary causal graphs (SCGs), provide a simplified representation of causal relationships, omitting temporal information and focusing on high-level causal structures. This simplification introduces new challenges concerning the types of queries of interest: macro queries, which involve relationships between clusters represented as vertices in the graph, and micro queries, which pertain to relationships between variables that are not directly visible through the vertices of the graph. In this paper, we first clearly distinguish between macro conditional independencies and micro conditional independencies and between macro total effects and micro total effects. Then, we demonstrate the soundness and completeness of the d-separation to identify macro conditional independencies in SCGs. Furthermore, we establish that the do-calculus is sound and complete for identifying macro total effects in SCGs. Conversely, we also show through various examples that these results do not hold when considering micro conditional independencies and micro total effects.

The primary objective of methods in continual learning is to learn tasks in a sequential manner over time from a stream of data, while mitigating the detrimental phenomenon of catastrophic forgetting. In this paper, we focus on learning an optimal representation between previous class prototypes and newly encountered ones. We propose a prototypical network with a Bayesian learning-driven contrastive loss (BLCL) tailored specifically for class-incremental learning scenarios. Therefore, we introduce a contrastive loss that incorporates new classes into the latent representation by reducing the intra-class distance and increasing the inter-class distance. Our approach dynamically adapts the balance between the cross-entropy and contrastive loss functions with a Bayesian learning technique. Empirical evaluations conducted on both the CIFAR-10 and CIFAR-100 dataset for image classification and images of a GNSS-based dataset for interference classification validate the efficacy of our method, showcasing its superiority over existing state-of-the-art approaches.

The brain is dynamic, associative and efficient. It reconfigures by associating the inputs with past experiences, with fused memory and processing. In contrast, AI models are static, unable to associate inputs with past experiences, and run on digital computers with physically separated memory and processing. We propose a hardware-software co-design, a semantic memory-based dynamic neural network (DNN) using memristor. The network associates incoming data with the past experience stored as semantic vectors. The network and the semantic memory are physically implemented on noise-robust ternary memristor-based Computing-In-Memory (CIM) and Content-Addressable Memory (CAM) circuits, respectively. We validate our co-designs, using a 40nm memristor macro, on ResNet and PointNet++ for classifying images and 3D points from the MNIST and ModelNet datasets, which not only achieves accuracy on par with software but also a 48.1% and 15.9% reduction in computational budget. Moreover, it delivers a 77.6% and 93.3% reduction in energy consumption.

A new variational inference method, SPH-ParVI, based on smoothed particle hydrodynamics (SPH), is proposed for sampling partially known densities (e.g. up to a constant) or sampling using gradients. SPH-ParVI simulates the flow of a fluid under external effects driven by the target density; transient or steady state of the fluid approximates the target density. The continuum fluid is modelled as an interacting particle system (IPS) via SPH, where each particle carries smoothed properties, interacts and evolves as per the Navier-Stokes equations. This mesh-free, Lagrangian simulation method offers fast, flexible, scalable and deterministic sampling and inference for a class of probabilistic models such as those encountered in Bayesian inference and generative modelling.