Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

To extend the limited scope of autonomy used in prior missions for operation in distant and complex environments, there is a need to further develop and mature autonomy that jointly reasons over multiple subsystems, which we term system-level autonomy. System-level autonomy establishes situational awareness that resolves conflicting information across subsystems, which may necessitate the refinement and interconnection of the underlying spacecraft and environment onboard models. However, with a limited understanding of the assumptions and tradeoffs of modeling to arbitrary extents, designing onboard models to support system-level capabilities presents a significant challenge. In this paper, we provide a detailed analysis of the increasing levels of model fidelity for several key spacecraft subsystems, with the goal of informing future spacecraft functional- and system-level autonomy algorithms and the physics-based simulators on which they are validated. We do not argue for the adoption of a particular fidelity class of models but, instead, highlight the potential tradeoffs and opportunities associated with the use of models for onboard autonomy and in physics-based simulators at various fidelity levels. We ground our analysis in the context of deep space exploration of small bodies, an emerging frontier for autonomous spacecraft operation in space, where the choice of models employed onboard the spacecraft may determine mission success. We conduct our experiments in the Multi-Spacecraft Concept and Autonomy Tool (MuSCAT), a software suite for developing spacecraft autonomy algorithms.

Motivation: The Mapper algorithm is an essential tool to explore shape of data in topology data analysis. With a dataset as an input, the Mapper algorithm outputs a graph representing the topological features of the whole dataset. This graph is often regarded as an approximation of a reeb graph of data. The classic Mapper algorithm uses fixed interval lengths and overlapping ratios, which might fail to reveal subtle features of data, especially when the underlying structure is complex. Results: In this work, we introduce a distribution guided Mapper algorithm named D-Mapper, that utilizes the property of the probability model and data intrinsic characteristics to generate density guided covers and provides enhanced topological features. Our proposed algorithm is a probabilistic model-based approach, which could serve as an alternative to non-prababilistic ones. Moreover, we introduce a metric accounting for both the quality of overlap clustering and extended persistence homology to measure the performance of Mapper type algorithm. Our numerical experiments indicate that the D-Mapper outperforms the classical Mapper algorithm in various scenarios. We also apply the D-Mapper to a SARS-COV-2 coronavirus RNA sequences dataset to explore the topological structure of different virus variants. The results indicate that the D-Mapper algorithm can reveal both vertical and horizontal evolution processes of the viruses. Availability: Our package is available at https://github.com/ShufeiGe/D-Mapper.

This paper focuses on the construction of non-intrusive Scientific Machine Learning (SciML) Reduced-Order Models (ROMs) for nonlinear, chaotic plasma turbulence simulations. In particular, we propose using Operator Inference (OpInf) to build low-cost physics-based ROMs from data for such simulations. As a representative example, we focus on the Hasegawa-Wakatani (HW) equations used for modeling two-dimensional electrostatic drift-wave plasma turbulence. For a comprehensive perspective of the potential of OpInf to construct accurate ROMs for this model, we consider a setup for the HW equations that leads to the formation of complex, nonlinear, and self-driven dynamics, and perform two sets of experiments. We first use the data obtained via a direct numerical simulation of the HW equations starting from a specific initial condition and train OpInf ROMs for predictions beyond the training time horizon. In the second, more challenging set of experiments, we train ROMs using the same dataset as before but this time perform predictions for six other initial conditions. Our results show that the OpInf ROMs capture the important features of the turbulent dynamics and generalize to new and unseen initial conditions while reducing the evaluation time of the high-fidelity model by up to five orders of magnitude in single-core performance. In the broader context of fusion research, this shows that non-intrusive SciML ROMs have the potential to drastically accelerate numerical studies, which can ultimately enable tasks such as the design and real-time control of optimized fusion devices.

One of the most important challenges in text generation systems is to produce outputs that are not only correct but also diverse. Recently, Minimum Bayes-Risk (MBR) decoding has gained prominence for generating sentences of the highest quality among the decoding algorithms. However, existing algorithms proposed for generating diverse outputs are predominantly based on beam search or random sampling, thus their output quality is capped by these underlying methods. In this paper, we investigate an alternative approach -- we develop diversity-promoting decoding algorithms by enforcing diversity objectives to MBR decoding. We propose two variants of MBR, Diverse MBR (DMBR) and $k$-medoids MBR (KMBR), methods to generate a set of sentences with high quality and diversity. We evaluate DMBR and KMBR on a variety of directed text generation tasks using encoder-decoder models and a large language model with prompting. The experimental results show that the proposed method achieves a better trade-off than the diverse beam search and sampling algorithms.

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily focus on an operator inference methodology that builds dynamical models, preferably in low-dimension, with a prior hypothesis on the model structure, often determined by known physics or given by experts. Then, for inference, we aim to learn the operators of a model by setting up an appropriate optimization problem. One of the critical properties of dynamical systems is stability. However, this property is not guaranteed by the inferred models. In this work, we propose inference formulations to learn quadratic models, which are stable by design. Precisely, we discuss the parameterization of quadratic systems that are locally and globally stable. Moreover, for quadratic systems with no stable point yet bounded (e.g., chaotic Lorenz model), we discuss how to parameterize such bounded behaviors in the learning process. Using those parameterizations, we set up inference problems, which are then solved using a gradient-based optimization method. Furthermore, to avoid numerical derivatives and still learn continuous systems, we make use of an integral form of differential equations. We present several numerical examples, illustrating the preservation of stability and discussing its comparison with the existing state-of-the-art approach to infer operators. By means of numerical examples, we also demonstrate how the proposed methods are employed to discover governing equations and energy-preserving models.

Defeasibility in causal reasoning implies that the causal relationship between cause and effect can be strengthened or weakened. Namely, the causal strength between cause and effect should increase or decrease with the incorporation of strengthening arguments (supporters) or weakening arguments (defeaters), respectively. However, existing works ignore defeasibility in causal reasoning and fail to evaluate existing causal strength metrics in defeasible settings. In this work, we present {\delta}-CAUSAL, the first benchmark dataset for studying defeasibility in causal reasoning. {\delta}-CAUSAL includes around 11K events spanning ten domains, featuring defeasible causality pairs, i.e., cause-effect pairs accompanied by supporters and defeaters. We further show current causal strength metrics fail to reflect the change of causal strength with the incorporation of supporters or defeaters in {\delta}-CAUSAL. To this end, we propose CESAR (Causal Embedding aSsociation with Attention Rating), a metric that measures causal strength based on token-level causal relationships. CESAR achieves a significant 69.7% relative improvement over existing metrics, increasing from 47.2% to 80.1% in capturing the causal strength change brought by supporters and defeaters. We further demonstrate even Large Language Models (LLMs) like GPT-3.5 still lag 4.5 and 10.7 points behind humans in generating supporters and defeaters, emphasizing the challenge posed by {\delta}-CAUSAL.

Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require deep domain expertise. Numerical simulations present an alternative to physical experiments but are usually infeasible for complex real-world domains due to the computational requirements of existing numerical methods. Artificial intelligence (AI) presents a potential paradigm shift by developing fast data-driven surrogate models. In particular, an AI framework, known as Neural Operators, presents a principled framework for learning mappings between functions defined on continuous domains, e.g., spatiotemporal processes and partial differential equations (PDE). They can extrapolate and predict solutions at new locations unseen during training, i.e., perform zero-shot super-resolution. Neural Operators can augment or even replace existing simulators in many applications, such as computational fluid dynamics, weather forecasting, and material modeling, while being 4-5 orders of magnitude faster. Further, Neural Operators can be integrated with physics and other domain constraints enforced at finer resolutions to obtain high-fidelity solutions and good generalization. Since Neural Operators are differentiable, they can directly optimize parameters for inverse design and other inverse problems. We believe that Neural Operators present a transformative approach to simulation and design, enabling rapid research and development.

E-commerce platforms usually present an ordered list, mixed with several organic items and an advertisement, in response to each user's page view request. This list, the outcome of ad auction and allocation processes, directly impacts the platform's ad revenue and gross merchandise volume (GMV). Specifically, the ad auction determines which ad is displayed and the corresponding payment, while the ad allocation decides the display positions of the advertisement and organic items. The prevalent methods of segregating the ad auction and allocation into two distinct stages face two problems: 1) Ad auction does not consider externalities, such as the influence of actual display position and context on ad Click-Through Rate (CTR); 2) The ad allocation, which utilizes the auction-winning ad's payment to determine the display position dynamically, fails to maintain incentive compatibility (IC) for the advertisement. For instance, in the auction stage employing the traditional Generalized Second Price (GSP) , even if the winning ad increases its bid, its payment remains unchanged. This implies that the advertisement cannot secure a better position and thus loses the opportunity to achieve higher utility in the subsequent ad allocation stage. Previous research often focused on one of the two stages, neglecting the two-stage problem, which may result in suboptimal outcomes...

Generating animation of physics-based characters with intuitive control has long been a desirable task with numerous applications. However, generating physically simulated animations that reflect high-level human instructions remains a difficult problem due to the complexity of physical environments and the richness of human language. In this paper, we present InsActor, a principled generative framework that leverages recent advancements in diffusion-based human motion models to produce instruction-driven animations of physics-based characters. Our framework empowers InsActor to capture complex relationships between high-level human instructions and character motions by employing diffusion policies for flexibly conditioned motion planning. To overcome invalid states and infeasible state transitions in planned motions, InsActor discovers low-level skills and maps plans to latent skill sequences in a compact latent space. Extensive experiments demonstrate that InsActor achieves state-of-the-art results on various tasks, including instruction-driven motion generation and instruction-driven waypoint heading. Notably, the ability of InsActor to generate physically simulated animations using high-level human instructions makes it a valuable tool, particularly in executing long-horizon tasks with a rich set of instructions.