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Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often model these separate (although possibly statistically dependent) random variables by fitting a large number of parametric probability distributions to historical data and then comparing goodness-of-fit statistics. However, this approach is highly susceptible to problems of overfitting because it gives insufficient weight to fundamental considerations of functional simplicity and adaptability. To address this shortcoming, we propose a formal mathematical measure for assessing the versatility of frequency and severity distributions prior to their application. We then illustrate this approach by computing and comparing values of the versatility measure for a variety of probability distributions commonly used in risk analysis.

Instruction following is one of the fundamental capabilities of large language models (LLMs). As the ability of LLMs is constantly improving, they have been increasingly applied to deal with complex human instructions in real-world scenarios. Therefore, how to evaluate the ability of complex instruction-following of LLMs has become a critical research problem. Existing benchmarks mainly focus on modeling different types of constraints in human instructions while neglecting the composition of different constraints, which is an indispensable constituent in complex instructions. To this end, we propose ComplexBench, a benchmark for comprehensively evaluating the ability of LLMs to follow complex instructions composed of multiple constraints. We propose a hierarchical taxonomy for complex instructions, including 4 constraint types, 19 constraint dimensions, and 4 composition types, and manually collect a high-quality dataset accordingly. To make the evaluation reliable, we augment LLM-based evaluators with rules to effectively verify whether generated texts can satisfy each constraint and composition. Furthermore, we obtain the final evaluation score based on the dependency structure determined by different composition types. ComplexBench identifies significant deficiencies in existing LLMs when dealing with complex instructions with multiple constraints composition., Comment: 20 pages, 7 figures

Human-robot collaboration (HRC) in a shared workspace has become a common pattern in real-world robot applications and has garnered significant research interest. However, most existing studies for human-in-the-loop (HITL) collaboration with robots in a shared workspace evaluate in either simplified game environments or physical platforms, falling short in limited realistic significance or limited scalability. To support future studies, we build an embodied framework named HumanTHOR, which enables humans to act in the simulation environment through VR devices to support HITL collaborations in a shared workspace. To validate our system, we build a benchmark of everyday tasks and conduct a preliminary user study with two baseline algorithms. The results show that the robot can effectively assist humans in collaboration, demonstrating the significance of HRC. The comparison among different levels of baselines affirms that our system can adequately evaluate robot capabilities and serve as a benchmark for different robot algorithms. The experimental results also indicate that there is still much room in the area and our system can provide a preliminary foundation for future HRC research in a shared workspace. More information about the simulation environment, experiment videos, benchmark descriptions, and additional supplementary materials can be found on the website: https://sites.google.com/view/humanthor/., Comment: In RSS 2024

Gas separation using polymer membranes promises to dramatically drive down the energy, carbon, and water intensity of traditional thermally driven separation, but developing the membrane materials is challenging. Here, we demonstrate a novel graph machine learning (ML) strategy to guide the experimental discovery of synthesizable polymer membranes with performances simultaneously exceeding the empirical upper bounds in multiple industrially important gas separation tasks. Two predicted candidates are synthesized and experimentally validated to perform beyond the upper bounds for multiple gas pairs (O2/N2, H2/CH4, and H2/N2). Notably, the O2/N2 separation selectivity is 1.6-6.7 times higher than existing polymer membranes. The molecular origin of the high performance is revealed by combining the inherent interpretability of our ML model, experimental characterization, and molecule-level simulation. Our study presents a unique explainable ML-experiment combination to tackle challenging energy material design problems in general, and the discovered polymers are beneficial for industrial gas separation.

Inverse molecular design with diffusion models holds great potential for advancements in material and drug discovery. Despite success in unconditional molecule generation, integrating multiple properties such as synthetic score and gas permeability as condition constraints into diffusion models remains unexplored. We present the Graph Diffusion Transformer (Graph DiT) for multi-conditional molecular generation. Graph DiT has a condition encoder to learn the representation of numerical and categorical properties and utilizes a Transformer-based graph denoiser to achieve molecular graph denoising under conditions. Unlike previous graph diffusion models that add noise separately on the atoms and bonds in the forward diffusion process, we propose a graph-dependent noise model for training Graph DiT, designed to accurately estimate graph-related noise in molecules. We extensively validate the Graph DiT for multi-conditional polymer and small molecule generation. Results demonstrate our superiority across metrics from distribution learning to condition control for molecular properties. A polymer inverse design task for gas separation with feedback from domain experts further demonstrates its practical utility., Comment: 21 pages, 9 figures, 7 tables

In this paper, we deal with a class of planar Schr\"{o}dinger-Poisson systems, namely, $-\Delta u+V(x)u+\frac{\gamma}{2\pi}\bigl(\log(|\cdot|)\ast|u|^{2}\bigr)u=b|u|^{p-2}u\ \text{in}\ \mathbb{R}^{2}$, where $\gamma > 0$, $b \geq 0$, $p>2$ and $V \in C(\mathbb{R}^2, \mathbb{R})$ is an unbounded potential function with $\inf_{\mathbb{R}^2} V >0$. Suppose moreover that the potential $V$ satisfies $\left|\{x \in \mathbb{R}^2:\: V(x)\leq M\}\right| < \infty$ for every $M>0$, we establish the existence of ground state solutions for this system via variational methods. Furthermore, we also explore the minimax characterization of ground state solutions. Our main results can be viewed as a counterpart of the result from Molle and Sardilli (Proc. Edinb. Math. Soc. 65:1133-1146, 2022), where the authors studied the existence of ground state solutions for the above planar Schr\"{o}dinger-Poisson system in the case where $b>0$ and $p >4$., Comment: arXiv admin note: substantial text overlap with arXiv:2312.07265

In this paper, we deal with the planar Schr\"{o}dinger-Poisson system \begin{equation*}\begin{cases} -\Delta u + V(x) u + \phi u = b|u|^{p-2} u \ &\text{in}\ \mathbb{R}^{2},\\\Delta \phi= u^{2} &\text{in}\ \mathbb{R}^{2},\end{cases} \end{equation*} where $b \geq 0$, $p > 2 $ and $V \in C(\mathbb{R}^2, \mathbb{R})$ is a potential function with $\inf_{\mathbb{R}^2} V >0$. Suppose moreover that $V$ exhibits a bounded potential well in the sense that $\lim_{|x|\rightarrow \infty} V(x)$ exists and is equal to $\sup_{\mathbb{R}^2} V$. By using variational methods, we obtain the existence of ground state solutions for this system in the case where $p \geq 3$. Furthermore, we also present a minimax characterization of ground state solutions. The main feature of this work is that we do not assume any periodicity or symmetry condition on the external potential $V$, which is essential to establish the compactness condition of Cerami sequences.

Graph property prediction tasks are important and numerous. While each task offers a small size of labeled examples, unlabeled graphs have been collected from various sources and at a large scale. A conventional approach is training a model with the unlabeled graphs on self-supervised tasks and then fine-tuning the model on the prediction tasks. However, the self-supervised task knowledge could not be aligned or sometimes conflicted with what the predictions needed. In this paper, we propose to extract the knowledge underlying the large set of unlabeled graphs as a specific set of useful data points to augment each property prediction model. We use a diffusion model to fully utilize the unlabeled graphs and design two new objectives to guide the model's denoising process with each task's labeled data to generate task-specific graph examples and their labels. Experiments demonstrate that our data-centric approach performs significantly better than fifteen existing various methods on fifteen tasks. The performance improvement brought by unlabeled data is visible as the generated labeled examples unlike the self-supervised learning., Comment: Accepted by NeurIPS 2023

Heavy-tailed random variables have been used in insurance research to model both loss frequencies and loss severities, with substantially more emphasis on the latter. In the present work, we take a step toward addressing this imbalance by exploring the class of heavy-tailed frequency models formed by continuous mixtures of Negative Binomial and Poisson random variables. We begin by defining the concept of a calibrative family of mixing distributions (each member of which is identifiable from its associated Negative Binomial mixture), and show how to construct such families from only a single member. We then introduce a new heavy-tailed frequency model -- the two-parameter ZY distribution -- as a generalization of both the one-parameter Zeta and Yule distributions, and construct calibrative families for both the new distribution and the heavy-tailed two-parameter Waring distribution. Finally, we pursue natural extensions of both the ZY and Waring families to a unifying, four-parameter heavy-tailed model, providing the foundation for a novel loss-frequency modeling approach to complement conventional GLM analyses. This approach is illustrated by application to a classic set of Swedish commercial motor-vehicle insurance loss data.

Rationale is defined as a subset of input features that best explains or supports the prediction by machine learning models. Rationale identification has improved the generalizability and interpretability of neural networks on vision and language data. In graph applications such as molecule and polymer property prediction, identifying representative subgraph structures named as graph rationales plays an essential role in the performance of graph neural networks. Existing graph pooling and/or distribution intervention methods suffer from lack of examples to learn to identify optimal graph rationales. In this work, we introduce a new augmentation operation called environment replacement that automatically creates virtual data examples to improve rationale identification. We propose an efficient framework that performs rationale-environment separation and representation learning on the real and augmented examples in latent spaces to avoid the high complexity of explicit graph decoding and encoding. Comparing against recent techniques, experiments on seven molecular and four polymer real datasets demonstrate the effectiveness and efficiency of the proposed augmentation-based graph rationalization framework., Comment: Accepted by KDD 2022

Finding amorphous polymers with higher thermal conductivity is important, as they are ubiquitous in heat transfer applications. With recent progress in material informatics, machine learning approaches have been increasingly adopted for finding or designing materials with desired properties. However, relatively limited effort has been put into finding thermally conductive polymers using machine learning, mainly due to the lack of polymer thermal conductivity databases with reasonable data volume. In this work, we combine high-throughput molecular dynamics (MD) simulations and machine learning to explore polymers with relatively high thermal conductivity (> 0.300 W/m-K). We first randomly select 365 polymers from the existing PolyInfo database and calculate their thermal conductivity using MD simulations. The data are then employed to train a machine learning regression model to quantify the structure-thermal conductivity relation, which is further leveraged to screen polymer candidates in the PolyInfo database with thermal conductivity > 0.300 W/m-K. 133 polymers with MD-calculated thermal conductivity above this threshold are eventually identified. Polymers with a wide range of thermal conductivity values are selected for re-calculation under different simulation conditions, and those polymers found with thermal conductivity above 0.300 W/m-K are mostly calculated to maintain values above this threshold despite fluctuation in the exact values. A classification model is also constructed, and similar results were obtained compared to the regression model in predicting polymers with thermal conductivity above or below 0.300 W/m-K. The strategy and results from this work may contribute to automating the design of polymers with high thermal conductivity.