Machine-learned interatomic potentials (MLIPs) are typically trained on datasets that encompass a restricted subset of possible input structures, which presents a potential challenge for their generalization to a broader range of systems outside the training set. Nevertheless, MLIPs have demonstrated impressive accuracy in predicting forces and energies in simulations involving intricate and complex structures. In this paper we aim to take steps towards rigorously explaining the excellent observed generalisation properties of MLIPs. Specifically, we offer a comprehensive theoretical and numerical investigation of the generalization of MLIPs in the context of dislocation simulations. We quantify precisely how the accuracy of such simulations is directly determined by a few key factors: the size of the training structures, the choice of training observations (e.g., energies, forces, virials), and the level of accuracy achieved in the fitting process. Notably, our study reveals the crucial role of fitting virials in ensuring the consistency of MLIPs for dislocation simulations. Our series of careful numerical experiments encompassing screw, edge, and mixed dislocations, supports existing best practices in the MLIPs literature but also provides new insights into the design of data sets and loss functions.
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機器學習(xi)系統設計系統評(ping)估標準(zhun)
The modifiable areal unit problem in geography or the change-of-support (COS) problem in statistics demonstrates that the interpretation of spatial (or spatio-temporal) data analysis is affected by the choice of resolutions or geographical units used in the study. The ecological fallacy is one famous example of this phenomenon. Here we investigate the ecological fallacy associated with the COS problem for multivariate spatial data with the goal of providing a data-driven discretization criterion for the domain of interest that minimizes aggregation errors. The discretization is based on a novel multiscale metric, called the Multivariate Criterion for Aggregation Error (MVCAGE). Such multi-scale representations of an underlying multivariate process are often formulated in terms of basis expansions. We show that a particularly useful basis expansion in this context is the multivariate Karhunen-Lo`eve expansion (MKLE). We use the MKLE to build the MVCAGE loss function and use it within the framework of spatial clustering algorithms to perform optimal spatial aggregation. We demonstrate the effectiveness of our approach through simulation and through regionalization of county-level income and hospital quality data over the United States and prediction of ocean color in the coastal Gulf of Alaska.
We study the problem of estimating the number of defective items in adaptive Group testing by using a minimum number of queries. We improve the existing algorithm and prove a lower bound that show that, for constant estimation, the number of tests in our algorithm is optimal.
The increasing digitization of smart grids has made addressing cybersecurity issues crucial in order to secure the power supply. Anomaly detection has emerged as a key technology for cybersecurity in smart grids, enabling the detection of unknown threats. Many research efforts have proposed various machine-learning-based approaches for anomaly detection in grid operations. However, there is a need for a reproducible and comprehensive evaluation environment to investigate and compare different approaches to anomaly detection. The assessment process is highly dependent on the specific application and requires an evaluation that considers representative datasets from the use case as well as the specific characteristics of the use case. In this work, we present an evaluation environment for anomaly detection methods in smart grids that facilitates reproducible and comprehensive evaluation of different anomaly detection methods.
We examine data-processing of Markov chains through the lens of information geometry. We first establish a theory of congruent Markov morphisms within the framework of stochastic matrices. Specifically, we introduce and justify the concept of a linear right inverse (congruent embedding) for lumping, a well-known operation used in Markov chains to extract coarse information. Furthermore, we inspect information projections onto geodesically convex sets of stochastic matrices, and show that under some conditions, projecting (m-projection) onto doubly convex submanifolds can be regarded as a form of data-processing. Finally, we show that the family of lumpable stochastic matrices can be meaningfully endowed with the structure of a foliated manifold and motivate our construction in the context of embedded models and inference.
Existing score-distilling text-to-3D generation techniques, despite their considerable promise, often encounter the view inconsistency problem. One of the most notable issues is the Janus problem, where the most canonical view of an object (\textit{e.g}., face or head) appears in other views. In this work, we explore existing frameworks for score-distilling text-to-3D generation and identify the main causes of the view inconsistency problem -- the embedded bias of 2D diffusion models. Based on these findings, we propose two approaches to debias the score-distillation frameworks for view-consistent text-to-3D generation. Our first approach, called score debiasing, involves cutting off the score estimated by 2D diffusion models and gradually increasing the truncation value throughout the optimization process. Our second approach, called prompt debiasing, identifies conflicting words between user prompts and view prompts using a language model, and adjusts the discrepancy between view prompts and the viewing direction of an object. Our experimental results show that our methods improve the realism of the generated 3D objects by significantly reducing artifacts and achieve a good trade-off between faithfulness to the 2D diffusion models and 3D consistency with little overhead. Our project page is available at~\url{//susunghong.github.io/Debiased-Score-Distillation-Sampling/}.
Generative Pre-trained Transformer (GPT) models have exhibited exciting progress in their capabilities, capturing the interest of practitioners and the public alike. Yet, while the literature on the trustworthiness of GPT models remains limited, practitioners have proposed employing capable GPT models for sensitive applications such as healthcare and finance -- where mistakes can be costly. To this end, this work proposes a comprehensive trustworthiness evaluation for large language models with a focus on GPT-4 and GPT-3.5, considering diverse perspectives -- including toxicity, stereotype bias, adversarial robustness, out-of-distribution robustness, robustness on adversarial demonstrations, privacy, machine ethics, and fairness. Based on our evaluations, we discover previously unpublished vulnerabilities to trustworthiness threats. For instance, we find that GPT models can be easily misled to generate toxic and biased outputs and leak private information in both training data and conversation history. We also find that although GPT-4 is usually more trustworthy than GPT-3.5 on standard benchmarks, GPT-4 is more vulnerable given jailbreaking system or user prompts, potentially because GPT-4 follows (misleading) instructions more precisely. Our work illustrates a comprehensive trustworthiness evaluation of GPT models and sheds light on the trustworthiness gaps. Our benchmark is publicly available at //decodingtrust.github.io/; our dataset can be previewed at //huggingface.co/datasets/AI-Secure/DecodingTrust; a concise version of this work is at //openreview.net/pdf?id=kaHpo8OZw2.
A basic experiment in probability theory is drawing without replacement from an urn filled with multiple balls of different colours. Clearly, it is physically impossible to overdraw, that is, to draw more balls from the urn than it contains. This paper demonstrates that overdrawing does make sense mathematically, once we allow signed distributions with negative probabilities. A new (conservative) extension of the familiar hypergeometric ('draw-and-delete') distribution is introduced that allows draws of arbitrary sizes, including overdraws. The underlying theory makes use of the dual basis functions of the Bernstein polynomials, which play a prominent role in computer graphics. Negative probabilities are treated systematically in the framework of categorical probability and the central role of datastructures such as multisets and monads is emphasised.
Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.
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