The Kolmogorov-Arnold Theorem (KAT), or more generally, the Kolmogorov Superposition Theorem (KST), establishes that any non-linear multivariate function can be exactly represented as a finite superposition of non-linear univariate functions. Unlike the universal approximation theorem, which provides only an approximate representation without guaranteeing a fixed network size, KST offers a theoretically exact decomposition. The Kolmogorov-Arnold Network (KAN) was introduced as a trainable model to implement KAT, and recent advancements have adapted KAN using concepts from modern neural networks. However, KAN struggles to effectively model physical systems that require inherent equivariance or invariance to $E(3)$ transformations, a key property for many scientific and engineering applications. In this work, we propose a novel extension of KAT and KAN to incorporate equivariance and invariance over $O(n)$ group actions, enabling accurate and efficient modeling of these systems. Our approach provides a unified approach that bridges the gap between mathematical theory and practical architectures for physical systems, expanding the applicability of KAN to a broader class of problems.

It has been 100 years since statistical process control (SPC) or statistical process monitoring (SPM) was first introduced for production processes and later applied to service, healthcare, and other industries. The techniques applied to SPM applications are mostly statistically oriented. Recent advances in Artificial Intelligence (AI) have reinvigorated the imagination of adopting AI for SPM applications. This manuscript begins with a concise review of the historical development of the statistically based SPM methods. Next, this manuscript explores AI and Machine Learning (ML) algorithms and methods applied in various SPM applications, addressing quality characteristics of univariate, multivariate, profile, and image. These AI methods can be classified into the following categories: classification, pattern recognition, time series applications, and generative AI. Specifically, different kinds of neural networks, such as artificial neural networks (ANN), convolutional neural networks (CNN), recurrent neural networks (RNN), and generative adversarial networks (GAN), are among the most implemented AI methods impacting SPM. Finally, this manuscript outlines a couple of future directions that harness the potential of the Large Multimodal Model (LMM) for advancing SPM research and applications in complex systems. The ultimate objective is to transform statistical process monitoring (SPM) into smart process control (SMPC), where corrective actions are autonomously implemented to either prevent quality issues or restore process performance.

Published as a conference paper at ICLR 2025M OLS PECTRA: P RETRAINING 3D M OLECULAR R EP-RESENTATION WITHM ULTI-MODALE NERGYS PECTRA Liang Wang 1,2 Shaozhen Liu 1 Y u Rong 3 Deli Zhao 3 Qiang Liu 1,2 Shu Wu 1,2 Liang Wang 1,2 1 New Laboratory of Pattern Recognition (NLPR), State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS), Institute of Automation, Chinese Academy of Sciences (CASIA) 2 School of Artificial Intelligence, University of Chinese Academy of Sciences 3 DAMO Academy, Alibaba Group A BSTRACT Establishing the relationship between 3D structures and the energy states of molecular systems has proven to be a promising approach for learning 3D molecular representations. However, existing methods are limited to modeling the molecular energy states from classical mechanics. This limitation results in a significant oversight of quantum mechanical effects, such as quantized (discrete) energy level structures, which offer a more accurate estimation of molecular energy and can be experimentally measured through energy spectra. In this paper, we propose to utilize the energy spectra to enhance the pre-training of 3D molecular representations (MolSpectra), thereby infusing the knowledge of quantum mechanics into the molecular representations. Specifically, we propose SpecFormer, a multi-spectrum encoder for encoding molecular spectra via masked patch reconstruction. By further aligning outputs from the 3D encoder and spectrum encoder using a contrastive objective, we enhance the 3D encoder's understanding of molecules. Evaluations on public benchmarks reveal that our pre-trained representations surpass existing methods in predicting molecular properties and modeling dynamics. Given the scarcity of molecular property labels, self-supervised representation pre-training has been proposed and utilized to provide generalizable representations (Hu et al., 2020; Rong et al., 2020; Ma et al., 2024). In contrast to contrastive learning (Wang et al., 2022; Kim et al., 2022) and masked modeling (Hou et al., 2022; Liu et al., 2023c; Wang et al., 2024b) on 2D molecular graphs and molecular languages (e.g., SMILES), the design of pre-training strategies on 3D molecular geometries is more closely aligned with physical principles. Previous studies (Zaidi et al., 2023; Jiao et al., 2023) have guided representation learning through denoising processes on 3D molecular geometries, theoretically demonstrating that denoising 3D geometries is equivalent to learning molecular force fields, specifically the negative gradient of molecular potential energy with respect to position. Essentially, these studies reveal that establishing the relationship between 3D geometries and the energy states of molecular systems is an effective pathway to learn 3D molecular representations.

Evaluating large language models (LLMs) poses significant challenges, particularly due to issues of data contamination and the leakage of correct answers. To address these challenges, we introduce ThinkBench, a novel evaluation framework designed to evaluate LLMs' reasoning capability robustly. ThinkBench proposes a dynamic data generation method for constructing out-of-distribution (OOD) datasets and offers an OOD dataset that contains 2,912 samples drawn from reasoning tasks. ThinkBench unifies the evaluation of reasoning models and non-reasoning models. We evaluate 16 LLMs and 4 PRMs under identical experimental conditions and show that most of the LLMs' performance are far from robust and they face a certain level of data leakage. By dynamically generating OOD datasets, ThinkBench effectively provides a reliable evaluation of LLMs and reduces the impact of data contamination.

Artificial intelligence (AI) is not a panacea for effortlessly solving the planet's environmental problems. AI still sparks passionate and dystopian predictions within some parts of the academic community, especially in the natural sciences. For some, the existence of AI tools means an existential threat to human creativity.10 Concerns about the increasing environmental costs of carbon emissions1 and water use demanded by information and communication technologies are also on the horizon. These viewpoints, however, overlook the advantages of employing AI in biodiversity research.

Large language models have become a powerful method for feature augmentation in recommendation systems. However, existing approaches relying on quick inference often suffer from incomplete feature coverage and insufficient specificity in feature descriptions, limiting their ability to capture fine-grained user preferences and undermining overall performance. Motivated by the recent success of inference scaling in math and coding tasks, we explore whether scaling inference can address these limitations and enhance feature quality. Our experiments show that scaling inference leads to significant improvements in recommendation performance, with a 12% increase in NDCG@10. The gains can be attributed to two key factors: feature quantity and specificity. In particular, models using extended Chain-of-Thought (CoT) reasoning generate a greater number of detailed and precise features, offering deeper insights into user preferences and overcoming the limitations of quick inference. We further investigate the factors influencing feature quantity, revealing that model choice and search strategy play critical roles in generating a richer and more diverse feature set. This is the first work to apply inference scaling to feature augmentation in recommendation systems, bridging advances in reasoning tasks to enhance personalized recommendation.

Reasoning about images with rich text, such as charts and documents, is a critical application of vision-language models (VLMs). However, VLMs often struggle in these domains due to the scarcity of diverse text-rich vision-language data. To address this challenge, we present CoSyn, a framework that leverages the coding capabilities of text-only large language models (LLMs) to automatically create synthetic text-rich multimodal data. Given input text describing a target domain (e.g., "nutrition fact labels"), CoSyn prompts an LLM to generate code (Python, HTML, LaTeX, etc.) for rendering synthetic images. With the underlying code as textual representations of the synthetic images, CoSyn can generate high-quality instruction-tuning data, again relying on a text-only LLM. Using CoSyn, we constructed a dataset comprising 400K images and 2.7M rows of vision-language instruction-tuning data. Comprehensive experiments on seven benchmarks demonstrate that models trained on our synthetic data achieve state-of-the-art performance among competitive open-source models, including Llama 3.2, and surpass proprietary models such as GPT-4V and Gemini 1.5 Flash. Furthermore, CoSyn can produce synthetic pointing data, enabling VLMs to ground information within input images, showcasing its potential for developing multimodal agents capable of acting in real-world environments.

Large Language Models (LLMs) have shown great promise in tool-making, yet existing frameworks often struggle to efficiently construct reliable toolsets and are limited to single-task settings. To address these challenges, we propose GATE (Graph-based Adaptive Tool Evolution), an adaptive framework that dynamically constructs and evolves a hierarchical graph of reusable tools across multiple scenarios. We evaluate GATE on open-ended tasks (Minecraft), agent-based tasks (TextCraft, DABench), and code generation tasks (MATH, Date, TabMWP). Our results show that GATE achieves up to 4.3x faster milestone completion in Minecraft compared to the previous SOTA, and provides an average improvement of 9.23% over existing tool-making methods in code generation tasks and 10.03% in agent tasks. GATE demonstrates the power of adaptive evolution, balancing tool quantity, complexity, and functionality while maintaining high efficiency. Code and data are available at \url{https://github.com/ayanami2003/GATE}.

Disruptions in energy imports, backlash in social acceptance, and novel technologies failing to develop are unexpected events that are often overlooked in energy planning, despite their ability to jeopardize the energy transition. We propose a method to explore unexpected events and assess their impact on the transition pathway of a large-scale whole-energy system. First, we evaluate unexpected events assuming "perfect foresight", where decision-makers can anticipate such events in advance. This allows us to identify dealbreakers, i.e., conditions that make the transition infeasible. Then, we assess the events under "limited foresight" to evaluate the robustness of early-stage decisions against unforeseen unexpected events and the costs associated with managing them. A case study for Belgium demonstrates that a lack of electrofuel imports in 2050 is the main dealbreaker, while accelerating the deployment of renewables is the most robust policy. Our transferable method can help policymakers identify key dealbreakers and devise robust energy transition policies.

Designing modern industrial systems requires balancing several competing objectives, such as profitability, resilience, and sustainability, while accounting for complex interactions between technological, economic, and environmental factors. Multi-objective optimization (MOO) methods are commonly used to navigate these tradeoffs, but selecting the appropriate algorithm to tackle these problems is often unclear, particularly when system representations vary from fully equation-based (white-box) to entirely data-driven (black-box) models. While grey-box MOO methods attempt to bridge this gap, they typically impose rigid assumptions on system structure, requiring models to conform to the underlying structural assumptions of the solver rather than the solver adapting to the natural representation of the system of interest. In this chapter, we introduce a unifying approach to grey-box MOO by leveraging network representations, which provide a general and flexible framework for modeling interconnected systems as a series of function nodes that share various inputs and outputs. Specifically, we propose MOBONS, a novel Bayesian optimization-inspired algorithm that can efficiently optimize general function networks, including those with cyclic dependencies, enabling the modeling of feedback loops, recycle streams, and multi-scale simulations - features that existing methods fail to capture. Furthermore, MOBONS incorporates constraints, supports parallel evaluations, and preserves the sample efficiency of Bayesian optimization while leveraging network structure for improved scalability. We demonstrate the effectiveness of MOBONS through two case studies, including one related to sustainable process design. By enabling efficient MOO under general graph representations, MOBONS has the potential to significantly enhance the design of more profitable, resilient, and sustainable engineering systems.