Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training of deep neural networks in artificial intelligence (AI) systems. Despite the popularity and the success of Adam it remains an \emph{open research problem} to provide a rigorous convergence analysis for Adam even for the class of strongly convex SOPs. In one of the main results of this work we establish convergence rates for Adam in terms of the number of gradient steps (convergence rate \nicefrac{1}{2} w.r.t. the size of the learning rate), the size of the mini-batches (convergence rate 1 w.r.t. the size of the mini-batches), and the size of the second moment parameter of Adam (convergence rate 1 w.r.t. the distance of the second moment parameter to 1) for the class of strongly convex SOPs. In a further main result of this work, which we refer to as \emph{Adam symmetry theorem}, we illustrate the optimality of the established convergence rates by proving for a special class of simple quadratic strongly convex SOPs that Adam converges as the number of gradient steps increases to infinity to the solution of the SOP (the unique minimizer of the strongly convex objective function) if and \emph{only} if the random variables in the SOP (the data in the SOP) are \emph{symmetrically distributed}. In particular, in the standard case where the random variables in the SOP are not symmetrically distributed we \emph{disprove} that Adam converges to the minimizer of the SOP as the number of Adam steps increases to infinity. We also complement the conclusions of our convergence analysis and the Adam symmetry theorem by several numerical simulations that indicate the sharpness of the established convergence rates and that illustrate the practical appearance of the phenomena revealed in the \emph{Adam symmetry theorem}.

Scientific experiment and manufacture rely on complex, multi-step procedures that demand continuous human expertise for precise execution and decision-making. Despite advances in machine learning and automation, conventional models remain confined to virtual domains, while real-world experiment and manufacture still rely on human supervision and expertise. This gap between machine intelligence and physical execution limits reproducibility, scalability, and accessibility across scientific and manufacture workflows. Here, we introduce human-AI co-embodied intelligence, a new form of physical AI that unites human users, agentic AI, and wearable hardware into an integrated system for real-world experiment and intelligent manufacture. In this paradigm, humans provide precise execution and control, while agentic AI contributes memory, contextual reasoning, adaptive planning, and real-time feedback. The wearable interface continuously captures the experimental and manufacture processes, facilitates seamless communication between humans and AI for corrective guidance and interpretable collaboration. As a demonstration, we present Agentic-Physical Experimentation (APEX) system, coupling agentic reasoning with physical execution through mixed-reality. APEX observes and interprets human actions, aligns them with standard operating procedures, provides 3D visual guidance, and analyzes every step. Implemented in a cleanroom for flexible electronics fabrication, APEX system achieves context-aware reasoning with accuracy exceeding general multimodal large language models, corrects errors in real time, and transfers expertise to beginners. These results establish a new class of agentic-physical-human intelligence that extends agentic reasoning beyond computation into the physical domain, transforming scientific research and manufacturing into autonomous, traceable, interpretable, and scalable processes.

BPM is the practice of documenting, measuring, improving, and automating enterprise workflows.

The emergence of AI-driven web automation through Large Language Models (LLMs) offers unprecedented opportunities for optimizing digital workflows. However, deploying such systems within industry's real-world environments presents four core challenges: (1) ensuring consistent execution, (2) accurately identifying critical HTML elements, (3) meeting human-like accuracy in order to automate operations at scale and (4) the lack of comprehensive benchmarking data on internal web applications. Existing solutions are primarily tailored for well-designed, consumer-facing websites (e.g., Amazon.com, Apple.com) and fall short in addressing the complexity of poorly-designed internal web interfaces. To address these limitations, we present Cybernaut, a novel framework to ensure high execution consistency in web automation agents designed for robust enterprise use. Our contributions are threefold: (1) a Standard Operating Procedure (SOP) generator that converts user demonstrations into reliable automation instructions for linear browsing tasks, (2) a high-precision HTML DOM element recognition system tailored for the challenge of complex web interfaces, and (3) a quantitative metric to assess execution consistency. The empirical evaluation on our internal benchmark demonstrates that using our framework enables a 23.2% improvement (from 72% to 88.68%) in task execution success rate over the browser_use. Cybernaut identifies consistent execution patterns with 84.7% accuracy, enabling reliable confidence assessment and adaptive guidance during task execution in real-world systems. These results highlight Cybernaut's effectiveness in enterprise-scale web automation and lay a foundation for future advancements in web automation.

Large Language Models (LLMs) have demonstrated significant success across diverse applications. However, enforcing content restrictions remains a significant challenge due to their expansive output space. One aspect of content restriction is preventing LLMs from generating harmful content via model alignment approaches such as supervised fine-tuning (SFT). Yet, the need for content restriction may vary significantly across user groups, change rapidly over time, and not always align with general definitions of harmfulness. Applying SFT to each of these specific use cases is impractical due to the high computational, data, and storage demands. Motivated by this need, we propose a new task called \textit{Adaptive Content Restriction} (AdaCoRe), which focuses on lightweight strategies -- methods without model fine-tuning -- to prevent deployed LLMs from generating restricted terms for specific use cases. We propose the first method for AdaCoRe, named \textit{Suffix Optimization (SOP)}, which appends a short, optimized suffix to any prompt to a) prevent a target LLM from generating a set of restricted terms, while b) preserving the output quality. To evaluate AdaCoRe approaches, including our SOP, we create a new \textit{Content Restriction Benchmark} (CoReBench), which contains 400 prompts for 80 restricted terms across 8 carefully selected categories. We demonstrate the effectiveness of SOP on CoReBench, which outperforms the system-level baselines such as system suffix by 15\%, 17\%, 10\%, 9\%, and 6\% on average restriction rates for Gemma2-2B, Mistral-7B, Vicuna-7B, Llama3-8B, and Llama3.1-8B, respectively. We also demonstrate that SOP is effective on POE, an online platform hosting various commercial LLMs, highlighting its practicality in real-world scenarios.

Deep learning-based approaches have demonstrated significant advancements in time series forecasting. Despite these ongoing developments, the complex dynamics of time series make it challenging to establish the rule of thumb for designing the golden model architecture. In this study, we argue that refining existing advanced models through a universal calibrating strategy can deliver substantial benefits with minimal resource costs, as opposed to elaborating and training a new model from scratch. We first identify a multi-target learning conflict in the calibrating process, which arises when optimizing variables across time steps, leading to the underutilization of the model's learning capabilities. To address this issue, we propose an innovative calibrating strategy called Socket+Plug (SoP). This approach retains an exclusive optimizer and early-stopping monitor for each predicted target within each Plug while keeping the fully trained Socket backbone frozen. The model-agnostic nature of SoP allows it to directly calibrate the performance of any trained deep forecasting models, regardless of their specific architectures. Extensive experiments on various time series benchmarks and a spatio-temporal meteorological ERA5 dataset demonstrate the effectiveness of SoP, achieving up to a 22% improvement even when employing a simple MLP as the Plug (highlighted in Figure 1). Code is available at https://github.com/hanyuki23/SoP.

Large Language Models (LLMs) demonstrate impressive general-purpose reasoning and problem-solving abilities. However, they struggle with executing complex, long-horizon workflows that demand strict adherence to Standard Operating Procedures (SOPs), a critical requirement for real-world industrial automation. Despite this need, there is a lack of public benchmarks that reflect the complexity, structure, and domain-specific nuances of SOPs. To address this, we present three main contributions. First, we introduce a synthetic data generation framework to create realistic, industry-grade SOPs that rigorously test the planning, reasoning, and tool-use capabilities of LLM-based agents. Second, using this framework, we develop SOP-Bench, a benchmark of over 1,800 tasks across 10 industrial domains, each with APIs, tool interfaces, and human-validated test cases. Third, we evaluate two prominent agent architectures: Function-Calling and ReAct Agents, on SOP-Bench, observing average success rates of only 27% and 48%, respectively. Remarkably, when the tool registry is much larger than necessary, agents invoke incorrect tools nearly 100% of the time. These findings underscore a substantial gap between current agentic capabilities of LLMs and the demands of automating real-world SOPs. Performance varies significantly by task and domain, highlighting the need for domain-specific benchmarking and architectural choices before deployment. SOP-Bench is publicly available at http://sop-bench.s3-website-us-west-2.amazonaws.com/. We also release the prompts underpinning the data generation framework to support new domain-specific SOP benchmarks. We invite the community to extend SOP-Bench with SOPs from their industrial domains.

We present Self-Organizing Visual Prototypes (SOP), a new training technique for unsupervised visual feature learning. Unlike existing prototypical self-supervised learning (SSL) methods that rely on a single prototype to encode all relevant features of a hidden cluster in the data, we propose the SOP strategy. In this strategy, a prototype is represented by many semantically similar representations, or support embeddings (SEs), each containing a complementary set of features that together better characterize their region in space and maximize training performance. We reaffirm the feasibility of non-parametric SSL by introducing novel non-parametric adaptations of two loss functions that implement the SOP strategy. Notably, we introduce the SOP Masked Image Modeling (SOP-MIM) task, where masked representations are reconstructed from the perspective of multiple non-parametric local SEs. We comprehensively evaluate the representations learned using the SOP strategy on a range of benchmarks, including retrieval, linear evaluation, fine-tuning, and object detection. Our pre-trained encoders achieve state-of-the-art performance on many retrieval benchmarks and demonstrate increasing performance gains with more complex encoders.

In this paper, we address the challenges of managing Standard Operating Procedures (SOPs), which often suffer from inconsistencies in language, format, and execution, leading to operational inefficiencies. Traditional process modeling demands significant manual effort, domain expertise, and familiarity with complex languages like Business Process Modeling Notation (BPMN), creating barriers for non-techincal users. We introduce SOP Structuring (SOPStruct), a novel approach that leverages Large Language Models (LLMs) to transform SOPs into decision-tree-based structured representations. SOPStruct produces a standardized representation of SOPs across different domains, reduces cognitive load, and improves user comprehension by effectively capturing task dependencies and ensuring sequential integrity. Our approach enables leveraging the structured information to automate workflows as well as empower the human users. By organizing procedures into logical graphs, SOPStruct facilitates backtracking and error correction, offering a scalable solution for process optimization. We employ a novel evaluation framework, combining deterministic methods with the Planning Domain Definition Language (PDDL) to verify graph soundness, and non-deterministic assessment by an LLM to ensure completeness. We empirically validate the robustness of our LLM-based structured SOP representation methodology across SOPs from different domains and varying levels of complexity. Despite the current lack of automation readiness in many organizations, our research highlights the transformative potential of LLMs to streamline process modeling, paving the way for future advancements in automated procedure optimization.