The present note studies \emph{surjective rational endomorphisms} $f: \mathbb{P}^2 \dashrightarrow \mathbb{P}^2$ with \emph{cubic} terms and the indeterminacy locus $I_f \ne \emptyset$. We develop an experimental approach, based on some Python programming and Machine Learning, towards the classification of such maps; a couple of new explicit $f$ is constructed in this way. We also prove (via pure projective geometry) that a general non-regular cubic endomorphism $f$ of $\mathbb{P}^2$ is surjective if and only if the set $I_f$ has cardinality at least $3$.

Concept activation vector (CAV) has attracted broad research interest in explainable AI, by elegantly attributing model predictions to specific concepts. However, the training of CAV often necessitates a large number of high-quality images, which are expensive to curate and thus limited to a predefined set of concepts. To address this issue, we propose Language-Guided CAV (LG-CAV) to harness the abundant concept knowledge within the certain pre-trained vision-language models (e.g., CLIP). This method allows training any CAV without labeled data, by utilizing the corresponding concept descriptions as guidance. To bridge the gap between vision-language model and the target model, we calculate the activation values of concept descriptions on a common pool of images (probe images) with vision-language model and utilize them as language guidance to train the LG-CAV.

This paper presents linear DML models for causal inference using the simplest Python code on a Jupyter notebook based on an Anaconda platform and compares the performance of different DML models. The results show that current Library API technology is not yet sufficient to enable novice Python users to build qualified and high-quality DML models with the simplest coding approach. Novice users attempting to perform DML causal inference using Python still have to improve their mathematical and computer knowledge to adapt to more flexible DML programming. Additionally, the issue of mismatched outcome variable dimensions is also widespread when building linear DML models in Jupyter notebook.

In recent years, masked diffusion models (MDMs) have emerged as a promising alternative approach for generative modeling over discrete domains. Compared to autoregressive models (ARMs), MDMs trade off complexity at training time with flexibility at inference time. At training time, they must learn to solve an exponentially large number of infilling problems, but at inference time, they can decode tokens in essentially arbitrary order. In this work, we closely examine these two competing effects. On the training front, we theoretically and empirically demonstrate that MDMs indeed train on computationally intractable subproblems compared to their autoregressive counterparts. On the inference front, we show that a suitable strategy for adaptively choosing the token decoding order significantly enhances the capabilities of MDMs, allowing them to sidestep hard subproblems. On logic puzzles like Sudoku, we show that adaptive inference can boost solving accuracy in pretrained MDMs from $<7$% to $\approx 90$%, even outperforming ARMs with $7\times$ as many parameters and that were explicitly trained via teacher forcing to learn the right order of decoding.

Recent advancements in AI for biological research focus on integrating molecular data with natural language to accelerate drug discovery. However, the scarcity of high-quality annotations limits progress in this area. This paper introduces LA$^3$, a Language-based Automatic Annotation Augmentation framework that leverages large language models to augment existing datasets, thereby improving AI training. We demonstrate the effectiveness of LA$^3$ by creating an enhanced dataset, LaChEBI-20, where we systematically rewrite the annotations of molecules from an established dataset. These rewritten annotations preserve essential molecular information while providing more varied sentence structures and vocabulary. Using LaChEBI-20, we train LaMolT5 based on a benchmark architecture to learn the mapping between molecular representations and augmented annotations. Experimental results on text-based *de novo* molecule generation and molecule captioning demonstrate that LaMolT5 outperforms state-of-the-art models. Notably, incorporating LA$^3$ leads to improvements of up to 301% over the benchmark architecture. Furthermore, we validate the effectiveness of LA$^3$ notable applications in *image*, *text* and *graph* tasks, affirming its versatility and utility.

Accurate solar flare prediction is crucial due to the significant risks that intense solar flares pose to astronauts, space equipment, and satellite communication systems. Our research enhances solar flare prediction by utilizing advanced data preprocessing and classification methods on a multivariate time series-based dataset of photospheric magnetic field parameters. First, our study employs a novel preprocessing pipeline that includes missing value imputation, normalization, balanced sampling, near decision boundary sample removal, and feature selection to significantly boost prediction accuracy. Second, we integrate contrastive learning with a GRU regression model to develop a novel classifier, termed ContReg, which employs dual learning methodologies, thereby further enhancing prediction performance. To validate the effectiveness of our preprocessing pipeline, we compare and demonstrate the performance gain of each step, and to demonstrate the efficacy of the ContReg classifier, we compare its performance to that of sequence-based deep learning architectures, machine learning models, and findings from previous studies. Our results illustrate exceptional True Skill Statistic (TSS) scores, surpassing previous methods and highlighting the critical role of precise data preprocessing and classifier development in time series-based solar flare prediction.

In recent years, urban safety has become a paramount concern for city planners and law enforcement agencies. Accurate prediction of likely crime occurrences can significantly enhance preventive measures and resource allocation. However, many law enforcement departments lack the tools to analyze and apply advanced AI and ML techniques that can support city planners, watch programs, and safety leaders to take proactive steps towards overall community safety. This paper explores the effectiveness of ML techniques to predict spatial and temporal patterns of crimes in urban areas. Leveraging police dispatch call data from San Jose, CA, the research goal is to achieve a high degree of accuracy in categorizing calls into priority levels particularly for more dangerous situations that require an immediate law enforcement response. This categorization is informed by the time, place, and nature of the call. The research steps include data extraction, preprocessing, feature engineering, exploratory data analysis, implementation, optimization and tuning of different supervised machine learning models and neural networks. The accuracy and precision are examined for different models and features at varying granularity of crime categories and location precision. The results demonstrate that when compared to a variety of other models, Random Forest classification models are most effective in identifying dangerous situations and their corresponding priority levels with high accuracy (Accuracy = 85%, AUC = 0.92) at a local level while ensuring a minimum amount of false negatives. While further research and data gathering is needed to include other social and economic factors, these results provide valuable insights for law enforcement agencies to optimize resources, develop proactive deployment approaches, and adjust response patterns to enhance overall public safety outcomes in an unbiased way.

Building Management System (BMS) through a data-driven method always faces data and model scalability issues. We propose a methodology to tackle the scalability challenges associated with the development of data-driven models for BMS by using Large Language Models (LLMs). LLMs' code generation adaptability can enable broader adoption of BMS by "automating the automation," particularly the data handling and data-driven modeling processes. In this paper, we use LLMs to generate code that processes structured data from BMS and build data-driven models for BMS's specific requirements. This eliminates the need for manual data and model development, reducing the time, effort, and cost associated with this process. Our hypothesis is that LLMs can incorporate domain knowledge about data science and BMS into data processing and modeling, ensuring that the data-driven modeling is automated for specific requirements of different building types and control objectives, which also improves accuracy and scalability. We generate a prompt template following the framework of Machine Learning Operations so that the prompts are designed to systematically generate Python code for data-driven modeling. Our case study indicates that bi-sequential prompting under the prompt template can achieve a high success rate of code generation and code accuracy, and significantly reduce human labor costs.