We first prove the direction Z T SI(Z;T) = 0, which is equivalent to prove I(Z;T) = 0 SI(Z;T) = 0. We prove the contrapositive, i.e. rather than show LHS = RHS, we show that RHS = LHS. Now assume that supwi,vj ρ(w i Z i,v j T j) > ϵ for some i,j. Then by setting those elements in w,v unrelated to Z i,T j to zero, and those related to Z i,T j exactlythesameaswi,vj,weknowthatsupw,vρ(w Z,v T) > ϵ. All neural networks are trained by Adam with its default settings and a learning rate η = 0.001. Early stopping is an useful technique for avoiding overfitting, however it needs to be carefully considered when applied to adversarial methods.

Regression with group-sparsity penalty plays acentral role in high-dimensional predictionproblems.

Neural architecture search (NAS) has demonstrated impressive performance in automatically designing high-performance neural networks. The power ofdeep neural networks is to be unleashed for analyzing a large volume of data (e.g.

Air pollution is one of the most concerns for urban areas. Many countries have constructed monitoring stations to hourly collect pollution values. Recently, there is a research in Daegu city, Korea for real-time air quality monitoring via sensors installed on taxis running across the whole city. The collected data is huge (1-second interval) and in both Spatial and Temporal format. In this paper, based on this spatiotemporal Big data, we propose a real-time air pollution prediction model based on Convolutional Neural Network (CNN) algorithm for image-like Spatial distribution of air pollution. Regarding to Temporal information in the data, we introduce a combination of a Long Short-Term Memory (LSTM) unit for time series data and a Neural Network model for other air pollution impact factors such as weather conditions to build a hybrid prediction model. This model is simple in architecture but still brings good prediction ability.

SSL algorithms would face in real-world applications.

We are only aware of few approaches devoted to infer the Group Lasso structure.

Small Language Models (SLMs) offer compelling advantages in deployment cost and latency, but their accuracy often lags behind larger models, particularly for complex domain-specific tasks. While supervised fine-tuning can help bridge this performance gap, it requires substantial manual effort in data preparation and iterative optimization. We present PaDA-Agent (Pattern-guided Data Augmentation Agent), an evaluation-driven approach that streamlines the data augmentation process for SLMs through coordinated operations. Unlike state-of-the-art approaches that focus on model training errors only and generating error-correcting samples, PaDA-Agent discovers failure patterns from the validation data via evaluations and drafts targeted data augmentation strategies aiming to directly reduce the generalization gap. Our experimental results demonstrate significant improvements over state-of-the-art LLM-based data augmentation approaches for Llama 3.2 1B Instruct model fine-tuning.