We thank all the reviewers for the valuable insights and feedback. Below please see our response to the questions. Brief description of SAEM: Thank you for the suggestion. Causal direction flipping is not an assumption. It is hard to handle with traditional methods.

The paper advocates for LLMs to enhance the accessibility, usage and explainability of rule-based legal systems, contributing to a democratic and stakeholder-oriented view of legal technology. A methodology is developed to explore the potential use of LLMs for translating the explanations produced by rule-based systems, from high-level programming languages to natural language, allowing all users a fast, clear, and accessible interaction with such technologies. The study continues by building upon these explanations to empower laypeople with the ability to execute complex juridical tasks on their own, using a Chain of Prompts for the autonomous legal comparison of different rule-based inferences, applied to the same factual case.

Databricks is giving users a set of new tools for big data processing with enhancements to Apache Spark. The new tools and features make it easier to do machine learning within Spark, process streaming data at high speeds, and run tasks in the cloud without provisioning servers. On the machine learning side, Databricks announced Deep Learning Pipelines, which are designed to make it possible for data scientists and AI novices to implement neural nets in their big data processing. It provides developers with high-level APIs designed to help with tasks like loading images, tuning a model's hyperparameters, and modifying a more general model to help in a specific case. The company has also integrated Spark's Structured Streaming feature into the beta of its enterprise product to accelerate the processing of real-time data.

We pick the cell size to be bounded by (r)/( (n)), so that each grid cell will contain at most one sample, and thus the grid can be implemented as a simple n-dimensional array of integers: the default 1 indicates no sample, a non-negative integer gives the index of the sample located in a cell. Step 1. Select the initial sample, x0, randomly chosen uniformly from the domain.

We pick the cell size to be bounded by (r)/( (n)), so that each grid cell will contain at most one sample, and thus the grid can be implemented as a simple n-dimensional array of integers: the default 1 indicates no sample, a non-negative integer gives the index of the sample located in a cell. Step 1. Select the initial sample, x0, randomly chosen uniformly from the domain.

We pick the cell size to be bounded by (r)/( (n)), so that each grid cell will contain at most one sample, and thus the grid can be implemented as a simple n-dimensional array of integers: the default 1 indicates no sample, a non-negative integer gives the index of the sample located in a cell. Step 1. Select the initial sample, x0, randomly chosen uniformly from the domain.

In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned work.