In practice, the target sequence often follows certain model properties or patterns (e.g., reasonable ranges, consecutive changes, resource constraint, temporal correlations between multiple variables, existence, unusual cases, etc.). However,RNNs cannot guarantee their learned distributions satisfy these properties.

We appreciate the valuable comments from the reviewers. We will answer reviewers' questions from three aspects, i.e., In respond to Reviewer 5, this paper's major novelty is developing a new STL-based learning framework to Our method creates a practical way to ensure the logic rules' satisfaction in an end-to-end manner. Our approach achieves promising results on real city datasets, i.e., significantly We have carefully compared our work with all the related papers pointed out by the reviewers. Therefore, we also choose STL to express the model properties. Using STL to specify CPS properties is not our novelty.

Recurrent Neural Networks (RNNs) have made great achievements for sequential prediction tasks. In practice, the target sequence often follows certain model properties or patterns (e.g., reasonable ranges, consecutive changes, resource constraint, temporal correlations between multiple variables, existence, unusual cases, etc.). However, RNNs cannot guarantee their learned distributions satisfy these model properties. It is even more challenging for predicting large-scale and complex Cyber-Physical Systems. Failure to produce outcomes that meet these model properties will result in inaccurate and even meaningless results. In this paper, we develop a new temporal logic-based learning framework, STLnet, which guides the RNN learning process with auxiliary knowledge of model properties, and produces a more robust model for improved future predictions. Our framework can be applied to general sequential deep learning models, and trained in an end-to-end manner with back-propagation. We evaluate the performance of STLnet using large-scale real-world city data. The experimental results show STLnet not only improves the accuracy of predictions, but importantly also guarantees the satisfaction of model properties and increases the robustness of RNNs.

Following, a population of such neural network models (referred to as model zoo) would form structures in weight space.

Recurrent Neural Networks (RNNs) have made great achievements for sequential prediction tasks. In practice, the target sequence often follows certain model properties or patterns (e.g., reasonable ranges, consecutive changes, resource constraint, temporal correlations between multiple variables, existence, unusual cases, etc.). However, RNNs cannot guarantee their learned distributions satisfy these model properties. It is even more challenging for predicting large-scale and complex Cyber-Physical Systems. Failure to produce outcomes that meet these model properties will result in inaccurate and even meaningless results.

Epistemic logics typically talk about knowledge of individual agents or groups of explicitly listed agents. Often, however, one wishes to express knowledge of groups of agents specified by a given property, as in `it is common knowledge among economists'. We introduce such a logic of common knowledge, which we term abstract-group epistemic logic (AGEL). That is, AGEL features a common knowledge operator for groups of agents given by concepts in a separate agent logic that we keep generic, with one possible agent logic being ALC. We show that AGEL is EXPTIME-complete, with the lower bound established by reduction from standard group epistemic logic, and the upper bound by a satisfiability-preserving embedding into the full $\mu$-calculus. Further main results include a finite model property (not enjoyed by the full $\mu$-calculus) and a complete axiomatization.

Machine Learning (ML) techniques are used by most data-driven organisations to extract insights. Machine-learning-as-a-service (MLaaS), where models are trained on potentially sensitive user data and then queried by external parties are becoming a reality. However, recently, these systems have been shown to be vulnerable to Membership Inference Attacks (MIA), where a target's data can be inferred to belong or not to the training data. While the key factors for the success of MIA have not been fully understood, existing defence mechanisms only consider the model-specific properties. We investigate the impact of both the data and ML model properties on the vulnerability of ML techniques to MIA. Our analysis indicates a strong relationship between the MIA success and the properties of the data in use, such as the data size and balance between the classes as well as the model properties including the fairness in prediction and the mutual information between the records and the model's parameters. We then propose new approaches to protect ML models from MIA by using several properties, e.g. the model's fairness and mutual information between the records and the model's parameters as regularizers, which reduces the attack accuracy by 25%, while yielding a fairer and a better performing ML model.

In safety-critical applications of machine learning, it is often necessary to look beyond standard metrics such as test accuracy in order to validate various qualitative properties such as monotonicity with respect to a feature or combination of features, checking for undesirable changes or oscillations in the response, and differences in outcomes (e.g. discrimination) for a protected class. To help answer this need, we propose a framework for approximately validating (or invalidating) various properties of a black box model by finding a univariate diagnostic curve in the input space whose output maximally violates a given property. These diagnostic curves show the exact value of the model along the curve and can be displayed with a simple and intuitive line graph. We demonstrate the usefulness of these diagnostic curves across multiple use-cases and datasets including selecting between two models and understanding out-of-sample behavior.