Typically,G would be set as the class of all arithmetic, polynomial, algebraic, closed-form, or analytic expressions.

Deformable shapes provide important and complex geometric features of objects presented in images. However, such information is oftentimes missing or underutilized as implicit knowledge in many image analysis tasks. This paper presents Geo-SIC, the first deep learning model to learn deformable shapes in a deformation space for an improved performance of image classification. We introduce a newly designed framework that (i) simultaneously derives features from both image and latent shape spaces with large intra-class variations; and (ii) gains increased model interpretability by allowing direct access to the underlying geometric features of image data. In particular, we develop a boosted classification network, equipped with an unsupervised learning of geometric shape representations characterized by diffeomorphic transformations within each class. In contrast to previous approaches using pre-extracted shapes, our model provides a more fundamental approach by naturally learning the most relevant shape features jointly with an image classifier. We demonstrate the effectiveness of our method on both simulated 2D images and real 3D brain magnetic resonance (MR) images. Experimental results show that our model substantially improves the image classification accuracy with an additional benefit of increased model interpretability. Our code is publicly available at https://github.com/jw4hv/Geo-SIC.

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on large data sets, due to their discrete parameters and structures. Ensemble methods and fuzzy/soft rules are commonly used to improve performance, but they sacrifice the model interpretability. To obtain both good scalability and interpretability, we propose a new classifier, named Rule-based Representation Learner (RRL), that automatically learns interpretable non-fuzzy rules for data representation and classification. To train the non-differentiable RRL effectively, we project it to a continuous space and propose a novel training method, called Gradient Grafting, that can directly optimize the discrete model using gradient descent. An improved design of logical activation functions is also devised to increase the scalability of RRL and enable it to discretize the continuous features end-to-end. Exhaustive experiments on nine small and four large data sets show that RRL outperforms the competitive interpretable approaches and can be easily adjusted to obtain a trade-off between classification accuracy and model complexity for different scenarios. Our code is available at: https://github.com/12wang3/rrl.

Several queries and scores have recently been proposed to explain individual predictions over ML models. Examples include queries based on "anchors", which are parts of an instance that are sufficient to justify its classification, and "feature-perturbation" scores such as SHAP. Given the need for flexible, reliable, and easy-to-apply interpretability methods for ML models, we foresee the need for developing declarative languages to naturally specify different explainability queries. We do this in a principled way by rooting such a language in a logic called FOIL, which allows for expressing many simple but important explainability queries, and might serve as a core for more expressive interpretability languages. We study the computational complexity of FOIL queries over two classes of ML models often deemed to be easily interpretable: decision trees and more general decision diagrams. Since the number of possible inputs for an ML model is exponential in its dimension, tractability of the FOIL evaluation problem is delicate but can be achieved by either restricting the structure of the models, or the fragment of FOIL being evaluated. We also present a prototype implementation of FOIL wrapped in a high-level declarative language and perform experiments showing that such a language can be used in practice.

-- Cardiovascular diseases (CVDs) are a main cause of mortality globally, accounting for 31% of all deaths. This study involves a cardiovascular disease (CVD) dataset comprising 68,119 records to explore the influence of numerical (age, height, weight, blood pressure, BMI) and categorical gender, cholesterol, glucose, smoking, alcohol, activity) factors on CVD occurrence. We have performed statistical analyses, including t - tests, Chi - square tests, and ANOVA, to identify strong associations between CVD and elde rly people, hypertension, higher weight, and abnormal cholesterol levels, while physical activity (a protective factor). A logistic regression model highlights age, blood pressure, and cholesterol as primary risk factors, with unexpected negative associati ons for smoking and alcohol, suggesting potential data issues. Model performance comparisons reveal CatBoost as the top performer with an accuracy of 0.734 and an ECE of 0.0064 and excels in probabilistic prediction (Brier score = 0.1824). Data challenges, including outliers and skewed distributions, indicate a need for improved preprocessing to enhance predictive reliability. Cardiovascular diseases (CVDs) encompass a range of conditions affecting the heart and blood vessels, including coronary heart disease, stroke, and heart failure.

In laparoscopy surgical training and evaluation, real-time detection of surgical actions with interpretable outputs is crucial for automated and real-time instructional feedback and skill development. Such capability would enable development of machine guided training systems. This paper presents a rapid deployment approach utilizing automated machine learning methods, based on surgical action data collected from both experienced and trainee surgeons. The proposed approach effectively tackles the challenge of highly imbalanced class distributions, ensuring robust predictions across varying skill levels of surgeons. Additionally, our method partially incorporates model transparency, addressing the reliability requirements in medical applications. Compared to deep learning approaches, traditional machine learning models not only facilitate efficient rapid deployment but also offer significant advantages in interpretability. Through experiments, this study demonstrates the potential of this approach to provide quick, reliable and effective real-time detection in surgical training environments

Superposition refers to encoding representations of multiple features within a single neuron, which is common in deep neural networks. This property allows neurons to combine and represent multiple features, enabling the model to capture intricate information and handle complex tasks. Despite promising performance, the model's interpretability has been diminished. This paper presents a novel approach to enhance model interpretability by regularizing feature superposition. We introduce SAFR, which simply applies regularizations to the loss function to promote monosemantic representations for important tokens while encouraging polysemanticity for correlated token pairs, where important tokens and correlated token pairs are identified via VMASK and attention weights respectively. We evaluate SAFR with a transformer model on two classification tasks. Experiments demonstrate the effectiveness of SAFR in improving model interpretability without compromising prediction performance. Besides, SAFR provides explanations by visualizing the neuron allocation within the intermediate layers.

This paper proposes a formal framework based on symbolic compression, integrating combinatory logic, information-theoretic optimal encoding, and context-aware inference techniques to achieve a step-change improvement in token efficiency while preserving semantic integrity. We establish a mathematical framework within a functional programming paradigm, derive the quantitative relationship between symbolic density and model interpretability, and propose a differentiable compression factor metric to evaluate encoding efficiency. Furthermore, we leverage parameter-efficient fine-tuning (PEFT) techniques to achieve a low-cost application of the GAEL language. Experimental results show that this method achieves a 78.3% token compression rate in code generation tasks while improving logical traceability by 62% through structural explicitness. This research provides new theoretical tools for efficient inference in LLMs and opens a symbolic path for model interpretability research.

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on large data sets, due to their discrete parameters and structures. Ensemble methods and fuzzy/soft rules are commonly used to improve performance, but they sacrifice the model interpretability. To obtain both good scalability and interpretability, we propose a new classifier, named Rule-based Representation Learner (RRL), that automatically learns interpretable non-fuzzy rules for data representation and classification. To train the non-differentiable RRL effectively, we project it to a continuous space and propose a novel training method, called Gradient Grafting, that can directly optimize the discrete model using gradient descent.

Deformable shapes provide important and complex geometric features of objects presented in images. However, such information is oftentimes missing or underutilized as implicit knowledge in many image analysis tasks. This paper presents Geo-SIC, the first deep learning model to learn deformable shapes in a deformation space for an improved performance of image classification. We introduce a newly designed framework that (i) simultaneously derives features from both image and latent shape spaces with large intra-class variations; and (ii) gains increased model interpretability by allowing direct access to the underlying geometric features of image data. In particular, we develop a boosted classification network, equipped with an unsupervised learning of geometric shape representations characterized by diffeomorphic transformations within each class.