Integrated Information Theory (IIT) provides a quantitative framework for explaining consciousness phenomenon, positing that conscious systems comprise elements integrated through causal properties. We apply IIT 3.0 and 4.0 -- the latest iterations of this framework -- to sequences of Large Language Model (LLM) representations, analyzing data derived from existing Theory of Mind (ToM) test results. Our study systematically investigates whether the differences of ToM test performances, when presented in the LLM representations, can be revealed by IIT estimates, i.e., $\Phi^{\max}$ (IIT 3.0), $\Phi$ (IIT 4.0), Conceptual Information (IIT 3.0), and $\Phi$-structure (IIT 4.0). Furthermore, we compare these metrics with the Span Representations independent of any estimate for consciousness. This additional effort aims to differentiate between potential "consciousness" phenomena and inherent separations within LLM representational space. We conduct comprehensive experiments examining variations across LLM transformer layers and linguistic spans from stimuli. Our results suggest that sequences of contemporary Transformer-based LLM representations lack statistically significant indicators of observed "consciousness" phenomena but exhibit intriguing patterns under $\textit{spatio}$-permutational analyses. The Appendix and code are available as Supplementary Materials at: https://doi.org/10.1016/j.nlp.2025.100163.
Interpretable machine learning is rapidly becoming a crucial tool for scientific discovery. Among existing approaches, variational autoencoders (VAEs) have shown promise in extracting the hidden physical features of some input data, with no supervision nor prior knowledge of the system at study. Yet, the ability of VAEs to create meaningful, interpretable representations relies on their accurate approximation of the underlying probability distribution of their input. When dealing with quantum data, VAEs must hence account for its intrinsic randomness and complex correlations. While VAEs have been previously applied to quantum data, they have often neglected its probabilistic nature, hindering the extraction of meaningful physical descriptors. Here, we demonstrate that two key modifications enable VAEs to learn physically meaningful latent representations: a decoder capable of faithfully reproduce quantum states and a probabilistic loss tailored to this task. Using benchmark quantum spin models, we identify regimes where standard methods fail while the representations learned by our approach remain meaningful and interpretable. Applied to experimental data from Rydberg atom arrays, the model autonomously uncovers the phase structure without access to prior labels, Hamiltonian details, or knowledge of relevant order parameters, highlighting its potential as an unsupervised and interpretable tool for the study of quantum systems.
While analyzing the importance of features has become ubiquitous in interpretable machine learning, the joint signal from a group of related features is sometimes overlooked or inadvertently excluded. Neglecting the joint signal could bypass a critical insight: in many instances, the most significant predictors are not isolated features, but rather the combined effect of groups of features. This can be especially problematic for datasets that contain natural groupings of features, including multimodal datasets. This paper introduces a novel approach to determine the importance of a group of features for Generalized Additive Models (GAMs) that is efficient, requires no model retraining, allows defining groups posthoc, permits overlapping groups, and remains meaningful in high-dimensional settings. Moreover, this definition offers a parallel with explained variation in statistics. We showcase properties of our method on three synthetic experiments that illustrate the behavior of group importance across various data regimes. We then demonstrate the importance of groups of features in identifying depressive symptoms from a multimodal neuroscience dataset, and study the importance of social determinants of health after total hip arthroplasty. These two case studies reveal that analyzing group importance offers a more accurate, holistic view of the medical issues compared to a single-feature analysis.
Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be represented by many different decision trees. The presence of models with identical decision boundaries but different evaluation processes makes model selection challenging. The models will have different variable importance and behave differently in the presence of missing values, but most optimization procedures will arbitrarily choose one such model to return. We present a boolean logical representation of decision trees that does not exhibit predictive equivalence and is faithful to the underlying decision boundary. We apply our representation to several downstream machine learning tasks. Using our representation, we show that decision trees are surprisingly robust to test-time missingness of feature values; we address predictive equivalence's impact on quantifying variable importance; and we present an algorithm to optimize the cost of reaching predictions.
Medical imaging plays a crucial role in assessing knee osteoarthritis (OA) risk by enabling early detection and disease monitoring. Recent machine learning methods have improved risk estimation (i.e., predicting the likelihood of disease progression) and predictive modelling (i.e., the forecasting of future outcomes based on current data) using medical images, but clinical adoption remains limited due to their lack of interpretability. Existing approaches that generate future images for risk estimation are complex and impractical. Additionally, previous methods fail to localize anatomical knee landmarks, limiting interpretability. We address these gaps with a new interpretable machine learning method to estimate the risk of knee OA progression via multi-task predictive modelling that classifies future knee OA severity and predicts anatomical knee landmarks from efficiently generated high-quality future images. Such image generation is achieved by leveraging a diffusion model in a class-conditioned latent space to forecast disease progression, offering a visual representation of how particular health conditions may evolve. Applied to the Osteoarthritis Initiative dataset, our approach improves the state-of-the-art (SOTA) by 2\%, achieving an AUC of 0.71 in predicting knee OA progression while offering ~9% faster inference time.
In scientific machine learning (SciML), a key challenge is learning unknown, evolving physical processes and making predictions across spatio-temporal scales. For example, in real-world manufacturing problems like additive manufacturing, users adjust known machine settings while unknown environmental parameters simultaneously fluctuate. To make reliable predictions, it is desired for a model to not only capture long-range spatio-temporal interactions from data but also adapt to new and unknown environments; traditional machine learning models excel at the first task but often lack physical interpretability and struggle to generalize under varying environmental conditions. To tackle these challenges, we propose the Attention-based Spatio-Temporal Neural Operator (ASNO), a novel architecture that combines separable attention mechanisms for spatial and temporal interactions and adapts to unseen physical parameters. Inspired by the backward differentiation formula (BDF), ASNO learns a transformer for temporal prediction and extrapolation and an attention-based neural operator for handling varying external loads, enhancing interpretability by isolating historical state contributions and external forces, enabling the discovery of underlying physical laws and generalizability to unseen physical environments. Empirical results on SciML benchmarks demonstrate that ASNO outperforms over existing models, establishing its potential for engineering applications, physics discovery, and interpretable machine learning.
Financial literacy is increasingly dependent on the ability to interpret complex financial data and utilize advanced forecasting tools. In this context, this study proposes a novel approach that combines transformer-based time series models with explainable artificial intelligence (XAI) to enhance the interpretability and accuracy of stock price predictions. The analysis focuses on the daily stock prices of the five highest-volume banks listed in the BIST100 index, along with XBANK and XU100 indices, covering the period from January 2015 to March 2025. Models including DLinear, LTSNet, Vanilla Transformer, and Time Series Transformer are employed, with input features enriched by technical indicators. SHAP and LIME techniques are used to provide transparency into the influence of individual features on model outputs. The results demonstrate the strong predictive capabilities of transformer models and highlight the potential of interpretable machine learning to empower individuals in making informed investment decisions and actively engaging in financial markets.
Postoperative stroke remains a critical complication in elderly surgical intensive care unit (SICU) patients, contributing to prolonged hospitalization, elevated healthcare costs, and increased mortality. Accurate early risk stratification is essential to enable timely intervention and improve clinical outcomes. We constructed a combined cohort of 19,085 elderly SICU admissions from the MIMIC-III and MIMIC-IV databases and developed an interpretable machine learning (ML) framework to predict in-hospital stroke using clinical data from the first 24 hours of Intensive Care Unit (ICU) stay. The preprocessing pipeline included removal of high-missingness features, iterative Singular Value Decomposition (SVD) imputation, z-score normalization, one-hot encoding, and class imbalance correction via the Adaptive Synthetic Sampling (ADASYN) algorithm. A two-stage feature selection process-combining Recursive Feature Elimination with Cross-Validation (RFECV) and SHapley Additive exPlanations (SHAP)-reduced the initial 80 variables to 20 clinically informative predictors. Among eight ML models evaluated, CatBoost achieved the best performance with an AUROC of 0.8868 (95% CI: 0.8802--0.8937). SHAP analysis and ablation studies identified prior cerebrovascular disease, serum creatinine, and systolic blood pressure as the most influential risk factors. Our results highlight the potential of interpretable ML approaches to support early detection of postoperative stroke and inform decision-making in perioperative critical care.
This paper evaluates the performance of prominent machine learning (ML) algorithms in predicting Indonesia's inflation using the payment system, capital market, and macroeconomic data. We compare the forecasting performance of each ML model, namely shrinkage regression, ensemble learning, and super vector regression, to that of the univariate time series ARIMA and SARIMA models. We examine various out-of-bag sample periods in each ML model to determine the appropriate data-splitting ratios for the regression case study. This study indicates that all ML models produced lower RMSEs and reduced average forecast errors by 45.16 percent relative to the ARIMA benchmark, with the Extreme Gradient Boosting model outperforming other ML models and the benchmark. Using the Shapley value, we discovered that numerous payment system variables significantly predict inflation. We explore the ML forecast using local Shapley decomposition and show the relationship between the explanatory variables and inflation for interpretation. The interpretation of the ML forecast highlights some significant findings and offers insightful recommendations, enhancing previous economic research that uses a more established econometric method. Our findings advocate ML models as supplementary tools for the central bank to predict inflation and support monetary policy.
The use of appropriate methods of Interpretable Machine Learning (IML) and eXplainable Artificial Intelligence (XAI) is essential for adopting black-box predictive models in fields where model and prediction explainability is required. As a novel tool for interpreting black-box models, we introduce the R package midr, which implements Maximum Interpretation Decomposition (MID). MID is a functional decomposition approach that derives a low-order additive representation of a black-box model by minimizing the squared error between the model's prediction function and this additive representation. midr enables learning from black-box models by constructing a global surrogate model with advanced analytical capabilities. After reviewing related work and the theoretical foundation of MID, we demonstrate the package's usage and discuss some of its key features.
Evolving Fuzzy Systems (eFS) have gained significant attention due to their ability to adaptively update their structure in response to data dynamics while maintaining interpretability. However, the lack of publicly available implementations of these models limits their accessibility and widespread adoption. To address this gap, we present evolvingfuzzysystems, a Python library that provides implementations of several well-established eFS models, including ePL-KRLS-DISCO, ePL+, eMG, ePL, exTS, Simpl\_eTS, and eTS. The library facilitates model evaluation and comparison by offering built-in tools for training, visualization, and performance assessment. The models are evaluated using the fetch\_california\_housing dataset, with performance measured in terms of normalized root-mean-square error (NRMSE), non-dimensional error index (NDEI), and mean absolute percentage error (MAPE). Additionally, computational complexity is analyzed by measuring execution times and rule evolution during training and testing phases. The results highlight ePL as a simple yet efficient model that balances accuracy and computational cost, making it particularly suitable for real-world applications. By making these models publicly available, evolvingfuzzysystems aims to foster research and practical applications in adaptive and interpretable machine learning.
Association Rule Mining (ARM) is the task of mining patterns among data features in the form of logical rules, with applications across a myriad of domains. However, high-dimensional datasets often result in an excessive number of rules, increasing execution time and negatively impacting downstream task performance. Managing this rule explosion remains a central challenge in ARM research. To address this, we introduce Aerial+, a novel neurosymbolic ARM method. Aerial+ leverages an under-complete autoencoder to create a neural representation of the data, capturing associations between features. It extracts rules from this neural representation by exploiting the model's reconstruction mechanism. Extensive evaluations on five datasets against seven baselines demonstrate that Aerial+ achieves state-of-the-art results by learning more concise, high-quality rule sets with full data coverage. When integrated into rule-based interpretable machine learning models, Aerial+ significantly reduces execution time while maintaining or improving accuracy.
The transition from traditional power grids to smart grids, significant increase in the use of renewable energy sources, and soaring electricity prices has triggered a digital transformation of the energy infrastructure that enables new, data driven, applications often supported by machine learning models. However, the majority of the developed machine learning models rely on univariate data. To date, a structured study considering the role meta-data and additional measurements resulting in multivariate data is missing. In this paper we propose a taxonomy that identifies and structures various types of data related to energy applications. The taxonomy can be used to guide application specific data model development for training machine learning models. Focusing on a household electricity forecasting application, we validate the effectiveness of the proposed taxonomy in guiding the selection of the features for various types of models. As such, we study of the effect of domain, contextual and behavioral features on the forecasting accuracy of four interpretable machine learning techniques and three openly available datasets. Finally, using a feature importance techniques, we explain individual feature contributions to the forecasting accuracy.
Traumatic Brain Injury (TBI) is a major contributor to mortality among older adults, with geriatric patients facing disproportionately high risk due to age-related physiological vulnerability and comorbidities. Early and accurate prediction of mortality is essential for guiding clinical decision-making and optimizing ICU resource allocation. In this study, we utilized the MIMIC-III database to identify geriatric TBI patients and applied a machine learning framework to develop a 30-day mortality prediction model. A rigorous preprocessing pipeline-including Random Forest-based imputation, feature engineering, and hybrid selection-was implemented to refine predictors from 69 to 9 clinically meaningful variables. CatBoost emerged as the top-performing model, achieving an AUROC of 0.867 (95% CI: 0.809-0.922), surpassing traditional scoring systems. SHAP analysis confirmed the importance of GCS score, oxygen saturation, and prothrombin time as dominant predictors. These findings highlight the value of interpretable machine learning tools for early mortality risk stratification in elderly TBI patients and provide a foundation for future clinical integration to support high-stakes decision-making in critical care.
Brain stroke remains one of the principal causes of death and disability worldwide, yet most tabular-data prediction models still hover below the 95% accuracy threshold, limiting real-world utility. Addressing this gap, the present work develops and validates a completely data-driven and interpretable machine-learning framework designed to predict strokes using ten routinely gathered demographic, lifestyle, and clinical variables sourced from a public cohort of 4,981 records. We employ a detailed exploratory data analysis (EDA) to understand the dataset's structure and distribution, followed by rigorous data preprocessing, including handling missing values, outlier removal, and class imbalance correction using Synthetic Minority Over-sampling Technique (SMOTE). To streamline feature selection, point-biserial correlation and random-forest Gini importance were utilized, and ten varied algorithms-encompassing tree ensembles, boosting, kernel methods, and a multilayer neural network-were optimized using stratified five-fold cross-validation. Their predictions based on probabilities helped us build the proposed model, which included Random Forest, XGBoost, LightGBM, and a support-vector classifier, with logistic regression acting as a meta-learner. The proposed model achieved an accuracy rate of 97.2% and an F1-score of 97.15%, indicating a significant enhancement compared to the leading individual model, LightGBM, which had an accuracy of 91.4%. Our study's findings indicate that rigorous preprocessing, coupled with a diverse hybrid model, can convert low-cost tabular data into a nearly clinical-grade stroke-risk assessment tool.
This study introduces an interpretable machine learning (ML) framework to extract macroeconomic alpha from global news sentiment. We process the Global Database of Events, Language, and Tone (GDELT) Project's worldwide news feed using FinBERT -- a Bidirectional Encoder Representations from Transformers (BERT) based model pretrained on finance-specific language -- to construct daily sentiment indices incorporating mean tone, dispersion, and event impact. These indices drive an XGBoost classifier, benchmarked against logistic regression, to predict next-day returns for EUR/USD, USD/JPY, and 10-year U.S. Treasury futures (ZN). Rigorous out-of-sample (OOS) backtesting (5-fold expanding-window cross-validation, OOS period: c. 2017-April 2025) demonstrates exceptional, cost-adjusted performance for the XGBoost strategy: Sharpe ratios achieve 5.87 (EUR/USD), 4.65 (USD/JPY), and 4.65 (Treasuries), with respective compound annual growth rates (CAGRs) exceeding 50% in Foreign Exchange (FX) and 22% in bonds. Shapley Additive Explanations (SHAP) affirm that sentiment dispersion and article impact are key predictive features. Our findings establish that integrating domain-specific Natural Language Processing (NLP) with interpretable ML offers a potent and explainable source of macro alpha.
As machine learning systems are increasingly used in high-stakes domains, there is a growing emphasis placed on making them interpretable to improve trust in these systems. In response, a range of interpretable machine learning (IML) methods have been developed to generate human-understandable insights into otherwise black box models. With these methods, a fundamental question arises: Are these interpretations reliable? Unlike with prediction accuracy or other evaluation metrics for supervised models, the proximity to the true interpretation is difficult to define. Instead, we ask a closely related question that we argue is a prerequisite for reliability: Are these interpretations stable? We define stability as findings that are consistent or reliable under small random perturbations to the data or algorithms. In this study, we conduct the first systematic, large-scale empirical stability study on popular machine learning global interpretations for both supervised and unsupervised tasks on tabular data. Our findings reveal that popular interpretation methods are frequently unstable, notably less stable than the predictions themselves, and that there is no association between the accuracy of machine learning predictions and the stability of their associated interpretations. Moreover, we show that no single method consistently provides the most stable interpretations across a range of benchmark datasets. Overall, these results suggest that interpretability alone does not warrant trust, and underscores the need for rigorous evaluation of interpretation stability in future work. To support these principles, we have developed and released an open source IML dashboard and Python package to enable researchers to assess the stability and reliability of their own data-driven interpretations and discoveries.
Though neural networks trained on large datasets have been successfully used to describe and predict many physical phenomena, there is a sense among scientists that, unlike traditional scientific models comprising simple mathematical expressions, their findings cannot be integrated into the body of scientific knowledge. Critics of machine learning's inability to produce human-understandable relationships have converged on the concept of "interpretability" as its point of departure from more traditional forms of science. As the growing interest in interpretability has shown, researchers in the physical sciences seek not just predictive models, but also to uncover the fundamental principles that govern a system of interest. However, clarity around a definition of interpretability and the precise role that it plays in science is lacking in the literature. In this work, we argue that researchers in equation discovery and symbolic regression tend to conflate the concept of sparsity with interpretability. We review key papers on interpretable machine learning from outside the scientific community and argue that, though the definitions and methods they propose can inform questions of interpretability for scientific machine learning (SciML), they are inadequate for this new purpose. Noting these deficiencies, we propose an operational definition of interpretability for the physical sciences. Our notion of interpretability emphasizes understanding of the mechanism over mathematical sparsity. Innocuous though it may seem, this emphasis on mechanism shows that sparsity is often unnecessary. It also questions the possibility of interpretable scientific discovery when prior knowledge is lacking. We believe a precise and philosophically informed definition of interpretability in SciML will help focus research efforts toward the most significant obstacles to realizing a data-driven scientific future.
Photonic chip design has seen significant advancements with the adoption of inverse design methodologies, offering flexibility and efficiency in optimizing device performance. However, the black-box nature of the optimization approaches, such as those used in inverse design in order to minimize a loss function or maximize coupling efficiency, poses challenges in understanding the outputs. This challenge is prevalent in machine learning-based optimization methods, which can suffer from the same lack of transparency. To this end, interpretability techniques address the opacity of optimization models. In this work, we apply interpretability techniques from machine learning, with the aim of gaining understanding of inverse design optimization used in designing photonic components, specifically two-mode multiplexers. We base our methodology on the widespread interpretability technique known as local interpretable model-agnostic explanations, or LIME. As a result, LIME-informed insights point us to more effective initial conditions, directly improving device performance. This demonstrates that interpretability methods can do more than explain models -- they can actively guide and enhance the inverse-designed photonic components. Our results demonstrate the ability of interpretable techniques to reveal underlying patterns in the inverse design process, leading to the development of better-performing components.
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data through learning Riemannian geometry algorithms can achieve improved performance and interpretability in tasks like clustering, dimensionality reduction, and interpolation. In particular, learned pullback geometry has recently undergone transformative developments that now make it scalable to learn and scalable to evaluate, which further opens the door for principled non-linear data analysis and interpretable machine learning. However, there are still steps to be taken when considering real-world multi-modal data. This work focuses on addressing distortions and modeling errors that can arise in the multi-modal setting and proposes to alleviate both challenges through isometrizing the learned Riemannian structure and balancing regularity and expressivity of the diffeomorphism parametrization. We showcase the effectiveness of the synergy of the proposed approaches in several numerical experiments with both synthetic and real data.