Interpretable ML

The ability to interpret machine learning model decisions is critical in such domains as healthcare, where trust in model predictions is as important as their accuracy. Inspired by the development of prototype parts-based deep neural networks in computer vision, we propose a new model for tabular data, specifically tailored to medical records, that requires discretization of diagnostic result norms. Unlike the original vision models that rely on the spatial structure, our method employs trainable patching over features describing a patient, to learn meaningful prototypical parts from structured data. These parts are represented as binary or discretized feature subsets. This allows the model to express prototypes in human-readable terms, enabling alignment with clinical language and case-based reasoning. Our proposed neural network is inherently interpretable and offers interpretable concept-based predictions by comparing the patient's description to learned prototypes in the latent space of the network. In experiments, we demonstrate that the model achieves classification performance competitive to widely used baseline models on medical benchmark datasets, while also offering transparency, bridging the gap between predictive performance and interpretability in clinical decision support.

Structural heart disease (SHD) is a prevalent condition with many undiagnosed cases, and early detection is often limited by the high cost and accessibility constraints of echocardiography (ECHO). Recent studies show that artificial intelligence (AI)-based analysis of electrocardiograms (ECGs) can detect SHD, offering a scalable alternative. However, existing methods are fully black-box models, limiting interpretability and clinical adoption. To address these challenges, we propose an interpretable and effective framework that integrates clinically meaningful ECG foundation-model predictors within a generalized additive model, enabling transparent risk attribution while maintaining strong predictive performance. Using the EchoNext benchmark of over 80,000 ECG-ECHO pairs, the method demonstrates relative improvements of +0.98% in AUROC, +1.01% in AUPRC, and +1.41% in F1 score over the latest state-of-the-art deep-learning baseline, while achieving slightly better performance even with only 30% of the training data. Subgroup analyses confirm robust performance across heterogeneous populations, and the estimated entry-wise functions provide interpretable insights into the relationships between risks of traditional ECG diagnoses and SHD. This work illustrates a complementary paradigm between classical statistical modeling and modern AI, offering a pathway to interpretable, high-performing, and clinically actionable ECG-based SHD screening.

Machine learning models support decision-making, yet the reasons behind their predictions are opaque. Clear and reliable explanations help users make informed decisions and avoid blindly trusting model outputs. However, many existing explanation methods fail to guarantee correctness. Logic-based approaches ensure correctness but often offer overly constrained explanations, limiting coverage. Recent work addresses this by incrementally expanding explanations while maintaining correctness. This process is performed separately for each feature, adjusting both its upper and lower bounds. However, this approach faces a trade-off: smaller increments incur high computational costs, whereas larger ones may lead to explanations covering fewer instances. To overcome this, we propose two novel methods. Onestep builds upon this prior work, generating explanations in a single step for each feature and each bound, eliminating the overhead of an iterative process. Twostep takes a gradual approach, improving coverage. Experimental results show that Twostep significantly increases explanation coverage (by up to 72.60% on average across datasets) compared to Onestep and, consequently, to prior work.

Machine learning accelerates molecular property prediction, yet state-of-the-art Large Language Models and Graph Neural Networks operate as black boxes. In drug discovery, where safety is critical, this opacity risks masking false correlations and excluding human expertise. Existing interpretability methods suffer from the effectiveness-trustworthiness trade-off: explanations may fail to reflect a model's true reasoning, degrade performance, or lack domain grounding. Concept Bottleneck Models (CBMs) offer a solution by projecting inputs to human-interpretable concepts before readout, ensuring that explanations are inherently faithful to the decision process. However, adapting CBMs to chemistry faces three challenges: the Relevance Gap (selecting task-relevant concepts from a large descriptor space), the Annotation Gap (obtaining concept supervision for molecular data), and the Capacity Gap (degrading performance due to bottleneck constraints). We introduce GlassMol, a model-agnostic CBM that addresses these gaps through automated concept curation and LLM-guided concept selection. Experiments across thirteen benchmarks demonstrate that \method generally matches or exceeds black-box baselines, suggesting that interpretability does not sacrifice performance and challenging the commonly assumed trade-off. Code is available at https://github.com/walleio/GlassMol.

Modern deep neural networks remain challenging to interpret due to the opacity of their latent representations, impeding model understanding, debugging, and debiasing. Concept Embedding Models (CEMs) address this by mapping inputs to human-interpretable concept representations from which tasks can be predicted. Yet, CEMs fail to represent inter-concept relationships and require concept annotations at different granularities during training, limiting their applicability. In this paper, we introduce Hierarchical Concept Embedding Models (HiCEMs), a new family of CEMs that explicitly model concept relationships through hierarchical structures. To enable HiCEMs in real-world settings, we propose Concept Splitting, a method for automatically discovering finer-grained sub-concepts from a pretrained CEM's embedding space without requiring additional annotations. This allows HiCEMs to generate fine-grained explanations from limited concept labels, reducing annotation burdens. Our evaluation across multiple datasets, including a user study and experiments on PseudoKitchens, a newly proposed concept-based dataset of 3D kitchen renders, demonstrates that (1) Concept Splitting discovers human-interpretable sub-concepts absent during training that can be used to train highly accurate HiCEMs, and (2) HiCEMs enable powerful test-time concept interventions at different granularities, leading to improved task accuracy.

Explaining opaque Machine Learning (ML) models has become an increasingly important challenge. However, current eXplanation in AI (XAI) methods suffer several shortcomings, including insufficient abstraction, limited user interactivity, and inadequate integration of symbolic knowledge. We propose ReasonX, an explanation tool based on expressions (or, queries) in a closed algebra of operators over theories of linear constraints. ReasonX provides declarative and interactive explanations for decision trees, which may represent the ML models under analysis or serve as global or local surrogate models for tabular-data black-box classifiers. Users can express background or common sense knowledge as linear constraints. This allows for reasoning at multiple levels of abstraction, ranging from fully specified examples to under-specified or partially constrained ones. ReasonX leverages Mixed-Integer Linear Programming (MILP) to reason over the features of factual and contrastive instances. We present here the architecture of ReasonX, which consists of a Python layer, closer to the user, and a Constraint Logic Programming (CLP) layer, which implements a meta-interpreter of the query algebra. The capabilities of ReasonX are demonstrated through qualitative examples, and compared to other XAI tools through quantitative experiments.

Can Machine Learning (ML) autonomously recover interpretable mathematical structure from raw numerical data? We aim to answer this question using the classification of real-root configurations of polynomials up to degree five as a structured benchmark. We tested an extensive set of ML models, including decision trees, logistic regression, support vector machines, random forest, gradient boosting, XGBoost, symbolic regression, and neural networks. Neural networks achieved strong in-distribution performance on quintic classification using raw coefficients alone (84.3% + or - 0.9% balanced accuracy), whereas decision trees perform substantially worse (59.9% + or - 0.9%). However, when provided with an explicit feature capturing sign changes at critical points, decision trees match neural performance (84.2% + or - 1.2%) and yield explicit classification rules. Knowledge distillation reveals that this single invariant accounts for 97.5% of the extracted decision structure. Out-of-distribution, data-efficiency, and noise robustness analyses indicate that neural networks learn continuous, data-dependent geometric approximations of the decision boundary rather than recovering scale-invariant symbolic rules. This distinction between geometric approximation and symbolic invariance explains the gap between predictive performance and interpretability observed across models. Although high predictive accuracy is attainable, we find no evidence that the evaluated ML models autonomously recover discrete, human-interpretable mathematical rules from raw coefficients. These results suggest that, in structured mathematical domains, interpretability may require explicit structural inductive bias rather than purely data-driven approximation.

Psychiatric questionnaires are highly context sensitive and often only weakly predict subsequent symptom severity, which makes the prognostic relationship difficult to learn. Although flexible nonlinear models can improve predictive accuracy, their limited interpretability can erode clinical trust. In fields such as imaging and omics, investigators commonly address visit- and instrument-specific artifacts by extracting stable signal through preprocessing and then fitting an interpretable linear model. We adopt the same strategy for questionnaire data by decoupling preprocessing from prediction: REFINE (Redundancy-Exploiting Follow-up-Informed Nonlinear Enhancement) uses follow-up information to learn a nonlinear, item-aligned preprocessing of baseline measurements, and then maps these stabilized baseline items to future severity through a linear coefficient matrix. This construction constrains where nonlinearity enters rather than restricting the end-to-end predictive function class, allowing the prognostic relationship to remain globally interpretable through a single coefficient matrix rather than through post hoc local attributions. In the population, the resulting predictor recovers the Bayes-optimal conditional mean, so global linear interpretability does not require sacrificing nonlinear predictive flexibility. In experiments, REFINE outperforms other interpretable approaches while preserving clear global attribution of prognostic factors across psychiatric and non-psychiatric longitudinal prediction tasks.

Recent deep learning methods for fMRI-based diagnosis have achieved promising accuracy by modeling functional connectivity networks. However, standard approaches often struggle with noisy interactions, and conventional post-hoc attribution methods may lack reliability, potentially highlighting dataset-specific artifacts. To address these challenges, we introduce PIME, an interpretable framework that bridges intrinsic interpretability with minimal-sufficient subgraph optimization by integrating prototype-based classification and consistency training with structural perturbations during learning. This encourages a structured latent space and enables Monte Carlo Tree Search (MCTS) under a prototype-consistent objective to extract compact minimal-sufficient explanatory subgraphs post-training. Experiments on three benchmark fMRI datasets demonstrate that PIME achieves state-of-the-art performance. Furthermore, by constraining the search space via learned prototypes, PIME identifies critical brain regions that are consistent with established neuroimaging findings. Stability analysis shows 90% reproducibility and consistent explanations across atlases.

Inspired by behavioral science, we propose Behavior Learning (BL), a novel general-purpose machine learning framework that learns interpretable and identifiable optimization structures from data, ranging from single optimization problems to hierarchical compositions. It unifies predictive performance, intrinsic interpretability, and identifiability, with broad applicability to scientific domains involving optimization. BL parameterizes a compositional utility function built from intrinsically interpretable modular blocks, which induces a data distribution for prediction and generation. Each block represents and can be written in symbolic form as a utility maximization problem (UMP), a foundational paradigm in behavioral science and a universal framework of optimization. BL supports architectures ranging from a single UMP to hierarchical compositions, the latter modeling hierarchical optimization structures. Its smooth and monotone variant (IBL) guarantees identifiability. Theoretically, we establish the universal approximation property of BL, and analyze the M-estimation properties of IBL. Empirically, BL demonstrates strong predictive performance, intrinsic interpretability and scalability to high-dimensional data. Code: https://github.com/MoonYLiang/Behavior-Learning ; install via pip install blnetwork.

Despite significant progress in post-hoc explanation methods for neural networks, many remain heuristic and lack provable guarantees. A key approach for obtaining explanations with provable guarantees is by identifying a cardinally-minimal subset of input features which by itself is provably sufficient to determine the prediction. However, for standard neural networks, this task is often computationally infeasible, as it demands a worst-case exponential number of verification queries in the number of input features, each of which is NP-hard. In this work, we show that for Neural Additive Models (NAMs), a recent and more interpretable neural network family, we can efficiently generate explanations with such guarantees. We present a new model-specific algorithm for NAMs that generates provably cardinally-minimal explanations using only a logarithmic number of verification queries in the number of input features, after a parallelized preprocessing step with logarithmic runtime in the required precision is applied to each small univariate NAM component. Our algorithm not only makes the task of obtaining cardinally-minimal explanations feasible, but even outperforms existing algorithms designed to find the relaxed variant of subset-minimal explanations - which may be larger and less informative but easier to compute - despite our algorithm solving a much more difficult task. Our experiments demonstrate that, compared to previous algorithms, our approach provides provably smaller explanations than existing works and substantially reduces the computation time. Moreover, we show that our generated provable explanations offer benefits that are unattainable by standard sampling-based techniques typically used to interpret NAMs.

Machine learning models are increasingly applied to biomedical data, yet their adoption in high stakes domains remains limited by poor robustness, limited interpretability, and instability of learned features under realistic data perturbations, such as missingness. In particular, models that achieve high predictive performance may still fail to inspire trust if their key features fluctuate when data completeness changes, undermining reproducibility and downstream decision-making. Here, we present CACTUS (Comprehensive Abstraction and Classification Tool for Uncovering Structures), an explainable machine learning framework explicitly designed to address these challenges in small, heterogeneous, and incomplete clinical datasets. CACTUS integrates feature abstraction, interpretable classification, and systematic feature stability analysis to quantify how consistently informative features are preserved as data quality degrades. Using a real-world haematuria cohort comprising 568 patients evaluated for bladder cancer, we benchmark CACTUS against widely used machine learning approaches, including random forests and gradient boosting methods, under controlled levels of randomly introduced missing data. We demonstrate that CACTUS achieves competitive or superior predictive performance while maintaining markedly higher stability of top-ranked features as missingness increases, including in sex-stratified analyses. Our results show that feature stability provides information complementary to conventional performance metrics and is essential for assessing the trustworthiness of machine learning models applied to biomedical data. By explicitly quantifying robustness to missing data and prioritising interpretable, stable features, CACTUS offers a generalizable framework for trustworthy data-driven decision support.

Generalized additive models (GAMs) offer interpretability through independent univariate feature effects but underfit when interactions are present in data. GA$^2$Ms add selected pairwise interactions which improves accuracy, but sacrifices interpretability and limits model auditing. We propose Conditionally Additive Local Models (CALMs), a new model class, that balances the interpretability of GAMs with the accuracy of GA$^2$Ms. CALMs allow multiple univariate shape functions per feature, each active in different regions of the input space. These regions are defined independently for each feature as simple logical conditions (thresholds) on the features it interacts with. As a result, effects remain locally additive while varying across subregions to capture interactions. We further propose a principled distillation-based training pipeline that identifies homogeneous regions with limited interactions and fits interpretable shape functions via region-aware backfitting. Experiments on diverse classification and regression tasks show that CALMs consistently outperform GAMs and achieve accuracy comparable with GA$^2$Ms. Overall, CALMs offer a compelling trade-off between predictive accuracy and interpretability.

In clinical tabular prediction, classical machine learning models with feature engineering often outperform neural methods. LLMs are increasingly used to automate this process, acting as domain experts that propose diverse feature transformations to boost downstream performance. However, the feature generation process of existing LLM-based methods is agnostic to the downstream learner: the LLM receives no signal about which features currently drive predictions or where the model's representational capacity falls short, so proposals are neither targeted to promising regions of the feature space nor tailored to the learner's inductive bias. This shortcoming is amplified in healthcare data, which simultaneously exhibits class imbalance, heterogeneous feature spaces, and strict interpretability requirements. In this paper, we propose MedFeat, the first feature engineering framework inspired by the workflow of machine learning practitioners, leveraging model-awareness and feature importance signals to iteratively guide feature discovery for clinical tabular learning. We evaluate MedFeat on a broad range of challenging real-world clinical tasks and show that it statistically significantly outperforms state-of-the-art baselines, with an average F1 improvement of more than 10% over the baseline across models with distinct inductive biases.

Adaptive Neuro-Fuzzy Inference System (ANFIS) was designed to combine the learning capabilities of neural network with the reasoning transparency of fuzzy logic. However, conventional ANFIS architectures suffer from structural complexity, where the product-based inference mechanism causes an exponential explosion of rules in high-dimensional spaces. We herein propose the Kolmogorov-Arnold Neuro-Fuzzy Inference System (KANFIS), a compact neuro-symbolic architecture that unifies fuzzy reasoning with additive function decomposition. KANFIS employs an additive aggregation mechanism, under which both model parameters and rule complexity scale linearly with input dimensionality rather than exponentially. Furthermore, KANFIS is compatible with both Type-1 (T1) and Interval Type-2 (IT2) fuzzy logic systems, enabling explicit modeling of uncertainty and ambiguity in fuzzy representations. By using sparse masking mechanisms, KANFIS generates compact and structured rule sets, resulting in an intrinsically interpretable model with clear rule semantics and transparent inference processes. Empirical results demonstrate that KANFIS achieves competitive performance against representative neural and neuro-fuzzy baselines.

Complex AI systems make better predictions but often lack transparency, limiting trustworthiness, interpretability, and safe deployment. Common post hoc AI explainers, such as LIME, SHAP, HSIC, and SAGE, are model agnostic but are too restricted in one significant regard: they tend to misrank correlated features and require costly perturbations, which do not scale to high dimensional data. We introduce ExCIR (Explainability through Correlation Impact Ratio), a theoretically grounded, simple, and reliable metric for explaining the contribution of input features to model outputs, which remains stable and consistent under noise and sampling variations. We demonstrate that ExCIR captures dependencies arising from correlated features through a lightweight single pass formulation. Experimental evaluations on diverse datasets, including EEG, synthetic vehicular data, Digits, and Cats-Dogs, validate the effectiveness and stability of ExCIR across domains, achieving more interpretable feature explanations than existing methods while remaining computationally efficient. To this end, we further extend ExCIR with an information theoretic foundation that unifies the correlation ratio with Canonical Correlation Analysis under mutual information bounds, enabling multi output and class conditioned explainability at scale.

Most major retailers today have multiple divisions focused on various aspects, such as marketing, supply chain, online customer experience, store customer experience, employee productivity, and vendor fulfillment. They also regularly collect data corresponding to all these aspects as dashboards and weekly/monthly/quarterly reports. Although several machine learning and statistical techniques have been in place to analyze and predict key metrics, such models typically lack interpretability. Moreover, such techniques also do not allow the validation or discovery of causal links. In this paper, we aim to provide a recipe for applying model interpretability and causal inference for deriving sales insights. In this paper, we review the existing literature on causal inference and interpretability in the context of problems in e-commerce and retail, and apply them to a real-world dataset. We find that an inherently explainable model has a lower variance of SHAP values, and show that including multiple confounders through a double machine learning approach allows us to get the correct sign of causal effect.

Kolmogorov--Arnold Networks (KANs) offer a promising path toward interpretable machine learning: their learnable activations can be studied individually while collectively fitting complex data accurately. In practice, however, trained activations often lack symbolic fidelity, learning pathological decompositions with no meaningful correspondence to interpretable forms. We propose Softly Symbolified Kolmogorov--Arnold Networks (S2KAN), which integrate symbolic primitives directly into training. Each activation draws from a dictionary of symbolic and dense terms, with learnable gates that sparsify the representation. Crucially, this sparsification is differentiable, enabling end-to-end optimization, and uses an optimization objective inspired by minimum description length. S2KAN can discover interpretable activation functions while retaining dense splines for flexible approximation. We introduce a quantitative measure of symbolic fidelity, assessing how closely learned activations can be approximated by short expressions from a specified symbolic language. Across real-world prediction tasks, dynamical-system forecasting, and synthetic symbolic benchmarks, S2KAN generally achieves higher symbolic fidelity and often far smaller models, while maintaining competitive predictive accuracy on real-world data and low prediction errors on most symbolic benchmark configurations. We also examine the models' learned responses on scientific data, including the contributions of their symbolic components. Together, these results show that incorporating symbolic structure during training can yield compact, accurate KAN models whose learned responses can be examined through their symbolic components.

Data sequences, such as time series, traces, and sensor streams, are words over large or infinite data domains. Their properties often depend on comparisons between values at different positions, which finite automata cannot express directly. We study synthesis and verification for Deterministic Register Automata (DRAs) over ordered data sequences. DRAs combine finite control with registers for remembered data values, providing compact symbolic descriptions of quantitative sequence languages. Our technical core is a local-search synthesis procedure and an exact robustness checker for DRAs. We fix the alphabet theory to ordered rationals $(\Q;<,=)$ with rational guard constants and use non-negative affine accumulator costs. For a fixed number of DRA registers, the checker runs in polynomial time; its dependence on that number is exponential. It reduces robustness to coverability and then to a shortest-path problem. Since the search ranges over $\Q^+$, it produces variable-length witnesses and, for RAA-definable alignment costs such as DTW, explores a counterexample space with no a priori length bound. As an application, we use learned DRAs as interpretable surrogates for queried neural sequence classifiers. A probably approximately correct (PAC) validation loop refines rejected candidates, returns genuine non-robustness witnesses for the classifier when found, and accepts a surrogate only with statistical guarantees for fidelity and local stability. We implement the framework in $\textsc{RAExc}$, enabling the synthesis of interpretable automata and the verification of their robustness. We evaluate the approach on benchmark languages and sequentialized MNIST, demonstrating high accuracy while verifying the robustness of the learned automata.

Decision trees are widely used in high-stakes fields like finance and healthcare due to their interpretability. This work introduces an efficient, scalable method for generating synthetic pre-training data to enable meta-learning of decision trees. Our approach samples near-optimal decision trees synthetically, creating large-scale, realistic datasets. Using the MetaTree transformer architecture, we demonstrate that this method achieves performance comparable to pre-training on real-world data or with computationally expensive optimal decision trees. This strategy significantly reduces computational costs, enhances data generation flexibility, and paves the way for scalable and efficient meta-learning of interpretable decision tree models.

Social scientists are increasingly turning to unstructured datasets to unlock new empirical insights, e.g., estimating descriptive statistics of or causal effects on quantitative measures derived from text, audio, or video data. In many settings, unsupervised analysis is of primary interest, in that the researcher does not want to (or cannot) manually pre-specify all important aspects of the unstructured data to measure; they are interested in "discovery." This paper proposes a general and flexible framework for pursuing such discovery from unstructured data in a statistically principled way. The framework leverages recent methods from the literature on AI interpretability to map unstructured data points to high-dimensional, sparse, and interpretable "concept embeddings"; computes statistics from these concept embeddings for testing interpretable, concept-by-concept hypotheses; performs selective inference on these hypotheses using algorithms validated by new results in high-dimensional central limit theory, producing a selected set ("discoveries"); and both generates and evaluates human-interpretable natural language descriptions of these discoveries. The proposed framework has few researcher degrees of freedom, is robust to data snooping and other post-selection inference concerns, and facilitates fast and inexpensive sensitivity analysis and replication. Applications to recent descriptive and causal analyses of unstructured data in empirical economics are explored.

Traditional machine learning relies on explicit models and domain assumptions, often limiting flexibility and interpretability. We introduce a "model-free" framework of instance-based learning using surprisal (information theoretic uncertainty) to directly analyze and perform inferences from raw data, eliminating distribution modeling, reducing bias, and enabling efficient updates including direct edits and deletion of training data. By quantifying relevance through uncertainty, the approach enables generalizable inference across tasks including generative inference, causal discovery, anomaly detection, and time series forecasting. Our approach emphasizes traceability, interpretability, and data-driven decision making, offering a unified, human-understandable framework for machine learning, can be adapted to virtually all machine learning tasks, achieving competency across all and state-of-the-art performance on anomaly detection and some supervised tasks. The mathematical foundations create a "physics" of information, which enable these techniques to apply effectively to a wide variety of complex data types, including missing data. Our results suggest that this may be a viable foundation upon which to build scalable machine learning and artificial intelligence that can maintain human understandability of the underlying mechanics.

Nanoporous materials hold promise for diverse sustainable applications, yet their vast chemical space poses challenges for efficient design. Machine learning offers a compelling pathway to accelerate the exploration, but existing models lack either interpretability or fidelity for elucidating the correlation between crystal geometry and property. Here, we report a three-dimensional periodic space sampling method that decomposes large nanoporous structures into local geometrical sites for combined property prediction and site-wise contribution quantification. Trained with a constructed database and retrieved datasets, our model achieves state-of-the-art accuracy and data efficiency for property prediction on gas storage, separation, and electrical conduction. Meanwhile, this approach enables the interpretation of the prediction and allows for accurate identification of significant local sites for targeted properties. Through identifying transferable high-performance sites across diverse nanoporous frameworks, our model paves the way for interpretable, symmetry-aware nanoporous materials design, which is extensible to other materials, like molecular crystals and beyond.

Traditional decision tree models, which rely exclusively on numerical variables, often face challenges in handling high-dimensional data and are limited in their ability to incorporate textual information effectively. To address these limitations, we propose the integrated multivariate segmentation tree (IMST), a comprehensive framework designed to improve credit evaluation for small- and medium-sized enterprises (SMEs) by integrating financial data with textual sources. This method comprises three core stages: (1) transforming textual data into numerical matrices through matrix factorization, (2) selecting salient financial features using Lasso regression, and (3) constructing a multivariate segmentation tree based on either the Gini index or entropy, with weakest-link pruning applied to control model complexity. Experimental results based on a dataset of 1,428 Chinese SMEs demonstrated that IMST achieved an accuracy rate of 88.9%, surpassing both baseline decision trees (87.4%) and conventional models such as support vector machines and neural networks. Furthermore, the proposed model demonstrated superior interpretability and computational efficiency, featuring a more streamlined architecture and improved risk detection capabilities.

Differentiable logic networks (DLNs) have shown promising results in tabular domains by combining accuracy, interpretability, and computational efficiency. In this work, we apply DLNs to the domain of TSC for the first time, focusing on univariate datasets. To enable DLN application in this context, we adopt feature-based representations relying on Catch22 and TSFresh, converting sequential time series into vectorized forms suitable for DLN classification. Unlike prior DLN studies that fix the training configuration and vary various settings in isolation via ablation, we integrate all such configurations into the hyperparameter search space, enabling the search process to select jointly optimal settings. We then analyze the distribution of selected configurations to better understand DLN training dynamics. We evaluate our approach on 51 publicly available univariate TSC benchmarks. The results confirm that classification DLNs maintain their core strengths in this new domain: they deliver competitive accuracy, retain low inference cost, and provide transparent, interpretable decision logic, thus aligning well with previous DLN findings in the realm of tabular classification and regression tasks.

We propose a novel, flexible, and efficient framework for designing Concept Bottleneck Models (CBMs) that enables practitioners to explicitly encode and extend their prior knowledge and beliefs about the concept-concept ($C-C$) and concept-task ($C \to Y$) relationships within the model's reasoning when making predictions. The resulting $\textbf{C}$oncept $\textbf{REA}$soning $\textbf{M}$odels (CREAMs) architecturally encode arbitrary types of $C-C$ relationships such as mutual exclusivity, hierarchical associations, and/or correlations, as well as potentially sparse $C \to Y$ relationships. Moreover, CREAM can optionally incorporate a regularized side-channel to complement the potentially {incomplete concept sets}, achieving competitive task performance while encouraging predictions to be concept-grounded. To evaluate CBMs in such settings, we introduce a $C \to Y$ agnostic metric that quantifies interpretability when predictions partially rely on the side-channel. In our experiments, we show that, without additional computational overhead, CREAM models support efficient interventions, can avoid concept leakage, and achieve black-box-level performance under missing concepts. We further analyze how an optional side-channel affects interpretability and intervenability. Importantly, the side-channel enables CBMs to remain effective even in scenarios where only a limited number of concepts are available.

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.

Electroencephalography (EEG) classification has shown significant promise in applications ranging from neurodegenerative disease detection to brain-computer interfaces (BCIs). Whilst deep learning methods have increasingly dominated the research landscape in recent years; these models remain largely opaque 'black boxes' with limited interpretability. In this paper, we revisit the utility of feature-based classification via a systematic pipeline designed to integrate per-electrode signal statistics with cross-brain connectivity metrics. The proposed "KnowEEG" pipeline extracts 783 per-electrode statistical features alongside between-electrode connectivity statistics, utilizing a balanced sampling strategy between high-dimensional per electrode features and connectivity. This feature-based pipeline achieves performance comparable to or exceeding state-of-the-art deep learning models across five diverse classification tasks: emotion detection, mental workload classification, eyes open/closed detection, abnormal EEG classification, and event detection. This performance is achieved without the need for Graphics Processing Unit (GPU) resources. Furthermore, the pipeline provides inherent explainability through feature importance rankings. We demonstrate via the eyes open/closed task that this explainability identifies discriminative biomarkers in the occipital region that are consistent with established neuroscience literature. These results suggest that despite significant advances in deep learning, structured feature engineering remains a high performance and interpretable method for EEG classification.

With the rapid development of machine learning and deep learning techniques, actuaries and the broader insurance industry face a persistent trade-off between predictive accuracy and interpretability. This paper provides a comprehensive applied assessment of Explainable Boosting Machines (EBM) in a car insurance framework, focusing on claim frequency and severity modeling. EBM combines the additive structure of generalized additive models (GAM) with a cyclic gradient boosting algorithm, resulting in a glass-box model whose predictions are interpretable by design. Using real-world data, we empirically illustrate its practical relevance and compare EBM with modern benchmark models used in non-life insurance pricing. The evaluation considers (i) out-of-sample predictive accuracy, including Murphy diagrams and Bregman dominance tests, and (ii) calibration assessment using T-reliability diagrams and Murphy's score decomposition. Finally, we highlight the link between EBM predictions and Shapley values, showing how predictions can be transparently decomposed into exact main and pairwise interaction effects, providing actionable insights beyond predictive performance.

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear combinations of predictor variables in their leaf nodes to form predictions, which can help achieve higher accuracy and smaller trees. Typical algorithms for learning model trees from training data work in a greedy fashion, growing the tree in a top-down manner by recursively splitting the data into smaller and smaller subsets. Crucially, the selected splits are only locally optimal, potentially rendering the tree overly complex and less accurate than a tree whose structure is globally optimal for the training data. In this paper, we empirically investigate the effect of constructing globally optimal model trees for classification and regression with linear support vector machines at the leaf nodes. To this end, we present mixed-integer linear programming formulations to learn optimal trees, compute such trees for a large collection of benchmark data sets, and compare their performance against greedily grown model trees in terms of interpretability and accuracy. We also compare to classic optimal and greedily grown decision trees, random forests, and support vector machines. Our results show that optimal model trees can achieve competitive accuracy with very small trees. We also investigate the effect on the accuracy of replacing axis-parallel splits with multivariate ones, foregoing interpretability while potentially obtaining greater accuracy.