Differentiable Interval Bottlenecks for Interpretable Anomaly Detection in Numerical Data

Reconstruction-based anomaly detectors are accurate but opaque: a deep autoencoder flags a sample without telling a practitioner which feature ranges made it anomalous. We propose DIFFINT, an autoencoder whose latent bottleneck is structured as a set of soft, axis-aligned interval memberships learned end-to-end directly from raw numerical data, without any discretization or binarization. Each latent unit corresponds to a human-readable hyper-rectangle in feature space; an instance is encoded by how strongly it falls inside each interval relative to the other units, and its reconstruction error is the anomaly score. This keeps the power of differentiable representation learning while exposing an inspectable internal structure. We make the inductive bias precise: a certified reconstruction-error lower bound for points that fall outside every active coordinate of the learned support (with a Lipschitz-enforced decoder), and a graded, empirically verified suppression mechanism for the usual case in which only a few features are abnormal; and we provide a closed-form, label-free importance that ranks each (unit, feature) pair from quantities the model already maintains, turning trained intervals into auditable candidate constraints without ever seeing an anomaly label. On 48 ADBench benchmarks against 22 baselines under a common [-1, 1]-normalized protocol, DIFFINT attains the best mean rank overall on both metrics (4.10 on ROC-AUC, 4.16 on AUPR); among inlier-only detectors it leads its regime clearly, and it is competitive with the strongest contaminated-data detectors (see the stratified and complete-case analyses). It is the only interpretable detector in the statistically-tied leading cluster of seven methods.

Adaptive Multi-Branching for Shallow Decision Tree Induction

Decision trees are attractive for tabular prediction tasks because each prediction follows an interpretable sequence of feature-threshold tests. Under a strict maximum-depth budget, however, conventional binary trees can be under-expressive, since each internal node makes only a single threshold decision. We study shallow-depth tree induction, where the goal is to improve accuracy while keeping root-to-leaf paths short. We propose the Multi-Branch Neural Decision Tree with Adaptive Pruning (MBNDT), a single axis-aligned tree trained end-to-end with differentiable multi-way splits. Each internal node learns ordered thresholds over a selected feature and a branch mask that adapts its effective arity, and the trained model is converted to a deterministic single-path tree for inference. Across 21 OpenML binary-classification benchmarks, MBNDT achieves the best average rank and mean balanced accuracy among depth-constrained single-tree baselines; a controlled ablation isolates multi-way splitting as the source of the gain. These gains come with an explicit trade-off: MBNDT realizes more leaves than the other single-tree baselines, making it best suited when accuracy under short, bounded decision paths is prioritized over minimal global tree size.

Importance Scoring of Transformer Attention Heads in Learning Tabular Data

Computationally demanding and opaque deep learning models can be better understood and optimized by analyzing how they transform data. While deep transformers have been widely studied in computer vision and natural language processing, their application in tabular data remains relatively underexplored. This paper presents one of the first applications of an importance-scoring metric to interpret multi-head transformer models in learning from tabular data. Experiments conducted on 40 diverse tabular datasets demonstrate robustness to head drops based on the proposed head importance score. In 72.5\% of experimental examples, the model remains most resilient to performance drops when heads with the lowest importance scores are gradually removed. In contrast, removing the most important attention head first results in the greatest reduction in classification performance. A closer look at individual head importance scores across six attention layers reveals that important heads are scattered across layers, with no consistent layer-specific trends. In contrast to the image and language domains, the importance of individual attention heads varies considerably across tabular datasets with different schemas and feature spaces. The proposed importance score can improve efficiency and redundancy within transformer architectures. We make the source code for measuring the importance of individual attention heads publicly available.

$\texttt{findr}$: Transparent and Fair Credit Risk Decisions through Semi-Structured Regressions

Credit risk models increasingly need to combine predictive accuracy with transparent explanations and auditable fairness constraints. Logistic regression remains attractive because its coefficients are easy to interpret, but it can miss nonlinear structure. Flexible models can improve prediction, but their explanations are often post-hoc and may not describe the decision rule itself. We introduce $\texttt{findr}$, short for flexible, interpretable deep regression, a semi-structured framework for binary credit risk modelling that decomposes the logit into an interpretable structured component and an orthogonal neural residual. The orthogonalisation separates coefficient-based effects from residual nonlinear variation, while an in-processing Wasserstein penalty mitigates group disparities by comparing score distributions during training. The framework also includes diagnostics that measure the structured component's contribution to logit variation, decision agreement, and local directional consistency. We evaluate $\texttt{findr}$ in a simulation study and on eight public credit datasets using score-level accuracy-fairness frontiers. The results show that $\texttt{findr}$ behaves close to logistic regression when the signal is approximately linear, while recovering much of the predictive gain of neural models when nonlinear structure is relevant. The diagnostics identify when coefficient-based explanations remain close to the full fitted model and when residual variation must also be examined. These findings support semi-structured modelling as a practical way to make performance, fairness, and interpretability trade-offs explicit in credit risk decisions.

A Heterogeneous Mixture of Experts Framework for Interpretable Machine Learning

Mixture-of-Experts (MoE) models provide a flexible framework for partitioning complex prediction problems into simpler local learning tasks through an input-dependent gating mechanism. Existing interpretable MoE approaches, such as Mixture of Decision Trees (MoDT), achieve transparency by employing homogeneous decision-tree experts, but this restricts the model to a single inductive bias across all regions of the feature space. We extend the MoDT framework by introducing heterogeneous expert families comprising decision trees, linear support vector machines, and quadratic discriminant analysis under a common probabilistic gating mechanism. To ensure coherent likelihood-based inference, non-probabilistic experts are calibrated to produce conditional class probabilities, allowing parameter estimation within the generalized Expectation-Maximization framework of MoDT. We further establish theoretical monotone ascent guarantees for the proposed heterogeneous gating updates, providing a justification for the optimization procedure. Experiments on a diverse collection of synthetic and real-world benchmark datasets demonstrate that the proposed framework adaptively specializes experts according to local data geometry, yielding interpretable expert assignments while achieving predictive performance competitive with homogeneous MoDT and Random Forests. The proposed approach combines interpretability, adaptive inductive bias selection, and probabilistic coherence within a unified mixture-of-experts framework.

Revenge of Monosemanticity: Specialized Neurons Improve Data Efficiency in MLPs

Understanding how neural networks learn and organize features is central to understanding their behavior. Much existing theory of feature learning has focused on the emergence of a global low-dimensional predictive geometry. We show that this picture is incomplete. In regression problems with clustered data, we demonstrate that multilayer perceptrons (MLPs) naturally develop monosemantic specialized neurons: individual neurons become strongly aligned with a specific predictive feature relevant to a particular region of the input space. Rather than learning a single global low-dimensional representation, MLPs learn a collection of local low-dimensional representations that can collectively span a high-dimensional space. This specialization provably gives MLPs a data-efficiency advantage over feature-learning methods based on a global low-dimensional representation.

Interpretable AI with Local Distillation

Modern AI models such as tabular foundation models and gradient-boosted ensembles can outpredict classical methods, but provide little basis for reasoning about their predictions. High-stakes decisions call for models that are both accurate and interpretable as built. Local linear modeling offers a path forward: a smooth regression function is locally well approximated by a linear one, allowing a linear fit near each query point to achieve high accuracy without sacrificing transparency. The challenges lie in learning what is "local" and developing statistical tools for interpretation. Here, we propose local distillation, in which a black-box "teacher" guides a regularized linear "student" model at each query point. The teacher (1) defines locality by upweighting training observations with similar predicted outcomes, and (2) anchors the fit with its prediction at the query point, included as a pseudo-observation whose weight is estimated from the data. For interpretation, we add a small amount of Gaussian randomization to the local objective and use refits to assess stability: selection frequencies identify reliable features at a query point, and clustering the randomized fits identifies stable subgroups across the data. Under the lasso penalty, we prove that this randomization yields feature-selection probabilities that are stable under small perturbations of the training responses. Across 17 benchmark datasets, local distillation nearly matches its AI teacher's accuracy while producing a sparse linear model at each test point. In a high-dimensional cancer gene expression example, the framework identifies patient subgroups whose local models use different genes; this heterogeneity is invisible to a global linear model, and difficult to surface in a black-box model.

Poisson Subspace Clustering: Focusing on the Essentials in Count Data

Count data represented as a matrix of non-negative integer values, such as contingency tables, are prevalent across diverse domains. When clustering such data sets, specific methods are required, as generic algorithms often fail to consider their unique distributional properties, leading to unreliable outputs. An effective strategy is to use well-established statistical models such as the Poisson and negative binomial distributions. We present 3CPO, a clustering algorithm based on statistically solid modeling of count data. In addition to the cluster labels, it identifies a subset of relevant columns, enhancing the interpretability of the results. We propose a simple iterative algorithm that maximizes the posterior probability to find good clustering solutions and discuss its properties. Extensive experiments demonstrate its ability to define high-quality clusters within associated subspaces for various data domains, ranging from gene expressions and texts to economics. Our findings suggest that 3CPO is a robust solution for clustering count data in a statistically sound and interpretable manner. Our code is available at https://github.com/collinleiber/3CPO.

Counterfactual Transition Graphs: Evaluating Cross-Class Transition Quality

Counterfactual (CF) explanations for time-series classifiers are usually evaluated one example at a time: what minimal edit flips this single window's prediction? We argue that the more informative question for diagnostic interpretability is structural: how does the classifier connect its own classes to each other? We propose a counterfactual transition graph (CGT) in which each node is a class and each edge weight is the CF reliability of the transition from one prototype to another under a proximity aware retrieval sweep. On a six-class hand-movement task, we induce a CGT that reveals a non-trivial topology, which is not predicted by the binary confusion matrix: it shows that counterfactual reachability does not align with classifier accuracy and even runs counter to it (Spearman $ρ=-0.37$ over the 15 pairs), i.e. the boundaries the classifier separates most confidently are among those an in-distribution edit can least often cross. Our framework is method agnostic, i.e. any CF-explainers can be used. Presently, we use it to juxtapose replacement-based CFs with gradient-based CFs; gradient-based methods reach almost any class by stepping off the data manifold, while replacement-based methods stay on it and fail on precisely the rigid boundaries.

ConceptTS: LLM-Guided Concept Bottlenecks for Interpretable Multivariate Time-Series Forecasting

State-of-the-art multivariate time-series forecasters can model complex temporal and cross-variable dependencies, yet their opaque representations provide limited insight into why a particular forecast is produced. This lack of transparency restricts their use in settings where practitioners must understand and assess the factors underlying a prediction. We introduce ConceptTS, an interpretable forecasting framework that organizes its predictions around named, human-readable concepts. ConceptTS uses a large language model to propose task-relevant concepts and generate executable labeling rules, translating the language model's domain knowledge into direct supervision without costly manual concept annotation. The proposed concepts are organized into three complementary bottlenecks that describe the historical context, local forecast intervals, and the full forecast horizon. A shared decoder combines representations derived from their predicted activations to construct the forecast, making the model's decision process explicit and supporting direct concept-level interventions. Experiments on the Beijing Multi-Site Air Quality dataset show that ConceptTS achieves accuracy competitive with strong black-box baselines while producing semantically meaningful concept activations.

Fuzzy-MoE: Interpretable Regime-Conditioned Expert Routing for Non-Stationary Multivariate Time Series Forecasting

In non-stationary multivariate time series, different variables and samples often exhibit heterogeneous latent dynamic states, while existing deep forecasting models usually compress them into a unified end-to-end mapping, leading to suboptimal modeling of time-varying dynamics and limited interpretability regarding which forecasting mechanism is activated under different latent states. To overcome these limitations, we reformulate time series forecasting as a unified framework of latent temporal state identification and interpretable expert routing, and propose Fuzzy-MoE, a fuzzy logic-based dynamic Mixture-of-Experts model. Fuzzy-MoE consists of multiple parallel expert mapping networks and a dual-view fuzzy router. By jointly exploiting local convolutional dynamics and global segmented statistics, the router infers latent temporal states and computes expert activation strengths through learnable Gaussian membership functions, enabling explicit IF-THEN rule-based expert selection. This fine-grained routing strategy allows different variables within the same sequence to activate different experts, effectively capturing heterogeneous temporal dynamics while improving model interpretability. Experimental results on multiple public time series benchmark datasets show that Fuzzy-MoE significantly outperforms mainstream forecasting methods in forecasting accuracy. Moreover, fuzzy memberships and rule activations provide interpretable routing diagnostics, demonstrating the effectiveness of the proposed framework in both forecasting performance and mechanism transparency. Unlike traditional MoE models that use black-box routing, Fuzzy-MoE`s routing is based on clear, interpretable fuzzy rules. This makes the expert selection transparent and traceable.

DecoVAE: a Lightweight Interpretable Trend-Seasonal VAE Framework for Efficient Probabilistic Time Series Forecasting

Probabilistic time series forecasting remains challenging, largely because modeling distinct trend and seasonal dynamics requires specialized approaches. Existing methods often fail to capture the unique inner properties of these components, lack interpretability, or suffer from heavy memory and runtime overhead. To address these limitations, we propose DecoVAE, a lightweight interpretable trend-seasonal VAE framework that explicitly decomposes time series into trend and seasonal components by applying domain-specific inductive biases. The trend stream enforces structural smoothness using a differential regularizer on the latent trajectory, analogous to the Hodrick-Prescott filter. Concurrently, the seasonal stream operates in the frequency domain via a complex Gaussian VAE, natively capturing the amplitude and phase of periodic patterns. Extensive evaluations across seven real-world benchmarks show that DecoVAE consistently outperforms strong baselines. It achieves reductions of up to 14.96\% in CRPS and 23.30\% in NMAE for short-term forecasting, and up to 52.68\% and 26.51\% for long-term horizons. Crucially, DecoVAE yields these accuracy gains while remaining highly efficient, reducing model weight by up to 93\% and accelerating speed by up to 74\% compared to the second-best method.

Beyond receptive fields: sequence-pooled normalization can supply most of a sequence labeler's context

A convolutional sequence labeler's receptive field is routinely treated as the extent of the model's usable context: it sets dilation schedules, bounds streaming horizons, and underwrites locality claims. However, we show that this can be false: when a normalization layer computes statistics from the current input along the sequence at inference, those statistics open a sequence-spanning path that bypasses the convolutional receptive field to provide global context. We derive this from the layer's Jacobian (the criterion needs no experiment), and what the path carries has a closed form. On a synthetic labeling process with computable optima, the global summary that a sequence-spanning normalization encodes already supplies almost all of what a larger receptive field would buy where labels come in long runs: a network reaching 9 positions comes within 0.009 of the whole-sequence optimum, against a near-chance bound for its reach. Closing the path, by taking the same statistics per position, multiplies what enlarging the receptive field is worth by up to an order of magnitude on simulated genomes at every difficulty level tested and on real 1000 Genomes haplotypes. The same path also confounds attribution: ablating a trained network's receptive-field-enlarging blocks severs part of the path, overstating their contribution 8.3-16.1-fold relative to retraining from scratch. The substitution of normalization for receptive field fades as labels switch more often. Where labels run long, neither the receptive-field justification nor the ablation is wrong about its numbers, but both credit the wrong component.

Hide&Seek: Learning to Explain in an End-to-End Differentiable Network

Instance-wise feature selection is a valuable tool for interpreting labeled data and the predictions of black-box models. In contrast to global feature selection techniques, instance-wise methods dynamically identify important features for each instance. A growing number of methods learn a selector, which identifies important features, and a predictor, which uses these to make predictions. However, these pioneering methods face challenges including information leakage and lack of differentiability, which can slow training. In this paper, we present Hide&Seek, an end-to-end differentiable model for instance-wise feature selection. We jointly learn feature selection and prediction under a single objective without information leakage. Hide&Seek outperforms existing state-of-the-art models across a range of experiments and is fast to train. We achieve this by reformulating feature removal as a differentiable operation where instead of discretely removing features, we replace a proportion of each feature. Training is further stabilized via a parsimony-weight annealing framework.

LiD-GLM: Lipschitz-constrained Deep Generalized Linear Models

The combination of traditional statistical models and neural network (NN) components into semi-structured hybrid models is an intriguing approach to construct models that, ideally, combine traditional interpretability with the unprecedented flexibility of NNs. In order to preserve interpretability, it is usually necessary to restrict the NN components to prevent them from dominating the model. However, existing methods that enforce structural constraints on their NN components severely limit their models' flexibility; in contrast, methods that only enforce weak, indirect constraints lose meaningful interpretability. The method we propose therefore leverages invertible residual neural networks (i-ResNets) to equip generalized linear models with both nonlinear parameter estimation and a flexible correction of their distributional assumptions while always retaining stochastic monotonicity of the modeled distribution in the (formerly linear) predictor. The i-ResNets correspond to a controlled deviation from identity and by constraining their Lipschitz constant one can rigorously limit and quantify how far the hybrid model deviates from its traditional counterpart. This enables a user-specifiable compromise between flexibility and interpretability without limiting the structure of nonlinear and interaction effects that can be learned. Furthermore, we develop specific inherent interpretation techniques for our model and enforce model identifiability through an adapted post-hoc orthogonalization.

Learning Auditable Classifier Models: Source-Disjoint Tree Ensembles

Predictive models in clinical and regulated settings must be accurate and fully auditable. Tree ensembles deliver strong accuracy on tabular data, but their sequential boosting couples structure discovery with coefficient estimation, making compact per-prediction auditing difficult. Interpretable alternatives impose structural constraints that limit expressiveness: generalized additive models typically restrict interactions to pairwise terms and post-hoc rule extractors produce overlapping rules that hinder compact interpretation. We introduce Residual Pattern Tree Ensemble (RPTE), a three-stage learning approach, that is built on three key principles: bounded feature budget, source disjointness, and separate coefficient estimation. Stage~1 builds a supervised symbolic feature vocabulary. Stage~2 grows shallow trees under a source-disjointness constraint, where each raw variable is allocated to at most one tree, and retains only the discovered tree structures. Stage~3 solves a single $\ell_1$-regularized logistic regression over leaf-region indicators, yielding jointly optimal sparse coefficients. This learning approach ensures that every prediction decomposes into an algebraic sum of named, non-overlapping rule contributions, enabling full auditability by design. Empirical evaluation on twelve clinical-domain binary classification benchmarks using repeated stratified 5-fold cross-validation shows that RPTE performs competitively against tuned opaque ensembles and interpretable baselines. RPTE reduces model inspection units by 9$\times$ to 87$\times$ relative to XGBoost and maintains lower audit complexity than EBM on all 12 datasets. RuleFit requires comparable or fewer inspection units on three datasets where its rule count is small, but without source-disjointness guarantees. The source code is available at \href{https://github.com/srikumar2050/hugiml-core}{this https URL}.

Measuring Structured Predictability in Neural Training Dynamics: A Cross-Regime Study

Modern deep networks are trained through long update trajectories, yet their temporal organization remains less systematically characterized than architectures, losses, or optimizers. We study short-horizon predictability as a measure of temporal redundancy: where, when, and under which training conditions recent updates contain information about near-future parameter motion. We combine three complementary probe families, displacement-direction, subspace-residual, and predictor-based probes, with convention-aware, null-calibrated group-level readouts, and apply them to multi-pass vision training on CIFAR and public Pythia pretraining checkpoints. Across both regimes, vector-like tensors such as normalization parameters and biases (auxiliary parameters) exhibit simpler short-horizon dynamics than matrix-like feature-transforming weights (bulk parameters), whose predictable behavior concentrates in localized, time-varying pockets. Agreement within and across probe families, and with independent trajectory diagnostics, indicates that these measurements capture intrinsic trajectory structure, while probe differences distinguish complementary forms of temporal organization. Controlled CIFAR comparisons further show that architecture and training recipe systematically modulate the measured structure. A Pythia-70M case study further exposes a sequence of role-, depth-, and scale-dependent events, including bulk ESA falling below the random sign-agreement level and the emergence and redistribution of predictable qkv pockets across layers. These results position short-horizon predictability as a retrospective, parameter-resolved diagnostic of training dynamics.

TabSOM: A tabular-to-image encoding method based on self-organizing maps

Tabular-to-image methods have emerged as novel approaches to leverage the high predictive performance of convolutional neural networks and vision transformers. They convert tabular data into image representations, mapping each feature at a fixed pixel location derived from a dimensionality-reduction method (e.g., t-SNE, UMAP, PCA). However, they encode only the marginal value of each feature and discard information about feature relationships. We propose TabSOM, a tabular-to-image encoding built on the Self-Organizing Map (SOM), which provides: (i) a spatial layout in which every input feature occupies a fixed canvas position derived from its component plane via collision-free Hungarian assignment; and (ii) a graph that captures pairwise feature relationships derived from the SOM component planes. The resulting image stacks two multi-scale node channels: one encodes feature values at fixed scales, while the other encodes pairwise feature interactions as spatial connections between related features. Two SOM-derived interpretability approaches are introduced: a prototype-inspired partial dependence plot and a class--separation importance score. Benchmarked against twelve existing tabular-to-image methods across public binary-classification datasets, TabSOM ranks first or second on every dataset and achieves the lowest variance of any method evaluated. Interpretability obtained with TabSOM was validated against Random Forest, XGBoost, and SHAP, the class-separation score shows reasonable agreement with established baselines on the top-ranked features while capturing complementary structural information from input data. These results demonstrate that TabSOM provides an effective and interpretable approach for applying deep learning architectures to tabular data, bridging the performance--interpretability gap in this domain.

HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry

The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning. However, existing ANFIS models generally construct rule antecedents and perform inference in Euclidean space, limiting their representational capacity and predictive performance. To address this issue, we propose Hyperbolic ANFIS (HyperANFIS), a hyperbolic extension of ANFIS. HyperANFIS preserves the fuzzy semantics and core architecture of conventional ANFIS while performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. It also retains the ability to generate interpretable IF-THEN rules. By exploiting the representational properties of hyperbolic geometry, HyperANFIS strengthens the fuzzy inference process, thereby improving predictive accuracy, inter-rule collaboration, and the credibility of its interpretable rules. Experimental results show that HyperANFIS consistently outperforms the standard ANFIS baseline and various ANFIS variants across all datasets, while also generating higher-quality fuzzy rules.

Do Time-Series Forecasters Use the Right History: Recoverability, Recovery, and Functional Use of Temporal Delays

Forecast accuracy does not tell us which past inputs produced a prediction. We separate three questions for time-series models with known delay structure: can the true delay be recovered from the observed data, does the model report it, and does the forecast actually use the same history? We first derive input-conditioned recoverability measures that separate intrinsic ambiguity from model error. We then prove that a delay report can become arbitrarily reliable while forecast risk approaches the oracle even though the predictor still uses the wrong lag. This failure also appears in finite samples on the point-delay task: among forecasts with a correct delay report and normalized excess risk within 10\% of the oracle, the reported history is functionally unused under our matched masking test in 55.4\% of N-HiTS cases and 92.7\% of TCN cases. Finally, we show that routing the prediction through the reported history removes off-report bypass paths; a hard one-hot control achieves exact fixed-report alignment. The main conclusion is simple: a good forecast, even with a correct delay report, does not show that the model used the right history.

How Simple Can It Get? From Interpretable Equations to Readable Rules for Financial Decision Making

In regulated domains such as finance, a model that cannot be explained cannot be deployed, yet many interpretable classifiers defeat their own purpose by producing formulas with dozens of features that no regulator could read. We take the reverse direction. Starting from an interpretable classifier expressed as a single equation over the input features, we progressively simplify it into more readable forms, including a pruned monomial, a directional if--then rule, and the integer scorecards and tallies that finance already deploys. Because the equation is itself the predictive model rather than a post-hoc explanation we can directly quantify what is lost under each simplification. Across four financial datasets, we find that pruning is nearly free and that fidelity can erode faster than predictive performance, allowing simpler rules to remain effective classifiers without faithfully reproducing the original model. A human assessment shows that simplification improves perceived readability, while preferences for different representations vary by professional background. Beyond measuring these losses empirically, we show that some can be anticipated from the original model: we derive a bound on the change caused by pruning and predict how faithfully a rule retaining only the direction of each feature's effect preserves the original ranking.

Beyond the Black Box: Interpretable Models of Human Randomisation Failures

Mixed strategy equilibrium predicts i.i.d play: past actions should not help predict future decisions. Human players, however, systematically depart from this benchmark, and in O'Neill's zero sum card game, these departures can be predicted by black box sequence models such as LSTMs. This paper asks whether that predictive power can be achieved by transparent alternatives that also reveal the behavioural structure behind it. Using 84,060 decisions from 2,802 pairs, the analysis first benchmarks naive and behavioral models against interpretable machine learning and deep learning models, then evaluates the modified EWA specifications of prior work against these benchmarks and uses the LASSO diagnostics to motivate a further nested frequency tracking extension. The results show that repeat or avoid behavior, especially players' management of their own recent action histories, accounts for most of the interpretable and strategically exploitable signal, while frequency tracking adds little out of sample.

IMFACT: Counterfactual Explanations for Time Series via Intrinsic Mode Function Substitution

Oscillatory signals, such as vibration, carry class-discriminative information in specific frequency bands; perturbing them in raw feature space for counterfactual analysis easily destroys their temporal structure and produces physically implausible results. In this work, we introduce IMFACT (IMF-based counterfACTuals), a model-agnostic framework for generating plausible counterfactual explanations for time series classifiers that operates in the decomposition space of Empirical Mode Decomposition. An input signal is split into Intrinsic Mode Functions (IMFs), and selected IMFs are progressively substituted with those of a Nearest Unlike Neighbour (NUN) until the classifier flips to the target class. We evaluate six IMF-selection strategies and a multi-NUN cycling extension on two UCR benchmarks (FaultDetectionA, FruitFlies). The variance-based strategy with three NUNs outperforms two prominent baseline techniques on reliability and plausibility metrics, while cycling across three NUNs yields the best proximity across both datasets.

A Generalized-Bayes Perspective on Counterfactual Explanations: Posterior-Based Decision-Making and Evaluation

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by identifying the smallest change to an input required to obtain a desired output. Although CEs are conventionally formulated as a distance-minimization problem, the theoretical basis of this formulation has received limited attention. We show that a distance-minimization-based CE is mathematically equivalent to the maximum a posteriori (MAP) estimate of a Gibbs posterior within the generalized Bayes framework, specifically when a distance-based prior is used. We call this formulation the Distance-Prior Generalized Bayes CE (DP-GBCE). Building on this posterior perspective, we introduce two decision rules beyond MAP within a unified framework: a Bayes decision that minimizes expected decision loss and CVaR-CE, a risk-averse decision rule. We also propose an extension that uses Bayesian model weights to mix the posterior distributions of multiple models, thereby accounting for model multiplicity, where several models have comparable predictive performance. Finally, we define metrics for evaluating both individual CEs and the posterior distribution as a whole, and use experiments on simulated data and Google Trends data to quantify the trade-offs among the decision rules.

Information Bottleneck Learning for Faithful Time Series Forecasting Explanations

As forecasts increasingly drive decisions in fields such as energy, transportation, and healthcare, understanding the historical data behind these predictions has become as crucial as the predictions themselves. Although existing interpretable-by-design forecasters reveal their internal structures, they offer no guarantee that these structures faithfully reflect the underlying evidence driving the predictions. In contrast, while faithfulness-oriented methods explicitly verify model behavior, they are almost exclusively designed for post-hoc classification tasks. To bridge this gap, we propose IB-Forecast, an inherently interpretable multivariate time-series forecasting framework. It decomposes forecasting into a learned periodic component and a residual component computed with explainable masks over input tokens. With a budget-constrained information bottleneck, end-to-end optimization enables users to directly control explanation sparsity. With a rigorous faithfulness evaluation protocol, extensive experiments demonstrate that IB-Forecast matches the forecasting error of leading black-box models while providing faithful explanations at no additional inference cost. Furthermore, under a matched sparsity budget, these native explanations consistently surpass gradient-based, occlusion-based, and optimization-based baselines across all evaluated datasets. Ultimately, whereas the native explanations of existing interpretable forecasters exhibit poor faithfulness, IB-Forecast guarantees high explanation fidelity, requiring only 14-20% of the observations to deliver low-error predictions.

Class-Aware Reinforcement Learning for Counterfactual Explanation Generation

Counterfactual explanations (CFEs) enhance the interpretability of black-box models by generating alternative instances with adjusted feature values that achieve a contrastive outcome. Reinforcement learning (RL) offers a promising approach for CFE generation, enabling efficient exploration of counterfactual instances while ensuring control over key metrics like validity, sparsity, and proximity. Previous studies have formulated RL states exclusively using features derived from the predictors in the supervised dataset. This study explores the impact of including an instance's predicted class, alongside features derived from the predictors, in the RL state representation for generating CFEs. The hypothesis is that class-awareness enhances exploration efficiency and improves policy optimality. We compare the proposed class-aware RL method with the class-blind RL method, which is similar but excludes the instance's class information from the state representation. The comparison was conducted using seven datasets from diverse domains, varying in size. The results show that during training, class-aware RL offers benefits in terms of convergence speed, reward optimization, and episode length reduction. Moreover, it generates significantly more valid CFEs compared to class-blind RL. Finally, the instance's class-based feature consistently ranks among the most influential predictors in RL's action-selection, as shown by the SHAP and LIME values, underscoring the significance of class-awareness in RL for CFE generation. The impact is heightened clarity, faster learning, improved validity, and more effective counterfactual generation across diverse datasets.

iFuzz-Meta: An Interpretable Fuzzy Learning Framework Bridging Top-Down and Bottom-Up Knowledge Integration

Interpretable representation learning remains a key challenge in modern neural computation, particularly when models are expected not only to perform but also to explain their reasoning. This paper introduces iFuzz-Meta, an interpretable fuzzy rule-based learning framework that preserves human-understandable reasoning structures within modern neural architectures. Each fuzzy rule corresponds to a semantic and spatial prototype defined in the original feature space, enabling transparent inference and direct interpretability. Meta-learning is employed as an analytical paradigm to examine how these interpretable rules reorganize across tasks and domains, providing a principled means to link algorithmic adaptation with cognitive representation. A knowledge-guided regularization mechanism further enables a top-down-bottom-up integration, in which theoretical priors act as soft inductive biases while data-driven learning refines and extends them. This dual process ensures that adaptation proceeds along semantically and physiologically meaningful trajectories, rather than arbitrary parameter shifts. Evaluations demonstrate that iFuzz-Meta achieves interpretable reasoning and stable cross-domain generalization, establishing a potential general pathway toward explainable and knowledge-aware fuzzy systems.

TreeCCA: Canonical Correlation Analysis via Gradient-Boosted Trees

Gradient-boosted trees dominate tabular machine learning, yet canonical correlation analysis has always relied on linear or neural encoders. We propose \textbf{TreeCCA}, the first method to train gradient-boosted tree ensembles end-to-end as CCA encoders, inheriting their plug-and-play reliability: no architecture design, familiar hyperparameters, and strong performance with defaults. The technical enabler is the Eckart-Young (EY) loss, which supplies closed-form per-sample gradients that slot directly into any standard GBT library (XGBoost, LightGBM) as a custom objective. TreeCCA is the first CCA method to combine nonlinear accuracy with native interpretability: every tree split selects one feature, so gain importances reveal which inputs drive cross-view correlation at no extra cost. We demonstrate these properties on synthetic benchmarks, where TreeCCA matches or exceeds Deep CCA (2.61 vs.\ 2.43 on Signed Power; 2.93 vs.\ 2.89 on Hermite), and on a sparse benchmark with zero linear cross-view covariance, where TreeCCA recovers the true support with $\text{Precision@}S = 1.00$ at $p=50$ while PMD finds no signal. On the UCI HAR sensor-fusion benchmark, TreeCCA achieves comparable accuracy to Deep CCA at $5\times$ lower cost, while XGBoost gain importances directly validate a physics-motivated hypothesis about the data --- an interpretation not readily available with neural encoders. Across five popular tabular multi-view datasets, TreeMCCA consistently matches or exceeds linear CCA in both nonlinear correlation extraction and downstream classification accuracy.

Rashomon Alignment

We propose Rashomon Alignment (RA), a new measure to assess functional similarity between two models. Existing functional similarity measures are distributional, quantifying differences between outputs of models applied to real-world data. However, these measures can be regarded as ecologically valid only for regions in the input space represented by the available data. We introduce a geometrical perspective on functional model similarity, which estimates it across the entire data space, offering a comprehensive view of decision boundary alignment independent of any specific data distribution. We also propose geometric Rashomon Alignment as a measure of geometrical similarity, which is computed using data uniformly sampled from the instance space. We perform an experimental analysis on more than 90 datasets, examining critical cases where model alignment diverges from predictive accuracy. Our results show that geometrical and distributional alignment provide different and complementary perspectives on the similarity between models and algorithms. RA can be used for multiple purposes, including model selection, ensemble construction, and enhanced interpretability of machine learning models and algorithms.

Interpretable Column Annotation with LLM-Symbolized Decision Process Materialization

Column annotation (CA), including column type annotation (CTA) and column property annotation (CPA), aims to identify the meanings of table columns and the semantic relationships among them. Recent CA methods usually use various neural models to learn column representations and directly map them to label categories, thereby (1) sacrificing model interpretability and adaptivity, and (2) overlooking rich label semantics and ultimately limiting accuracy. To address these limitations, we propose SymCA, an LLM-empowered interpretable CA framework that materializes column annotation as a global-to-local symbolic decision process. SymCA consists of two components: (1) global skeleton induction, which constructs a semantic skeleton over the label space, and (2) local substrate evolution, which evolves predictive substrates within the skeleton. Specifically, to exploit label semantics while preserving an interpretable decision process, the global skeleton induction module leverages LLMs to generate candidate hypernym-inspired tree-structured semantic skeletons and employs a Minimum Bayes Risk (MBR)-based consensus strategy to select a robust skeleton against generation variance. Since different internal nodes require different evidence to distinguish among their child nodes, the local substrate evolution module materializes each internal node as an executable and evolvable predictive substrate. Over multiple evolution rounds, each substrate trains an interpretable random forest classifier with the current operator set, leverages the LLM to propose node-specific operator modifications, and uses an exploration-exploitation strategy to prioritize promising substrates. Extensive experiments demonstrate that SymCA is accurate, robust, and interpretable, outperforming the strongest baselines by an average of 6.42% in Micro-F1 and 11.03% in Macro-F1.