Neural Network Interpretability

Follow this topic Ask about this topic

Neural network interpretability asks what a model has learned, which internal computations support its predictions, and whether those computations are understandable and reliable. Post-hoc methods include saliency and attribution, concept-based explanations, counterfactuals, and formal logical explanations; mechanistic work uses probes, sparse autoencoders, circuit analysis, and interventions on neurons or features. Another approach builds interpretability into models through sparse or additive architectures, prototypes, symbolic rules, and concept bottlenecks, with evaluations spanning image, language, time-series, and scientific tasks. A central challenge is showing that an explanation is both human-meaningful and faithful to the model: readable features or sparse circuits alone do not establish causal importance, and methods can vary in robustness and reliability across settings.

Latest papers

333 papers37 papers in the last four weeks, up 23% on the four weeks before. 0.2% of all new papers.

Mar 6, 2026

Sparse Crosscoders for diffing MoEs and Dense models

Mixture of Experts (MoE) achieve parameter-efficient scaling through sparse expert routing, yet their internal representations remain poorly understood compared to dense models. We present a systematic comparison of MoE and dense model internals using crosscoders, a variant of sparse autoencoders, that jointly models multiple activation spaces. We train 5-layer dense and MoEs (equal active parameters) on 1B tokens across code, scientific text, and english stories. Using BatchTopK crosscoders with explicitly designated shared features, we achieve

\sim 87\%

fractional variance explained and uncover concrete differences in feature organization. The MoE learns significantly fewer unique features compared to the dense model. MoE-specific features also exhibit higher activation density than shared features, whereas dense-specific features show lower density. Our analysis reveals that MoEs develop more specialized, focused representations while dense models distribute information across broader, more general-purpose features.

Marmik Chaudhari, Nishkal Hundia, Idhant Gulati

University of California, Berkeley · University of Maryland

Mixture-of-Experts Interpretability Mixture-of-Experts Models Neural Network Interpretability Sparse Autoencoders Representation Geometry in Language Models

Mar 5, 2026

Model Medicine: A Clinical Framework for Understanding, Diagnosing, and Treating AI Models

Model Medicine is the science of understanding, diagnosing, treating, and preventing disorders in AI models, grounded in the principle that AI models -- like biological organisms -- have internal structures, dynamic processes, heritable traits, observable symptoms, classifiable conditions, and treatable states. This paper introduces Model Medicine as a research program, bridging the gap between current AI interpretability research (anatomical observation) and the systematic clinical practice that complex AI systems increasingly require. We present five contributions: (1) a discipline taxonomy organizing 15 subdisciplines across four divisions -- Basic Model Sciences, Clinical Model Sciences, Model Public Health, and Model Architectural Medicine; (2) the Four Shell Model (v3.3), a behavioral genetics framework empirically grounded in 720 agents and 24,923 decisions from the Agora-12 program, explaining how model behavior emerges from Core--Shell interaction; (3) Neural MRI (Model Resonance Imaging), a working open-source diagnostic tool mapping five medical neuroimaging modalities to AI interpretability techniques, validated through four clinical cases demonstrating imaging, comparison, localization, and predictive capability; (4) a five-layer diagnostic framework for comprehensive model assessment; and (5) clinical model sciences including the Model Temperament Index for behavioral profiling, Model Semiology for symptom description, and M-CARE for standardized case reporting. We additionally propose the Layered Core Hypothesis -- a biologically-inspired three-layer parameter architecture -- and a therapeutic framework connecting diagnosis to treatment.

Jihoon Jeong

Department of Electrical Engineering and Computer Science, Daegu Gyeongbuk Institute of Science and Technology (DGIST) · ModuLabs

Explainable Artificial Intelligence Neural Network Interpretability

Mar 4, 2026

SCAN: Visual Explanations with Self-Confidence and Analysis Networks

Explainable AI (XAI) has become essential in computer vision to make the decision-making processes of deep learning models transparent. However, current visual explanation (XAI) methods face a critical trade-off between the high fidelity of architecture-specific methods and the broad applicability of universal ones. This often results in abstract or fragmented explanations and makes it difficult to compare explanatory power across diverse model families, such as CNNs and Transformers. This paper introduces the Self-Confidence and Analysis Networks (SCAN), a novel universal framework that overcomes these limitations for both convolutional neural network and transformer architectures. SCAN utilizes an AutoEncoder-based approach to reconstruct features from a model's intermediate layers. Guided by the Information Bottleneck principle, it generates a high-resolution Self-Confidence Map that identifies information-rich regions. Extensive experiments on diverse architectures and datasets demonstrate that SCAN consistently achieves outstanding performance on various quantitative metrics such as AUC-D, Negative AUC, Drop%, and Win%. Qualitatively, it produces significantly clearer, object-focused explanations than existing methods. By providing a unified framework that is both architecturally universal and highly faithful, SCAN enhances model transparency and offers a more reliable tool for understanding the decision-making processes of complex neural networks.

Gwanghee Lee, Sungyoon Jeong, Kyoungson Jhang

the Department of Computer Science and Engineering, Chungnam National University, Daejeon 34134, Republic of Korea · the Department of Artificial Intelligence, Chungnam National University, Daejeon 34134, Republic of Korea

Neural Network Interpretability Explainable Image Classification

Mar 4, 2026

Towards Explainable Deep Learning for Ship Trajectory Prediction in Inland Waterways

Accurate predictions of ship trajectories in crowded environments are essential to ensure safety in inland waterways traffic. Recent advances in deep learning promise increased accuracy even for complex scenarios. While the challenge of ship-to-ship awareness is being addressed with growing success, the explainability of these models is often overlooked, potentially obscuring an inaccurate logic and undermining the confidence in their reliability. This study examines an LSTM-based vessel trajectory prediction model by incorporating trained ship domain parameters that provide insight into the attention-based fusion of the interacting vessels' hidden states. This approach has previously been explored in the field of maritime shipping, yet the variety and complexity of encounters in inland waterways allow for a more profound analysis of the model's interpretability. The prediction performance of the proposed model variants are evaluated using standard displacement error statistics. Additionally, the plausibility of the generated ship domain values is analyzed. With an final displacement error of around 40 meters in a 5-minute prediction horizon, the model performs comparably to similar studies. Though the ship-to-ship attention architecture enhances prediction accuracy, the weights assigned to vessels in encounters using the learnt ship domain values deviate from the expectation. The observed accuracy improvements are thus not entirely driven by a causal relationship between a predicted trajectory and the trajectories of nearby ships. This finding underscores the model's explanatory capabilities through its intrinsically interpretable design. Future work will focus on utilizing the architecture for counterfactual analysis and on the incorporation of more sophisticated attention mechanisms.

Tom Legel, Dirk Söffker, Roland Schätzle +1

Department Hydraulic Engineering in Inland Areas, Federal Waterways Engineering and Research Institute, Germany · Chair of Dynamics and Control, University of Duisburg-Essen, Germany · Department of Technology (Computer Science), Baden-Wuerttemberg Cooperative State University, Germany +1

Vessel Trajectory Prediction Multi-Agent Trajectory Prediction Neural Network Interpretability Explainability Evaluation

Mar 3, 2026

Sparse autoencoders reveal organized biological knowledge but minimal regulatory logic in single-cell foundation models: a comparative atlas of Geneformer and scGPT

Background: Single-cell foundation models such as Geneformer and scGPT encode rich biological information, but whether this includes causal regulatory logic rather than statistical co-expression remains unclear. Sparse autoencoders (SAEs) can resolve superposition in neural networks by decomposing dense activations into interpretable features, yet they have not been systematically applied to biological foundation models. Results: We trained TopK SAEs on residual stream activations from all layers of Geneformer V2-316M (18 layers, d=1152) and scGPT whole-human (12 layers, d=512), producing atlases of 82525 and 24527 features, respectively. Both atlases confirm massive superposition, with 99.8 percent of features invisible to SVD. Systematic characterization reveals rich biological organization: 29 to 59 percent of features annotate to Gene Ontology, KEGG, Reactome, STRING, or TRRUST, with U-shaped layer profiles reflecting hierarchical abstraction. Features organize into co-activation modules (141 in Geneformer, 76 in scGPT), exhibit causal specificity (median 2.36x), and form cross-layer information highways (63 to 99.8 percent). When tested against genome-scale CRISPRi perturbation data, only 3 of 48 transcription factors (6.2 percent) show regulatory-target-specific feature responses. A multi-tissue control yields marginal improvement (10.4 percent, 5 of 48 TFs), establishing model representations as the bottleneck. Conclusions: These models have internalized organized biological knowledge, including pathway membership, protein interactions, functional modules, and hierarchical abstraction, yet they encode minimal causal regulatory logic. We release both feature atlases as interactive web platforms enabling exploration of more than 107000 features across 30 layers of two leading single-cell foundation models.

Ihor Kendiukhov

Department of Computer Science, University of Tübingen, Tübingen, Germany

Genomic Foundation Models Single-Cell Transcriptomics Neural Network Interpretability Transformer Interpretability

Mar 3, 2026

Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results

Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain difficult to train and interpret. In this work, a novel modeling approach is proposed, which relies on the use of Domain-aware Fourier Features (DaFFs) for the positional encoding of the input space. These features encapsulate all the domain-specific characteristics, such as the geometry and boundary conditions, and unlike Random Fourier Features (RFFs), eliminate the need for explicit boundary condition loss terms and loss balancing schemes, while simplifying the optimization process and reducing the computational cost associated with training. We further develop an LRP-based explainability framework tailored to PINNs, enabling the extraction of relevance attribution scores for the input space. It is demonstrated that PINN-DaFFs achieve orders-of-magnitude lower errors and allow faster convergence compared to vanilla PINNs and RFFs-based PINNs. Furthermore, LRP analysis reveals that the proposed leads to more physically consistent feature attributions, while PINN-RFFs and vanilla PINNs display more scattered and less physics-relevant patterns. These results demonstrate that DaFFs not only enhance PINNs' accuracy and efficiency but also improve interpretability, laying the ground for more robust and informative physics-informed learning.

Alberto Miño Calero, Luis Salamanca, Konstantinos E. Tatsis

Department of Engineering Cybernetics NTNU, Trondheim, Norway · Swiss Data Science Center (SDSC) ETH Zürich, Zürich, Switzerland

Fourier Feature Embeddings Neural Network Interpretability Physics-Informed ML Layer-Wise Relevance Propagation

Mar 3, 2026

Embedding interpretable $\ell_1$ -regression into neural networks for uncovering temporal structure in cell imaging

While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by

\ell_1

regularization, enabling identification of which factors drive observed dynamics. We investigate how these two types of approaches can be optimally combined, exemplarily considering two-photon calcium imaging data where sparse autoregressive dynamics are to be extracted. We propose embedding a vector autoregressive (VAR) model as an interpretable regression technique into a convolutional autoencoder, which provides dimension reduction for tractable temporal modeling. A skip connection separately addresses non-sparse static spatial information, selectively channeling sparse structure into the

\ell_1

-regularized VAR.

\ell_1

-estimation of regression parameters is enabled by differentiating through the piecewise linear solution path. This is contrasted with approaches where the autoencoder does not adapt to the VAR model. Having an embedded statistical model also enables a testing approach for comparing temporal sequences from the same observational unit. Additionally, contribution maps visualize which spatial regions drive the learned dynamics.

Fabian Kabus, Maren Hackenberg, Julia Hindel +6

Institute of Medical Biometry and Statistics (IMBI), Faculty of Medicine and Medical Center, University of Freiburg, Germany · Department of Computer Science, University of Freiburg, Germany · Institute of Physiology I, Faculty of Medicine, University of Freiburg, Germany +2

Autoregressive Modeling Neural Network Interpretability Microscopy Image Analysis Convolutional Autoencoder

Mar 2, 2026

Explanation-Guided Adversarial Training for Robust and Interpretable Models

Deep neural networks (DNNs) have achieved remarkable performance in many tasks, yet they often behave as opaque black boxes. Explanation-guided learning (EGL) methods steer DNNs using human-provided explanations or supervision on model attributions. These approaches improve interpretability but typically assume benign inputs and incur heavy annotation costs. In contrast, both predictions and saliency maps of DNNs could dramatically alter facing imperceptible perturbations or unseen patterns. Adversarial training (AT) can substantially improve robustness, but it does not guarantee that model decisions rely on semantically meaningful features. In response, we propose Explanation-Guided Adversarial Training (EGAT), a unified framework that integrates the strength of AT and EGL to simultaneously improve prediction performance, robustness, and explanation quality. EGAT generates adversarial examples on the fly while imposing explanation-based constraints on the model. By jointly optimizing classification performance, adversarial robustness, and attributional stability, EGAT is not only more resistant to unexpected cases, including adversarial attacks and out-of-distribution (OOD) scenarios, but also offer human-interpretable justifications for the decisions. We further formalize EGAT within the Probably Approximately Correct learning framework, demonstrating theoretically that it yields more stable predictions under unexpected situations compared to standard AT. Empirical evaluations on OOD benchmark datasets show that EGAT consistently outperforms competitive baselines in both clean accuracy and adversarial accuracy +37% while producing more semantically meaningful explanations, and requiring only a limited increase +16% in training time.

Chao Chen, Yanhui Chen, Shanshan Lin +4

Harbin Institute of Technology (Shenzhen) · Fuzhou University · NLPR, MAIS, Institute of Automation, Chinese Academy of Sciences

Adversarial Training Adversarial Robustness Neural Network Interpretability Distribution Shift Robustness

Mar 2, 2026

Bound Propagation meets Constraint Simplification: Improving Logic-based XAI for Neural Networks

Logic-based methods for explaining neural network decisions offer formal guarantees of correctness and non-redundancy, but they often suffer from high computational costs, especially for large networks. In this work, we improve the efficiency of such methods by combining bound propagation with constraint simplification. These simplifications, derived from the propagation, tighten neuron bounds and eliminate unnecessary binary variables, making the explanation process more efficient. Our experiments suggest that combining these techniques reduces explanation time by up to 89.26%, particularly for larger neural networks.

Ronaldo Gomes, Jairo Ribeiro, Luiz Queiroz +1

Department of Computer Science, Instituto Federal do Ceará (IFCE), Maracanaú, Brazil

Explainable Artificial Intelligence Neural Network Interpretability

Feb 28, 2026

Interpretable Cross-Network Attention for Resting-State fMRI Representation Learning

Understanding how large-scale functional brain networks reorganize during cognitive decline remains a central challenge in neuroimaging. While recent self-supervised models have shown promise for learning representations from resting-state fMRI, their internal mechanisms are difficult to interpret, limiting mechanistic insight. We propose BrainInterNet, a network-aware self-supervised framework based on masked reconstruction with cross-attention that explicitly models inter-network dependencies in rs-fMRI. By selectively masking predefined functional networks and reconstructing them from remaining context, our approach enables direct quantification of network predictability and interpretable analysis of cross-network interactions. We train BrainInterNet on multi-cohort fMRI data (from the ABCD, HCP Development, HCP Young Adults, and HCP Aging datasets) and evaluate on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, in total comprising 5,582 recordings. Our method reveals systematic alterations in the brain's network interactions under AD, including in the default mode, limbic, and attention networks. In parallel, the learned representations support accurate Alzheimer's-spectrum classification and yield a compact summary marker that tracks disease severity longitudinally. Together, these results demonstrate that network-guided masked modeling with cross-attention provides an interpretable and effective framework for characterizing functional reorganization in neurodegeneration.

Karanpartap Singh, Adam Turnbull, Mohammad Abbasi +3

Stanford University, Stanford, CA 94305

Brain Network Analysis Functional Connectivity Self-Supervised Time Series Representation Learning Neural Network Interpretability Alzheimer's Disease Classification Cross-Attention

Feb 27, 2026

A Case Study on Concept Induction for Neuron-Level Interpretability in CNN

Deep Neural Networks (DNNs) have advanced applications in domains such as healthcare, autonomous systems, and scene understanding, yet the internal semantics of their hidden neurons remain poorly understood. Prior work introduced a Concept Induction-based framework for hidden neuron analysis and demonstrated its effectiveness on the ADE20K dataset. In this case study, we investigate whether the approach generalizes by applying it to the SUN2012 dataset, a large-scale scene recognition benchmark. Using the same workflow, we assign interpretable semantic labels to neurons and validate them through web-sourced images and statistical testing. Our findings confirm that the method transfers to SUN2012, showing its broader applicability.

Moumita Sen Sarma, Samatha Ereshi Akkamahadevi, Pascal Hitzler

Department of Computer Science, Kansas State University, Manhattan, Kansas, USA

Neuron-Level Interpretability Neural Network Interpretability Concept-Based Explanations Convolutional Neural Networks Mechanistic Interpretability

Feb 25, 2026

Slice and Explain: Logic-Based Explanations for Neural Networks through Domain Slicing

Neural networks (NNs) are pervasive across various domains but often lack interpretability. To address the growing need for explanations, logic-based approaches have been proposed to explain predictions made by NNs, offering correctness guarantees. However, scalability remains a concern in these methods. This paper proposes an approach leveraging domain slicing to facilitate explanation generation for NNs. By reducing the complexity of logical constraints through slicing, we decrease explanation time by up to 40% less time, as indicated through comparative experiments. Our findings highlight the efficacy of domain slicing in enhancing explanation efficiency for NNs.

Luiz Fernando Paulino Queiroz, Carlos Henrique Leitão Cavalcante, Thiago Alves Rocha

Instituto Federal do Ceará (IFCE), Maracanaú, Ceará, Brazil

Neural Network Interpretability

Feb 25, 2026

Physics-Informed Machine Learning for Vessel Shaft Power and Fuel Consumption Prediction: Interpretable KAN-based Approach

Accurate prediction of shaft rotational speed, shaft power, and fuel consumption is crucial for enhancing operational efficiency and sustainability in maritime transportation. Conventional physics-based models provide interpretability but struggle with real-world variability, while purely data-driven approaches achieve accuracy at the expense of physical plausibility. This paper introduces a Physics-Informed Kolmogorov-Arnold Network (PI-KAN), a hybrid method that integrates interpretable univariate feature transformations with a physics-informed loss function and a leakage-free chained prediction pipeline. Using operational and environmental data from five cargo vessels, PI-KAN consistently outperforms the traditional polynomial method and neural network baselines. The model achieves the lowest mean absolute error (MAE) and root mean squared error (RMSE), and the highest coefficient of determination (R^2) for shaft power and fuel consumption across all vessels, while maintaining physically consistent behavior. Interpretability analysis reveals rediscovery of domain-consistent dependencies, such as cubic-like speed-power relationships and cosine-like wave and wind effects. These results demonstrate that PI-KAN achieves both predictive accuracy and interpretability, offering a robust tool for vessel performance monitoring and decision support in operational settings.

Hamza Haruna Mohammed, Dusica Marijan, Arnbjørn Maressa

Simula Research Laboratory, Oslo, Norway · Navtor AS, Egersund, Norway

Maritime Transportation Physics-Informed ML Kolmogorov-Arnold Networks Neural Network Interpretability

Feb 24, 2026

SymTorch: Symbolic Distillation of Neural Networks

What mathematical functions do neural network components learn? Symbolic distillation addresses this question by expressing neural network components with interpretable, closed-form mathematical expressions that expose the functional structure learned during training. We develop symbolic distillation as a systematic, architecture-agnostic methodology, and release our approach as the open-source SymTorch package - a PySR-powered library built natively for the PyTorch ecosystem. Applying this methodology across diverse architectures, we find that SymTorch is successful in the automated discovery of physical laws. Specifically, our approach (1) recovers pairwise interaction forces from graph neural networks trained on empirical

n

-body observations, (2) distills the exact closed-form PDE/ODE solutions of multiple physical systems, including the value of constants, from physics-informed neural networks trained on sparse data, and (3) uncovers the chaotic dynamics of the Lorenz system from high-dimensional data, ultimately outperforming the base neural network on downstream prediction tasks. We further demonstrate the utility of our framework for model interpretability by providing an optimized implementation of SLIME - a symbolic extension to the LIME explainability method. SLIME consistently outperforms LIME across predictive metrics across eight popular classification and regression benchmarks, while still providing an interpretable local symbolic model. Lastly, we investigate replacing transformer MLP layers with symbolic surrogates: replacing 1-7 layers with symbolic approximations yields 2-19% throughput improvements and up to 18.7% VRAM reduction, with the resulting hybrid models lying on the Pareto front of throughput versus perplexity among open-source LLMs of comparable scale.

Elizabeth S. Z. Tan, Adil Soubki, Miles Cranmer

Department of Applied Mathematics and Theoretical Physics University of Cambridge

Neural Network Interpretability Scientific Discovery Symbolic Regression

Feb 24, 2026

Beyond Accuracy: An Explainability-Driven Analysis of Harmful Content Detection

Although automated harmful content detection systems are frequently used to monitor online platforms, moderators and end users frequently cannot understand the logic underlying their predictions. While recent studies have focused on increasing classification accuracy, little focus has been placed on comprehending why neural models identify content as harmful, especially when it comes to borderline, contextual, and politically sensitive situations. In this work, a neural harmful content detection model trained on the Civil Comments dataset is analyzed explainability-drivenly. Two popular post-hoc explanation methods, Shapley Additive Explanations and Integrated Gradients, are used to analyze the behavior of a RoBERTa-based classifier in both correct predictions and systematic failure cases. Despite strong overall performance, with an area under the curve of 0.93 and an accuracy of 0.94, the analysis reveals limitations that are not observable from aggregate evaluation metrics alone. Integrated Gradients appear to extract more diffuse contextual attributions while Shapley Additive Explanations extract more focused attributions on explicit lexical cues. The consequent divergence in their outputs manifests in both false negatives and false positives. Qualitative case studies reveal recurring failure modes such as indirect toxicity, lexical over-attribution, or political discourse. The results suggest that explainable AI can foster human-in-the-loop moderation by exposing model uncertainty and increasing the interpretable rationale behind automated decisions. Most importantly, this work highlights the role of explainability as a transparency and diagnostic resource for online harmful content detection systems rather than as a performance-enhancing lever.

Trishita Dhara, Siddhesh Sheth

Upper Hand, Indianapolis, IN 46204, USA · Ace Rent a Car, Indianapolis, IN 46204, USA

Content Moderation Neural Network Interpretability Transformer Interpretability

Feb 23, 2026

The Confusion is Real: GRAPHIC -- A Network Science Approach to Confusion Matrices in Deep Learning

Explainable artificial intelligence has emerged as a promising field of research to address reliability concerns in artificial intelligence. Despite significant progress in explainable artificial intelligence, few methods provide a systematic way to visualize and understand how classes are confused and how their relationships evolve as training progresses. In this work, we present GRAPHIC, an architecture-agnostic approach that analyzes neural networks on a class level. It leverages confusion matrices derived from intermediate layers using linear classifiers. We interpret these as adjacency matrices of directed graphs, allowing tools from network science to visualize and quantify learning dynamics across training epochs and intermediate layers. GRAPHIC provides insights into linear class separability, dataset issues, and architectural behavior, revealing, for example, similarities between flatfish and man and labeling ambiguities validated in a human study. In summary, by uncovering real confusions, GRAPHIC offers new perspectives on how neural networks learn. The code is available at https://github.com/Johanna-S-Froehlich/GRAPHIC.

Johanna S. Fröhlich, Bastian Heinlein, Jan U. Claar +3

Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen, Germany · Technical University of Darmstadt Darmstadt, Germany

Neural Network Interpretability Explainable Artificial Intelligence Neural Network Training Dynamics Classification

Feb 19, 2026

Systematic Evaluation of Single-Cell Foundation Model Interpretability Reveals Attention Captures Co-Expression Rather Than Unique Regulatory Signal

We present a systematic evaluation framework - thirty-seven analyses, 153 statistical tests, four cell types, two perturbation modalities - for assessing mechanistic interpretability in single-cell foundation models. Applying this framework to scGPT and Geneformer, we find that attention patterns encode structured biological information with layer-specific organisation - protein-protein interactions in early layers, transcriptional regulation in late layers - but this structure provides no incremental value for perturbation prediction: trivial gene-level baselines outperform both attention and correlation edges (AUROC 0.81-0.88 versus 0.70), pairwise edge scores add zero predictive contribution, and causal ablation of regulatory heads produces no degradation. These findings generalise from K562 to RPE1 cells; the attention-correlation relationship is context-dependent, but gene-level dominance is universal. Cell-State Stratified Interpretability (CSSI) addresses an attention-specific scaling failure, improving GRN recovery up to 1.85x. The framework establishes reusable quality-control standards for the field.

Ihor Kendiukhov

Department of Computer Science, University of Tübingen, Tübingen, Germany

Mechanistic Interpretability Neural Network Interpretability Attention Head Analysis Gene Regulatory Network Inference Single-Cell Transcriptomics Single-Cell Perturbation Modeling

Feb 19, 2026

Provably Explaining Neural Additive Models

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.

Shahaf Bassan, Yizhak Yisrael Elboher, Tobias Ladner +4

Hebrew University of Jerusalem, Israel · Technical University of Munich, Germany · Masaryk University, Czech Republic

Interpretable ML Neural Network Interpretability

Feb 19, 2026

Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding elastic and inelastic potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.

Chenyi Ji, Kian P. Abdolazizi, Hagen Holthusen +2

Computational Mechanics in Medicine, Applied Medical Engineering, RWTH Aachen University Pauwelsstraße 20, 52074 Aachen, Germany · Institute for Continuum and Material Mechanics, Hamburg University of Technology Eißendorfer Straße 42, 21073 Hamburg, Germany · Institute of Applied Mechanics, University of Erlangen-Nuremberg Egerlandstrasse 5, 91058 Erlangen, Germany +1

Materials Science Neural Network Interpretability Kolmogorov-Arnold Networks Computational Materials Science Symbolic Regression

Feb 17, 2026

What Do Neurons Listen To? A Neuron-level Dissection of a General-purpose Audio Model

In this paper, we analyze the internal representations of a general-purpose audio self-supervised learning (SSL) model from a neuron-level perspective. Despite their strong empirical performance as feature extractors, the internal mechanisms underlying the robust generalization of SSL audio models remain unclear. Drawing on the framework of mechanistic interpretability, we identify and examine class-specific neurons by analyzing conditional activation patterns across diverse tasks. Our analysis reveals that SSL models foster the emergence of class-specific neurons that provide extensive coverage across novel task classes. These neurons exhibit shared responses across different semantic categories and acoustic similarities, such as speech attributes and musical pitch. We also confirm that these neurons have a functional impact on classification performance. To our knowledge, this is the first systematic neuron-level analysis of a general-purpose audio SSL model, providing new insights into its internal representation.

Takao Kawamura, Daisuke Niizumi, Nobutaka Ono

Graduate School of Systems Design, Tokyo Metropolitan University, Tokyo, Japan

Audio Representation Learning Neural Network Interpretability Self-Supervised Learning

Jan 29, 2026

Mechanistic Evidence for Spectral Structures in Prior-Data Fitted Networks

Prior-Data Fitted Networks (PFNs) perform approximate Bayesian inference in a single forward pass, and tabular foundation models (TFMs) built on them are now widely used. To understand what networks infer internally, recent mechanistic studies of TFMs locate where predictions form, but treat these models as tabular predictors rather than as PFNs. It therefore remains unknown whether PFNs represent the spectral content of their context, the quantity that specifies a stationary kernel, and whether this content can be read out as an explicit kernel. We answer both questions. First, across seven PFNs, including four pretrained TFMs and a model trained only on a decision-tree prior, a linear probe on the residual stream recovers the frequency of the context with

R^2 \geq 0.95

. This structure is led by a single principal direction. Second, activation and subspace patching show that the network uses the structure through a low-dimensional subspace, where a few spectral directions move predictions far more than random ones. This holds even for the decision-tree model, so a spectral training prior is not required. On real datasets with up to 499 features, 64 of the 192 directions of TabPFN, chosen without labels, carry 85 to 95% of the causal effect of the context in all but one pair. Third, we introduce a Filter Bank Decoder that turns frozen PFN representations into an explicit stationary kernel through Bochner's theorem. Without any test-time optimization, the decoded kernel supports Gaussian process regression competitive with deep kernel learning and random Fourier features at about

200\times

lower cost. PFN latents therefore hold spectral structure that is causally used and recoverable as a portable kernel.

Kaustubh Sharma, Srijan Tiwari, Ojasva Nema +1

Indian Institute of Technology Roorkee, India

Prior-Data Fitted Networks Neural Network Interpretability Frequency-Domain Feature Learning Kernel Methods Mechanistic Interpretability Kernel Regression

Jan 10, 2026

Architecture Before the Formula: Training-Dependent Computational Semantics in Transformers

An operation's input-output function does not, by itself, determine its computational role within a represented process. That role also depends on the processes producing its inputs and receiving its outputs, a philosophical stance termed deep learning externalism (DLE). We develop a mathematical account of represented computation that distinguishes functional equivalence, retained predecessor distinctions, restricted receiver capability, and context-dependent effective architectures. The resulting equivalences depend on which computational relations a scientific description must preserve. We prove that two injective producer contexts can preserve every predecessor distinction while changing whether fixed local and attention receiver families are equivalent. We investigate these relations in a dimension-labelled PreNorm Transformer and their evolution under training. Residual bypasses restrict complete-state information identifications to two merges per block, while finer branches can change receiver accessibility. Exact gradient-descent models yield covariance-dependent geometric attenuation under learned producer routing and algebraic

(t^{-1/2})

attenuation under Q/K-softmax training, with optimal bounded-receiver recovery errors derived in both cases. Coupled producer-attention dynamics establish how learning jointly reorganizes the presented features and receiver allocation. Finally, present functional or receiver-profile equivalence need not determine future behavior under an optimizer. In an input-conditioned attention model, two accessibility measurements form an exact reduced predictive state, whereas one alone does not.

Luis F. Rosario Freytes

Transformer Training Dynamics Transformer Attention Neural Network Interpretability Neural Network Training Dynamics

Dec 3, 2025

When, How Long and How Much? Interpretable Neural Networks for Time Series Regression by Learning to Mask and Aggregate

Time series extrinsic regression (TSER) refers to the task of predicting a continuous target variable from an input time series. It appears in many domains, including healthcare, finance, environmental monitoring, and engineering. In these settings, accurate predictions and trustworthy reasoning are both essential. Although state-of-the-art TSER models achieve strong predictive performance, they typically operate as black boxes, making it difficult to understand which temporal patterns drive their decisions. Post-hoc interpretability techniques, such as feature attribution, aim to to explain how the model arrives at its predictions, but often produce coarse, noisy, or unstable explanations. Recently, inherently interpretable approaches based on concepts, additive decompositions, or symbolic regression, have emerged as promising alternatives. However, these approaches remain limited: they require explicit supervision on the concepts themselves, often cannot capture interactions between time-series features, lack expressiveness for complex temporal patterns, and struggle to scale to high-dimensional multivariate data. To address these limitations, we propose MAGNETS (Mask-and-AGgregate NEtwork for Time Series), an inherently interpretable neural architecture for TSER. MAGNETS learns a compact set of human-understandable concepts without requiring any annotations. Each concept corresponds to a learned, mask-based aggregation over selected input features, explicitly revealing both which features drive predictions and when they matter in the sequence. Predictions are formed as combinations of these learned concepts through a transparent, additive structure, enabling clear insight into the model's decision process. The code implementation and datasets are publicly available at https://github.com/FlorentF9/MAGNETS.

Florent Forest, Amaury Wei, Olga Fink

1IMOS Laboratory, EPFL, Lausanne, CH-1015, Switzerland.

Concept-Based Explanations Neural Network Interpretability

Oct 1, 2025

Activation-Deactivation: A General Framework for Robust Post-hoc Explainable AI

Perturbation-based explainability methods face criticism due to their reliance on out-of-distribution mutants. This raises doubts about the quality of the explanations. In this paper, we introduce a novel forward pass paradigm, Activation-Deactivation (AD), which obviates the need for perturbation of the input. AD replaces perturbation of input features with switching off parts of the model corresponding to to the intended perturbations. We implement ConvAD, an AD approximation algorithm for CNNs. ConvAD is a drop-in mechanism that can be easily added to any trained CNN and, without any additional training, generates more robust and more transferable explanations. We provide evaluation results across multiple architectures, datasets, methods and perturbation strategies, demonstrating the superior quality of ConvAD compared to the SOTA.

Akchunya Chanchal, David A. Kelly, Hana Chockler

Department of Informatics King’s College London Strand, WC2R 2LS, London, UK

Explainable Artificial Intelligence Explanation Stability Neural Network Interpretability Explainability Evaluation

Aug 29, 2025

The Algorithm Is Not the Behavior: Learned Priors Override Look-Ahead in a Chess-Playing Neural Network

Recent mechanistic work has uncovered learned algorithms within neural networks, from modular arithmetic to search and planning in game-playing agents. But does algorithmic structure guarantee algorithmic behavior? We investigate this in Leela Chess Zero, the strongest neural chess engine, where prior work identified learned look-ahead. By extending the logit lens to its move-selecting policy network, we discover that correct puzzle solutions--including immediate checkmates--often appear in intermediate layers but are systematically overridden in the final output, a phenomenon we term "forgotten puzzles". Replicating prior analyses on these positions, we find that look-ahead operates normally--future moves of the correct continuation are represented, causally important, and linearly decodable--ruling out a failure of the algorithm. Instead, late layers increasingly shift toward safe play over aggression. To test whether this shift drives the override, we steer the model against these preferences and recover 71.7% of forgotten puzzles, providing causal evidence that safety priors override algorithmically computed solutions. These findings show that algorithmic structure does not guarantee algorithmic behavior: a model can internally solve a problem and still output the wrong answer.

Elias Sandmann, Sebastian Lapuschkin, Wojciech Samek

Fraunhofer HHI · TU Dublin · TU Berlin

Neural Algorithmic Reasoning Neural Network Interpretability Game-Playing Agents

Aug 11, 2025

Neural Logic Networks for Interpretable Classification

Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a logical mechanism relating the inputs and outputs with AND and OR operations. We generalize these networks with NOT operations and biases that take into account unobserved data and develop a rigorous logical and probabilistic modeling in terms of concept combinations to motivate their use. We also propose a novel factorized IF-THEN rule structure for the model as well as a modified learning algorithm. Our method improves the state-of-the-art in Boolean networks discovery and is able to learn relevant, interpretable rules in tabular classification, notably on examples from the medical and industrial fields where interpretability has tangible value.

Vincent Perreault, Katsumi Inoue, Richard Labib +1

Department of Mathematics and Industrial Engineering Polytechnique Montréal · National Institute of Informatics, Tokyo

Boolean Function Learning Neural Network Interpretability Neurosymbolic Learning

Jun 30, 2025

Position: Use Sparse Autoencoders to Discover Unknowns

While sparse autoencoders (SAEs) have generated significant excitement, a series of negative results have added to skepticism about their usefulness. Here, we establish a conceptual distinction that reconciles competing narratives surrounding SAEs. We argue that even if SAEs may be less effective for acting on known concepts, SAEs are especially powerful tools for discovering unknown concepts. This distinction separates existing negative results from positive results, and suggests several classes of SAE applications. Specifically, we outline use cases for SAEs in (i) ML interpretability, explainability, fairness, auditing, and safety, and (ii) social and health sciences.

Kenny Peng, Rajiv Movva, Jon Kleinberg +2

1Cornell University · 2UC Berkeley

Explainable Artificial Intelligence Sparse Autoencoders Neural Network Interpretability

May 29, 2025

Learning Interpretable Differentiable Logic Networks for Tabular Regression

Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed Differentiable Logic Networks (DLNs) to address these issues for tabular classification based on relaxing discrete logic into a differentiable form, thereby enabling gradient-based learning of networks built from binary logic operations. DLNs offer interpretable reasoning and substantially lower inference cost. We extend the DLN framework to supervised tabular regression. We first redesign the final output layer (the SumLayer) to support continuous targets. More critically, we find the original two-phase training procedure used for classification is suboptimal for regression, and thus develop a unified, single-stage optimization procedure. We also demonstrate that temperature annealing of the network's differentiable relaxations is decisive for achieving stable convergence and high accuracy. We evaluate the resulting model on 15 public regression benchmarks, comparing it with modern neural networks and classical regression baselines. Regression DLNs match or exceed baseline accuracy while preserving interpretability and fast inference. Our results show that DLNs are a viable, cost-effective alternative for regression tasks, especially where model transparency and computational efficiency are important.

Chang Yue, Niraj K. Jha

Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA

Efficient Neural Network Inference Differentiable Logic Gate Networks Neural Network Interpretability Tabular Regression Differentiable Logic

May 26, 2025

Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression strategy for large-scale neural networks. However, despite encouraging empirical results, tensorized neural networks (TNNs) remain underutilized in mainstream deep learning. In this position paper, we offer a perspective on both the potential and current limitations of TNNs. We argue that TNNs represent a powerful yet underexplored framework for deep learning--one that deserves greater attention from both engineering and theoretical communities. Beyond compression, we highlight the value of TNNs as a flexible class of architectures with distinctive scaling properties and increased interpretability. A central feature of TNNs is the presence of bond indices, which introduce new latent spaces not found in conventional networks. These internal representations may provide deeper insight into the evolution of features across layers, potentially advancing the goals of mechanistic interpretability. We conclude by outlining several key research directions aimed at overcoming the practical barriers to scaling and adopting TNNs in modern deep learning workflows.

Safa Hamreras, Sukhbinder Singh, Román Orús

Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain · Multiverse Computing, Spadina Ave., Toronto, ON M5T 2C2, Canada · Multiverse Computing, Paseo de Miramón 170, E-20014 San Sebastián, Spain

Tensor Networks Neural Network Interpretability Neural Network Compression

May 21, 2025

Explainable embeddings with Distance Explainer

While eXplainable AI (XAI) has advanced significantly, few methods address interpretability in embedded vector spaces where dimensions represent complex abstractions. We introduce Distance Explainer, a novel method for generating local, post-hoc explanations of embedded spaces in machine learning models. Our approach adapts saliency-based techniques from RISE to explain the distance between two embedded data points by assigning attribution values through selective masking and distance-ranked mask filtering. We evaluate Distance Explainer on cross-modal embeddings (image-image and image-caption pairs) using established XAI metrics including Faithfulness, Sensitivity/Robustness, and Randomization. Experiments with ImageNet and CLIP models demonstrate that our method effectively identifies features contributing to similarity or dissimilarity between embedded data points while maintaining high robustness and consistency. We also explore how parameter tuning, particularly mask quantity and selection strategy, affects explanation quality. This work addresses a critical gap in XAI research and enhances transparency and trustworthiness in deep learning applications utilizing embedded spaces.

Christiaan Meijer, E. G. Patrick Bos

Netherlands eScience Center, Science Park 402, 1098 XH Amsterdam, Netherlands · Center for Information Technology, University of Groningen, P.O. Box 11044, 9700 CA Groningen, Netherlands

Feature Attribution Perturbation-Based Feature Attribution VLM Interpretability Neural Network Interpretability