Neural Network Interpretability

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Overview

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.

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

Apr 17, 2026

The Query Channel: Information-Theoretic Limits of Masking-Based Explanations

Masking-based post-hoc explanation methods, such as KernelSHAP and LIME, estimate local feature importance by querying a black-box model under randomized perturbations. This paper formulates this procedure as communication over a query channel, where the latent explanation acts as a message and each masked evaluation is a channel use. Within this framework, the complexity of the explanation is captured by the entropy of the hypothesis class, while the query interface supplies information at a rate determined by an identification capacity per query. We derive a strong converse showing that, if the explanation rate exceeds this capacity, the probability of exact recovery necessarily converges to one in error for any sequence of explainers and decoders. We also prove an achievability result establishing that a sparse maximum-likelihood decoder attains reliable recovery when the rate lies below capacity. A Monte Carlo estimator of mutual information yields a non-asymptotic query benchmark that we use to compare optimal decoding with Lasso- and OLS-based procedures that mirror LIME and KernelSHAP. Experiments reveal a range of query budgets where information theory permits reliable explanations but standard convex surrogates still fail. Finally, we interpret super-pixel resolution and tokenization for neural language models as a source-coding choice that sets the entropy of the explanation and show how Gaussian noise and nonlinear curvature degrade the query channel, induce waterfall and error-floor behavior, and render high-resolution explanations unattainable.

Erciyes Karakaya, Ozgur Ercetin

*Department of Electrical and Computer Engineering, University of Maryland, College Park, USA · †Faculty of Engineering and Natural Sciences, Sabanci University, Turkiye

Feature AttributionExplainable Artificial IntelligenceNeural Network InterpretabilityExplainability EvaluationInformation-Theoretic Lower Bounds
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Apr 16, 2026

ProtoTTA: Prototype-Guided Test-Time Adaptation

Deep networks that rely on prototypes-interpretable representations that can be related to the model input-have gained significant attention for balancing high accuracy with inherent interpretability, which makes them suitable for critical domains such as healthcare. However, these models are limited by their reliance on training data, which hampers their robustness to distribution shifts. While test-time adaptation (TTA) improves the robustness of deep networks by updating parameters and statistics, the prototypes of interpretable models have not been explored for this purpose. We introduce ProtoTTA, a general framework for prototypical models that leverages intermediate prototype signals rather than relying solely on model outputs. ProtoTTA minimizes the entropy of the prototype-similarity distribution to encourage more confident and prototype-specific activations on shifted data. To maintain stability, we employ geometric filtering to restrict updates to samples with reliable prototype activations, regularized by prototype-importance weights and model-confidence scores. Experiments across four prototypical backbones on four diverse benchmarks spanning fine-grained vision, histopathology, and NLP demonstrate that ProtoTTA improves robustness over standard output entropy minimization while restoring correct semantic focus in prototype activations. We also introduce novel interpretability metrics and a vision-language model (VLM) evaluation framework to explain TTA dynamics, confirming ProtoTTA restores human-aligned semantic focus and correlates reliably with VLM-rated reasoning quality. Code is available at: https://github.com/DeepRCL/ProtoTTA.

Mohammad Mahdi Abootorabi, Parvin Mousavi, Purang Abolmaesumi +1

University of British Columbia · Queen’s University · Vector Institute

Prototype-Based LearningTest-Time AdaptationNeural Network Interpretability
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Apr 16, 2026

Improving Sparse Autoencoder with Dynamic Attention

Recently, sparse autoencoders (SAEs) have emerged as a promising technique for interpreting activations in foundation models by disentangling features into a sparse set of concepts. However, identifying the optimal level of sparsity for each neuron remains challenging in practice: excessive sparsity can lead to poor reconstruction, whereas insufficient sparsity may harm interpretability. While existing activation functions such as ReLU and TopK provide certain sparsity guarantees, they typically require additional sparsity regularization or cherry-picked hyperparameters. We show in this paper that dynamically sparse attention mechanisms using sparsemax can bridge this trade-off, due to their ability to determine the activation numbers in a data-dependent manner. Specifically, we first explore a new class of SAEs based on the cross-attention architecture with the latent features as queries and the learnable dictionary as the key and value matrices. To encourage sparse pattern learning, we employ a sparsemax-based attention strategy that automatically infers a sparse set of elements according to the complexity of each neuron, resulting in a more flexible and general activation function. Through comprehensive evaluation and visualization, we show that our approach successfully achieves lower reconstruction loss while producing high-quality concepts, particularly in top-n classification tasks.

Dongsheng Wang, Jinsen Zhang, Dawei Su +1

College of Computer Science and Software Engineering, Shenzhen University, China

Sparse AutoencodersNeural Network InterpretabilitySparse Attention
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Apr 15, 2026

Zero-Ablation Overstates Register Content Dependence in DINO Vision Transformers

Zero-ablation -- replacing token activations with zero vectors -- is widely used to probe token function in vision transformers. Register zeroing in DINOv2+registers and DINOv3 produces large drops (up to −36.6-36.6,pp classification, −30.9-30.9,pp segmentation), suggesting registers are functionally indispensable. However, three replacement controls -- mean-substitution, noise-substitution, and cross-image register-shuffling -- preserve performance across classification, correspondence, and segmentation, remaining within ∼1{\sim}1,pp of the unmodified baseline. Per-patch cosine similarity shows these replacements genuinely perturb internal representations, while zeroing causes disproportionately large perturbations, consistent with why it alone degrades tasks. We conclude that zero-ablation overstates dependence on exact register content. In the frozen-feature evaluations we test, performance depends on plausible register-like activations rather than on exact image-specific values. Registers nevertheless buffer dense features from [CLS] dependence and are associated with compressed patch geometry. These findings, including the replacement-control results, replicate at ViT-B scale.

Felipe Parodi, Jordan Matelsky, Melanie Segado

University of Pennsylvania · Johns Hopkins Applied Physics Laboratory

Vision TransformerNeural Network InterpretabilitySelf-Supervised Visual Representation Learning
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Apr 15, 2026

Geometric Routing Enables Causal Expert Control in Mixture of Experts

Sparse Mixture-of-Experts (MoE) models scale parameters while fixing active computation per token, but the specialization of individual experts remains opaque. In a companion paper we showed that routing topology is quality-neutral: five structurally different configurations converge to statistically equivalent language modeling quality. Here we show that expert identity is nonetheless causally meaningful: individual rank-1 experts are monosemantic by construction, and cosine-similarity routing in a low-dimensional metric space makes their specialization directly inspectable. We present four lines of evidence. First, projecting expert output vectors through the unembedding matrix yields a Semantic Dictionary: 15% of experts are monosemantic specialists spanning 10 categories (temporal, geographic, cardinal, discourse, emotional, financial, military, scientific). Second, routing exhibits a frequency-to-syntax gradient: early layers separate tokens by word frequency, deeper layers by syntactic class (Zipf-confound controls, all p<0.001p < 0.001). Third, causal interventions confirm these labels: steering toward a temporal expert's centroid increases P(temporal) by +321% (median across 44 prompts); suppressing a geographic expert drops P(geographic) by -23%; rewriting an expert's output vector halves target-category probability, and effects compose additively across layers. Fourth, the interventions are not unique to cosine routing: linear routers support comparable steering, but only cosine routing provides geometric transparency -- expert specialization is readable directly from the centroid matrix. MoE expert-level specialization is a first-class interpretability primitive: architecturally monosemantic, causally validated, and controllable at inference with zero overhead.

Ivan Ternovtsii, Yurii Bilak

Department of Software Systems, Uzhhorod National University, Narodna sq. 3, Uzhhorod, Ukraine, 88000 · HengeBytes

Mixture-of-Experts InterpretabilityMixture-of-Experts Expert SpecializationMixture of ExpertsMixture-of-Experts ModelsNeural Network InterpretabilityRepresentation Geometry in Language Models
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Apr 15, 2026

Hardware-Efficient Neuro-Symbolic Networks with the Exp-Minus-Log Operator

Deep neural networks (DNNs) deliver state-of-the-art accuracy on regression and classification tasks, yet two structural deficits persistently obstruct their deployment in safety-critical, resource-constrained settings: (i) opacity of the learned function, which precludes formal verification, and (ii) reliance on heterogeneous, library-bound activation functions that inflate latency and silicon area on edge hardware. The recently introduced Exp-Minus-Log (EML) Sheffer operator, eml(x, y) = exp(x) - ln(y), was shown by Odrzywolek (2026) to be sufficient - together with the constant 1 - to express every standard elementary function as a binary tree of identical nodes. We propose to embed EML primitives inside conventional DNN architectures, yielding a hybrid DNN-EML model in which the trunk learns distributed representations and the head is a depth-bounded, weight-sparse EML tree whose snapped weights collapse to closed-form symbolic sub-expressions. We derive the forward equations, prove computational-cost bounds, analyse inference and training acceleration relative to multilayer perceptrons (MLPs) and physics-informed neural networks (PINNs), and quantify the trade-offs for FPGA/analog deployment. We argue that the DNN-EML pairing closes a literature gap: prior neuro-symbolic and equation-learner approaches (EQL, KAN, AI-Feynman) work with heterogeneous primitive sets and do not exploit a single hardware-realisable Sheffer element. A balanced assessment shows that EML is unlikely to accelerate training, and on commodity CPU/GPU it is also unlikely to accelerate inference; however, on a custom EML cell (FPGA logic block or analog circuit) the asymptotic latency advantage can reach an order of magnitude with simultaneous gain in interpretability and formal-verification tractability.

Eymen Ipek

Institute of Automotive Engineering, Graz University of Technology, Austria

Neurosymbolic LearningEfficient Neural Network InferenceNeural Network InterpretabilityFPGA-Based Neural Network AccelerationNeural Network Verification
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Apr 13, 2026

The Linear Centroids Hypothesis: Features as Directions Learned by Local Experts

The Linear Representation Hypothesis (LRH) identifies features of a trained deep network (DN) as linear directions in the activation spaces, i.e., output spaces of intermediate layers. This characterization decouples the input-output maps learned by a DN from the organization of feature directions in its activation spaces. We introduce the Linear Centroids Hypothesis (LCH), which instead identifies features with linear directions among a DN's centroid spaces -- where any vector denotes a centroid or summary of a local affine expert characterizing the learned input-output maps of the DN exactly (e.g., for piecewise-affine DNs) or approximately (e.g., for smooth DNs like transformers). We show that replacing intermediate activations with centroids yields a functional drop-in alternative for standard interpretability tools. Empirically, this change yields sparser, more downstream-useful feature dictionaries on DINO ViTs, suppresses spurious directions on a controlled task, recovers interpretable circuits in GPT2-Large, and produces faithful gradient-based saliency maps. LCH unifies dictionaries, probing, circuits, and saliency maps into a single geometric object grounded in the network's input-output map -- making interpretability mechanistic by construction rather than post hoc. Code to study the LCH https://github.com/ThomasWalker1/LinearCentroidsHypothesis .

Thomas Walker, Ahmed Imtiaz Humayun, Randall Balestriero +1

Rice University · Google Research · Brown University

Neural Network InterpretabilityMechanistic InterpretabilityTransformer InterpretabilityRepresentation Geometry in Language Models
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Apr 13, 2026

THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture

We present THEIA, a 2.75M-parameter modular neural architecture that learns the complete Kleene three-valued logic (K3) truth table from task data without external symbolic inference or hand-encoded K3 gate primitives. Across 5 seeds it passes all 39 K3 rules at >99% per-rule accuracy. K3 learnability is not the central finding: Transformer baselines also pass all 39 rules, and flat MLPs match THEIA on Phase-1 accuracy within 0.04pp. The contributions are two properties of the learned system. (1) Uncertainty-verdict asymmetric propagation. THEIA preserves Has-Unknown at every upstream boundary (80.0/91.1/90.8/99.7% across Arith/Order/Set/Logic vs. ~52% majority) while final-verdict decodability stays at or below a 73.4% U-vs-non-U oracle reference under linear and nonlinear probes. Activation patching on non-absorbent T->U cases flips 4,898/4,898 OR and 4,719/4,719 AND pairs across 5 seeds, ruling out residual shortcuts. (2) Reliability spectrum under discretized end-to-end training, on tasks decomposable along the engine boundaries. A mod-3 sequential composition task generalizes from 5- to 500-step evaluation at 99.96+-0.04% (5 seeds). Under identical Gumbel-softmax training, flat MLPs collapse to chance by 50 steps; a 2x2 ResMLP grid reaches >=99% on only 3/20 (config, seed) trials; a pre-LN Transformer reaches 99.24+-0.34%. Straight-through discretization prevents 0.999^500 compounding; the architectural separator is sustaining Phase-1 accuracy under Phase-3 training, where flat MLPs fail. Auxiliary: under per-architecture development defaults (not optimizer-controlled), THEIA reaches 12/12 Kleene coverage 6.5x faster than a parameter-comparable 8L Transformer; this narrows to ~3.6x with Transformer-standard tuning and 4.93x with the same recipe on both. Ratios are config-specific, not asymptotic.

Augustus Haoyang Li

Irvine Valley College Irvine, CA, USA

Neural Network InterpretabilityCompositional GeneralizationModular Neural Networks
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Apr 12, 2026

Visualising the Attractor Landscape of Neural Cellular Automata

As Neural Cellular Automata (NCAs) are increasingly applied outside of the toy models in Artificial Life, there is a pressing need to understand how they behave and to build appropriate routes to interpret what they have learnt. By their very nature, the benefits of training NCAs are balanced with a lack of interpretability: we can engineer emergent behaviour, but have limited ability to understand what has been learnt. In this paper, we apply a variety of techniques to pry open the NCA black box and glean some understanding of what it has learnt to do. We apply techniques from manifold learning (principal components analysis and both dense and sparse autoencoders) along with techniques from topological data analysis (persistent homology) to capture the NCA's underlying behavioural manifold, with varying success. Results show that when analysis is performed at a macroscopic level (i.e. taking the entire NCA state as a single data point), the underlying manifold is often quite simple and can be captured and analysed quite well. When analysis is performed at a microscopic level (i.e. taking the state of individual cells as a single data point), the manifold is highly complex and more complicated techniques are required in order to make sense of it.

James Stovold, Mia-Katrin Kvalsund, Harald Michael Ludwig +2

University of York, UK · University of Oslo, Norway · Machine Learning Research Unit, TU Wien, Austria +2

Neural Cellular AutomataNeural Network InterpretabilityDynamical Systems
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Apr 9, 2026

On-board Telemetry Monitoring in Autonomous Satellites: Challenges and Opportunities

The increasing autonomy of spacecraft demands fault-detection systems that are both reliable and explainable. This work addresses eXplainable Artificial Intelligence for onboard Fault Detection, Isolation and Recovery within the Attitude and Orbit Control Subsystem by introducing a framework that enhances interpretability in neural anomaly detectors. We propose a method to derive low-dimensional, semantically annotated encodings from intermediate neural activations, called peepholes. Applied to a convolutional autoencoder, the framework produces interpretable indicators that enable the identification and localization of anomalies in reaction-wheel telemetry. Peepholes analysis further reveals bias detection and supports fault localization. The proposed framework enables the semantic characterization of detected anomalies while requiring only a marginal increase in computational resources, thus supporting its feasibility for on-board deployment.

Lorenzo Capelli, Leandro de Souza Rosa, Maurizio De Tommasi +8

University of Bologna, Italy · Thales Alenia Space Italia, Rome, Italy · European Space Agency (ESA-ESTEC), Netherlands

Interpretable Anomaly DetectionFault DetectionAnomaly DetectionNeural Network InterpretabilityFault Localization
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Apr 9, 2026

Neural-Symbolic Knowledge Tracing: Injecting Educational Knowledge into Deep Learning for Responsible Learner Modelling

The growing use of artificial intelligence (AI) in education, particularly large language models (LLMs), has increased interest in intelligent tutoring systems. However, LLMs often show limited adaptivity and struggle to model learners' evolving knowledge over time, highlighting the need for dedicated learner modelling approaches. Although deep knowledge tracing methods achieve strong predictive performance, their opacity and susceptibility to bias can limit alignment with pedagogical principles. To address this, we propose Responsible-DKT, a neural-symbolic deep knowledge tracing approach that integrates symbolic educational knowledge (e.g., mastery and non-mastery rules) into sequential neural models for responsible learner modelling. Experiments on a real-world dataset of students' math interactions show that Responsible-DKT outperforms both a neural-symbolic baseline and a fully data-driven PyTorch DKT model across training settings. The model achieves over 0.80 AUC with only 10% of training data and up to 0.90 AUC, improving performance by up to 13%. It also demonstrates improved temporal reliability, producing lower early- and mid-sequence prediction errors and the lowest prediction inconsistency rates across sequence lengths, indicating that prediction updates remain directionally aligned with observed student responses over time. Furthermore, the neural-symbolic approach offers intrinsic interpretability via a grounded computation graph that exposes the logic behind each prediction, enabling both local and global explanations. It also allows empirical evaluation of pedagogical assumptions, revealing that repeated incorrect responses (non-mastery) strongly influence prediction updates. These results indicate that neural-symbolic approaches enhance both performance and interpretability, mitigate data limitations, and support more responsible, human-centered AI in education.

Danial Hooshyar, Gustav Šír, Yeongwook Yang +6

School of Digital Technologies Tallinn University, Estonia · Faculty of Information Technology University of Jyväskylä Finland · Faculty of Education and Psychology University of Jyväskylä Finland +7

Knowledge TracingAI in EducationNeurosymbolic LearningNeural Network Interpretability
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Apr 9, 2026

LINE: LLM-based Iterative Neuron Explanations for Vision Models

Interpreting individual neurons in deep neural networks is a crucial step towards understanding their complex decision-making processes and ensuring AI safety. Despite recent progress in neuron labeling, existing methods often limit the search space to predefined concept vocabularies or produce overly specific descriptions that fail to capture higher-order, global concepts. We introduce LINE, a novel, training-free iterative approach tailored for open-vocabulary concept labeling in vision models. Operating in a strictly black-box setting, LINE leverages a large language model and a text-to-image generator to iteratively propose and refine concepts in a closed loop, guided by activation history. LINE achieves state-of-the-art performance across multiple model architectures, yielding AUC improvements of up to 0.11 on ImageNet and 0.05 on Places365, while discovering, on average, 27% of new concepts missed by predefined vocabularies. Beyond identifying the top concept, LINE provides a complete generation history, enabling polysemanticity evaluation and producing visual explanations that rival gradient-dependent activation maximization methods. The source code will be made available soon.

Vladimir Zaigrajew, Michał Piechota, Gaspar Sekula +2

Centre for Credible AI Warsaw University of Technology · Warsaw University of Technology Warsaw, Poland · Centre for Credible AI, Warsaw University of Technology University of Warsaw, Poland

Neuron-Level InterpretabilityNeural Network Interpretability
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Apr 8, 2026

ConceptTracer: Interactive Analysis of Concept Saliency and Selectivity in Neural Representations

Neural networks deliver impressive predictive performance across a variety of tasks, but they are often opaque in their decision-making processes. Despite a growing interest in mechanistic interpretability, tools for systematically exploring the representations learned by neural networks in general, and tabular foundation models in particular, remain limited. In this work, we introduce ConceptTracer, an interactive application for analyzing neural representations through the lens of human-interpretable concepts. ConceptTracer integrates two information-theoretic measures that quantify concept saliency and selectivity, enabling researchers and practitioners to identify neurons that respond strongly to individual concepts. We demonstrate the utility of ConceptTracer on representations learned by TabPFN and show that our approach facilitates the discovery of interpretable neurons. Together, these capabilities provide a practical framework for investigating how neural networks like TabPFN encode concept-level information. ConceptTracer is available at https://github.com/ml-lab-htw/concept-tracer.

Ricardo Knauer, Andre Beinrucker, Erik Rodner

KI-Werkstatt, University of Applied Sciences Berlin, Berlin, Germany

Neural Network InterpretabilityNeuron-Level InterpretabilityMechanistic InterpretabilityConcept-Based Explanations
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Apr 8, 2026

Explaining Neural Networks in Preference Learning: a Post-hoc Inductive Logic Programming Approach

In this paper, we propose using Learning from Answer Sets to approximate black-box models, such as Neural Networks (NN), in the specific case of learning user preferences. We specifically explore the use of ILASP (Inductive Learning of Answer Set Programs) to approximate preference learning systems through weak constraints. We have created a dataset on user preferences over a set of recipes, which is used to train the NNs that we aim to approximate with ILASP. Our experiments investigate ILASP both as a global and a local approximator of the NNs. These experiments address the challenge of approximating NNs working on increasingly high-dimensional feature spaces while achieving appropriate fidelity on the target model and limiting the increase in computational time. To handle this challenge, we propose a preprocessing step that exploits Principal Component Analysis to reduce the dataset's dimensionality while keeping our explanations transparent. Under consideration for publication in Theory and Practice of Logic Programming (TPLP).

Daniele Fossemò, Filippo Mignosi, Giuseppe Placidi +3

Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Italy · ICAR-CNR, Palermo, Italy · Department of Life, Health and Environmental Sciences, University of L’Aquila, Italy +2

Neural Network InterpretabilityPreference LearningInductive Logic Programming
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Apr 7, 2026

Beyond Semantics: Disentangling Information Scope in Sparse Autoencoders for CLIP

Sparse Autoencoders (SAEs) have emerged as a powerful tool for interpreting the internal representations of CLIP vision encoders, yet existing analyses largely focus on the semantic meaning of individual features. We introduce information scope as a complementary dimension of interpretability that characterizes how broadly an SAE feature aggregates visual evidence, ranging from localized, patch-specific cues to global, image-level signals. We observe that some SAE features respond consistently across spatial perturbations, while others shift unpredictably with minor input changes, indicating a fundamental distinction in their underlying scope. To quantify this, we propose the Contextual Dependency Score (CDS), which separates positionally stable local scope features from positionally variant global scope features. Our experiments show that features of different information scopes exert systematically different influences on CLIP's predictions and confidence. These findings establish information scope as a critical new axis for understanding CLIP representations and provide a deeper diagnostic view of SAE-derived features.

Yusung Ro, Jaehyun Choi, Junmo Kim

KAIST · Korea AI Safety Institute, ETRI

Neural Network InterpretabilityVLM InterpretabilitySparse AutoencodersMultimodal Model Interpretability
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Apr 7, 2026

PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network

Data-driven machine learning approaches have become increasingly attractive for nonlinear system identification, but standard models often fail to preserve the underlying physical structure and remain difficult to interpret, especially when no analytical model is available. In this context, port-Hamiltonian (pH) models provide a natural physics-informed representation. However, when these models are parameterized with standard multilayer perceptrons (MLPs), the learned constitutive components often remain poorly interpretable. In this paper, we propose a structure-preserving identification framework for nonlinear port-Hamiltonian systems based on Kolmogorov-Arnold Networks (KANs). The proposed PH-KAN model parameterizes the interconnection matrix, dissipation matrix, Hamiltonian, and input mapping using dedicated KAN blocks, while enforcing the port-Hamiltonian constraints by construction. This yields constitutive representations in which the nonlinear functions defining the identified pH components can be explicitly inspected, leading to a more interpretable model than with standard MLP-based parameterizations.

Achraf El Messaoudi, Karim Cherifi, Yann Le Gorrec +1

UMLP, ENSMM, FEMTO-ST · Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, institut FEMTO-ST, F-25000 Besançon, France

Nonlinear System IdentificationPort-Hamiltonian SystemsNeural Network Interpretability
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Apr 4, 2026

Functional Similarity Metric for Neural Networks: Overcoming Parametric Ambiguity via Activation Region Analysis

As modern deep learning architectures grow in complexity, representational ambiguity emerges as a critical barrier to their interpretability and reliable merging. For ReLU networks, identical functional mappings can be achieved through entirely different weight configurations due to algebraic symmetries: neuron permutation and positive diagonal scaling. Consequently, traditional parameter-based comparison methods exhibit extreme instability to slight weight perturbations during training. This paper proposes a mathematically grounded approach to constructing a stable canonical representation of neural networks and a robust functional similarity metric. We shift focus from comparing raw weights to analyzing the topology of neuron activation regions. The algorithm first eliminates scaling ambiguity via L2-normalization of weight vectors with subsequent layer compensation. Next, discrete approximations of activation regions are generated as binary functional signatures evaluated over a data sample. To overcome the computational bottleneck of comparing large binary vectors, we adapt Locality-Sensitive Hashing, specifically MinHash, providing a fast and statistically precise approximation of the Jaccard index. The final cross-network neuron matching is formulated as a linear sum assignment problem solved via the Hungarian algorithm. We demonstrate theoretically and experimentally that our metric mitigates the neuron "flickering" effect and exhibits exceptional robustness to minor weight perturbations. This framework provides a solid foundation for model merging, transfer learning, objective assessment during pruning, and Explainable AI paradigms.

Kutomanov Hennadii

Representational Similarity AnalysisNeural Network Interpretability
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Apr 4, 2026

Interpretable Fuzzy Modeling Reveals Population-Level Representation Differences in P300 Brain Computer Interfaces Across Neurodivergent and Neurotypical Cohorts

P300-based brain-computer interfaces (BCIs) are widely used for communication, but population heterogeneity may alter the neural patterns available for decoding. Prior work has mainly examined such differences at the signal or performance level, while the representation structure learned by the decoder remains underexplored. In this study, we propose an interpretable fuzzy spatiotemporal framework for P300 classification and use it to analyze population-level differences across amyotrophic lateral sclerosis (ALS), autism (AUT), and neurotypical (NT) cohorts. The model employs spatial and temporal fuzzy filters with learnable prototypes, enabling both classification and reconstruction of cohort-specific fuzzy centers. Experiments were conducted on ALS and NT subsets from bigP3BCI and on the BCIAUT-P300 benchmark in a within-subject setting. The proposed model achieved competitive performance against multiple deep learning baselines. More importantly, the reconstructed fuzzy centers revealed systematic cohort-dependent differences in waveform morphology and representation geometry. Point-wise statistical analysis identified significant temporal differences between cohorts, including intervals overlapping with the canonical P300 window, and low-dimensional embeddings showed partially separated cohort-specific prototype organizations. These results suggest that population heterogeneity in P300-BCI is reflected not only in decoding performance but also in the discriminative structure learned by the model. The proposed framework provides an interpretable route toward population-aware P300-BCI analysis and design.

Xiaowei Jiang, Sudong Shang, Adrian Wilkinson +4

Computational Intelligence and Brain-Computer Interfaces lab, Australian AI Institute, Faculty of Engineering and Information Technology, University of Technology Sydney, 2007, Australia · Department of Management, Griffith Business School, 4215, Australia · Department of Neuroscience, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, 19104, USA +2

Brain-Computer InterfacesEEG DecodingPrototype-Based ClassificationFuzzy LogicNeural Network Interpretability
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Apr 2, 2026

The Expert Strikes Back: Interpreting Mixture-of-Experts Language Models at Expert Level

Mixture-of-Experts (MoE) architectures have become the dominant choice for scaling Large Language Models (LLMs), activating only a subset of parameters per token. While MoE architectures are primarily adopted for computational efficiency, it remains an open question whether their sparsity makes them inherently easier to interpret than dense feed-forward networks (FFNs). We compare MoE experts and dense FFNs using kk-sparse probing and find that expert neurons are consistently less polysemantic, with the gap widening as routing becomes sparser. This suggests that sparsity pressures both individual neurons and entire experts toward monosemanticity. Leveraging this finding, we zoom out from the neuron to the expert level as a more effective unit of analysis. We validate this approach by automatically interpreting hundreds of experts. This analysis allows us to resolve the debate on specialization: experts are neither broad domain specialists (e.g., biology) nor simple token-level processors. Instead, they function as fine-grained task experts, specializing in linguistic operations or semantic tasks (e.g., closing brackets in LaTeX\LaTeX{}). Our findings suggest that MoEs are inherently interpretable at the expert level, providing a clearer path toward large-scale model interpretability. Code is available at: https://github.com/jerryy33/MoE_analysis.

Jeremy Herbst, Stefan Wermter, Jae Hee Lee

Department of Informatics, University of Hamburg, Hamburg, Germany.

Mixture-of-Experts InterpretabilityMixture-of-Experts ModelsMixture-of-Experts Language ModelsLLM InterpretabilityNeural Network Interpretability
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Apr 2, 2026

PhiNet: Speaker Verification with Phonetic Interpretability

Despite remarkable progress, automatic speaker verification (ASV) systems typically lack the transparency required for high-accountability applications. Motivated by how human experts perform forensic speaker comparison (FSC), we propose a speaker verification network with phonetic interpretability, PhiNet, designed to enhance both local and global interpretability by leveraging phonetic evidence in decision-making. For users, PhiNet provides detailed phonetic-level comparisons that enable manual inspection of speaker-specific features and facilitate a more critical evaluation of verification outcomes. For developers, it offers explicit reasoning behind verification decisions, simplifying error tracing and informing hyperparameter selection. In our experiments, we demonstrate PhiNet's interpretability with practical examples, including its application in analyzing the impact of different hyperparameters. We conduct both qualitative and quantitative evaluations of the proposed interpretability methods and assess speaker verification performance across multiple benchmark datasets, including VoxCeleb, SITW, and LibriSpeech. Results show that PhiNet achieves performance comparable to traditional black-box ASV models while offering meaningful, interpretable explanations for its decisions, bridging the gap between ASV and forensic analysis.

Yi Ma, Shuai Wang, Tianchi Liu +1

Department of Electrical and Computer Engineering, National University of Singapore, 119077, Singapore · School of Intelligence Science and Technology, Nanjing University, Suzhou, 215163, China · Shenzhen Loop Area Institute, Shenzhen, China +2

Speaker VerificationNeural Network Interpretability
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Mar 31, 2026

Real-Time Explanations for Tabular Foundation Models

Interpretability is central for scientific machine learning, as understanding why models make predictions enables hypothesis generation and validation. While tabular foundation models show strong performance, existing explanation methods like SHAP are computationally expensive, limiting interactive exploration. We introduce ShapPFN, a foundation model that integrates Shapley value regression directly into its architecture, producing both predictions and explanations in a single forward pass. On standard benchmarks, ShapPFN achieves competitive performance while producing high-fidelity explanations (R2R^2=0.96, cosine=0.99) over 1000\times faster than KernelSHAP (0.06s vs 610s). Our code is available at https://github.com/kunumi/ShapPFN

Luan Borges Teodoro Reis Sena, Francisco Galuppo Azevedo

Kunumi Institute, Belo Horizonte, Minas Gerais, Brazil · Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil

Neural Network InterpretabilityTabular Foundation ModelsSHAP Feature AttributionShapley Value Attribution
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Mar 31, 2026

From Density Matrices to Phase Transitions in Deep Learning: Spectral Early Warnings and Interpretability

A key problem in the modern study of AI is predicting and understanding emergent capabilities in models during training. Inspired by methods for studying reactions in quantum chemistry, we present the ``2-datapoint reduced density matrix". We show that this object provides a computationally efficient, unified observable of phase transitions during training. By tracking the eigenvalue statistics of the 2RDM over a sliding window, we derive two complementary signals: the spectral heat capacity, which we prove provides early warning of second-order phase transitions via critical slowing down, and the participation ratio, which reveals the dimensionality of the underlying reorganization. Remarkably, the top eigenvectors of the 2RDM are directly interpretable making it straightforward to study the nature of the transitions. We validate across four distinct settings: deep linear networks, induction head formation, grokking, and emergent misalignment. We then discuss directions for future work using the 2RDM.

Max Hennick, Guillaume Corlouer

Phase Transitions in Neural NetworksNeural Network Training DynamicsStatistical Physics of LearningNeural Network Interpretability
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Mar 30, 2026

Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their intrinsic geometry, they may fail to capture subtle yet crucial distinctions between fundamentally different neural network solutions. Here, we introduce metric similarity analysis (MSA), a novel method which leverages tools from Riemannian geometry to compare the intrinsic geometry of neural representations under the manifold hypothesis. We show that MSA can be used to i) disentangle features of neural computations in deep networks with different learning regimes, ii) compare nonlinear dynamics, and iii) investigate diffusion models. Hence, we introduce a mathematically grounded and broadly applicable framework to understand the mechanisms behind neural computations by comparing their intrinsic geometries.

N Alex Cayco-Gajic, Arthur Pellegrino

Gatsby Unit, University College London

Neural Representation GeometryRepresentational Similarity AnalysisNeural Network Interpretability
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Mar 30, 2026

Post-hoc Self-explanation of CNNs

Although standard Convolutional Neural Networks (CNNs) can be mathematically reinterpreted as Self-Explainable Models (SEMs), their built-in prototypes do not on their own accurately represent the data. Replacing the final linear layer with a kk-means-based classifier addresses this limitation without compromising performance. This work introduces a common formalization of kk-means-based post-hoc explanations for the classifier, the encoder's final output (B4), and combinations of intermediate feature activations. The latter approach leverages the spatial consistency of convolutional receptive fields to generate concept-based explanation maps, which are supported by gradient-free feature attribution maps. Empirical evaluation with a ResNet34 shows that using shallower, less compressed feature activations, such as those from the last three blocks (B234), results in a trade-off between semantic fidelity and a slight reduction in predictive performance.

Ahcène Boubekki, Line H. Clemmensen

Department of Mathematical Sciences, University of Copenhagen, Denmark

Prototype-Based ExplanationNeural Network InterpretabilityExplainable Image ClassificationConcept-Based ExplanationsConvolutional Neural Networks
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Mar 27, 2026

TTE-CAM: Self-Explainable Class Activation Maps for Pretrained Black-Box CNNs

Convolutional neural networks (CNNs) achieve state-of-the-art performance in medical image analysis yet remain opaque, limiting adoption in high-stakes clinical settings. Existing approaches face a fundamental trade-off: post-hoc methods provide unfaithful approximate explanations, while inherently interpretable architectures are faithful but often sacrifice predictive performance. We introduce TTE-CAM, a test-time framework that bridges this gap by converting pretrained black-box CNNs into self-explainable models via a convolution-based replacement of their classification head, initialized from the original weights. The resulting model preserves black-box predictive performance while delivering built-in faithful explanations competitive with post-hoc methods, both qualitatively and quantitatively. The code is available at https://github.com/kdjoumessi/Test-Time-Explainability

Kerol Djoumessi, Philipp Berens

Hertie Institute for AI in Brain Health, University of Tübingen, Germany · Tübingen AI Center, University of Tübingen, Germany

Explainable Image ClassificationNeural Network InterpretabilityExplainable Medical Image AnalysisFeature AttributionConvolutional Neural Networks
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Mar 26, 2026

End-to-end Feature Alignment: A Simple CNN with Intrinsic Class Attribution

We present Feature-Align CNN (FA-CNN), a prototype CNN architecture with intrinsic class attribution through end-to-end feature alignment. Our intuition is that the use of unordered operations such as Linear and Conv2D layers cause unnecessary shuffling and mixing of semantic concepts, thereby making raw feature maps difficult to understand. We introduce two new order preserving layers, the dampened skip connection, and the global average pooling classifier head. These layers force the model to maintain an end-to-end feature alignment from the raw input pixels all the way to final class logits. This end-to-end alignment enhances the interpretability of the model by allowing the raw feature maps to intrinsically exhibit class attribution. We prove theoretically that FA-CNN penultimate feature maps are identical to Grad-CAM saliency maps. Moreover, we prove that these feature maps slowly morph layer-by-layer over network depth, showing the evolution of features through network depth toward penultimate class activations. FA-CNN performs well on benchmark image classification datasets. Moreover, we compare the averaged FA-CNN raw feature maps against Grad-CAM and permutation methods in a percent pixels removed interpretability task. We conclude this work with a discussion and future, including limitations and extensions toward hybrid models.

Parniyan Farvardin, David Chapman

University of Miami

Neural Network InterpretabilityExplainable Image ClassificationConvolutional Neural NetworksFeature AttributionGradient-Based AttributionSaliency Map Evaluation
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Mar 26, 2026

Vision Hopfield Memory Networks for Image Recognition

Recent vision backbones, such as Transformer families and state-space models like Mamba, have achieved remarkable progress on image recognition. Despite their empirical success, these architectures remain far from the computational principles of the human brain, often demanding enormous amounts of training data while offering limited interpretability. We propose the Vision Hopfield Memory Network (V-HMN), a brain-inspired vision backbone that integrates hierarchical memory mechanisms across layers with iterative refinement updates. Specifically, V-HMN incorporates local Hopfield modules that provide associative memory dynamics at the image patch level, global Hopfield modules that function as episodic memory for contextual modulation, and a predictive-coding-inspired refinement rule for iterative error correction. By organizing these memory-based modules hierarchically, V-HMN captures both local and global dynamics in a unified framework. Memory retrieval exposes the relationship between inputs and stored patterns, providing a prototype-based form of interpretability through explicit memory retrieval, while the reuse of stored patterns improves data efficiency. This brain-inspired design therefore enhances data efficiency and provides a prototype-based form of interpretability compared to existing self-attention- or state-space-based approaches. We conducted extensive experiments on public image classification benchmarks. V-HMN achieves strong performance on small- and medium-scale benchmarks, and remains competitive with widely adopted backbone architectures on ImageNet despite minimal architectural tuning, while offering improved data efficiency and a prototype-based form of interpretability. These findings highlight the potential of V-HMN as a memory-centric alternative to standard vision backbones, thereby bridging brain-inspired computation with modern machine learning.

Jianfeng Wang, Amine M'Charrak, Luk Koska +6

Department of Computer Science, University of Oxford, United Kingdom · Faculty of Informatics, Vienna University of Technology, Austria

Memory-Augmented Neural NetworksHopfield NetworksImage ClassificationNeural Network Interpretability
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Mar 26, 2026

Select, Hypothesize and Verify: Towards Verified Neuron Concept Interpretation

It is essential for understanding neural network decisions to interpret the functionality (also known as concepts) of neurons. Existing approaches describe neuron concepts by generating natural language descriptions, thereby advancing the understanding of the neural network's decision-making mechanism. However, these approaches assume that each neuron has well-defined functions and provides discriminative features for neural network decision-making. In fact, some neurons may be redundant or may offer misleading concepts. Thus, the descriptions for such neurons may cause misinterpretations of the factors driving the neural network's decisions. To address the issue, we introduce a verification of neuron functions, which checks whether the generated concept highly activates the corresponding neuron. Furthermore, we propose a Select-Hypothesize-Verify framework for interpreting neuron functionality. This framework consists of: 1) selecting activation samples that best capture a neuron's well-defined functional behavior through activation-distribution analysis; 2) forming hypotheses about concepts for the selected neurons; and 3) verifying whether the generated concepts accurately reflect the functionality of the neuron. Extensive experiments show that our method produces more accurate neuron concepts. Our generated concepts activate the corresponding neurons with a probability approximately 1.5 times that of the current state-of-the-art method.

ZeBin Ji, Yang Hu, Xiuli Bi +2

Chongqing Key Laboratory of Image Cognition, Chongqing University of Posts and Telecommunications, Chongqing, China · Jinan Inspur Data Technology Co., Ltd., Jinan, China

Neuron-Level InterpretabilityNeural Network InterpretabilityConcept-Based Explanations
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Mar 25, 2026

A Practical Guide Towards Interpreting Time-Series Deep Clinical Predictive Models: A Reproducibility Study

Clinical decisions are high-stakes and require explicit justification, making model interpretability essential for auditing deep clinical models prior to deployment. As the ecosystem of model architectures and explainability methods expands, critical questions remain: Do architectural features like attention improve explainability? Do interpretability approaches generalize across clinical tasks? While prior benchmarking efforts exist, they often lack extensibility and reproducibility, and critically, fail to systematically examine how interpretability varies across the interplay of clinical tasks and model architectures. To address these gaps, we present a comprehensive benchmark evaluating interpretability methods across diverse clinical prediction tasks and model architectures. Our analysis reveals that: (1) attention when leveraged properly is a highly efficient approach for faithfully interpreting model predictions; (2) black-box interpreters like KernelSHAP and LIME are computationally infeasible for time-series clinical prediction tasks; and (3) several interpretability approaches are too unreliable to be trustworthy. From our findings, we discuss several guidelines on improving interpretability within clinical predictive pipelines. To support reproducibility and extensibility, we provide our implementations via PyHealth, a well-documented open-source framework: https://github.com/sunlabuiuc/PyHealth.

Yongda Fan, John Wu, Andrea Fitzpatrick +3

University of Illinois Urbana-Champaign, Champaign, IL 61801, USA · PyHealth · University of Illinois College of Medicine, Chicago, IL 60612, USA

Explainable Time Series ForecastingNeural Network InterpretabilityExplainability EvaluationClinical Prediction
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Mar 25, 2026

From Weights to Concepts: Data-Free Interpretability of CLIP via Singular Vector Decomposition

As vision-language models are deployed at scale, understanding their internal mechanisms becomes increasingly critical. Existing interpretability methods predominantly rely on activations, making them dataset-dependent, vulnerable to data bias, and often restricted to coarse head-level explanations. We introduce SITH (Semantic Inspection of Transformer Heads), a fully data-free, training-free framework that directly analyzes CLIP's vision transformer in weight space. For each attention head, we decompose its value-output matrix into singular vectors and interpret each one via COMP (Coherent Orthogonal Matching Pursuit), a new algorithm that explains them as sparse, semantically coherent combinations of human-interpretable concepts. We show that SITH yields coherent, faithful intra-head explanations, validated through reconstruction fidelity and interpretability experiments. This allows us to use SITH for precise, interpretable weight-space model edits that amplify or suppress specific concepts, improving downstream performance without retraining. Furthermore, we use SITH to study model adaptation, showing how fine-tuning primarily reweights a stable semantic basis rather than learning entirely new features.

Francesco Gentile, Nicola Dall'Asen, Francesco Tonini +3

University of Trento · University of Pisa · Fondazione Bruno Kessler

Transformer InterpretabilityVLM InterpretabilityNeural Network InterpretabilityConcept-Based ExplanationsVLM Adaptation
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