Layer-Wise Relevance Propagation

Hyperbolic neural networks introduce geometric operations that require explicit treatment in relevance propagation. Equivalent geometric realizations can produce different feature attributions, even when local relevance is conserved. We study this problem through Geometric Representation Invariance (GRI), a specialization of Implementation Invariance, and zero-curvature consistency, which requires identity relevance propagation when a geometric module approaches the identity. We propose LRP-radial-all for origin-centered radial modules, treating geometric scaling as modulation and assigning relevance entirely to the signal branch. The rule conserves relevance, is invariant to equivalent radial factorizations, and satisfies zero-curvature consistency, yielding GRI for a specified Poincaré-Lorentz logarithmic-map construction. In contrast, a conservative LRP-half baseline can violate both consistency criteria. Experiments on hyperbolic MNIST, sEEG, and CIFAR-10 classifiers assess attribution fidelity, qualitative explanations, and runtime. LRP-radial-all achieves competitive attribution fidelity across datasets with runtime comparable to Gradient$\times$Input and substantially lower than Integrated Gradients. These findings motivate geometry-aware propagation rules that distinguish relevance conservation from consistency across equivalent computations.

Vision Transformers (ViTs) are central to most modern vision models, yet obtaining input attributions that are fine-grained, faithful, and stable remains challenging. Layer-wise Relevance Propagation (LRP) has been adapted to transformer attention, but in ViTs it often produces noisy, unfaithful explanations. We show that the missing ingredient is the treatment of residual connections: cancellation effects in residual pathways lead to attribution explosion. Moreover, we find that these cancellations are substantially stronger in ViTs than in language transformers. To address this issue, we introduce Residual-aware Layer-wise Relevance Propagation (ResLRP), a simple extension of LRP whose propagation rules explicitly account for cancellations in residual branches, are exactly conservative, and provably bound relevance explosion. Causal channel-wise interventions confirm that residual cancellation, not a generic regularization effect, drives the instability. ResLRP substantially improves attribution quality across faithfulness and localization, evaluated on ViT architectures spanning supervised, self-supervised, contrastive, hierarchical, and multimodal families, as well as on the ground-truth-controlled FunnyBirds benchmark. The largest gains arise in modern Vision Language Models (VLMs), with +27-29% localization and up to 3.4x faithfulness scores. Beyond benchmarks, ResLRP localizes Sparse Autoencoder (SAE) features in input space, and our residual amplification measure serves as an architecture-level diagnostic predicting where attribution degrades.

Vision Transformer (ViT) design has become increasingly diverse, with backbones combining convolutional stems, windowed, linear, or multi-axis attention, patch merging, and spatial reduction in various configurations. This diversity poses challenges for existing attribution methods, whose assumptions often do not hold across ViT variants: Grad-CAM requires a terminal spatial feature map, attention rollout assumes global softmax attention, and layer-wise relevance propagation (LRP) requires module-specific rules. To the best of our knowledge, no existing method provides a unified attribution framework across this architectural space. We show that this architectural diversity can be captured by a simpler underlying structure. The attention and resolution-reduction operators in current ViTs can be decomposed into four operation types: linear maps, bilinear mixing, normalization or gating, and reindexing. Each operation admits a relevance rule that satisfies conservation. Based on these rules, HiLRP supports new backbones by construction rather than by architecture-specific derivation, and its attribution maps decompose the prediction rather than relying on heuristic assumptions. We prove conservation and conditional equivariance and verify both to machine precision. Across 14 attribution methods and 10 architectures, we find that no prior method remains reliable across ViT families, while Faithfulness Correlation becomes uninformative for backbones robust to spatial masking. HiLRP alone preserves conservation across windowed, spatial-reduction, multi-axis, and linear-attention models, where naive extensions can produce zero or inflated relevance. It also localizes attribution failures in class activation mapping, achieving 0.97 Pointing compared with 0.55 for competing methods on EfficientViT.

Vision Transformers (ViTs) are difficult to interpret because current methods of relevance propagation and attention flow do not fully consider some key architectural features, such as the uneven importance of attention heads and residual connections. Prior approaches typically assume uniform importance across attention heads; furthermore, they model skip connections as identity paths, leading to inaccurate relevance attribution. To address these issues, we introduce GradSkip, a novel relevance propagation method for ViTs based on adaptive head weighting and skip-aware propagation. GradSkip models the different importance of the attention heads and dynamically distributes relevance between the attention and residual paths. Experiments on ImageNet1K and BloodMNIST demonstrate a state-of-the-art faithfulness of GradSkip while requiring over 14 times fewer GFLOPs than the best-performing existing approaches. Additional evaluations using transformer-based segmentation confirm improved localization and alignment with ground-truth regions.

We ask a simple question about decoder-only transformers: between which two layers is the probability of a predicted token actually produced? Existing layer-wise readout tools answer only approximately. The logit lens and its trained variant report a per-layer level of probability but give no additive decomposition; their estimates are biased and non-monotone across depth. Direct Logit Attribution and related residual-stream methods are additive, but only in logit space, the softmax nonlinearity breaks additivity in probability space, precisely the quantity one usually cares about. Layer Conductance integrates gradients per layer, but attributes each to its own baseline and so does not sum to the total change in prediction. We introduce IG-Lens, a telescoping application of Integrated Gradients along a single path through the hidden states from a baseline to the final layer. Crediting each segment to the layer it terminates at yields a layer-wise attribution whose sum is exactly the change in target probability, with the softmax inside the integration path rather than linearized away. Our default estimator credits each integration step its observed change in target probability (a prediction-aware reweighting in the spirit of IDGI) rather than its raw gradient. Because the readout is a one-dimensional probability, this collapses each segment to a telescoping sum of endpoint values, so completeness holds exactly (to floating point) at any step count, removing Riemann discretization error while suppressing steps that show gradient sensitivity without a change in output. We give the telescoping identity and its proof, verify completeness to floating point, and describe a single-pass batched implementation computing the full token-by-layer map without any backward call. Code: https://github.com/anhnda/IGLens.

Graph Neural Networks (GNNs) have become important machine learning tools for graph analysis, and its explainability is crucial for safety, fairness, and robustness. Layer-wise relevance propagation for GNNs (GNN-LRP) evaluates the relevance of \emph{walks} to reveal important information flows in the network, and provides higher-order explanations, which have been shown to be superior to the lower-order, i.e., node-/edge-level, explanations. However, identifying relevant walks by GNN-LRP requires {\em exponential} computational complexity with respect to the network depth, which we will remedy in this paper. Specifically, we propose {\em polynomial-time} algorithms for finding top-$K$ relevant walks, which drastically reduces the computation and thus increases the applicability of GNN-LRP to large-scale problems. Our proposed algorithms are based on the \emph{max-product} algorithm -- a common tool for finding the maximum likelihood configurations in probabilistic graphical models -- and can find the most relevant walks exactly at the neuron level and approximately at the node level. Our experiments demonstrate the performance of our algorithms at scale and their utility across application domains, i.e., on epidemiology, molecular, and natural language benchmarks. We provide our codes under github.com/xiong-ping/rel_walk_gnnlrp.

Explaining graph neural networks (GNNs) has become more and more important recently. Higher-order interpretation schemes, such as GNN-LRP (layer-wise relevance propagation for GNN), emerged as powerful tools for unraveling how different features interact thereby contributing to explaining GNNs. GNN-LRP gives a relevance attribution of walks between nodes at each layer, and the subgraph attribution is expressed as a sum over exponentially many such walks. In this work, we demonstrate that such exponential complexity can be avoided. In particular, we propose novel algorithms that enable to attribute subgraphs with GNN-LRP in linear-time (w.r.t. the network depth). Our algorithms are derived via message passing techniques that make use of the distributive property, thereby directly computing quantities for higher-order explanations. We further adapt our efficient algorithms to compute a generalization of subgraph attributions that also takes into account the neighboring graph features. Experimental results show the significant acceleration of the proposed algorithms and demonstrate the high usefulness and scalability of our novel generalized subgraph attribution method.

Emerging foundation models (FMs) in electroencephalography (EEG) promise a path to scale deep learning in diagnostics and brain-computer interfaces despite data scarcity, yet their opaque nature remains a barrier to wider adoption. We investigate attention-aware Layer-wise relevance propagation (LRP) as a post-hoc attribution method for EEG-FMs, extending LRP's use on convolutional neural network (CNN)-based EEG models to the Transformer architectures that current FMs are based on. We find that LRP can both verify EEG-FM decisions and surface novel, biologically plausible hypotheses from them. In motor imagery, it unmasks 'Clever Hans' behavior where models prioritize task correlated ocular signals over the intended motor correlates. In a naturalistic paradigm for affect prediction, it reveals a recurring reliance on a central electrode cluster, suggesting a candidate sensorimotor signature of arousal. Though heatmap interpretation remains ambiguous in this complex domain, the results position LRP as a tool for both verification and exploration of EEG-FMs, a role that will grow in both importance and discovery potential as the underlying models mature.

Attribution methods explain which input features drive a model's prediction, making them central to model debugging and mechanistic interpretability. Yet backward attribution methods, including gradients, LRP, and transformer-specific rules, lack a shared framework in which to compare the underlying backward calculations. We introduce such a framework by recasting backward attribution as a two-player game on an extended network graph, building on Gaubert and Vlassopoulos' ReLU Net Game. Gradients and the full alpha-beta-LRP family arise as integrals over game trajectories under specific equilibria, so attribution maps become projections of trajectory distributions rather than the primary object. Desired explanation properties, such as localisation focus, robustness to input noise, or stable attention routing, can be specified as game-theoretic concepts, including policy regularization, risk aversion, and extended action sets, and translate directly into novel adaptations of the well-known backward rules. On ViT-B/16, one such selected adaptation of alpha-beta-LRP outperforms prior transformer-specific backward methods across all considered localisation metrics.

Multimodal large language models (MLLMs) achieve strong performance on vision- and audio-language tasks, yet can generate responses that conflict with the given visual or auditory inputs, a problem known as multimodal hallucinations. Prior work suggests that this occurs when models rely more on textual cues and learned language patterns than on evidence from the perceptual input. To obtain a more direct account of this imbalance, we apply Layer-wise Relevance Propagation (LRP), which attributes predictions to individual input tokens, and use the resulting relevance scores to analyze and mitigate hallucinations. First, we examine whether this imbalance leads to multimodal hallucinations. We find that hallucinations often arise when the model relies less on perceptual inputs, and that changing this reliance affects its predictions. We further leverage LRP and propose a training-free framework that shifts relevance toward perceptual tokens by optimizing key-value representations during decoding, without modifying model parameters or requiring training data. We call this method Learning Inference-time Modality Enhancement (LIME). Despite using no spatial or temporal supervision, LIME concentrates relevance on query-relevant regions. We evaluate LIME across multiple multimodal benchmarks in both vision and audio domains, demonstrating consistent reductions in hallucinations and enhanced grounding while preserving generation quality.

Explaining deep neural network predictions on genome sequences enables biological insight and hypothesis generation-often of greater interest than predictive performance alone. While explanations of convolutional neural networks (CNNs) have been shown to capture relevant patterns in genome sequences, it is unclear whether this transfers to more expressive Transformer-based genome language models (gLMs). To answer this question, we adapt AttnLRP, an extension of layer-wise relevance propagation to the attention mechanism, and apply it to the state-of-the-art gLM DNABERT-2. Thereby, we propose strategies to transfer explanations from token and nucleotide level. We evaluate the adaption of AttnLRP on genomic datasets using multiple metrics. Further, we provide an extensive comparison between the explanations of DNABERT-2 and a baseline CNN. Our results demonstrate that AttnLRP yields reliable explanations corresponding to known biological patterns. Hence, like CNNs, gLMs can also help derive biological insights. This work contributes to the explainability of gLMs and addresses the comparability of relevance attributions across different architectures.

Interpretability tools are increasingly used to analyze failures of Large Language Models (LLMs), yet prior work largely focuses on short prompts or toy settings, leaving their behavior on commonly used benchmarks underexplored. To address this gap, we study contrastive, LRP-based attribution as a practical tool for analyzing LLM failures in realistic settings. We formulate failure analysis as \textit{contrastive attribution}, attributing the logit difference between an incorrect output token and a correct alternative to input tokens and internal model states, and introduce an efficient extension that enables construction of cross-layer attribution graphs for long-context inputs. Using this framework, we conduct a systematic empirical study across benchmarks, comparing attribution patterns across datasets, model sizes, and training checkpoints. Our results show that this token-level contrastive attribution can yield informative signals in some failure cases, but is not universally applicable, highlighting both its utility and its limitations for realistic LLM failure analysis. Our code is available at: https://aka.ms/Debug-XAI.

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.