Scale-Aware Interpretability

• Scale-aware interpretability is a framework that reveals neural network features organized across multiple scales, from fine details to global context.
• It employs methodologies like multi-scale feature extraction, uncertainty mapping, and attention-based scale selection to robustly characterize model predictions.
• The approach provides formal guarantees and error bounds, enhancing model transparency in applications such as medical imaging and semantic segmentation.

Scale-aware interpretability refers to a class of interpretability frameworks and methods for neural networks that explicitly account for, and leverage, the inherent multi-scale structure of data and representations. Rather than treating a model as a flat mapping from inputs to outputs, scale-aware interpretability seeks to uncover, disentangle, and robustly characterize the ways in which features at different spatial, temporal, or semantic resolutions are composed, interact, and influence model predictions. This paradigm aims to address the inadequacies of traditional interpretability tools, which often provide only local, input-output attributions or ignore the hierarchical organization of network internals.

1. Formal Foundations and Definitions

Scale-aware interpretability is grounded in the idea that neural networks internally organize features across multiple scales—ranging from fine (local details or atomic operations) to coarse (global context or high-level concepts). A principled scale-aware interpretability method is characterized by:

• Tracking feature composition as resolution changes: It explicitly describes how features at one scale are aggregated, marginalized, or interact to produce features at higher (coarser) scales or to influence network outputs.
• Separation of relevant and irrelevant information: Degrees of freedom that are unimportant for the observable of interest at a given scale are systematically identified and, if discarded, their impact on observables is quantitatively bounded.
• Worst-case guarantees: The method provides explicit, formal bounds on the change in a chosen observable when fine-scale structure is marginalized, e.g.,

$$\sup_{F^\text{fine}, F^{\text{fine}\prime}} |O(R_\Lambda(\Theta;F^\text{coarse},F^\text{fine})) - O(R_\Lambda(\Theta;F^\text{coarse},F^{\text{fine}\prime}))| \leq \epsilon(\Lambda)$$

where $R_\Lambda$ is a coarse-graining operator at scale $\Lambda$ (Greenspan et al., 5 Feb 2026).

This approach extends traditional feature attribution or saliency by making explicit the scale (or hierarchy of scales) at which interpretability claims are made, and under what conditions those claims remain robust.

2. Methodological Approaches

A range of algorithmic and theoretical techniques have been developed to achieve scale-aware interpretability, spanning vision, language, and multimodal domains. Representative methodologies include:

• Multi-scale feature extraction and fusion: Architectures such as U-Net variants and fully convolutional networks (FCNs) explicitly construct multi-resolution representations, which are then fused with mechanisms (attention, gating, etc.) that enable per-location and per-scale weighting (Chen et al., 2015, Zhang et al., 2023, Sinha et al., 16 Jan 2025).
• Uncertainty-based scale tracking: Uncertainty maps (epistemic and aleatoric, often estimated via Monte Carlo dropout) are computed at multiple scales and spatial resolutions, revealing where and at which scale the network is most uncertain about its predictions (Zhang et al., 2023).
• Attention-based scale selection: Attention mechanisms that learn per-location, per-scale weights over feature maps, providing both improved accuracy and the capacity to visualize which scale determined each prediction (Chen et al., 2015, Sinha et al., 16 Jan 2025).
• Manifold alignment: Decomposition of latent spaces into nested semantic manifolds (e.g., global, intermediate, local), with mappings between scales optimized for geometric alignment and mutual information preservation. This enables explicit tracking of how semantic information propagates and transforms across scales and layers (Zhang et al., 24 May 2025).
• Renormalization group (RG) and kernel truncation approaches: Techniques from statistical physics are adapted to define coarse-graining operators, quantify spectral (or information-theoretic) scales, and provide error bounds for discarding irrelevant fine-scale features (Greenspan et al., 5 Feb 2026).

These approaches are often combined with visualization tools (e.g., scale-specific heatmaps, saliency overlays), ablation or pruning studies (to identify scale-specific redundancy or importance), and functional metrics to quantify scale-wise attributions.

3. Architectural Instantiations

Scale-aware interpretability has been operationalized across several model classes:

• Medical image segmentation: SSU-Net augments a U-Net with spatial and scale uncertainty maps (computed via MC dropout), Gated Soft Uncertainty-Aware modules, and Multi-Scale Uncertainty-Aware fusion. This yields per-location, per-scale epistemic and aleatoric uncertainty visualizations, tightly binding the prediction at each spatial point to the scale at which the network is confident (Zhang et al., 2023).
• Semantic segmentation in vision: Attention to Scale models process multi-resolution inputs with shared encoders, using an attention head to produce per-scale weights at each spatial location. Visualization of these attention maps reveals which scale is trusted for which object or structure, and auxiliary scale supervision is used to enhance both accuracy and interpretability (Chen et al., 2015).
• Concept-aligned ViT models: ASCENT-ViT utilizes a multi-scale CNN feature pyramid, merges these with ViT patch embeddings via deformable attention, and then aligns to human-labeled concepts using attention heads. The framework directly provides interpretable, scale-aware heatmaps indicating which patches and scales contributed to the detection of specific semantic concepts (Sinha et al., 16 Jan 2025).
• Multi-modal diagnosis networks: Dual-branch (global/local) CNN streams fused via attention gates have been used to combine wide-context and fine-patch information, with saliency maps over both channels visualized and quantified for their anatomical specificity and clinical trustworthiness (Onari et al., 2 Aug 2025).

In LLMs, multi-scale analysis includes:

• Multi-scale manifold alignment: Partitioning layers into clusters (global, sentence, word) and learning cross-scale mappings constrained to be geometrically and information-theoretically faithful, enabling controlled interventions or inspection at arbitrary semantic granularity (Zhang et al., 24 May 2025).
• Redundancy and necessary component analysis: Systematic pruning and ablation reveal that only a small core of components (e.g., “induction heads”) are critical for in-context generalization, with the rest being largely redundant—thus providing interpretability at the scale of architectural modules or units (Bansal et al., 2022).
• Causal abstraction and invertible alignment: Methods such as Boundless DAS discover low-dimensional, functionally meaningful subspaces aligned to symbolic algorithms, providing a coarse-grained causal abstraction of LLM computations (Wu et al., 2023).

4. Quantitative Guarantees and Evaluation Metrics

A distinguishing objective of scale-aware interpretability is the provision of formal guarantees regarding the faithfulness and robustness of the interpretations as resolution changes. This includes:

• Worst-case error bounds: Under spectral truncation or coarse-graining operations, observable quantities (e.g., regression output, safety probes) are bounded by the norm of discarded feature components, e.g.,

$$\| \hat{y}_\text{full} - \hat{y}_\text{trunc} \|_2 \leq \mu^{-1} \sum_{j>k} \lambda_j \|y\|_2$$

where $\lambda_j$ are kernel eigenvalues and $\mu$ a regularization parameter (Greenspan et al., 5 Feb 2026).

• Hierarchical conditional independence: If the RG map is block-diagonal, the influence of fine-scale (irrelevant) features on a given observable is upper-bounded by the corresponding Jacobian singular values.
• Feature Consistency Rate (FCR): Proportion of samples with consistent feature assignment under scale-conditioned inversion—quantitatively assesses whether features at different layers/scales encode the same information (Luo et al., 9 Jun 2025).
• Interchange Intervention Accuracy (IIA): For causal abstraction alignment, measures the rate at which low-dimensional, interpretable interventions faithfully transfer through the network, matching ground-truth algorithmic decisions (Wu et al., 2023).
• Ablation and redundancy quantification: For large models, the fraction of components pruned with minimal accuracy loss delineates which scales or modules are necessary vs. superfluous for generalization and thus interpretable responsibility (Bansal et al., 2022).
• Coherence, RMA, and RRA: In medical imaging, metrics such as Relevance Mass Accuracy and Relevance Rank Accuracy quantify the correspondence between model attributions (e.g., from fused attention maps) and ground-truth anatomical labels at different scales (Onari et al., 2 Aug 2025).

These metrics are often visualized as error curves, histograms of per-scale attribution, or correspondence matrices across tasks and resolutions.

5. Practical Applications and Empirical Findings

Empirical validation across multiple domains demonstrates the utility of scale-aware interpretability:

• Medical imaging: Scale- and uncertainty-aware approaches yield improved segmentation accuracy and better-calibrated confidence in ambiguous regions, especially for elongated or low-contrast structures (Zhang et al., 2023). However, current fused saliency maps often lack the anatomical specificity required by clinicians, suggesting a need for further refinement (Onari et al., 2 Aug 2025).
• Semantic segmentation: Attention-based multi-scale fusion with auxiliary supervision outperforms fixed pooling schemes and offers pixel-wise, interpretable visualizations of scale importance, which systematically track object sizes and regions (Chen et al., 2015).
• Vision transformers: Explicit encoding and fusion of multi-scale features aligned with semantic concepts confer robustness to object scale changes and improve concept heatmap localization without significant parameter overhead (Sinha et al., 16 Jan 2025).
• LLMs: Multi-scale manifold alignment frameworks provide control over geometric and information-theoretic fidelity when mapping between semantic levels (Zhang et al., 24 May 2025); pruning studies show interpretability “nuclei” drive in-context learning (Bansal et al., 2022); scalable alignment methods robustly identify causal subspaces aligned to high-level algorithms (Wu et al., 2023).
• Robustness and safety: RG-based coarse-graining formalizes the goal of preserving safety-critical observables under worst-case perturbations of fine-scale features, with explicit error quantification (Greenspan et al., 5 Feb 2026).

A recurring theme is that scale-aware methods enable more robust, faithful, and intervention-ready explanations, though in practice, high-resolution visualizations may still require additional clinical or application-specific structuring.

6. Challenges, Limitations, and Future Directions

Despite substantial progress, key challenges and open questions remain:

• Objective design for interpretability: Scaling model size alone does not automatically yield more mechanistically interpretable networks; explicit architectural or objective modifications are required to favor disentangled, semantically coherent features (Zimmermann et al., 2023).
• Definition and identification of “scale”: In non-vision architectures, “scale” can be defined by layer depth, spectral frequency, semantic hierarchy, or information-theoretic criteria. Determining the most “model-natural” decomposition remains an open topic.
• Automatization of scale discovery: While RG-inspired tools provide a principled foundation, developing practical algorithms that discover the relevant scales and coarse variables with reliable error bounds in arbitrary architectures is an ongoing research agenda (Greenspan et al., 5 Feb 2026).
• Human-in-the-loop evaluation: Quantitative metrics do not always track end-user trust or utility, particularly in clinical or safety-critical contexts. Structured feedback loops—where human corrections inform the refinement of scale-aware attention or uncertainty modules—are recommended (Onari et al., 2 Aug 2025).
• Faithfulness and completeness: Alignment methods may be hypothesis-dependent, linear in alignment class, or overlook nonlinear or distributed causal subcircuits. Comprehensive coverage of all functionally relevant scales is a persistent challenge (Wu et al., 2023).
• Integration with training objectives: Future work may incorporate scale-aware interpretability objectives directly into model pre-training or architecture design phases, thereby ensuring that transparency is achieved at deployable model scales (Bansal et al., 2022, Zimmermann et al., 2023).

In summary, scale-aware interpretability formalizes and implements the principle that neural network explanations must respect and expose the multi-scale structure of both data and model representations. By providing methods that decompose, visualize, and bound the contributions of different scales, this approach advances both the technical rigor of interpretability research and its practical relevance for robust, trustworthy AI systems.