Dual-Perspective Interpretability Framework

• Dual-Perspective Interpretability Framework is a method that balances fidelity and human comprehensibility by exploring Pareto-optimal trade-offs in machine learning models.
• It employs mathematical formalization and optimization strategies, including weighted constraint solvers and composite loss functions, to ensure sound and complete analysis.
• The framework integrates local instance-level explanations with global population-level insights, enhancing model trustworthiness and usability in practical applications.

A Dual-Perspective Interpretability Framework is a formalism for developing, describing, and evaluating interpretations of machine learning models from two fundamentally distinct, but complementary, standpoints—typically corresponding to correctness (fidelity to model behavior) and explainability (human comprehensibility), or, alternatively, to local (instance-level) and global (population-level) reasoning. The core motivation is to ensure that machine learning models are not merely black boxes, but admit reasoning that can be inspected, critiqued, and trusted by stakeholders with varying expertise and needs. This article provides a detailed account of the key methodologies, mathematical formalization, optimization strategies, application domains, and empirical results that constitute the state-of-the-art in dual-perspective interpretability frameworks, with a central focus on frameworks that define, operationalize, and systematically navigate trade-offs between competing interpretability objectives.

1. Foundational Principles of Dual-Perspective Interpretability

The dual-perspective paradigm recognizes that interpretability in machine learning must balance two or more desiderata that may be inherently at odds—such as predictive accuracy (correctness, or fidelity to the black-box model) and human explainability (simplicity, comprehensibility, or syntactic transparency). Rather than collapsing these objectives by scalarization (e.g., via weighted sums), the dual-perspective framework treats them as distinct axes and searches for Pareto-optimal solutions that represent different trade-offs (Torfah et al., 2021). This ensures that all maximal solutions are discoverable and selectable according to context-specific stakeholder requirements.

In parallel, interpretability itself is multi-faceted: it can be instantiated as properties of models (structural transparency), explanations of outputs (post-hoc local or global explanations), or as the process by which a model or explanation is optimized vis-à-vis both semantic fidelity and usability. The dual-perspective formalism thus subsumes both inherent (glassbox) and post-hoc (black-box) interpretability (Garouani et al., 27 Mar 2025, Parekh et al., 2020, Nori et al., 2019).

2. Mathematical Formalization and Optimization

Dual-perspective frameworks typically define a candidate space of interpretations—e.g., a syntactic class of models $\mathcal{E}$ (decision diagrams, rule lists, small neural nets)—and two quantifiable objectives:

• Correctness (C): Agreement between the interpretation $E \in \mathcal{E}$ and the black-box model on a finite representative sample $S$ (often formalized as empirical accuracy: $$C(E) = \frac{|\{(i, o) \in S \mid f_E(i) = o\}|}{|S|}$$).
• Explainability (E): A measure of human comprehensibility, typically based on model size or use of preferred predicates (e.g., $$E(E) = \sum_{i: \text{unused}} w_{\text{node}} + \sum_{(i, p): \text{used}} w_p$$) (Torfah et al., 2021).

The synthesis problem is then:

$\max_{E \in \mathcal{E}}~(C(E), E(E))$

with maximality defined under the product partial order to recover the Pareto frontier.

Typically, each individual optimization subproblem (e.g., maximizing $C(E)$ subject to a window $E(E) \in [\delta^l, \delta^u]$) is reduced to an instance of weighted MaxSAT or other constraint-satisfaction framework, encoding both hard syntactic restrictions and soft correctness/explainability rewards (Torfah et al., 2021).

For frameworks centered on deep models with attribute-based interpretations, the optimization is performed over a composite loss:

$$L = L_{\text{pred}} + \beta L_{\text{of}} + \gamma L_{\text{if}} + \delta L_{\text{cd}}$$

comprising the standard predictive loss, output-fidelity and input-fidelity terms (e.g., via cross-entropy on predictive outputs and reconstruction losses), and explicit entropy- or sparsity-based penalties for concise, diverse attribute activation (Parekh et al., 2020).

3. Local and Global Interpretability: Dual Modes of Reasoning

The dual-perspective principle commonly expresses itself as the provision of both local (per-instance) and global (population-level or class-level) interpretability.

• Local interpretability targets explanations of single decisions—e.g., computing (normalized) relevance scores for high-level attributes driving the prediction for a given input $x$. In the FLINT architecture, this is operationalized as $r_k(x) = \alpha_k(x) / \max_j |\alpha_j(x)|$, with attribute $k$ declared "active" if $|r_k(x)| > 1/\tau$ (Parekh et al., 2020).
• Global interpretability is statistical or logical, highlighting which attributes, concepts, or features are predictive for entire classes. This is often accomplished by batching and averaging relevance scores over all instances of a given predicted class (Parekh et al., 2020, Schrouff et al., 2021).

In some frameworks, the distinction is made rigorous through the complexity-theoretic lens: local sufficient reason queries (for a single input) and global sufficient reason queries (over all inputs) can differ drastically in computational hardness, implying a precise duality in feasible explanations for different model families (Bassan et al., 5 Jun 2024).

Table 1: Complexity of Local vs. Global Sufficient Reason Queries (excerpt from (Bassan et al., 5 Jun 2024)):

Model	Local (MSR)	Global (MSR)
Perceptron	P	coNP-c
Decision Tree	NP-c	P
MLP (ReLU)	$\Sigma_2^P$-c	coNP-c

This result underlines that neither local nor global interpretability is universally computationally superior; the relative tractability depends on model class.

4. Pareto-Optimal Interpretations and Multi-Objective Navigation

A distinguishing feature of dual-perspective frameworks is explicit enumeration of the Pareto frontier of interpretations, each point capturing a distinct trade-off between correctness and explainability (Torfah et al., 2021). The optimization proceeds by divide-and-conquer or branch-and-bound algorithms managing bounded explainability windows, using quantitative encodings that permit constraint solvers to optimize correctness and explainability independently.

This paradigm guarantees that no feasible interpretation is omitted and that strictly increasing aggregators (e.g., $w_1 C + w_2 E$ for positive $w_i$) cannot recover all solutions unless the entire frontier is characterized. The approach also enables human-in-the-loop adaptation—end-users can interactively select points on the frontier based on task-specific needs or regulatory demands.

In high-stakes medical domains, this approach is extended in frameworks such as Medical Priority Fusion (MPF), combining probabilistic models and explicit rules via weight-tuned fusion to satisfy stringent constraints on both sensitivity and interpretability, with mathematically imposed interpretability floors (Ge et al., 22 Sep 2025).

5. Application Architectures and Methods

Several canonical architectures realize the dual-perspective principle:

• Dictionary-based attribute models: End-to-end frameworks where predictor and interpreter are jointly learned; the latter provides a small set of high-level attributes feeding a linear classifier, with regularization to enforce conciseness, diversity, input/output fidelity, and visualizability (Parekh et al., 2020).
• Multi-objective decision diagram synthesis: Search over explicit syntactic classes of interpretations (decision diagrams, rule lists), quantifying trade-offs and delivering the full Pareto set (Torfah et al., 2021).
• Fusion frameworks: Weighted combination of heterogeneous base predictors (e.g., Naive Bayes and Decision Trees) under explicit constraints and with closed-form fusion weights derived from both sensitivity and interpretability scores (Ge et al., 22 Sep 2025).
• Hybrid symbolic–neural models: Direct injection of symbolic rules into neural architectures or staged knowledge distillation while maintaining explicit accountability for both transparency and accuracy (Garouani et al., 27 Mar 2025, Dhurandhar et al., 2017).
• Evaluation and meta-evaluation: In domains such as NLG, dual-perspective meta-evaluation frameworks independently assess global (ordinal category assignment) and local (fine-grained discrimination) metric capability for explainability, revealing orthogonal strengths not visible from scalar correlations alone (Hu et al., 17 Feb 2025).

6. Visualization, Evaluation, and Human-Centric Metrics

Effective visualization pipelines are integral to dual-perspective interpretability frameworks. For attribute-based approaches, sample selection (maximum-activation sets), activation maximization, and decoder-based feature ablations provide human-interpretable representations of underlying abstract features or concepts (Parekh et al., 2020). Empirical studies consistently include human-subject evaluations, forced-choice tasks, or forward simulation exercises to assess if explanations are both technically faithful and useful for real-world stakeholders (Parekh et al., 2020, Schrouff et al., 2021, Pinto et al., 22 May 2024). In frameworks founded on evaluation theory, criteria such as intelligibility, stability, plausibility, and faithfulness are operationalized with explicit dependencies (e.g., plausibility as a prerequisite for intelligibility), and assessment is stratified across functionally grounded, human-grounded, and application-grounded levels (Pinto et al., 22 May 2024).

7. Limitations, Formal Guarantees, and Outlook

Dual-perspective frameworks provide formal guarantees on completeness (all Pareto-optimal points found for finite template classes), soundness (all interpretations valid for specified correctness and explainability measures), and, when instantiated as post-hoc surrogates, statistical bounds on overfitting due to finite sample sizes (Torfah et al., 2021).

Limitations include dependence on proxy explainability metrics, reliance on finite or discrete template spaces (though generalizations to infinite VC-dimension classes are noted), and scalability challenges as the number or complexity of templates increases (Torfah et al., 2021). Some frameworks are sensitive to hyper-parameter selection in sparsity or conciseness penalties, or to issues of subjective alignment between technical measures and stakeholder intuition (Parekh et al., 2020, Ge et al., 22 Sep 2025). Nevertheless, the dual-perspective approach defines a principled and extensible template for future interpretability research, providing mathematically sound and empirically validated tools for navigating the interpretability–performance landscape in machine learning.