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PACE: A Neuro-Symbolic Framework for Plausible and Actionable Counterfactual Explanations

This paper introduces PACE, a modular neuro-symbolic framework that combines neural predictive models with symbolic reasoning to generate counterfactual explanations that are not only valid but also realistic and actionable by explicitly enforcing domain-specific constraints and feasible interventions.

Original authors: Pavel Iakovets, Liyanapathiranage Sudeepika Wajirakumari Samarathunga, Martin Thomas Horsch, Fadi Al Machot

Published 2026-07-03

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CC BY 4.0

Original authors: Pavel Iakovets, Liyanapathiranage Sudeepika Wajirakumari Samarathunga, Martin Thomas Horsch, Fadi Al Machot

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are using a machine learning "black box" to decide if you qualify for a loan or a job. The computer says "No." You ask, "What do I need to change to get a 'Yes'?"

A standard AI might give you an answer like, "If you were 150 years old and worked 200 hours a week, you'd get the loan." While mathematically true (it changes the prediction), it's useless because it's impossible to do.

This paper introduces PACE, a new system designed to give you answers that are not just mathematically correct, but also realistic and doable.

Here is how PACE works, broken down into simple concepts:

1. The Problem: The "Unrealistic" Advice

Think of standard AI explanation tools as a reckless travel agent. If you ask, "How do I get from New York to London?" they might say, "Fly at the speed of light." It gets you there (valid), but you can't actually do it (not plausible).

Existing methods often focus only on changing the result (getting the "Yes") without checking if the steps to get there make sense in the real world. They might suggest changing your age or your gender, which are things you simply cannot change.

2. The Solution: The "Neuro-Symbolic" Team

The authors created PACE, which acts like a two-person team working together to give you advice:

The Neural Network (The "Gambler"): This is the AI that knows how to predict the outcome. It's good at guessing, "If you change X, the result will likely flip to Y." But it doesn't know the rules of the real world.
The Symbolic Reasoner (The "Rulebook"): This is a strict logic engine that holds a list of real-world rules. It knows that you can't change your age, that you can't work 200 hours a week, and that you can only move from a "High School" education to "Some College," not jump straight to "PhD" in one step.

PACE forces the "Gambler" to only suggest changes that the "Rulebook" approves.

3. How It Works: The "Search with a Fence"

Imagine you are looking for a specific key in a giant field.

Old methods run around the whole field randomly. They might find the key quickly, but they might also suggest you dig up a mountain to find it.
PACE builds a fence around the field. This fence represents the "feasible intervention space." The system knows you can only walk inside the fence. It systematically checks every spot inside the fence until it finds the key.

If the key isn't inside the fence (meaning no realistic change can get you a "Yes"), PACE admits it. It won't lie and tell you to break the laws of physics.

4. The Test: The "Adult Income" Case Study

To test this, the researchers used a dataset about people's incomes. They asked the system: "What small, realistic changes can a person make to increase their income from under $50k to over $50k?"

They compared PACE against other popular methods (like DiCE, Wachter, and Random Search).

The Results:

The "Reckless" Methods (Random Search, DiCE): They were very good at finding some way to change the prediction (High "Validity"). However, most of their suggestions were nonsense (Low "Plausibility"). For example, they might suggest changing a person's sex or age.
PACE: It was slightly slower at finding any answer because it was strictly following the rules. However, 100% of the answers it gave were realistic.
- It suggested things like: "Increase your education level by one step" or "Work a few more hours a week."
- It never suggested impossible changes.

5. The Trade-Off

The paper highlights a clear trade-off, like choosing between speed and safety.

If you want the fastest answer that changes the result, you might get a suggestion that is impossible to follow.
If you want a suggestion you can actually do, you need a system like PACE that checks the rules first.

Summary

PACE is a framework that combines a smart AI predictor with a strict logic checker. It ensures that when an AI tells you how to change your life to get a better outcome, the advice is actionable. It won't tell you to become a different person; it will tell you what realistic steps you can actually take.

The paper concludes that while this approach sometimes takes a bit longer to find an answer, it is much better at providing trustworthy, real-world advice than methods that ignore the rules of reality.

Technical Summary: PACE – A Neuro-Symbolic Framework for Plausible and Actionable Counterfactual Explanations

Problem Statement
Counterfactual explanations (CEs) are a prominent approach in Explainable AI (XAI) designed to provide actionable recommendations by identifying minimal changes to an input instance that would alter a machine learning model's prediction. While existing methods effectively generate prediction-changing alternatives, they frequently produce unrealistic or infeasible recommendations. This occurs because many approaches optimize primarily for prediction change and proximity to the original instance, often lacking explicit mechanisms to incorporate domain knowledge or intervention constraints. Consequently, generated explanations may violate domain-specific rules (e.g., suggesting an impossible change in immutable attributes like age or sex) or fail to represent realistic human actions. There is a critical need for methods that ensure explanations are not only valid (changing the prediction) but also plausible and feasible within the constraints of the application domain.

Methodology
The paper proposes PACE (Plausible and Actionable Counterfactual Explanations), a modular neuro-symbolic framework that integrates data-driven predictive models with symbolic reasoning to enforce feasibility. The methodology is structured around three core components:

Problem Formulation:
The generation of a counterfactual is formalized as a constrained search problem. Given a black-box model $f$ and an input $x$ with prediction $y$ , the goal is to find a counterfactual $x_{cf}$ such that $f(x_{cf}) \neq f(x)$ . The search minimizes a distance metric $d$ (defined as the number of modified features) subject to the constraint that $x_{cf}$ must lie within a feasible intervention space $\Omega$ . This space is strictly defined by domain-specific rules, ensuring that immutable attributes remain unchanged and editable attributes follow logical dependencies.
Neuro-Symbolic Architecture:
- Neural Component: A predictive model (e.g., a Multilayer Perceptron) acts as an oracle to evaluate candidate instances and verify if the prediction flip condition is met.
- Symbolic Component: A symbolic reasoning layer, implemented using Answer Set Programming (ASP), encodes the domain knowledge. This layer defines the feasible space $\Omega$ by partitioning features into immutable ( $X_I$ ) and editable ( $X_E$ ) sets. It enforces logical rules, such as directional invariants (e.g., education levels can only change to adjacent levels) and relational invariants (e.g., specific occupation transitions).
- Search Procedure: The framework employs an iterative "generate-and-verify" loop. The symbolic engine generates candidate interventions within a specific budget $K$ (limiting the number of simultaneous feature changes). Candidates are filtered against the symbolic constraints before being evaluated by the neural model. The search starts with a minimal budget and incrementally expands until a valid counterfactual is found or the maximum bound is reached.

Case Study and Experimental Setup
The framework was evaluated on the Adult Income dataset, a benchmark for tabular classification. The task involved predicting whether an individual's income exceeds $50,000.

Model: A Multilayer Perceptron (MLP) with 82% accuracy served as the predictive model.
Features: Five features were used: Age and Sex (immutable), and Education, Occupation, and Hours per Week (editable).
Constraints: The symbolic knowledge base enforced rules such as:
- Age and Sex cannot be modified.
- Education changes are restricted to adjacent levels.
- Occupation changes must follow a predefined transition graph.
- Working hours must change within bounded steps.
Baselines: PACE was compared against Random Search, DiCE, Wachter-style optimization, VCNet-style, and C-CHVAE-style approaches.

Key Results
The experiments, conducted on 1,000 test instances, highlighted a distinct trade-off between validity (successfully changing the prediction) and plausibility (satisfying domain constraints):

Plausibility: PACE achieved 100% plausibility, as all generated explanations strictly adhered to the symbolic constraints. In contrast, unconstrained methods like Random Search (2.7% plausibility) and DiCE (4.2% plausibility) frequently produced infeasible recommendations.
Validity: Unconstrained methods generally achieved higher validity scores (e.g., Random Search at 0.778, DiCE at 0.742) compared to PACE (0.240). This indicates that restricting the search space to feasible interventions reduces the number of instances for which a counterfactual can be found.
Minimality: PACE generated relatively compact explanations, requiring an average of 1.242 feature modifications, which was lower than most baselines (e.g., DiCE at 1.953).
Search Efficiency: PACE demonstrated high efficiency, requiring an average of 5.271 iterations to flip a prediction and a runtime of 0.076 seconds per instance, significantly outperforming the Wachter-style baseline.
Additional Analysis: When all methods were restricted to the same feasible space $\Omega$ , their plausibility scores converged to 1.0, confirming that the plausibility gains in PACE stem from explicit constraint specification. Furthermore, PACE counterfactuals were found to be closer to the empirical data manifold (mean distance to nearest neighbors: 0.354) compared to unconstrained search (0.944).

Significance and Contributions
The paper claims that PACE addresses the gap between high-validity counterfactual generation and the explicit enforcement of feasibility. Its primary contributions are:

A Modular Framework: It integrates machine learning with symbolic reasoning to enable constrained counterfactual generation.
Feasibility-Aware Formulation: It defines counterfactual generation as a search where symbolic constraints explicitly delineate the admissible intervention space.
Implementation: It provides an ASP-based implementation that enforces domain-specific constraints during the search process.
Empirical Evidence: It demonstrates through the Adult Income case study that incorporating symbolic constraints yields explanations that better satisfy domain-specific feasibility requirements, albeit with a trade-off in the rate of finding valid counterfactuals for all instances.

The authors conclude that while there is a trade-off between validity and plausibility, neuro-symbolic methods like PACE offer a promising direction for generating transparent, feasibility-aware explanations in high-stakes decision-support systems. The paper acknowledges limitations, noting the reliance on a single dataset and manually specified constraints, and suggests future work should explore automated constraint acquisition and richer forms of domain knowledge.