Journal of Artificial Intelligence Research

Causal Explanations for Image Classifiers

2026-02-13T08:54:00+00:00

Existing algorithms for explaining the output of image classifiers use different definitions of explanations and a variety of techniques to find them. However, none of the existing tools use a principled approach based on formal definitions of cause and explanation.

In this paper we present a novel black-box approach to computing explanations grounded in the theory of actual causality. We prove relevant theoretical results and present an algorithm for computing approximate explanations based on these definitions. We prove termination of our algorithm and discuss its complexity and the amount of approximation compared to the precise definition.

We implemented the framework in a tool, ReX, and we present experimental results and a comparison with state-of-the-art tools. We demonstrate that ReX is the most efficient black-box tool and produces the smallest explanations, in addition to outperforming other black-box tools on standard quality measures.

Honey, I Shrunk the Hypothesis Space (Through Logical Preprocessing)

2026-01-29T00:07:47+00:00

Inductive logic programming (ILP) is a form of logical machine learning. The goal is to search a hypothesis space for a hypothesis that generalises training examples and background knowledge. We introduce an approach that shrinks the hypothesis space before an ILP system searches it. Our approach uses background knowledge to find rules that cannot be in an optimal hypothesis regardless of the training examples. For instance, our approach discovers relationships such as even numbers cannot be odd and prime numbers greater than 2 are odd. It then removes violating rules from the hypothesis space. We implement our approach using answer set programming and use it to shrink the hypothesis space of a constraint-based ILP system. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach can substantially reduce learning times whilst maintaining predictive accuracies. For instance, given just 10 seconds of preprocessing time, our approach can reduce learning times from over 10 hours to only 2 seconds.

R-Mod: Minimal Structural Revision of S5 Epistemic Models

2026-01-15T05:11:35+00:00

Revising what an agent knows in response to new information is a central problem in formal epistemology. In doxastic logics such as KD45, belief revision proceeds by reordering plausibility: the agent simply re-ranks which worlds it considers most credible. This strategy fails for S5 knowledge. Because knowledge is factive (Kφ → φ), an agent cannot come to know phi merely by finding φ-worlds more plausible; if the actual world falsifies φ, then Kφ remains unsatisfiable regardless of any reordering. Accommodating new modal information in S5 therefore requires genuine model transformation: adjusting the equivalence-based accessibility structure, the valuation, or both.

We develop R-Mod, a selection-based revision operator that realizes this transformation as minimal structural repair. Given an S5 model and a target formula, R-Mod searches for a closest model, measured by a bisimulation-aware distance on quotient structures, that satisfies the formula while preserving S5 constraints. At the skeptical level, R-Mod satisfies success, consistency preservation, and deductive closure; classical AGM postulates such as Inclusion and Superexpansion fail due to permissible structural amplification, though we identify conditions under which they re-emerge. Computationally, the decision problem is NP-complete, and we provide tractable fragments exploiting structural locality.

While recent work has advanced AGM-style postulate analysis for S5 and topological semantics via simplicial complexes, these approaches do not provide goal-driven optimization with algorithmic guarantees. R-Mod fills this gap by combining modal invariance, explicit distance minimization, and fine-grained complexity analysis. Our results reframe revision in S5 as knowledge-model revision rather than belief revision, offering a foundation for algorithmic implementations and extensions to richer epistemic semantics.

Formal Logic Inference Guided Uncertainty Quantification for Personalized Federated Learning

2026-01-16T05:23:35+00:00

Federated Learning (FL) enables privacy-preserving model training across heterogeneous distributed systems, such as smartgrid forecasting or traffic-flow prediction from geographically dispersed sensors and devices. A key challenge in such settings is capturing client-specific patterns while addressing data heterogeneity and uncertainty at scale. Existing approaches, including Bayesian Neural Networks (BNNs) and clustering-based methods, struggle with scalability and consistent personalization. We propose LogiCP, a novel FL framework that integrates formal logic reasoning with uncertainty quantification (UQ) to support scalable and personalized learning with theoretical guarantees. LogiCP uses Signal Temporal Logic (STL) to extract temporal patterns and form semantically coherent client clusters, controlling intra-cluster heterogeneity. Within each cluster, LogiCP applies decentralized Conformal Prediction (CP) to produce distribution-free prediction intervals with mathematical guarantees that encompass the real value. LogiCP dynamically assigns clients to clusters at runtime without retraining, improving practicality. Evaluations on three real-world datasets—traffic, temperature, and electricity—show that LogiCP consistently outperforms BNN-, clustering-, and CP-based baselines, achieving up to a 95% improvement in client-level MSE while maintaining strong scalability.

Explaining Multivariate Decision Trees: Characterising Tractable Languages

2025-12-20T06:48:44+00:00

We study multivariate decision trees (MDTs), in particular, classes of MDTs determined by the language of relations that can be used to split feature space. An abductive explanation (AXp) of the classification of a particular instance, viewed as a set of feature-value assignments, is a minimal subset of the instance which is sufficient to lead to the same decision. We investigate when finding a single AXp is tractable. We identify tractable languages for real, integer and boolean features. Indeed, in the case of boolean languages, we provide a P/NP-hard dichotomy. We extend this dichotomy to languages defined by formulas whose literals correspond to splits of ordered domains of arbitrary finite size. Experiments indicate that MDTs can provide more compact models than classical decision trees while conserving accuracy and explainability.

Efficiently Negative: Complexity and Approximations of Targeted Negative Campaigning

2025-12-15T11:22:00+00:00

Given the ubiquity of negative campaigning in recent political elections, we find it important to study its properties from a theoretical computational perspective. To this end, we present a model where elections can be manipulated by convincing voters to demote specific non-favored candidates, and study its properties in the classic setting of scoring rules.

When the goal is constructive (making a preferred candidate win), we prove that finding such a demotion strategy is easy for Plurality and Veto, while generally hard for t-approval and Borda. We also provide a min(t, m - t)-factor approximation for t-approval for every t ∈ {1,..., m - 1} (where m is the number of candidates), and a 3-factor approximation algorithm for Borda. Interestingly enough---following recent trends in political science that show that the effectiveness of negative campaigning depends on the type of candidate and demographic---when assigning varying prices to different possible demotion operations, we are able to provide inapproximability results.

When the goal is destructive (making the leading opponent lose), we show that the problem is easy for a broad class of scoring rules and provide an FPTAS for the general case.

TeamTTA: Efficient Multi-Device Collaboration for Open-Set Test-Time Adaptation via Cloud Integration

2026-01-11T13:39:16+00:00

Deep neural networks (DNNs) deployed on edge devices often suffer from severe performance degradation when exposed to dynamic and continually shifting environments. Test-time adaptation (TTA) has emerged as a promising solution by updating models online with incoming test data. However, edge deployment poses unique challenges: limited computational resources, latency caused by adaptation delays, and knowledge isolation across devices. The situation becomes even more complex in open-world scenarios, where the presence of unknown categories further disrupts adaptation. To overcome these limitations, we propose TeamTTA, a cloud-integrated framework designed for efficient multi-device collaboration open-set test-time adaptation. Specifically, TeamTTA aggregates reliable samples from multiple edge devices through crowdsourcing, uploads them to the cloud, and maintains a memory buffer for continual adaptation. A large vision model (LVM) in the cloud leverages its zero-shot generalization ability to filter out open-set samples and acts as a teacher model, distilling its knowledge into a replicated student edge model stored in the cloud. The adapted model parameters, or alternatively global statistics under poor network conditions, are then transmitted back to the edge devices for efficient inference. Extensive experiments on standard public TTA benchmarks, including corrupted and open-set datasets, show that TeamTTA achieves superior adaptation accuracy, robustness to distribution shifts, and communication efficiency, outperforming state-of-the-art TTA baselines. These results validate the effectiveness of integrating cloud-edge collaboration and LVM-driven knowledge distillation for real-world edge intelligence.

Differential Parity: Relative Fairness Between Two Sets of Decisions

2026-02-13T04:35:18+00:00

Background: With AI systems increasingly being applied to assist humans in decision-making processes such as talent hiring, school admissions, and loan approvals, there is a growing need to ensure that the resulting decisions are fair. A major challenge in analyzing fairness is that standards are highly subjective and context-dependent —- there is no consensus on what absolute fairness means in every scenario. Moreover, different standards of fairness often conflict with each other.

Objectives: To address this issue, this work aims to evaluate the relative fairness between decisions.

Methods: Instead of defining what constitutes “absolutely” fair decisions, we propose assessing the relative fairness of one decision set against another using differential parity —- two sets of decisions are considered relatively fair with respect to each other if and only if the difference between them is independent of a given sensitive attribute. The proposed notion of differential parity fairness offers three key benefits: (1) it avoids the ambiguity and contradictions inherent in defining “absolutely” fair decisions; (2) it reveals relative preferences and biases between two decision sets; and (3) it can serve as a new notion of group fairness when a reference set of decisions (e.g., ground truth) is available. One limitation of differential parity is that the two sets of decisions being compared must be made on the same data subjects. To overcome this limitation, we propose to utilize a machine learning model to bridge the gap between the two sets of decisions made on different data and approximate the differential parity metrics. In addition to differential parity and inspired by the statistical parity fairness notion, we also define relative statistical parity – the difference between the means of two sets of decisions is required to be independent of the sensitive attribute – as a weaker notion of relative fairness compared to differential parity.

Results: Theoretically, we show how the proposed metrics statistically evaluate differential parity and relative statistical parity. We also proved the feasibility of using the proposed biased bridge algorithm to approximate differential parity metrics between decisions made on different data. Empirically, we evaluated the Type I and Type II error rates of differential parity and relative statistical parity both between decisions made on the same data and on different data. Experimental results suggest that differential parity outperforms relative statistical parity by having a much lower Type II error rate in both scenarios.

Conclusions: With lower than 0.1 Type I and Type II error rates in both scenarios, the effectiveness of differential parity demonstrated in this article suggests that it is feasible and beneficial to evaluate relative bias between decisions made by different entities. We expect this to pave the way for the analysis of relative fairness in AI and beyond.

How to DP-Fy Your Data: A Practical Guide to Generating Synthetic Data With Differential Privacy

2025-12-28T00:28:22+00:00

High quality data is of vital importance for unlocking the full potential of AI for end users. Villalobos et al. stated in 2024 that finding new sources of such data is getting harder as most publicly-available human generated data will soon have been used. Additionally, publicly available data often is not representative of users of a particular system — for example, a research speech dataset of contractors interacting with an AI assistant will likely be more homogeneous, well articulated and self-censored that real world commands that end users will issue. Therefore unlocking high-quality data grounded in real user interactions is of vital interest to both system creators and end users themselves. However, the direct use of user data comes with significant privacy risks, which must be addressed before the data can be used. Differential Privacy (DP) is a well established framework for reasoning about and limiting information leakage, and is a gold standard for protecting user privacy. The focus of this work, Differentially Private Synthetic data, refers to synthetic data that preserves the overall trends of source data (often user-generated), while providing strong privacy guarantees to individuals that contributed to the source dataset. DP synthetic data can unlock the value of datasets that have previously been inaccessible due to privacy concerns. Additionally, DP synthetic data can replace the use of sensitive datasets that previously have only had rudimentary protections like ad-hoc rule-based anonymization.

In this survey we explore the full suite of techniques surrounding DP synthetic data, the types of privacy protections different generation approaches can offer, and the state-of-the-art for various modalities including image, tabular, text and federated (decentralized) data. We outline all the components needed in a system that generates DP synthetic data, from sensitive data handling and preparation, to tracking the use of synthetic data and empirical privacy testing.

We hope that work will result in increased adoption of DP synthetic data, spur additional research in still underexplored domains, and additionally increase trust in DP synthetic data approaches.

Scaling Neuro-symbolic Problem Solving: Solver-Free Learning of Constraints and Objectives

2025-11-20T01:04:07+00:00

Background: In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimisation problems from natural inputs, a task that Large Language Models seem to struggle with.

Objectives: We introduce a differentiable neuro-symbolic architecture and a loss function dedicated to learning how to solve NP-hard reasoning problems.

Methods: Our new probabilistic loss allows for learning both the constraints and the objective – possibly non-linear – of a combinatorial problem. Thus, it delivers a complete model that can be scrutinized and completed with side constraints. By pushing the combinatorial solver out of the training loop, our architecture also offers scalable training while exact inference gives access to maximum accuracy.

Results: We empirically show that it can efficiently learn how to solve NP-hard reasoning problems from natural inputs. On three variants of the Sudoku benchmark – symbolic, visual, and many-solution –, our approach requires a fraction of data and training time of other hybrid methods. On a visual Min-Cut/Max-cut task, it optimizes the regret as well as a Decision-Focused-Learning regret-dedicated loss. Finally, it efficiently learns the energy optimisation formulation of the large real-world problem of designing proteins.