Informative Post-Hoc Explanations Only Exist for Simple Functions

• URL: http://arxiv.org/abs/2508.11441v1
• Date: Fri, 15 Aug 2025 12:46:18 GMT
• Title: Informative Post-Hoc Explanations Only Exist for Simple Functions
• Authors: Eric Günther, Balázs Szabados, Robi Bhattacharjee, Sebastian Bordt, Ulrike von Luxburg,
• Abstract summary: We introduce a general, learning-theory-based framework for what it means for an explanation to provide information about a decision function.<n>We show that many popular explanation algorithms are not informative when applied to complex decision functions.<n>We argue that it holds strong implications for the practical applicability of these algorithms, particularly for auditing, regulation, and high-risk applications of AI.
• Score: 12.017822772474576
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many researchers have suggested that local post-hoc explanation algorithms can be used to gain insights into the behavior of complex machine learning models. However, theoretical guarantees about such algorithms only exist for simple decision functions, and it is unclear whether and under which assumptions similar results might exist for complex models. In this paper, we introduce a general, learning-theory-based framework for what it means for an explanation to provide information about a decision function. We call an explanation informative if it serves to reduce the complexity of the space of plausible decision functions. With this approach, we show that many popular explanation algorithms are not informative when applied to complex decision functions, providing a rigorous mathematical rejection of the idea that it should be possible to explain any model. We then derive conditions under which different explanation algorithms become informative. These are often stronger than what one might expect. For example, gradient explanations and counterfactual explanations are non-informative with respect to the space of differentiable functions, and SHAP and anchor explanations are not informative with respect to the space of decision trees. Based on these results, we discuss how explanation algorithms can be modified to become informative. While the proposed analysis of explanation algorithms is mathematical, we argue that it holds strong implications for the practical applicability of these algorithms, particularly for auditing, regulation, and high-risk applications of AI.

Related papers

• On the Hardness of Computing Counterfactual and Semifactual Explanations in XAI [5.172213041663734]
  We show that in many cases, generating explanations is computationally hard.<n>We discuss the implications for the XAI community and for policymakers seeking to regulate explanations in AI.
  arXiv  Detail & Related papers  (2026-01-14T13:02:24Z)
• Coherent Local Explanations for Mathematical Optimization [0.0]
  We introduce Coherent Local Explanations for Mathematical Optimization (CLEMO)<n>CLEMO provides explanations for multiple components of optimization models, the objective value and decision variables, which are coherent with the underlying model structure.<n>Our sampling-based procedure can provide explanations for the behavior of exact and exact solution algorithms.
  arXiv  Detail & Related papers  (2025-02-07T11:18:04Z)
• Pyreal: A Framework for Interpretable ML Explanations [51.14710806705126]
  Pyreal is a system for generating a variety of interpretable machine learning explanations. Pyreal converts data and explanations between the feature spaces expected by the model, relevant explanation algorithms, and human users. Our studies demonstrate that Pyreal generates more useful explanations than existing systems.
  arXiv  Detail & Related papers  (2023-12-20T15:04:52Z)
• Disagreement amongst counterfactual explanations: How transparency can be deceptive [0.0]
  Counterfactual explanations are increasingly used as Explainable Artificial Intelligence technique. Not every algorithm creates uniform explanations for the same instance. Ethical issues arise when malicious agents use this diversity to fairwash an unfair machine learning model.
  arXiv  Detail & Related papers  (2023-04-25T09:15:37Z)
• Learning with Explanation Constraints [91.23736536228485]
  We provide a learning theoretic framework to analyze how explanations can improve the learning of our models. We demonstrate the benefits of our approach over a large array of synthetic and real-world experiments.
  arXiv  Detail & Related papers  (2023-03-25T15:06:47Z)
• Explainable Data-Driven Optimization: From Context to Decision and Back Again [76.84947521482631]
  Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. We introduce a counterfactual explanation methodology tailored to explain solutions to data-driven problems. We demonstrate our approach by explaining key problems in operations management such as inventory management and routing.
  arXiv  Detail & Related papers  (2023-01-24T15:25:16Z)
• Don't Explain Noise: Robust Counterfactuals for Randomized Ensembles [50.81061839052459]
  We formalize the generation of robust counterfactual explanations as a probabilistic problem. We show the link between the robustness of ensemble models and the robustness of base learners. Our method achieves high robustness with only a small increase in the distance from counterfactual explanations to their initial observations.
  arXiv  Detail & Related papers  (2022-05-27T17:28:54Z)
• Learning outside the Black-Box: The pursuit of interpretable models [78.32475359554395]
  This paper proposes an algorithm that produces a continuous global interpretation of any given continuous black-box function. Our interpretation represents a leap forward from the previous state of the art.
  arXiv  Detail & Related papers  (2020-11-17T12:39:44Z)
• Efficient computation of contrastive explanations [8.132423340684568]
  We study the relation of contrastive and counterfactual explanations. We propose a 2-phase algorithm for efficiently computing (plausible) positives of many standard machine learning models.
  arXiv  Detail & Related papers  (2020-10-06T11:50:28Z)
• A framework for step-wise explaining how to solve constraint satisfaction problems [21.96171133035504]
  We study the problem of explaining the inference steps that one can take during propagation, in a way that is easy to interpret for a person. Thereby, we aim to give the constraint solver explainable agency, which can help in building trust in the solver.
  arXiv  Detail & Related papers  (2020-06-11T11:35:41Z)
• The data-driven physical-based equations discovery using evolutionary approach [77.34726150561087]
  We describe the algorithm for the mathematical equations discovery from the given observations data. The algorithm combines genetic programming with the sparse regression. It could be used for governing analytical equation discovery as well as for partial differential equations (PDE) discovery.
  arXiv  Detail & Related papers  (2020-04-03T17:21:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.