Title: Cyclic Counterfactuals under Shift–Scale Interventions
Venue: NeurIPS 2025
Accepted: yes
Keywords: Counterfactuals

Causality

cyclic SCM
Abstract: Most counterfactual inference frameworks traditionally assume acyclic structural causal models (SCMs), i.e. directed acyclic graphs (DAGs). However, many real-world systems (e.g. biological systems) contain feedback loops or cyclic dependencies that violate acyclicity. In this work, we study counterfactual inference in cyclic SCMs under shift–scale interventions, i.e., soft, policy-style changes that rescale and/or shift a variable’s mechanism.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper focuses on cyclic SCMs and more precisely on their behavior under a type of soft interventions, the shift-scale interventions do(aX+b). A number of theoretical results is proved, including the unique solvability of twin SCMs, used for modelling counterfactual distributions, under ss interventions. The latter implies that counterfactual distributions associated with such interventions are well-defined for cyclic SCMs.\n\nSTRENGTHS AND WEAKNESSES:\n+ The paper is clearly written, and results are well explained.\n+ I read the proofs of the two theorems only. Their exposition was nice, and I found them easy to follow. The proofs seemed correct.\n+ The field of cyclic SCMs is indeed under explored and important. Thus, efforts to shed more light in this domain have value.\n\n- I found the connection of this paper to prior work poor. I strongly advise the authors to: (1) mention previous results from Bongers et al in cyclic SCMs, and especially their results related to hard interventions; (2) highlight any potential overlap in methodology and draw a connection to this paper and your explicitly mentioning the extra challenges you had to face in order to prove your results. See my questions for some examples\n\n- The contributions of the paper are rather limited. It would be interested to see a similar study for other subfamilies of soft interventions and/or the case with more than one simultaneous soft interventions. The latter produces counterfactual distributions which might include more than two counterfactual worlds and hence cannot be modeled by twin SCMs.\n\nQUESTIONS:\nQ1. What are the key differences between Theorem 2 from your paper and Proposition 8.2 from Bogers et.al.?\n\nQ2. Could I kindly ask the authors to explain what P-almost surely means in Definition 2? It could be helpful if you add an explanation in the paper for completeness.\n\nQ3. Could you elaborate on the last sentence from the paragraph in Section 5?\n\nLIMITATIONS:\nLimitations are mentioned. Maybe some more discussion on the challenges that other types of soft interventions pose would be helpful.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-20"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the challenge of counterfactual inference in cyclic structural causal models (SCMs), which better reflect the feedback loops and cyclical dependencies found in many real-world systems such as biological networks. While traditional counterfactual methods assume acyclic models (DAGs), this work departs from that norm and explores shift-scale interventions within cyclic SCMs. The authors propose a new framework for conducting counterfactual analysis under these conditions and demonstrate its theoretical soundness and practical utility, laying groundwork for more realistic causal reasoning in complex systems.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- Addresses a major gap by extending counterfactual inference to cyclic SCMs, which better model feedback loops in real systems (e.g., biology).\n\nWeaknesses\n- The paper never clearly highlights which sections or results are specifically responsible for handling cyclic structures, making it harder for readers to identify where cycles are addressed.\n- The paper lacks empirical validation. No simulations or real-data experiments are provided to illustrate practical performance.\n- Computational aspects (e.g., how to verify contraction or solve high-dimensional twin SCMs) are not discussed, which could hinder adoption in large-scale systems.\n\nQUESTIONS:\n1. Which part of the paper explains how the proposed method handles cyclic structures?\n2. Could the authors elaborate where the twin-SCM construction interacts with the cyclic structure?\n3. What is the computational cost of solving the (shift-scale) twin SCM in high dimensions, and are there efficient algorithms?\n4. Can the authors provide simulations or real-data case studies to demonstrate (a) cycles in action, (b) contraction diagnostics, and (c) counterfactual estimation under shift-scale interventions?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 1, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nStructural causal models are the classical framework in counterfactual inference. However, these models typically require an directed acyclic graph, which excludes the possibility of feedback loops. The article introduces a notion of counterfactuals that generalizes beyond acyclic graphs and can handle cycles. The underlying mathematics is based on contraction mappings and Banach fixed point theory.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The manuscript is well-written and clear. I enjoyed reading it.\n- The manuscript could provide a foundation for follow-up works, as well-posedness of structural causal models with cycles and well-posedness of a corresponding set of interventions is thorougly discussed.\n\nWeaknesses:\n- While the mathematical exposition is on point, the main results e.g. Thm.1 and Thm.2 follow in a relatively straightforward manner from Banach fixed point theory. The technical contributions are therefore somewhat limited.\n- The authors could expand the discussion on the meaning and interpretations (including a philosophical level) of structural causal models with cyclic graphs. In many physical process there are no feedback effects that are immediate as modelled by the authors. I am thinking of thermodynamic systems, mechanical systems, fluid dynamical systems, etc. that have some sort of \"inertia\", which means that there is a clear temporal sequence that characterizes how the variables affect each other over time. In such a case modelling with a directed acyclic graph is maybe more appropriate... Can the authors provide simple examples where cyclic graphs are known to occur?\n\nOn a similar note, the field of control theory (i.e. the science of feedback) has dealt with feedback loops for a long time although the focus is maybe more on physical and engineering systems, wheras in causal inference the focus lies more on social and economical systems. In control theory there is the notion of well-posedness that has been studied extensively, which is very related to the content of the manuscript (although approached from a different angle). Here is for example a survey on well-posedness for a control-theoretic lens: \"Well-posed systems-The LTI case and beyond\" by Marius Tucsnak, George Weiss, Automatica, 2014.\n\nQUESTIONS:\nsee above.\n\nLIMITATIONS:\nyes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a theoretical framework for counterfactual inference in cyclic structural causal models (SCMs) using shift–scale interventions. While most existing counterfactual frameworks assume acyclic structures (DAGs), many real-world systems, specifically dynamical systems, involve feedback loops. By leveraging a global ℓp-contraction condition, the authors ensure unique solvability of cyclic SCMs even after shift–scale interventions. The paper further establishes closure properties under composition and derives sub-Gaussian concentration bounds for counterfactual outcomes under additional Lipschitz regularity assumptions in the exogenous noise.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- The paper makes a clear contribution by extending counterfactual reasoning to cyclic causal models.\n- The mathematical arguments are carefully detailed and all definitions, theorems, and proofs are clearly presented.\n\n## Weaknesses\n- The framework relies heavily on a global contraction condition (k < 1), which is difficult to check or guarantee in practical settings.\n- There are no toy examples to help readers understand how the theory plays out in practice.\n- The results are limited to shift–scale interventions and a discussion on how the results for these interventions can be generalized to other interventions is missing.  \n\n## Minor Comments\n- Page 3: The equation between line 83 and 84, 2nd line. ) is not needed.\n\nQUESTIONS:\n- Could you include a simple, illustrative example of a cyclic SCM to help demonstrate your theoretical results more concretely and make them easier to understand?\n\n- How might your results be used as a foundation to extend the framework to more general types of interventions beyond shift–scale?\n\nLIMITATIONS:\nIt is addressed in the weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}