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REVIEW 4 major objections 6 minor 28 references

Causal Explanations Over Time: Articulated Reasoning for Interactive Environments

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper introduces T-SCE, a temporal generalization of Structural Causal Explanations that turns a causal graph and time-indexed data into natural-language why-answers for dynamic agent behavior.

desk verdict Worthwhile temporal extension of SCE, but the formal core has fixable bugs that make the algorithm under-specified as written. read the letter →

arxiv 2506.03915 v1 pith:MGDCAYEN submitted 2025-06-04 cs.AI

Sebastian Rödling , Matej Zečević , Devendra Singh Dhami , Kristian Kersting This is my paper
classification cs.AI
keywords causalexplanationstructuralmodelstemporalreasoningtreestime-seriescausalityexplainableAIagentbehaviorXIL
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper introduces Temporal Structural Causal Explanations (T-SCE), a generalization of Structural Causal Explanations (SCEs) that turns a causal graph and time-indexed data into natural-language answers to 'why' questions. Unlike the original SCE, which handles small static variable sets, T-SCE represents explanations as recursive trees whose nodes link causes and effects across time steps, and it supports both retrospective explanations of why an event happened and anticipative explanations of what an action will bring about. The authors argue this matters because real-world behavior, especially an agent acting in an environment, is driven by temporal dependencies and feedback loops that static explanations miss. They demonstrate the framework on a synthetic time-series version of the Causal Hans example and on a 2D grid game, where T-SCE produces per-action explanations such as why an agent targets an enemy. If correct, T-SCE offers a way to make interactive, dynamic AI behavior explainable in human-readable causal terms.

What carries the argument

The central object is the Explanation Tree (Definition 2), a directed acyclic graph whose root is the variable in a valid why-question. Edges run from a node to its causally explanatory parents in the retrospective case, or to its causal children in the anticipative case. The tree is built by the Temporal SCE recursion (Definition 3), which at each depth selects the relevant parent/child set $\Phi_1$ from the context-appropriate SCM, resolves the Explanation Indicators through the Fundamental Rules (and optionally the 'mostly' rule) into values in $\{-1, 0, 1\}$, uses $\Phi_2$ to avoid duplicates, and recurses up to depth $K$. Because the explanation is a tree rather than nested prose, the algorithm can attach sequence indicators, mask intermediate variables, restrict explanations to a path, and merge interrupted sequences; these operations are what let it summarize temporal explanations cleanly.

What would settle it

Run T-SCE on rollouts from a simulator with a known structural causal model that includes one feedback loop and one delayed effect, then compare every edge and lag in the produced explanation tree against the true structural parents at each time step. If the tree names an edge absent from the true SCM, or attributes a cause to the wrong time step, the claim that T-SCE yields causal temporal explanations is refuted for that case.

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Extended reading notes

Core claim

On its own terms, the paper claims that Structural Causal Explanations can be lifted from static linked-list sentences to a recursive formulation over explanation trees that captures the temporal interactions between reasons. Given a valid why-question $Q_X$, a set of context-specific proxy structural causal models, and a dataset $D$, the recursion $E(Q_R, Q_X, \mathcal{M}, D, j)$ selects the relevant causal parents in the retrospective case or causal children in the anticipative case, prunes them by a threshold $\theta$ or a top-$n$ selection, prevents reattaching duplicated time-variable pairs, and stops at a maximum recursion depth $K$. Explanation rules evaluate each edge with a sign function and a binary ordering relation, encoding relations as 'because' or 'although', possibly across different time steps; a sequence indicator then summarizes stable relations, producing sentences such as 'Hans's Mobility has been consistently below average ... mostly because of his low Mobility one year before and his low Health in the current year.' The authors show that the same machinery, using behavior-specific rules, yields both retrospective and anticipative explanations for a CoinRunner agent's actions, and they demonstrate the method on synthetic time series and the 2D game, comparing against the original SCE and other causal explanation methods.

Load-bearing premise

The load-bearing premise is that the causal graph handed to T-SCE is a faithful representation of the true causal structure; in the game experiments those graphs are learned from the same rollouts being explained and are only assumed to be causal, and within each context the process is assumed stationary.

Editorial extensions

If this is right

  • T-SCE can answer why-questions about time-series data when causes and effects lie in different time steps, naming both immediate and delayed reasons in one explanation tree.
  • The same explanation tree can be read in reverse to state what an agent's current action will cause, which is useful for explaining and inspecting behavior during a rollout.
  • Pruning by threshold, top-$n$, and recursion depth keeps tree size manageable even when the underlying causal graph has many weak or irrelevant edges.
  • Sequence indicators turn repeated per-timestep clauses into summaries such as 'consistently below average for the past three years', improving readability without changing the underlying causal claims.
  • The temporal formulation is backward compatible, so on static, single-context data the algorithm reduces to the original SCE-style explanation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implication the authors leave implicit: T-SCE could serve as a policy debugger for reinforcement-learning agents, since the anticipative explanations it prints can be checked against actual next-frame transitions in held-out rollouts; mismatches would localize where the learned graph or the model is wrong.
  • The context-switching mechanism suggests a testable extension: replace the hand-defined contexts (e.g., 'powerup exists' versus 'enemy exists') with learned context labels and T-SCE becomes an interpretable change-point detector for agent behavior.
  • Because the explanation rules rest on signs of edge weights, a likely boundary case is nonlinear dynamics; a concrete follow-up would test whether adding interaction or nonlinear structural equations changes which tree is returned and whether the resulting explanations remain readable.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper generalizes Structural Causal Explanations (SCE) to temporally extended and interactive settings. It introduces Temporal SCE (T-SCE), which constructs an 'Explanation Tree' over time-indexed variables using a provided or learned causal graph, supports retrospective and anticipative modes, and handles multiple context-specific SCMs. The method is demonstrated on a synthetic time-series variant of the 'Causal Hans' example and on a 2D grid game (CoinRunner) with an agent behavior; comparisons are made with LEWIS and Causal Shapley Values.

Significance. The paper addresses a real gap: SCE is static and limited to small variable sets, and generating human-readable causal explanations for time-series or agent behavior is an important problem. The proposed tree structure, context-dependent SCM selection, and sequence indicators are sensible ingredients. The paper is transparent about a key limitation: in the CoinRunner demonstration, the causal graphs are learned from the same rollouts and merely assumed causal, which limits the causal claims. However, the formal core—Definitions 3-5—contains several under-specifications that block unambiguous implementation: the θ/top-n filtering is vacuous by construction, the recursive call is ill-typed, and ER3 is never defined. These issues undermine the central claim that T-SCE is a well-defined generalization of SCE. If repaired, the framework could be a useful contribution. The paper does not ship machine-checked proofs or a reproducible code package; the code URL is not provided, so the evaluation cannot be reproduced by a reader.

major comments (4)
  1. [Definition 4 and Definition 5] Definition 4 (Retrospective) and Definition 5 (Anticipative): Since PaX_t,θ ⊆ PaX_t and PaX_t,n ⊆ PaX_t, the union Φ1 = PaX_t ∪ PaX_t,θ ∪ PaX_t,n equals PaX_t (and analogously for ChX_t). Consequently, the threshold θ and top-n parameter n have no effect on the selected parent set, and the 'flexible limitation of explanatory variables' claimed in Section 6 and the pruning by Φ2 cannot actually depend on these parameters. Please redefine Φ1 so that the filtering is effective (e.g., by replacing the union with a single selection rule controlled by θ or n, or by defining the selection as a function of the parameters).
  2. [Definition 3 (Temporal SCE)] The recursive call E(QX, Z, M, D, j+1) passes a variable Z as the second argument, whereas the function is defined with a why-question as its second argument (initially QX = QR). As written, the recursion is ill-typed and cannot be evaluated. The paper must specify how each parent Z is converted into a valid why-question QZ (e.g., via Generalization 1 with an appropriate instance and population statistic) before the recursive call is made. In addition, the surrounding text states that 'Φ1 further select the appropriate approx. SCM from M', but Definitions 4 and 5 define Φ1 as a set of variables, not an SCM; this mismatch needs to be resolved.
  3. [Generalization 3 (Explanation Rules)] ER3 is mentioned in Section 3 ('ER3X→Y serves as an additional indicator') and is used in Appendix A ('included the complementary rule ER3 (Mostly-Rule)'), but no formal definition of ER3 is given in the main text or appendix. Since the explanation rule triplet is central to the EI(·) evaluation in Definition 3, the paper should either provide the definition of ER3 or revise all references to it.
  4. [Section 4 (CoinRunner) and Appendix B] The causal graphs used as inputs to T-SCE are learned from the same 500 rollouts that are later explained, using Granger, VARLiNGAM, or Lasso, and are only 'assume[d] as causal for the moment' (Section 4) and used 'if we consider the graphs to be causal' (Appendix B). Since the generated explanations directly report the structure and coefficients of these graphs (e.g., Tables 1-3 list coefficients such as 0.056 and 4.338), any spurious edges or estimation error in the learned graphs is inherited by the explanations. The paper's claim to have 'illustrated ... causal explanations to agent behavior' (Section 6) is therefore stronger than what the evaluation supports. Please either validate the learned graphs against the known game mechanics (e.g., by comparing with the true generative process of the implemented agent) or explicitly restrict the claim to explanations conditioned on an assumed causal model.
minor comments (6)
  1. [Section 3, Definition 1] ER rules are referenced as 'Def. 3', but Generalization 3 appears in Section 4; add a forward reference or renumber.
  2. [Figure 3 caption] The word 'Trucanated' should be 'Truncated'.
  3. [Tables 1-3] The label 'Varlingam' should be 'VARLiNGAM'.
  4. [Section 4, Dynamic Time Series paragraph] In the text 'as outlined in Def. 3 (see ϕ1 and M)', the symbol 'ϕ1' should be 'Φ1' (uppercase Phi) to match the notation used in Definitions 4 and 5.
  5. [Appendix B, Code availability] The code availability statement gives only a repository name ('Why-Was-That-Happening_Offering-Reasons-For-Events-0C4E') and a domain placeholder rather than a resolvable URL; please provide the full link or state that code will be released upon publication.
  6. [Generalization 3 (Explanation Rules)] In the definitions of δ1 and δ2, both formulas use R2 for the x comparison; please check whether one occurrence should be R1, as the intended contrast between 'because' and 'although' seems to require different relations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: T-SCE is an explicit graph-to-explanation transformation; the learned-graph caveat is a stated limitation, not a fitted prediction.

full rationale

T-SCE's chain of derivation is self-contained with respect to circularity: the algorithm takes a (possibly learned) causal graph and a why-question as explicit inputs and produces an explanation tree by traversing that graph (Defs. 3-5). The CoinRunner demonstration is explicitly conditional: 'we then used Lasso, VARLiNGAM, and Granger on conditioned frame sections, depending on our contexts C, to generate graphs that we want to assume as causal for the moment' (Section 4; Appendix B), so the reported explanations inherit the input graph's coefficients rather than predicting them from the same data. That is a stated limitation, not a circular reduction. The base SCE is formally restated in Definition 1 rather than imported solely via [ZDRK23]; the self-citations are provenance for the SCE/XIL framing and are not load-bearing. I therefore find no input-output equivalence that would make the central claim circular. The paper does contain serious formal defects—Definition 4's union makes the theta and top-n filters vacuous, and Definition 3's recursive call passes a variable where a why-question is expected—but these are under-specification and correctness problems, not circular dependencies, and they do not change the circularity verdict.

Assumptions & free parameters 3 free parameters · 4 assumptions · 1 invented entities

The method's output is a rendering of an input causal graph; the graph itself, its edge weights, and the hand-defined contexts carry most of the causal content. The formal definition of the filtering rule has a bug that makes the stated variable-selection mechanism vacuous. No new physical entities are introduced; the Explanation Tree is an algorithmic construct rather than a substantive entity.

free parameters (3)
  • Causal edge weights alpha_{X->Y} in learned graphs = e.g., 0.056 (targeting->colliding), 4.338 (colliding->score), -0.479 (colliding->enemy existence)
    Fit by Lasso/VARLiNGAM/Granger from 500 rollouts; used directly by Explanation Rules (Gen. 3) to decide positive or negative effects.
  • Maximum recursion depth K = 2 in the Section 4 example; 3 in Appendix A
    Chosen by hand; limits tree depth and directly changes explanation length.
  • Threshold theta and top-n parent count = Unspecified in experiments
    Retrospective/anticipative definitions rely on these, but the union in Def. 4 makes them vacuous and no concrete values are reported.
assumptions (4)
  • domain assumption Time series are strictly stationary within each context
    Background states 'the time series is typically assumed to be a strictly stationary stochastic process'; the sequence indicator and context selection rely on this.
  • domain assumption Provided or learned causal graph is correct
    Section 4: graphs 'we want to assume as causal for the moment'; false edges make explanations non-causal.
  • domain assumption Linear signed edge weights capture causal effect direction and strength
    Concluding remarks: 'T-SCE inherits the linearity assumption of SCE'; ER rules use sign(alpha) and threshold magnitudes.
  • ad hoc to paper Hand-defined sprite-existence contexts cover the relevant stationary regimes
    Three contexts C_K,1..3 are defined for the Killer agent without evidence they capture all behavior regimes (Section 4).
invented entities (1)
  • Explanation Tree
    purpose: DAG representation of time-indexed causal explanations; replaces the linked-list output of SCE
    New algorithmic construct introduced by the paper; it does not by itself make falsifiable predictions outside the algorithm.

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Cite this review

Pith. "Pith review of Causal Explanations Over Time: Articulated Reasoning for Interactive Environments." pith.science (2026). https://pith.science/paper/MGDCAYEN

@misc{pith2026250603915,
  author       = {Pith},
  title        = {Pith review of: Causal Explanations Over Time: Articulated Reasoning for Interactive Environments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MGDCAYEN}},
  note         = {Machine review of arXiv:2506.03915}
}
read the original abstract

Structural Causal Explanations (SCEs) can be used to automatically generate explanations in natural language to questions about given data that are grounded in a (possibly learned) causal model. Unfortunately they work for small data only. In turn they are not attractive to offer reasons for events, e.g., tracking causal changes over multiple time steps, or a behavioral component that involves feedback loops through actions of an agent. To this end, we generalize SCEs to a (recursive) formulation of explanation trees to capture the temporal interactions between reasons. We show the benefits of this more general SCE algorithm on synthetic time-series data and a 2D grid game, and further compare it to the base SCE and other existing methods for causal explanations.

Figures

Figures reproduced from arXiv: 2506.03915 by the authors.

Figure 1
Figure 1. “Why Was That Happening?” Causal explanation for the behavior of two agents (referred to as Luigi and Mario) from the same player type in different game situations of the 2D CoinRunner game using the generalized T-SCE framework. (Best viewed in color) developed for explaining predictions for different scenarios involving causality. For instance, methods such as Causal Shapley Values [HSBC20], causality-based counter… view at source ↗
Figure 2
Figure 2. Causal Graph for the Causal Hans Exam￾ple. The edge values represent the causal effect from one variable onto another. (Best viewed in color.) If real valued weights are used, this rep￾resents some quantitative knowledge on the causal effect (which for linear SCM would be the regression coefficients). The most important aspect of the coefficients is their sign facilitating a distinction between adverse and supportiv… view at source ↗
Figure 3
Figure 3. Trucanated full-time graph for the Causal Hans Example. Red edges depict a delayed effect over time. In contrast, black edges represent immediate effects. Best viewed in color. Incorporating Temporality: We expand the Causal Hans example by incorporat￾ing a time dimension into the analysis. As shown in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Example of Explanation Tree. Sub-tree regarding the question, “Why is Hans’ Health below average?”. Sequences are color-coded. In the following, we provide an example illustrating human-readable causal explana￾tions in response to the question “Why is Hans’ Health belo…
Figure 5
Figure 5. Figure 5: SotA methods are not designed to offer structural explanations. Suf. Score and Shapley Values for 100 random patients with below avg. mobility prediction. Same Score/Value sequences are grouped together (group size n). Small groups are again combined. emy are present, …
Figure 6
Figure 6. Figure 6: Explanation Tree for the Causal Hans Example with changing explanations over time. Visualized are the individual nodes together with their indicators (ind) for the Fundamental Rules, Complementary Rule and the time (t). Color-coded are sequences tags indicating that th…
Figure 7
Figure 7. Figure 7: Basic CoinRunner game board including information board on the right side. Agent, gold coin and powerup have been initialized and are placed at random positions in the environment. The target sprite is placed at one of the four corners. Best viewed in colors [PITH_FUL…
Figure 8
Figure 8. Figure 8: Comparative Causal Diagrams for Behaviour Type Killer Using Granger, Lasso, and VARLiNGAM for CK,1, CK,2, CK,3. Red indicates positive influences, while blue represents negative effects. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Necessity Scores for all features of 100 patients from the ‘above average’ Mobility group. [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: Causal XIL Paradigm in action. A practical example featuring a developer and a doctor collaboratively working on optimizing a causal model. The feedback loop enables iterative improvement of the model, drawing on the expert knowledge of the doctor and the adjustments …

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Reviewed August 7, 2026 · model on record in the stance chip above.