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REVIEW 2 major objections 5 minor 55 references

Temporal causal discovery can be cast as a zero-shot, single-pass prediction problem once the training corpus is large and diverse enough.

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2026-08-04 05:58 UTC pith:V32XLCWP

load-bearing objection A genuine scaling result for zero-shot temporal causal discovery, with the realistic-benchmark leg substantially circular and the scaling claim overdrawn at the top end. the 2 major comments →

arxiv 2602.18662 v2 pith:V32XLCWP submitted 2026-02-20 cs.LG

Large Causal Models for Temporal Causal Discovery

Nikolaos Kougioulis , Nikolaos Gkorgkolis , MingXue Wang , Bora Caglayan , Dario Simionato , Andrea Tonon , Ioannis Tsamardinos This is my paper
classification cs.LG
keywords temporal causal discoverylarge causal modelsfoundation modelszero-shot generalizationtime seriesstructural causal modelstransformersamortized inference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that earlier attempts to build pre-trained neural models for temporal causal discovery failed because they trained on narrow, mostly synthetic distributions, not because transformers cannot handle the task. It builds a large-scale training corpus that mixes randomized synthetic temporal structural causal models with realistic time series simulated from real-world data, and trains a transformer—the 'large causal model'—to output a lagged adjacency tensor of edge probabilities from a time series in one pass. On synthetic, semi-synthetic, and realistic benchmarks that were never seen in training, the pretrained model matches or beats classical per-dataset algorithms, including on out-of-distribution data, while running in constant time relative to input size. The central claim is that scaling failures reported in prior work stem from insufficient training-distribution diversity rather than architectural limitations.

Core claim

The paper's central claim is that a single pretrained network can amortize temporal causal discovery: given a multivariate time series, an LCM predicts the probability of every directed lagged edge simultaneously, without per-dataset fitting. Training uses a 275k-sample corpus built from two sources: a synthetic generator that draws random lagged directed acyclic graphs with linear/nonlinear additive-noise mechanisms, and a realistic pipeline that learns temporal structural causal models from real time series and simulates new samples from them. The trained LCM achieves competitive or superior AUC compared with classical methods on in-distribution holdouts and on out-of-distribution semi-syn

What carries the argument

The machinery centres on the lagged adjacency tensor, which encodes all candidate directed edges at lags up to a fixed maximum, and the architecture is a convolution-enhanced transformer: a 1D-convolution embedding with sinusoidal position encodings, a stack of self-attention encoder blocks with optional temporal distillation, and a feedforward head with sigmoid output that yields edge probabilities. Two training aids are concatenated to the encoder state—lagged cross-correlations and a correlation-regularization loss that biases confident predictions toward observed statistical dependencies. The corpus itself is the load-bearing component: roughly 230k synthetic pairs plus 45k realistic pai

Load-bearing premise

The realistic training and evaluation labels are produced by an algorithmic causal-discovery pipeline, so the 'ground truth' graphs are outputs of an existing method; if that method is biased or wrong, the model's apparent superiority may be agreement with the labeler rather than discovery of actual causes.

What would settle it

Run the label-generating pipeline on a synthetic temporal structural causal model whose true graph is known exactly but whose dynamics violate the pipeline's assumptions (e.g., nonstationary noise or contemporaneous effects), verify that the pipeline's inferred graph diverges from the true graph, then check whether the LCM's zero-shot predictions match the true graph or the pipeline's graph. If the LCM tracks the pipeline's incorrect labels, the generalization claim collapses.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • A pre-trained LCM can replace per-dataset causal discovery: one forward pass outputs the lagged causal graph, so real-time or high-throughput applications become feasible.
  • Zero-shot transfer to new time-series domains becomes practical for datasets that satisfy the model's causal assumptions (stationarity, no unobserved confounders, no contemporaneous effects).
  • Scaling strategy for temporal causal discovery shifts from architecture search to data curation; models should be trained on as diverse a corpus as possible rather than deeper networks alone.
  • The released corpus of 275k time-series/graph pairs becomes a standardized testbed for evaluating future temporal causal discovery methods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the realistic labels are produced by an algorithmic causal-discovery pipeline, the benchmark may measure agreement with that labeler; an independent evaluation with hand-verified mechanistic ground truth is the natural next test.
  • The success of correlation injection suggests the model may lean heavily on statistical dependence; under hidden confounders or contemporaneous effects this heuristic could degrade, making relaxation of causal sufficiency the key stress test.
  • Runtime independence of input size hints at embedded use in closed-loop experiment design—choosing interventions in real time—which the paper leaves implicit.
  • The scaling behavior implies a 'universal' temporal causal discovery model may be reachable with even larger, cross-domain corpora, especially in fields where randomized trials are prohibitively expensive.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper introduces Large Causal Models (LCMs), transformer-based foundation models for temporal causal discovery. LCMs are trained supervised on a large corpus of time-series/causal-graph pairs, mixing synthetic TSCM-generated data with 'realistic' data produced by the TCS pipeline, and are then applied zero-shot to unseen datasets. The authors report that LCMs outperform or match classical temporal CD baselines (PCMCI, DYNOTEARS, VARLiNGAM) and the prior neural method CP on synthetic, semi-synthetic, and realistic benchmarks, while providing fast single-pass inference. They further claim that scaling failures in prior work are due to insufficient training-distribution diversity rather than architectural limits.

Significance. If the main claims hold, the paper is a substantial step toward foundation models for temporal causal discovery. Its strengths include a large released corpus of paired time-series and causal graphs, public model weights/code, careful ablation of training aids, and strong zero-shot results on semi-synthetic benchmarks with known simulators (fMRI and Kuramoto, Table 4, AUC roughly 0.92-0.98). These semi-synthetic results are non-circular and provide genuine evidence that a pretrained transformer can amortize causal discovery out of distribution. The weaker points are the realistic-data evaluation, which is confounded by the label-generation procedure, and the scaling narrative, which is not uniformly supported by the largest model's performance. The paper is therefore a promising contribution, but its central realistic and scaling claims need substantial revision before publication.

major comments (2)
  1. [Appendix .3, Tables 10-11; Tables 5 and 2] The realistic benchmark labels are not independent ground truth. TCS takes real time series, runs PCMCI, DYNOTEARS, and CP (Table 10) to infer a 'ground truth' graph, then simulates series from that graph. The same TCS pipeline is used to create both the realistic training pairs and the OOD evaluation pairs (Table 11), and one of the labelers, CP [48], is itself a baseline. High AUC on the realistic collections in Table 5 therefore measures agreement with the labeler algorithms rather than discovery of actual causes, and Table 2's gains from adding realistic data inherit the same issue. The non-circular semi-synthetic evidence is strong, but the realistic claims should be reframed as 'agreement with TCS-inferred structure' or validated against an independent gold standard; per-labeler AUC would be a useful diagnostic.
  2. [Section 7.3, Tables 3 and 5] The headline scaling claim is not supported by the full table. Table 3 shows LCM24M is significantly worse than LCM12.2M on all three synthetic collections (e.g., Synthetic_2: 0.865 vs 0.909; CDML: 0.727 vs 0.773). Table 5 also shows LCM24M significantly below LCM2.5M on AirQualityMS and Power. Thus the evidence does not 'confirm that scaling failures stem from insufficient training distributions rather than architectural limitations'; the largest model degrades on several benchmarks. The authors should either reconcile this with the scaling narrative or weaken the claim to 'scaling improves up to 12M on semi-synthetic transfer' and report the full model-size/benchmark interaction.
minor comments (5)
  1. [Section 5.1 and Table 6] The main text says Synthetic_2 contains 230k instances, but Table 6 reports 270k. The stated LS total of 275k is consistent with 230k synthetic + 45k realistic, so Table 6 likely needs correction.
  2. [Abstract and final page] The code URL in the abstract ends with /LCM/ while the final page gives /LCM-paper/. Please unify.
  3. [Appendix .11, Figure 9] Figure 9's caption says paired differences are computed relative to LCM_2.5M, but the text and Table 3 use LCM12.2M as the best-performing reference on synthetic collections. This inconsistency makes the figure hard to interpret.
  4. [Section 4.1] The correlation loss is written as Lcorr = E[(A - CC)^2 ⊙ CC^γ] without specifying the distribution over which the expectation is taken. Please define it explicitly as an empirical average over batch elements and lagged edge entries.
  5. [Section 11] The limitations section acknowledges assumption violations but does not mention that the realistic training and evaluation labels are algorithmic outputs of TCS. A sentence clarifying that realistic-benchmark performance is agreement with TCS-inferred graphs would help readers calibrate the claims.

Circularity Check

3 steps flagged

Realistic OOD benchmarks are TCS-pipeline labels, not ground truth: LCMs trained on the same TCS outputs 'predict' the labeler (PCMCI/DYNOTEARS/CP), so realistic and Power/Climate claims are partly circular; synthetic and semi-synthetic legs remain independent.

specific steps
  1. self definitional [Appendix .3 (Realistic), Tables 10-11; Section 5.1]
    "To generate realistic (simulated) time-series datasets paired with ground-truth temporal causal graphs, we employ the methodology of [20]. TCS takes as input real multivariate time-series data, learns a Temporal Structural Causal Model (TSCM) consisting of a directed causal graph, functional mechanisms, and noise models, and synthesizes arbitrary numbers of time-series samples from the learned causal model. This procedure produces fully supervised dataset–graph pairs suitable for training LCMs."

    The 'ground-truth' graph is the output of TCS's causal-discovery phase, which runs PCMCI, DYNOTEARS, and CP (Table 10). The same TCS pipeline produces both the realistic training pairs and the OOD realistic evaluation collections (ETTm2, Climate, Garments, Power, Gearbox, AirQualityMS in Table 5). Therefore the LCM is trained to predict TCS's inferred graphs, and its 'zero-shot' realistic AUC measures agreement with the labeler's algorithm, not recovery of true causal structure. The Table 2 Power/Climate OOD columns are likewise TCS labels, so mixture gains there are partly forced by matching the training labeler.

  2. fitted input called prediction [Appendix .3 Table 10 vs Section 6.2 Baselines; Tables 3-4]
    "Causal Discovery Method Description PCMCI [43] Constraint-Based Algorithm DYNOTEARS [38] Constraint Optimization Algorithm CP [48] Pre-trained Transformer"

    TCS's causal-discovery phase for realistic data uses CP [48] as one of the labelers, and CP is also one of the neural baselines against which LCMs are compared (Section 6.2, Tables 3-4). LCMs are trained on dataset–graph pairs whose 'ground truth' can be CP's own output; hence high LCM AUC over CP on realistic collections may reflect learning to imitate CP's output pattern rather than outperforming it as an independent method. The comparison is therefore not independent for the realistic leg.

  3. self citation load bearing [Section 5.1 Realistic; reference [20]]
    "We incorporate realistic TSCMs derived from real-world time series following [20], to the best of our knowledge the only method constructing calibrated causal twins from observed, real data."

    Reference [20] is the authors' own prior work (Gkorgkolis, Kougioulis, Wang, Caglayan, Tonon, Simionato, Tsamardinos). The entire realistic training corpus and the realistic OOD benchmarks rest on this self-cited pipeline; the 'only method' claim is self-referential and is not backed by an external gold standard for the inferred graphs. This makes the realistic leg load-bearing on a self-citation whose outputs are themselves algorithmic CD results, rather than on independent causal ground truth.

full rationale

Most of the derivation chain is non-circular: synthetic benchmarks use known TSCM graphs (Appendix .3) and semi-synthetic fMRI/Kuramoto benchmarks use known simulators never used in training, so zero-shot AUC there is genuine evidence. The circularity is confined to the realistic leg: the 'ground-truth temporal causal graphs' for realistic data are not gold standards but outputs of the authors' TCS pipeline [20], whose causal-discovery phase runs PCMCI, DYNOTEARS, and CP (Appendix .3, Table 10). The same pipeline generates both the realistic training pairs and the OOD realistic evaluation collections (Table 11; Table 5), so high AUC on AQ/Clim/Gar/ETT/Gear/Pow measures agreement with TCS's labeler rather than discovery of true causes. This also affects Table 2's Power/Climate OOD columns and makes 'beating' CP on realistic data partly circular, since CP is one of the labelers. The paper's own Limitations section concedes that when assumptions are violated predictions may reflect training-distribution biases. Score 6 reflects partial circularity: the synthetic and semi-synthetic evidence stands, but the realistic OOD claims reduce by construction to reproducing TCS labels.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 0 invented entities

The central empirical claims rest on standard TSCM assumptions plus a load-bearing ad hoc assumption: that TCS-generated graphs, produced by running classical CD algorithms on real data, are trustworthy enough to serve as training labels and OOD ground truth. No new physical/ontological entities are postulated.

free parameters (4)
  • λ_corr (correlation regularization weight) = 0.75
    Selected via grid search on the Synthetic_1 holdout (Section 7.1); the reported improvement on that holdout is therefore partly selection-biased.
  • Synthetic/realistic mixing ratio = 80/20
    Adopted after comparing OOD fMRI/Power/Climate performance in Table 2; a design choice tuned on benchmark performance rather than fixed a priori.
  • γ (correlation loss exponent)
    Defined in Section 4.1 as γ>1 but the actual value is never reported, a reproducibility gap affecting the auxiliary loss.
  • Padding noise standard deviation = 0.01
    Gaussian noise σ=0.01 used for temporal padding (Appendix .2); a hand-set design choice.
axioms (7)
  • domain assumption Causal Markov Condition
    Appendix .1 Definition 1; assumed for interpreting lagged graphs from observational data.
  • domain assumption Faithfulness
    Appendix .1 Definition 2; required for the graph to be identifiable from conditional independences in principle.
  • domain assumption Causal Sufficiency (no latent confounders)
    Appendix .1 Definition 3 and Section 1; explicitly assumed and relaxed only in future work.
  • domain assumption Causal stationarity
    Appendix .1 Definition 4; the graph and noise distribution are time-invariant.
  • domain assumption Additive noise TSCM, no contemporaneous effects, fixed maximum lag
    Section 1 defines the data-generating process as additive noise with Pa(V^j_t) restricted to past lags up to ℓ_max.
  • ad hoc to paper TCS-generated graphs from real series are valid ground truth
    Realistic training and OOD evaluation rely on [20], where causal graphs are inferred by CD algorithms; if those inferred graphs are wrong, the realistic AUC results do not measure true causal discovery.
  • ad hoc to paper Bounded wrappers (tanh/sigmoid) preserve causal structure while ensuring stationarity
    Appendix .3 uses tanh/sigmoid to cap unbounded functional dependencies, asserting causal relationships are preserved; this is plausible but not formally demonstrated.

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Cite this review

Pith. "Pith review of Large Causal Models for Temporal Causal Discovery." pith.science (2026). https://pith.science/paper/V32XLCWP

@misc{pith2026260218662,
  author       = {Pith},
  title        = {Pith review of: Large Causal Models for Temporal Causal Discovery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V32XLCWP}},
  note         = {Machine review of arXiv:2602.18662}
}
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read the original abstract

Causal discovery for both cross-sectional and temporal data has traditionally followed a dataset-specific paradigm, where a new model is fitted for each individual dataset. Such an approach limits the potential of multi-dataset pretraining. The concept of large causal models (LCMs) envisions a class of pre-trained neural architectures specifically designed for temporal causal discovery. Prior approaches are constrained to small variable counts, degrade with larger inputs, and rely heavily on synthetic data, limiting generalization. We propose a principled framework for LCMs, combining diverse synthetic generators with realistic time-series datasets, allowing learning at scale. Extensive experiments on synthetic, semi-synthetic and realistic benchmarks show that LCMs scale effectively to higher variable counts and deeper architectures while maintaining strong performance. Trained models achieve competitive or superior accuracy compared to classical and neural baselines, particularly in out-of-distribution settings, while enabling fast, single-pass inference. Results demonstrate LCMs as a promising foundation-model paradigm for temporal causal discovery. Experiments and model weights are available at https://github.com/kougioulis/LCM/.

Figures

Figures reproduced from arXiv: 2602.18662 by Andrea Tonon, Bora Caglayan, Dario Simionato, Ioannis Tsamardinos, Mingxue Wang, Nikolaos Gkorgkolis, Nikolaos Kougioulis.

Figure 1
Figure 1. Figure 1: Temporal causal dependencies represented as a (a) lagged causal graph and (b) binary adjacency tensor. Each slice A (ℓ−1) encodes edges at a discrete lag ℓ ≤ ℓmax, where entry A (ℓ−1) j,i = 1 denotes V i t−ℓ → V j t . ℓ ∈ {1, . . . , ℓmax}. Edges are oriented forward in time and denote direct causal effects, while indirect effects are encoded via directed paths. Adjacency Tensor Representation. For V varia… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the large causal model (LCM) pipeline. (1) Synthetic and realistic TSCM generators produce training pairs of multivariate time series and their lagged causal graphs. (2) The LCM is trained via supervised learning on these pairs to discover a lagged adjacency tensor Aˆ for a time series X ∈ R L×V , padded and normalized for stability. (3) At inference (CD phase), the pre-trained LCM predicts cau… view at source ↗
Figure 3
Figure 3. Figure 3: A multivariate time series is embedded via Conv1D layers and positional encod￾ings, processed through a Transformer encoder stack with optional distillation blocks, and augmented with lagged cross-correlations (training aids). A feedforward head out￾puts a lagged adjacency tensor representing the discovered temporal causal graph. the TSCMs. Rather than performing dataset-specific DAG search, the model lear… view at source ↗
Figure 4
Figure 4. Figure 4: Running times (in seconds) for LCMs and baseline algorithms on the Synthetic_2 holdout set, averaged over 10 runs. Traditional methods (e.g., PCMCI & DYNOTEARS) scale superlinearly with lag and variable count, while Transformer￾based LCMs remain effectively independent of input dimensionality due to their constant-time forward pass. Ptotal = (dmodelVmax · k + dmodel) + B [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
Figure 5
Figure 5. Figure 5: Empirical convergence of LCMs with increasing training data. Test AUC for 500K, 1M, and 2M parameter models trained on subsampled datasets. Validation/test sets are fixed to isolate the effect of data scale. not claim a universal scaling law; rather, these findings inform practical design choices for large-scale temporal CD. 10 Concluding Remarks & Future Work Large Causal Models (LCMs) are foundation mode… view at source ↗
Figure 6
Figure 6. Figure 6: Hidden state representations with and without auxiliary training aids. In order to handle variable-length time-series, variable numbers of time-series and differing maximum lags across datasets, we adopt a set of standardized padding strategies, both for the input time-series and the ground truth lagged adjacency tensor. This enables consistent batch processing and generalization of trained models across h… view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of the padding strategies in LCMs. Left: Gaussian noise padding for time-series where V < Vmax and L < Lmax. Right: Zero padding of lagged adjacency tensors when V < Vmax or ℓ < ℓmax. Red dashed boxes indicate padded regions. N denotes N (0, 0.01) for brevity. .3 Datasets Synthetic In line with the synthetic temporal data generators provided in Tigramite [45], we implement a temporal SCM-based… view at source ↗
Figure 8
Figure 8. Figure 8: Heatmap visualization of the discovered lagged adjacency matrix (bottom row) compared to the ground truth (top row) in an example with nmax = 12 and ℓmax = 3 using the pretrained LCM-2.4M model. Brighter colors in the predicted adjacency indicate stronger confidence for edge existence. In [PITH_FULL_IMAGE:figures/full_fig_p029_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Paired median AUC differences relative to the reference model across Synthetic collections. Positive values indicate improved performance. Statistical significance is determined via Wilcoxon signed-rank test with Bonferroni correction [PITH_FULL_IMAGE:figures/full_fig_p030_9.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p031_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Paired median AUC differences across Realistic collections. Positive values indicate improved performance. Statistical significance is determined via Wilcoxon signed-rank test with Bonferroni correction [PITH_FULL_IMAGE:figures/full_fig_p032_11.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.