{"id":"5ead81b2-338f-4f58-9def-b8158312f9c4","arxiv_id":"2508.18873","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A temporal point process model that represents multi-order causal influence as multi-hop paths over a time-varying DAG, trained end-to-end for likelihood and sparse acyclic structure.","lead":"MOCHA is a neural model that learns time-varying causal graphs between event types and uses multi-hop paths through those graphs to predict future events. It reports lower prediction errors than existing temporal point process models on seven real-world datasets and claims to recover known clinical causal chains.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (5)-(6) leave intermediate timestamps t_1...t_{l-1} undefined, so the multi-order intensity is not computable; the paper's central causal mechanism is under-specified.","rationale":"The reader's verdict identifies the same load-bearing concern: the multi-order intensity in Eqs. (5)-(6) is under-specified because intermediate timestamps are undefined and no generative mechanism connects the type-level paths to observed events. I independently reach the same conclusion. The paper's central contribution is the multi-order causal path formulation; if that formulation is not computable, the model cannot be trained or evaluated as described, and the experimental results (Table I) do not provide evidence for the abstract's claim that 'MOCHA not only achieves state-of-the-art performance... but also reveals meaningful and interpretable causal structures.' Other problems—lack of error bars, no code/data, and a causal-readout evaluation without a baseline—are real but secondary; they would not alone invalidate the core idea if the math were well-defined. The mathematical gap is primary and fatal to the current write-up. I therefore agree with the reader's REJECT verdict and do not adjust it. A well-defined revision that specifies how intermediate event times enter the path sum, or that replaces the type-level sum with an event-level sum, could make the approach testable, but that is not present in this version.","tokens_in":11181,"tokens_out":4460,"duration_ms":42015,"concrete_test":"Analytically instantiate Eq. (6) for a minimal example: K=3, a single past event of type 1 at time 0, and a length-2 type path 1->2->3 at current time t. Write out λ_3^(2)(t|H_t) using only definitions in §IV-A. If the expression contains an undefined t_1, or if the only consistent evaluation (e.g., t_1=0) yields κ(0)=0 and hence a zero contribution, then the model as stated is not implementable. In addition, if the authors release code, check how t_1 is resolved: if the code sums over observed times of type 2 in the history, then Eq. (6) omits an essential sum that is required for the claimed multi-order effect.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that explicitly modeling multi-order dynamic causality improves prediction and interpretability—rests entirely on the definition of the multi-order intensity λ_k^(l) in Eq. (6), which sums path influences Φ_π^(l) from Eq. (5). Eq. (5) writes a length-l path as (t0,k0)->(t1,k1)->...->(tl,kl) with (tl,kl)=(t,k), and multiplies factors w_{k_{r-1}->k_r}(t_r-t_{r-1})·κ(t_r-t_{r-1}). However, the intermediate timestamps t_1,...,t_{l-1} are never defined. The paths summed in Eq. (6) are type sequences π=(k0->...->k); the sum ranges only over starting events (t_i,k_i) and type paths, not over intermediate event times. Moreover, the structural weight w is defined in §IV-A1 as a function of current time t (W_t[u,v]=w_{u->v}(t)), yet Eq. (5) evaluates it at t_r-t_{r-1}, an inconsistent argument. If one tries to fill the gap by setting all t_r=t_i, then κ(0)=0 as defined in §IV-A2, making every l≥2 contribution vanish. If one instead uses observed intermediate event times, Eq. (6) is missing the combinatorial sum over those times. The manuscript itself asserts (after Eq. 7) that 'intermediate events act as carriers of causal signals' but provides no formula for selecting or aggregating their timestamps. Thus λ_k^(l) is not a well-defined function of the history, and the reported NLL improvements cannot be attributed to the described multi-hop mechanism. This is a load-bearing mathematical gap, not a mere notational inconvenience.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes MOCHA, a neural temporal point process (TPP) model that claims to discover multi-order dynamic causal structure. The intensity of each event type is expressed as a sum of first-order and higher-order terms, where higher-order influences are propagated along paths in a time-varying DAG with learned structural weights and learned decay kernels. The DAG is regularized with continuous acyclicity and sparsity penalties, and training is end-to-end via negative log-likelihood. Experiments on seven real-world datasets (four clinical, three social) report state-of-the-art negative log-likelihood, an ablation study, and recovery of known clinical causal paths for AKI. The main claim is that explicitly modeling multi-hop dynamic causality improves both prediction and interpretability.","tokens_in":11705,"tokens_out":2722,"duration_ms":28177,"significance":"If the proposed formulation were rigorously defined and the empirical claims held, the paper would make a useful contribution to interpretable TPP modeling: jointly learning time-varying DAGs and using path-based influence is a natural and potentially valuable extension of Hawkes-type processes. The authors also connect to external clinical ground truth for path recovery, which is a positive step beyond purely predictive evaluation. However, the central mathematical object—the multi-order intensity in Eqs. (5)–(6)—is not well defined, and the experimental evidence lacks elementary statistical safeguards. As written, the paper's main claims are not supported.","major_comments":[{"comment":"The l-th order path influence Φ_π^(l)(t − t0) in Eq. (5) is defined over a path (t0, k0) → (t1, k1) → ... → (tl, kl) with (tl, kl) = (t, k), but the intermediate timestamps t1, ..., t_{l−1} are never defined. Eq. (6) then sums over observed starting events (ti, ki) and type-level paths π ∈ P_l(k_i → k), but there is no sum over intermediate event times. If one sets all intermediate t_r = t_i, then κ(0) = 0 (as defined in §IV-A2), making every l ≥ 2 contribution vanish. If one instead intends to use observed event times, Eq. (6) is missing the combinatorial summation over those times. Furthermore, the structural weight w is defined in §IV-A1 as a function of current time t (W_t[u,v] = w_{u→v}(t)), yet Eq. (5) evaluates it at t_r − t_{r−1}, an inconsistent argument. Consequently, λ_k^(l)(t|H_t) is not a well-defined function of the history, and the reported NLL improvements in Tables I–II","section":null},{"comment":"NLL values are reported as point estimates with no error bars, repeated-seed standard deviations, or statistical significance tests. Differences such as CAD 0.69 vs. 1.81 and TB −0.36 vs. previous 0.74 are large, but without variance estimates we cannot rule out run-to-run or initialization artifacts. The claim of consistent SOTA across all seven datasets is therefore not established. At minimum, the paper should report mean ± std over multiple seeds and a paired significance test.","section":null},{"comment":"The causal path recovery evaluation reports matching rates against a set of clinically known paths, but it provides no comparison to other causal discovery baselines, nor to a simple baseline that reads off transitive closures of the learned first-order DAG. The average first-order matching rate is 92.10%, while higher-order path matching appears to vary widely (e.g., one third-order path at 99.39%, but others are lower in Figure 3). Without such comparisons, it is unclear whether the path matching results reflect genuine multi-order causal learning or simply direct edges that happen to cover the selected paths. Also, the theoretical maximum matching rate is said to be below 100% due to patient subgroups, but no null model is given to calibrate the reported rates.","section":null},{"comment":"The manuscript asserts causal validity primarily from the DAG constraint and the SCM framing, but the learned graph is a prediction model with a sparsity/acyclicity penalty, not a result of identifiable causal discovery from interventional or counterfactual data. The external validation in RQ3 is independent and is a strength, but the broader claim that MOCHA 'reveals meaningful and interpretable causal structures' goes beyond what the experiments support. The paper should either temper the causal language or add a formal identifiability discussion. This concern is secondary to the definitional gap in Eqs. (5)–(6), but it affects the interpretation of the results.","section":null}],"minor_comments":[{"comment":"No dataset statistics (number of sequences, event types, event counts, time horizon) are provided. This makes the reported NLL values difficult to interpret and reproduce.","section":null},{"comment":"The text says RMSE and type accuracy are 'shown in the supplementary materials,' but the submission appears to have no supplementary material. Either include those results or remove the reference.","section":null},{"comment":"The regularization sums over all N events in each training sequence, which couples the penalty strength to sequence length. The authors should clarify whether this is intended and how γ_acyclic and γ_sparse are chosen across datasets differing in length.","section":null},{"comment":"The decay function κ(Δ t) is defined as Sigmoid(MLP(PE(Δ t))), which is bounded between 0 and 1 but is not necessarily monotonically decreasing in Δ t. If the intention is to model fading influence, this should be stated explicitly; otherwise the 'decay' terminology is misleading.","section":null},{"comment":"No code or repository is provided. For a paper whose experiments are central to the claims, releasing code and hyperparameter settings would greatly help reproducibility.","section":null}],"recommendation":"reject","confidential_remarks":"The central problem is the undefined intermediate timestamps in Eqs. (5)–(6), which the reader's report correctly identifies. I agree that this is a load-bearing gap: the model's core mechanism cannot be computed as written, so the empirical results do not validate the proposed multi-order causal contribution. The paper could in principle be fixed by redefining the model (e.g., summing over observed intermediate events or using a kernel over type paths only), but that would be a substantial rewrite and the experiments would need to be redone. The lack of error bars and the absent baseline comparisons for causal path recovery further weaken the work. I would not encourage a revision at this journal unless the authors can close the definitional gap and provide statistically grounded experiments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Thanks for the pass. My take: this is a real idea with a load-bearing hole. The multi-order intensity via multi-hop paths over a time-varying DAG is a fresh framing, and the clinical path-matching evaluation is the right kind of external check. But as written, the central equations do not define a computable intensity, and the experiments lack the basics (error bars, code) that would let us trust the reported gains.\n\nThe path-based decomposition of Hawkes-style influence into first- and higher-order terms is not in the cited baselines. The dynamic DAG with NOTEARS-style acyclicity and sparsity is a sensible way to keep the structure interpretable. And the AKI clinical validation against known disease pathways is a good idea: it is independent of the learned weights and gives at least one downstream check on the graph. The ablation, too, is a useful decomposition, even if incomplete.\n\nThe stress-test is right. Eq. (5) defines the l-th order path influence using intermediate timestamps t_1...t_{l-1} that never appear in any history-based sum. Eq. (6) sums over starting events and type-level paths, but not over intermediate event times. So λ_k^(l) is not a function of the observed history. Also, the structural weight W_t[u,v] is a function of current time t, but Eq. (5) evaluates it at t_r - t_{r-1}, which is a duration. That is a type mismatch, not a minor notation issue. If the intended mechanism is 'intermediate events act as carriers', then there must be a sum over observed intermediate events, and the paper does not provide it. This is load-bearing because the reported NLL improvements are attributed to the multi-order mechanism.\n\nBeyond that, the experiments have no variance or significance tests across the seven datasets, no code or data release, and the causal path matching has no baseline—what would a first-order-only model score on those same paths? The ablation is suggestive but again without variance.\n\nCredit where due: the idea is concrete and likely salvageable. The clinical validation is a step beyond synthetic benchmarks. But the paper in its current form cannot be evaluated on its central claim.\n\nWho it is for: anyone working on interpretable TPPs or causal discovery in event streams. It deserves a serious referee, but the referee should demand a major revision with a well-defined generative mechanism for intermediate event times and much more careful experimental reporting. I would send it to peer review rather than desk reject, because the framing is new and the gap is fixable. I would not cite it until the math is made consistent.","headline":"Genuinely new multi-hop causal TPP architecture, but Eq. (5)-(6) leave intermediate timestamps undefined, so the central mechanism is not actually computable as written.","tokens_in":12146,"tokens_out":2845,"would_cite":false,"duration_ms":27434,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Modeling indirect multi-hop causal paths over a time-varying DAG improves event modeling and reveals interpretable structures.","keywords":["temporal point processes","causal discovery","multi-order causality","dynamic DAG","Hawkes process","event sequence modeling","interpretable machine learning","neural point processes"],"falsifier":"Take synthetic event sequences generated by a multivariate Hawkes process with known first-order-only kernels, and fit MOCHA alongside a version with L=1. If the multi-order version has lower held-out negative log-likelihood, or if its learned graph contains paths of length greater than one, the multi-order claim is falsified; true first-order data should not reward longer paths.","tokens_in":11081,"feed_emoji":"🔗","tokens_out":7206,"duration_ms":71179,"temperature":0.7,"pith_summary":"MOCHA sets out to show that event sequences are better explained when influences can travel along multi-hop chains of event types, not just direct pairwise links. It builds a time-varying directed acyclic graph over event types, learns dynamic edge weights from event histories, and lets the conditional intensity of each type accumulate contributions from all causal paths up to length L. On seven real-world datasets, including four clinical event datasets, it reports the lowest negative log-likelihood among the compared neural temporal point process models. It also reports high matching rates with clinically established causal paths leading to acute kidney injury, and identifies a new multi-step path that later clinical literature supports. The intended consequence is that causal structure and predictive accuracy can be learned jointly rather than traded off.","feed_headline":"Causal chains lift event prediction","feed_subtitle":"A dynamic DAG that lets influence travel multiple hops beats first-order baselines on all seven datasets.","key_machinery":"The central object is a time-varying weighted DAG over event types. Its edge weights are generated by a graph attention network that attends over embeddings of event types and their elapsed times since last occurrence, and its influence kernel is a learned MLP-based decay. Higher-order influence along a length-l path is the product of edge weights and decays along the path, so the multi-order intensity is base intensity plus weighted sums of these path products. A continuous acyclicity constraint h(W_t) = Tr(exp(|W_t|∘|W_t|)) - K = 0 keeps every snapshot acyclic, which guarantees the longest path is at most K-1 and makes the hierarchy finite.","core_discovery":"The central claim is that the total influence of one event type on another is not exhausted by direct excitation; it propagates as products of dynamic edge weights and time-decay kernels along multi-hop paths in a latent time-varying DAG. MOCHA makes this claim concrete by defining an l-th-order intensity that sums, over all past events and all length-l type paths, the product of edge weights and decay factors along the path. Dynamic edge weights come from a graph attention network fed with sinusoidal recency embeddings and learnable type embeddings, and a differentiable acyclicity constraint keeps the graph acyclic, bounding the maximum order by K-1. The paper reports that this model attain","pith_inferences":["The path-product formula is not a self-contained generative model: it multiplies decay kernels at intermediate times that are never defined, and the intensity sum runs over type-level paths rather than over actual intermediate events. A fully grounded version would need latent event times or a sum over observed intermediate events; without that, the multi-order intensity is not computable as writt","If the likelihood gains survive a synthetic test with known first-order-only dynamics, they would demonstrate genuine higher-order discovery; if not, the gains may come from extra capacity in the dynamic weights and decay rather than from multi-order paths.","The path matching rate checks edge presence in the learned DAG, not temporal precedence in the data, so it measures consistency with clinical knowledge rather than proof that the model found the true causal mechanism.","The recency embeddings tied to last occurrence times make the graph state depend on the most recent event of each type; a fuller history representation could change which edges appear, so the discovered graphs are history-summary-dependent."],"forward_implications":["If the central claim is right, neural TPPs should stop treating pairwise kernels as complete; indirect chains are a separate, identifiable component of the intensity.","Dynamic edge weights mean the causal graph can be queried at each event time, so the output is a time-stamped structure, not a single static graph.","The path-matching results imply that early-warning systems could use learned multi-hop paths as risk markers before the terminal event, not just at it.","The framework gives a template for imposing acyclicity on any recurrent or attention-based point process without sacrificing end-to-end differentiability.","Because the model generalizes the Hawkes kernel to a path product, it inherits the interpretability of Hawkes-type models while widening the class of dependencies they can express."],"supporting_citations":[{"why":"Defines the Hawkes self- and mutually-exciting kernel that the paper extends into multi-order path products.","marker":"[4]"},{"why":"Recurrent marked TPP baseline; serves as a first-order neural comparison for the likelihood tables.","marker":"[7]"},{"why":"Neural Hawkes baseline; the main first-order neural point process MOCHA must outperform.","marker":"[8]"},{"why":"Self-attentive Hawkes baseline; supplies the attention-based TPP comparison.","marker":"[9]"},{"why":"Provides the continuous acyclicity constraint used to keep learned graphs acyclic.","marker":"[26]"},{"why":"Supplies the graph attention mechanism used to compute time-varying structural weights.","marker":"[32]"},{"why":"Source of the four clinical event datasets used in the evaluation.","marker":"[36]"},{"why":"Clinical guideline used to define ground-truth AKI causal paths for the matching-rate evaluation.","marker":"[38]"}],"fun_headline_variants":["Multi-hop causal paths sharpen event forecasts","Time-evolving causal graphs beat first-order models","Dynamic DAG uncovers multi-order causality","Event prediction gains from multi-hop influence"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The load-bearing premise is that an influence can travel along a chain of event types even when the intermediate events in the chain never actually occur in the observed sequence, and that the strength of that influence can be computed from times that the model never specifies.","fun_headline_variants_meta":{"raw":{"variants":["Multi-hop causal paths sharpen event forecasts","Time-evolving causal graphs beat first-order models","Dynamic DAG uncovers multi-order causality","Event prediction gains from multi-hop influence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000251,"raw_usage":{"total_tokens":1357,"prompt_tokens":673,"completion_tokens":684,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":417,"completion_tokens_details":{"reasoning_tokens":631}},"tokens_in":417,"tokens_out":684,"duration_ms":6281,"temperature":1.0,"reasoning_tokens":631,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T16:07:39.444261+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take synthetic event sequences generated by a multivariate Hawkes process with known first-order-only kernels, and fit MOCHA alongside a version with L=1. If the multi-order version has lower held-out negative log-likelihood, or if its learned graph contains paths of length greater than one, the multi-order claim is falsified; true first-order data should not reward longer paths.","supporting_citations":[{"cited_title":"Recurrent marked temporal point processes: Embedding event history to vector,","cited_arxiv_id":null,"evidence_quote":"Recurrent marked TPP baseline; serves as a first-order neural comparison for the likelihood tables."},{"cited_title":"The neural hawkes process: A neurally self-modulating multivariate point process,","cited_arxiv_id":null,"evidence_quote":"Neural Hawkes baseline; the main first-order neural point process MOCHA must outperform."},{"cited_title":"Self-attentive hawkes process,","cited_arxiv_id":null,"evidence_quote":"Self-attentive Hawkes baseline; supplies the attention-based TPP comparison."},{"cited_title":"Dags with no tears: Continuous optimization for structure learning,","cited_arxiv_id":null,"evidence_quote":"Provides the continuous acyclicity constraint used to keep learned graphs acyclic."},{"cited_title":"The mimic code repository: Enabling reproducibility in critical care research,","cited_arxiv_id":null,"evidence_quote":"Source of the four clinical event datasets used in the evaluation."},{"cited_title":"Kdigo clinical practice guideline for acute kidney injury,","cited_arxiv_id":null,"evidence_quote":"Clinical guideline used to define ground-truth AKI causal paths for the matching-rate evaluation."}],"review_version":1}