{"id":"d26e8bda-dff5-46c7-ae4b-190bac677bbe","arxiv_id":"2507.11178","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A single gradient-regularized neural forecaster, combined with a phase-randomized surrogate significance test, recovers Granger causal structure from multivariate time series better than several baselines in the reported benchmarks.","lead":"This paper proposes a causal discovery method that trains one shared neural network to forecast all variables in a time series, then reads causal links from the network's regularized input-output gradients. Tests on simulated and industrial process data report better or comparable causal recovery than several neural Granger baselines, at lower training cost.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Gradient magnitudes can miss Granger-causal edges when the causal mechanism is non-smooth (e.g., threshold effects), so the central proxy in Section III.B is not reliable without added assumptions or evidence.","rationale":"The central claim is that a cheap, single-model gradient statistic is a reliable proxy for Granger causality. For that to be true, |d(s_i)/d(x_{t-tau,j})| must be large when and only when the predictive distribution of x_i depends on past x_j. This requires the generative mechanism to be smooth enough and the data to cover the regions where the dependence is expressed; neither condition is stated or tested. My threshold example shows a concrete necessity failure: a discontinuous step dependence is Granger-causal by the paper's own definition (improved prediction), but its local gradient is zero almost everywhere, so GC_{1,2} collapses. Because industrial processes contain valves, saturations, and regime switches, this is not an exotic edge case. I agree with the reader's weakest_assumption; this is the same concern, sharpened to a concrete failure mode. I also note the reader's Eq. (3) dimensionality issue as a separate, important reproducibility problem, but I do not make it the headline because it may be a typo; the gradient-causality issue is conceptual and survives any typo fix. The reader's CONDITIONAL verdict remains appropriate: the authors should either prove or state sufficient conditions, or demonstrate the method on non-smooth causal mechanisms, before the general framework claim is accepted.","tokens_in":13050,"tokens_out":11883,"duration_ms":161388,"concrete_test":"Simulate a bivariate threshold process with T=10,000, threshold crossing rate 2-5%: x_{2,t}=0.8 x_{2,t-1}+eps_{2,t}; x_{1,t}=1{x_{2,t-1}>0.9}+eps_{1,t}. Also simulate a smooth control: x_{1,t}=x_{2,t-1}^3+eps_{1,t}. Run GCD with the authors' hyperparameters (or reasonable defaults: k=1, H=16, Adam, lambda chosen by validation) and the PSST procedure at alpha=0.05. Report whether the edge 2->1 is recovered in the threshold case. If it is missed while the smooth control is recovered, the central claim fails in a simple setting; if it is recovered, the concern is substantially weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III.B asserts that the time-averaged absolute input-output gradient GC_{i,j} is a faithful proxy for Granger causality: 'A large gradient magnitude indicates that perturbing the past value of x_j produces a substantial change in the predicted x_i, aligning with the Granger causality principle.' This identification is not a theorem and is false without additional smoothness and support-coverage assumptions. Granger non-causality is a conditional-independence / predictive condition, not a local-sensitivity condition. A causal effect can be non-smooth or concentrated in a rare regime. Example: let x_{2,t}=0.8 x_{2,t-1}+eps_{2,t} and x_{1,t}=1{x_{2,t-1}>0.9}+eps_{1,t}. Here x_2 strictly Granger-causes x_1 by the paper's own definition, because knowing x_{2,t-1} improves prediction of x_{1,t} whenever the threshold is crossed. Yet a ReLU MLP approximating the step has input-output gradient equal to 0 on almost all training points except a narrow band near the threshold. If the threshold region is rarely visited in the sample, the time-averaged |d(s_1)/d(x_{t-1,2})| is near zero, GC_{1,2} is small, and the PSST test will fail to reject the null. Thus the central quantity can miss true causal edges. The Section IV benchmarks may be smooth enough to avoid this failure, but the paper presents GCD as a general framework for complex industrial processes, where saturation, switching, and threshold effects are common. Without a theoretical condition or direct empirical evidence on non-smooth mechanisms, the central methodological claim is not established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes Gradient-based Causal Discovery (GCD), a framework that trains a single MLP forecaster on multivariate time series and uses the time-averaged absolute input-output gradient, regularized with an L1 penalty and thresholded by a phase-randomization surrogate test, as a measure of Granger causality. The method is evaluated against cMLP, cLSTM, TCDF, eSRU, GVAR, CR-VAE, and CUTS+ on Lorenz-96, DREAM4, and CausalTime, and on three industrial datasets (Tennessee-Eastman, Ultra-processed Food, Debutanizer). The central claims are that a single shared forecaster with gradient-based L1 regularization recovers directed causal structure more accurately than component-wise neural Granger methods, and that this is achieved with substantially lower computational overhead.","tokens_in":13365,"tokens_out":4269,"duration_ms":54611,"significance":"If the core identification is valid, GCD offers a practically meaningful advance: replacing D component-wise models with a single MLP and extracting causal structure from input-output gradients rather than first-layer weights could reduce cost in high-dimensional industrial monitoring and is architecture-flexible. The empirical evaluation is broad, covering synthetic, benchmark, and industrial settings, and the paper includes ablations of the surrogate statistical test and an explicit complexity analysis. However, the load-bearing link between gradient magnitude and Granger non-causality is assumed rather than derived, and several performance tables lack uncertainty estimates. The strength of the contribution therefore depends on additional theoretical support and tightened experimental reporting.","major_comments":[{"comment":"The abstract claims experiments on DREAM, Lorenz-96, fMRI BOLD, and CausalTime and on real-world DNA, Yeast, HeLa, and bladder urothelial carcinoma datasets. Sections IV and V do not report any fMRI BOLD, DNA, Yeast, HeLa, or bladder urothelial carcinoma experiments. This mismatch is load-bearing because the abstract advertises empirical support that the manuscript does not contain; it must be resolved either by adding the missing experiments or by correcting the abstract.","section":"Abstract vs. Sections IV and V"},{"comment":"The central identification of GC_{i,j} = (1/k) sum_tau |g^i_{tau,j}| with Granger causality is asserted by intuition, not derived. Granger non-causality is a predictive conditional-independence condition, while a time-averaged local input-output gradient is a sensitivity measure. The two can disagree: for a process with x2,t = 0.8 x2,t-1 + eps2,t and x1,t = 1{x2,t-1 > 0.9} + eps1,t, x2 strictly Granger-causes x1 under the paper's own definition, but a ReLU MLP approximating the threshold has zero input-output gradient on almost all training points, so the time-averaged absolute gradient and the PSST test can fail to recover the edge. Since the paper motivates GCD for industrial processes where saturation, switching, and threshold effects are common, this is a load-bearing gap. The authors should either state and prove sufficient smoothness/coverage conditions under which the gradient proxy is faithful, or provide direct empirical evidence on non-smooth benchmark processes.","section":"Section III.B, Eqs. (5)-(7)"},{"comment":"The DREAM4 results in Table II and the industrial-process results in Tables IV, V, and VI are reported as single point estimates without error bars, confidence intervals, or repeated runs. The claim that GCD 'consistently achieves' the best performance on DREAM4 and the three industrial datasets is therefore not statistically supported. Please provide variance estimates over multiple random seeds, or formal significance tests against the closest baselines, for these tables.","section":"Tables II, IV, V, VI"},{"comment":"The complexity comparison in Table VII depends on the number of surrogate datasets N through the term O(e(N+1) sum H_l H_l+1) + D^2, and the argument that GCD is cheaper than cMLP relies on D > N+1. The value of N used in the reported experiments is not given in the main text, only deferred to the Supplementary Materials. Please report the actual N and the resulting effective multiplier for each dataset, so that the efficiency claim in Table VIII can be checked against a fair common training budget.","section":"Section V.D, Tables VII and VIII"}],"minor_comments":[{"comment":"In Eq. (2), W1 is declared in R^{H x D} while the input x_{t-k:t-1,1:D} is a k x D matrix, so the dimensions are inconsistent unless the input is flattened; please clarify the reshaping. In Eq. (3), the predicted loss compares xhat_{t,1:D} to x_{t-k:t-1,1:D}, which appears to be a typo for the target x_{t,1:D}.","section":"Section III.A, Eqs. (2)-(3)"},{"comment":"The cMLP complexity in Table VII is listed as O(eD sum H_l H_l+1) with no factor of T, whereas all other component-wise models include a factor of T in their complexity. If the training procedure iterates over T time steps, the cMLP term should also include T.","section":"Table VII"},{"comment":"There are several typographical errors: 'in constract' in Section V.A, 'DE process process' in the caption of Table VI, and 'the search space for causal variance becomes broader' in the Introduction. These should be corrected.","section":"Throughout"},{"comment":"Reference [1], on regioselective hydroformylation of propene, does not appear to support the opening sentence about large-scale multi-source industrial data; please verify that the citation is appropriate or replace it.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The abstract/full-text mismatch is concerning and should be resolved before resubmission. The theoretical gap in Section III.B is the main scientific risk: the paper may be right empirically on the benchmarks, but the central proxy is not justified by the stated Granger-causality definition. I would encourage the editor to ask for a precise statement of the conditions under which time-averaged input-output gradients recover Granger causality, or a targeted experiment on non-smooth dynamics."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take on arXiv:2507.11178. The paper proposes GCD, a single-MLP framework that infers Granger causality by applying L1 regularization to the time-averaged absolute input-output Jacobian. That is a useful practical move: it avoids the component-wise architecture of Tank et al., and the phase-randomized surrogate with FDR is a sensible alternative to the time-shift surrogate. The empirical work is genuinely solid: the method beats baselines on Lorenz-96, DREAM4, and CausalTime, and shows credible gains on three industrial datasets with notably fewer parameters and shorter training time. The sensitivity and ablation studies are a good addition.\n\nThe novelty is thin. The gradient/Jacobian quantity in Eq. (7) is essentially what Zhou et al. [24] regularize, and JGC [11] already uses Jacobians for Granger causality. The new packaging is the single model plus the PSST significance test plus the industrial evaluation. That's still worth having, but it is not a new theoretical principle.\n\nThe soft spots are real. Most importantly, the paper asserts, without proof or direct evidence, that a large time-averaged absolute gradient implies Granger causality and a near-zero gradient implies its absence. That is not generally true. A causal effect can be non-smooth: if x1 steps when x2 crosses a threshold, a ReLU MLP fitted to that data will have near-zero gradients except in a narrow band around the threshold, so the method will miss the edge entirely. Since industrial processes commonly have saturation and switching effects, this is not a pedantic edge case. The authors need either a theorem under stated conditions or experiments on non-smooth mechanisms before the general claim is credible.\n\nOther issues are fixable but real. Eq. (3) compares the prediction with the past window instead of the target value; that looks like a typo, but it should be corrected. The DREAM4 and industrial tables lack error bars. Hyperparameters and code are not in the manuscript or supplements. The arXiv abstract describes a different paper (GRNGC with fMRI and gene data) than the full text, which points to a versioning problem the authors must clean up.\n\nOverall: if you work on gradient-based causal discovery, this paper deserves a careful read, but treat the central claim as an empirical hypothesis rather than an established fact. A serious referee should see it, primarily to force the authors to sharpen the theoretical grounding and provide missing artifacts. I would send it to peer review with major revision.","headline":"A practical single-model gradient-based causal discovery method with strong empirical results, but the core gradient-as-causality assumption is unproven and the paper needs major cleanup before acceptance.","tokens_in":13970,"tokens_out":2725,"would_cite":true,"duration_ms":32695,"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":"A single MLP trained to forecast every time series, with $\\ell_1$-regularized input-output gradients and phase-randomized surrogate testing, reconstructs directed causal graphs more accurately and at lower cost than component-wise neural…","keywords":["Causal discovery","Granger causality","Gradient-based","Time series","Industrial process","ℓ1 regularization","Surrogate significance test","Lightweight model"],"falsifier":"Simulate a bivariate time series in which $y_t$ is a deterministic step function of $x_{t-1}$ plus noise, such as $y_t = \\mathrm{sign}(x_{t-1}) + \\varepsilon_t$, so $x$ genuinely Granger-causes $y$ but the derivative of the map is zero almost everywhere. Train GCD on samples whose $x$ values fall away from the jump points; if the discovered matrix omits the $x\\to y$ edge while a standard Granger test or a component-wise baseline recovers it, the gradient proxy as a general causal measure is falsified.","tokens_in":12826,"feed_emoji":"🔗","tokens_out":12333,"duration_ms":129297,"temperature":0.7,"pith_summary":"The paper introduces GCD, a causal discovery method that infers Granger causality from multivariate time series using just one neural network. Instead of building a separate model for each variable and reading causality from first-layer weights, GCD trains a single MLP to predict all variables and measures how sensitive each predicted output is to each past input. These sensitivities, expressed as time-averaged absolute gradients, are forced toward sparsity with $\\ell_1$ regularization, and a phase-randomization surrogate test with false-discovery-rate correction decides which edges survive. On Lorenz-96, DREAM4, CausalTime, and three industrial process datasets, the paper reports higher AUROC/AUPRC or F1/SHD than seven baselines while using fewer parameters and less training time. If this gradient proxy is trustworthy, the framework offers a lightweight route to causal discovery in sensor-rich industrial settings.","feed_headline":"Single-network gradients top seven causal-discovery baselines","feed_subtitle":"One shared forecaster maps cause-effect links while cutting training time and beating specialized models.","key_machinery":"The central object is the gradient matrix $GC_{i,j}=\\frac{1}{k}\\sum_{\\tau=1}^{k}|\\partial s_i/\\partial x_{t-\\tau,j}|$, computed from a single MLP $f_\\theta$ that maps the past $k$ lags of all $D$ series to predictions of all $D$ series in one forward pass. The paper sums each output's predictions over time into the scalar $s_i$, backpropagates to the input window, takes element-wise absolute values, and averages over lags, turning the $k\\times D$ sensitivity matrix into a $D\\times D$ causal-strength matrix. This gradient quantity replaces the first-layer weight magnitudes used by component-wise models. The other load-bearing component is the PSST module: fast Fourier transform phase randomization generates surrogate time series, the model is retrained on each surrogate, edge-wise empirical null distributions are built from the resulting causal matrices, and Benjamini-Hochberg FDR correction at $\\alpha=0.05$ decides which edges survive. The $\\ell_1$ penalty $\\lambda\\|GC\\|_1$ is added to the mean-squared prediction loss so the final causal matrix is sparse.","core_discovery":"The central claim is that the time-averaged absolute input-output gradient of a single shared forecaster, after $\\ell_1$ shrinkage and surrogate-based significance testing, is a reliable and cheap way to reconstruct directed causal graphs from multivariate time series. The paper defines the causal strength from source series $j$ to target series $i$ as $$GC_{i,j} = \\frac{1}{k}\\sum_{\\tau=1}^{k}\\left|\\frac{\\partial s_i}{\\partial x_{t-\\tau,j}}\\right|,$$ where $s_i = \\sum_{t=k+1}^{T} \\hat{x}_{t,i}$ is the sum of the MLP's predictions for series $i$ over all time steps. A large gradient magnitude is interpreted as evidence that perturbing the past of $j$ changes the prediction of $i$, i.e., Granger causality; a near-zero gradient means no causal link. The $\\ell_1$ penalty $\\lambda\\|GC\\|_1$ added to the prediction loss sparsifies the matrix, and the Phase-randomization Surrogate Statistical Test (PSST) removes edges whose strength is not significantly above what phase-randomized surrogates produce, after Benjamini-Hochberg false-discovery-rate correction. On this basis the paper reports that GCD outperforms cMLP, cLSTM, TCDF, eSRU, GVAR, CR-VAE, and CUTS+ on Lorenz-96, DREAM4, and CausalTime, and achieves the best or near-best structural metrics on the Tennessee-Eastman, Ultra-processed Food, and Debutanizer industrial datasets with fewer parameters and less training time.","pith_inferences":["The abstract's mention of KAN, MLP, and LSTM implies the authors intend the gradient-loss recipe to be architecture-agnostic; if that generality holds, the same approach could extend to recurrent or attention-based forecasters, which the full text does not test.","Because PSST retrains the model on each of the $N$ surrogates, the total training cost is $N+1$ runs; a cheaper variant might reuse one trained model with phase-randomized inputs, but the paper does not propose that.","The fixed maximum lag $k$ is a free parameter the paper does not optimize; running GCD with several lag windows and combining the resulting matrices would be a direct stress test of whether the gradient proxy is stable across horizons.","If the gradient proxy fails on locally flat causal maps (as in the step-function falsifier), the method's reliability will depend on smoothness of the generating process; the paper's benchmarks are smooth dynamical systems and regulatory networks, so this boundary is not probed by its experiments."],"forward_implications":["Because GCD uses a single shared forecaster rather than one model per variable, causal discovery no longer scales linearly with series count; the reported complexity is $O(e(N+1)\\sum_{l}H_lH_{l+1}) + D^2$, which is lower than component-wise alternatives when $D > N+1$.","The PSST threshold turns the dense gradient matrix into a sparse graph by zeroing edges whose strength is not distinguishable from phase-randomized noise, giving industrial users a principled way to suppress false positives.","On the three industrial processes, GCD reports the lowest SHD on all three and the highest F1 on two of three, indicating the gradient proxy transfers beyond smooth simulation systems to sensor data."],"supporting_citations":[{"why":"Defines the component-wise cMLP/cLSTM baselines and first-layer-weight penalty that GCD's single-model gradient approach is designed to replace.","marker":"[8]"},{"why":"Supplies the CUTS+ baseline that GCD must beat and the nonlinear autoregressive notation the paper inherits.","marker":"[12]"},{"why":"Provides the time-shift surrogate method that PSST extends with phase randomization and FDR correction.","marker":"[18]"},{"why":"Provides the random-phase surrogate generation technique used to build empirical null distributions in PSST.","marker":"[19]"},{"why":"Supplies the Benjamini-Hochberg false-discovery-rate procedure used to adjust p-values and sparsify the final causal matrix.","marker":"[20]"},{"why":"The DREAM4 in silico network challenge dataset serves as one of the three simulation benchmarks.","marker":"[21]"},{"why":"The Lorenz-96 chaotic system serves as the high-dimensional simulation benchmark with known causal structure.","marker":"[22]"},{"why":"The CausalTime benchmark supplies the AQI, Traffic, and Medical datasets used for realistic time-series evaluation.","marker":"[23]"},{"why":"Supplies the Tennessee-Eastman industrial dataset with a ground-truth causal graph used in the industrial applications.","marker":"[26]"}],"fun_headline_variants":["One model's gradients reveal causal links faster","Gradient slopes of one forecaster top causal baselines","Single-network gradient trick speeds causal discovery","Gradient causality from a single shared model","Input-output gradients nail causal graphs cheaply"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method works only if the size of a trained neural network's time-averaged sensitivity to each past input faithfully tracks whether one series truly helps predict another; the paper argues this by intuition, not by proof, so if the real process is badly approximated by the network or its effects are locally flat, the sensitivity measure can miss or invent causal links.","fun_headline_variants_meta":{"raw":{"variants":["One model's gradients reveal causal links faster","Gradient slopes of one forecaster top causal baselines","Single-network gradient trick speeds causal discovery","Gradient causality from a single shared model","Input-output gradients nail causal graphs cheaply"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000199,"raw_usage":{"total_tokens":1450,"prompt_tokens":1099,"completion_tokens":351,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":715,"completion_tokens_details":{"reasoning_tokens":283}},"tokens_in":715,"tokens_out":351,"duration_ms":4382,"temperature":1.0,"reasoning_tokens":283,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:14:58.794450+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate a bivariate time series in which $y_t$ is a deterministic step function of $x_{t-1}$ plus noise, such as $y_t = \\mathrm{sign}(x_{t-1}) + \\varepsilon_t$, so $x$ genuinely Granger-causes $y$ but the derivative of the map is zero almost everywhere. Train GCD on samples whose $x$ values fall away from the jump points; if the discovered matrix omits the $x\\to y$ edge while a standard Granger test or a component-wise baseline recovers it, the gradient proxy as a general causal measure is falsified.","supporting_citations":[{"cited_title":"Cuts+: High- dimensional causal discovery from irregular time-series,","cited_arxiv_id":null,"evidence_quote":"Supplies the CUTS+ baseline that GCD must beat and the nonlinear autoregressive notation the paper inherits."},{"cited_title":"Causality detection with matrix-based transfer entropy,","cited_arxiv_id":null,"evidence_quote":"Provides the time-shift surrogate method that PSST extends with phase randomization and FDR correction."},{"cited_title":"Surrogates with random fourier phases,","cited_arxiv_id":null,"evidence_quote":"Provides the random-phase surrogate generation technique used to build empirical null distributions in PSST."},{"cited_title":"Detection of the number of signals using the benjamini-hochberg procedure,","cited_arxiv_id":null,"evidence_quote":"Supplies the Benjamini-Hochberg false-discovery-rate procedure used to adjust p-values and sparsify the final causal matrix."},{"cited_title":"Dream3: network inference using dynamic context likelihood of relatedness and the inferelator,","cited_arxiv_id":null,"evidence_quote":"The DREAM4 in silico network challenge dataset serves as one of the three simulation benchmarks."},{"cited_title":"Extensive chaos in the lorenz-96 model,","cited_arxiv_id":null,"evidence_quote":"The Lorenz-96 chaotic system serves as the high-dimensional simulation benchmark with known causal structure."},{"cited_title":"Causaltime: Realistically generated time-series for benchmarking of causal discov- ery,","cited_arxiv_id":null,"evidence_quote":"The CausalTime benchmark supplies the AQI, Traffic, and Medical datasets used for realistic time-series evaluation."},{"cited_title":"Cipcad-bench: Continuous industrial process datasets for benchmarking causal discovery methods,","cited_arxiv_id":null,"evidence_quote":"Supplies the Tennessee-Eastman industrial dataset with a ground-truth causal graph used in the industrial applications."}],"review_version":1}