{"id":"3b777a8d-f91f-4ca0-afa9-a136b19314ae","arxiv_id":"2605.30348","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"LLMSurgeon recovers pretraining domain mixtures from LLM-generated text by estimating a calibrated soft confusion matrix and solving a constrained inverse problem under the label-shift assumption.","lead":"LLMSurgeon estimates the domain-level mixture of an LLM's hidden pretraining data by solving an inverse problem on text the model generates. A smart generalist might care because it offers a practical way to audit proprietary models' 'digital DNA' without seeing their training sets.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Label-shift assumption between generated text and pretraining corpus is unverified and central to recovery","rationale":"The reader's weakest_assumption directly identifies the same methodological hinge. With the full manuscript now available, the claim of 'high fidelity' recovery still rests on this untested equality rather than on an independent verification that the estimated C is transportable from generated to pretraining text. No other internal inconsistency (e.g., in the optimization or LLMScan construction) appears more load-bearing.","tokens_in":1653,"tokens_out":384,"duration_ms":14581,"concrete_test":"For each LLM in LLMScan, collect an auxiliary set of text snippets drawn from the known pretraining domains (using the same taxonomy and sampling protocol as the generated set), compute the empirical soft confusion matrix C_pre on this set, and compare it entrywise to the C_gen used by LLMSurgeon; if the Frobenius distance ||C_pre - C_gen||_F exceeds 0.05 on average across models, re-run the inverse solver with C_pre and measure degradation in mixture recovery error.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"LLMSurgeon recovers the mixture prior by estimating a soft confusion matrix C from domain classifier outputs on generated text and solving the constrained inverse problem π = argmin ||Cπ - p|| subject to simplex constraints (under the label-shift model P(pred|true) independent of the marginal on true domains). This requires that the conditional P(classifier output | true domain) estimated on generated samples equals the one that would be observed on the actual pretraining corpus. The paper provides no direct diagnostic (e.g., comparison of C on generated vs. held-out in-domain text from the same taxonomy) to confirm this equality holds for the LLMs and domains in LLMScan.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper formalizes Data Mixture Surgery (DMS) as the task of recovering the domain-level pretraining mixture of an LLM given only samples of its generated text and a fixed taxonomy. It introduces LLMSurgeon, which estimates a soft confusion matrix C from a domain classifier applied to generated text and recovers the mixture prior π by solving the constrained inverse problem argmin ||Cπ − p|| subject to simplex constraints, under the label-shift assumption that P(classifier output | true domain) is independent of the marginal on domains. The method is evaluated on the introduced LLMScan benchmark consisting of open-source LLMs with known mixtures, with the claim that LLMSurgeon recovers the mixtures with high fidelity under fixed protocols.","tokens_in":1785,"tokens_out":549,"duration_ms":20482,"significance":"If the recovery is reliable, the approach would offer a practical post-hoc auditing tool for LLM training data compositions, addressing an important transparency gap. The construction of LLMScan as a recipe-verifiable evaluation suite is a clear positive contribution that enables controlled testing of such inverse methods.","major_comments":[{"comment":"§3 (Method), label-shift model and Eq. for C: the central recovery step assumes that the soft confusion matrix estimated on generated text equals the one that would be observed on the actual pretraining corpus; no direct diagnostic (e.g., comparison of C on generated vs. held-out in-domain text from the same taxonomy) is reported to confirm this equality holds for the LLMs and domains in LLMScan.","section":"§3"},{"comment":"§4 (Experiments): the claim of 'high fidelity' recovery is stated without accompanying quantitative metrics, error analysis, ablation of the inverse step versus direct aggregation of classifier outputs, or comparison to the unconstrained case, making it impossible to assess whether the constrained optimization meaningfully improves over the baseline.","section":"§4"},{"comment":"§3.2 (Optimization): the constrained inverse problem is presented as the core technical contribution, yet the manuscript provides no analysis of solution stability, sensitivity to the estimated C, or conditions under which the simplex-constrained argmin is well-posed or unique.","section":"§3.2"}],"minor_comments":[{"comment":"The notation for the soft confusion matrix and the precise form of the objective should be introduced with explicit equations before the optimization is described.","section":"§3"},{"comment":"Figure captions and table headers in the LLMScan results should explicitly state the number of generated samples per model and the taxonomy granularity used.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive feedback. The comments correctly identify gaps in validation of the label-shift assumption, quantitative evaluation, and analysis of the optimization. We address each point below and will revise the manuscript to incorporate additional diagnostics, metrics, and analyses.","responses":[{"response":"We agree that a direct diagnostic comparing C on generated text to held-out pretraining text would strengthen validation of the label-shift assumption. However, the actual pretraining corpora are unavailable by design of the DMS task, so the exact comparison suggested is not possible. In revision we will add a discussion of the assumption's plausibility, supported by recovery performance on LLMScan, and include proxy analyses using controlled in-domain generations where feasible. This limitation will be explicitly noted.","revision_made":"partial","referee_comment":"[§3] §3 (Method), label-shift model and Eq. for C: the central recovery step assumes that the soft confusion matrix estimated on generated text equals the one that would be observed on the actual pretraining corpus; no direct diagnostic (e.g., comparison of C on generated vs. held-out in-domain text from the same taxonomy) is reported to confirm this equality holds for the LLMs and domains in LLMScan."},{"response":"We acknowledge that the current results section would benefit from explicit quantitative support. The revised manuscript will add tables reporting L1 error, KL divergence, and other metrics between recovered and ground-truth mixtures on LLMScan, include error bars from multiple runs, and provide ablations comparing the constrained inverse problem to direct aggregation of classifier outputs as well as the unconstrained case.","revision_made":"yes","referee_comment":"[§4] §4 (Experiments): the claim of 'high fidelity' recovery is stated without accompanying quantitative metrics, error analysis, ablation of the inverse step versus direct aggregation of classifier outputs, or comparison to the unconstrained case, making it impossible to assess whether the constrained optimization meaningfully improves over the baseline."},{"response":"We agree that formal analysis of the optimization is needed. In the revision we will add discussion of solution stability (including empirical results across initializations), sensitivity of the recovered π to perturbations in the estimated C, and conditions for well-posedness and uniqueness (e.g., when the estimated C is well-conditioned or diagonally dominant). These will appear in §3.2 or an appendix.","revision_made":"yes","referee_comment":"[§3.2] §3.2 (Optimization): the constrained inverse problem is presented as the core technical contribution, yet the manuscript provides no analysis of solution stability, sensitivity to the estimated C, or conditions under which the simplex-constrained argmin is well-posed or unique."}],"tokens_in":1446,"tokens_out":589,"duration_ms":36299,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core contribution is casting data-mixture recovery as a constrained inverse problem that uses a soft confusion matrix to correct classifier errors instead of raw aggregation. That step is new relative to the classifier-aggregation baselines mentioned in the abstract, and the LLMScan suite with known open-model mixtures is a sensible way to test it.\n\nThe paper does a clean job of stating the label-shift model and the simplex-constrained optimization. If the full manuscript shows the actual solver, the matrix estimation procedure, and quantitative recovery errors on LLMScan, that would be the useful part.\n\nThe soft spot is exactly the one the stress-test flags: nothing in the abstract or the provided description checks whether the confusion matrix estimated on generated samples matches the one that would arise on the real pretraining corpus. Without that diagnostic or a sensitivity analysis, the “high fidelity” claim rests on an assumption whose violation would break the recovery. The abstract also gives no numbers, confidence intervals, or ablation on the constraint solver, so the practical reliability is still unclear.\n\nThis is for groups working on post-hoc auditing and transparency tooling. A reader who already cares about data provenance will get value from the formulation and the benchmark recipe even if the empirical claims need more support.\n\nI would send it to peer review. The idea is timely, the evaluation design is reproducible in principle, and the missing verification of the key assumption is the sort of thing referees can ask for directly.","headline":"LLMSurgeon gives a workable inverse-problem framing for mixture recovery but the label-shift assumption between generated text and pretraining data is unverified and load-bearing.","tokens_in":2251,"tokens_out":370,"would_cite":false,"duration_ms":12983,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"LLMSurgeon recovers the domain-level pretraining mixture of large language models from their generated text alone by solving a calibrated inverse problem.","keywords":["LLM pretraining data","data mixture estimation","domain distribution","inverse problem","label shift","model auditing","generated text analysis"],"falsifier":"Running LLMSurgeon on generated text from an open LLM with a known but mismatched domain mixture on LLMScan and observing whether the recovered distribution matches the known one within the reported fidelity.","tokens_in":2576,"feed_emoji":"","tokens_out":552,"duration_ms":20008,"temperature":0.7,"pith_summary":"The paper formalizes Data Mixture Surgery as the task of estimating an LLM's pretraining domain distribution from generated text samples under a fixed taxonomy. LLMSurgeon treats this as an inverse problem by estimating a soft confusion matrix from a domain classifier and solving for the latent mixture prior that accounts for classification errors. This enables post-hoc auditing of the data composition that shapes model behavior without needing the original training corpus. Evaluation on LLMScan, a set of open models with known mixtures, shows high-fidelity recovery under consistent protocols.","feed_headline":"LLMSurgeon infers LLM training domain mix from outputs","feed_subtitle":"By solving an inverse problem with a calibrated confusion matrix, the method audits pretraining data composition without direct access.","key_machinery":"A calibrated soft confusion matrix derived from domain classifier outputs on generated text, used to solve the constrained inverse problem for the mixture prior.","core_discovery":"Given only generated text from a target LLM, LLMSurgeon estimates the domain-level distribution of its pretraining corpus by estimating a calibrated soft confusion matrix and solving a constrained inverse problem to recover the latent mixture prior under the label-shift assumption.","pith_inferences":["Such auditing tools could support transparency requirements for deployed foundation models.","The approach might extend to identifying specific data sources or contamination within domains.","Refinements could handle cases where the label-shift assumption is violated by incorporating additional constraints."],"forward_implications":["Domain mixtures can be audited post-hoc from model outputs.","Systematic domain confusion in classifiers can be corrected to improve mixture estimates.","The method applies to any LLM under the label-shift assumption with a predefined domain taxonomy.","High fidelity recovery holds across the LLMScan evaluation suite."],"fun_headline_variants":["LLMSurgeon diagnoses LLM data mixtures from generated text","LLMSurgeon recovers pretraining domains via inverse problem","Estimating LLM training mixture with LLMSurgeon framework","LLMSurgeon solves constrained inverse problem for data mix"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The label-shift assumption holds between the domain classifier outputs on generated text and the true pretraining domain distribution.","fun_headline_variants_meta":{"raw":{"variants":["LLMSurgeon diagnoses LLM data mixtures from generated text","LLMSurgeon recovers pretraining domains via inverse problem","Estimating LLM training mixture with LLMSurgeon framework","LLMSurgeon solves constrained inverse problem for data mix"]},"model":"grok-4.3","cost_usd":0.01082,"raw_usage":{"total_tokens":4747,"prompt_tokens":623,"num_sources_used":0,"completion_tokens":65,"cost_in_usd_ticks":108199500,"prompt_tokens_details":{"text_tokens":623,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":4059,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":623,"tokens_out":65,"duration_ms":40868,"temperature":1.0,"reasoning_tokens":4059,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T07:56:02.101509+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Running LLMSurgeon on generated text from an open LLM with a known but mismatched domain mixture on LLMScan and observing whether the recovered distribution matches the known one within the reported fidelity.","supporting_citations":[],"review_version":1}