{"id":"40224118-b0f8-4c38-9343-bfbfcab2ddfa","arxiv_id":"2504.18992","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"DF-Merge unifies task arithmetic and Fisher merging and uses Bayesian optimization to tune per-task coefficients, reporting improved multi-task accuracy on T5 benchmarks.","lead":"This paper introduces DF-Merge, a model merging method that tunes per-task scaling coefficients with Bayesian optimization and weights parameters by Fisher information at the scaled locations. The authors report accuracy gains over prior merging methods on T5 models across six NLP tasks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unequal validation-evaluation budget: DF-Merge gets 60 coefficient evaluations versus ~11 for TA/TIES, so the reported gains may reflect search budget rather than the dynamic Fisher objective.","rationale":"The paper proposes a clean unification and the DF-Merge formulation is well motivated; the code is released and the main results are averaged over five runs with significance testing, which is real support. However, the headline comparison gives DF-Merge a substantially larger validation-search budget than the main baselines, so the claim that DF-Merge outperforms strong baselines is not yet established as a property of the method rather than of the search budget. The paper's own ablation reinforces this: the dominant gain is from BO-optimized coefficients, not from the dynamic Fisher weighting. A conditional acceptance requiring equal-budget comparisons and variance reporting is the appropriate outcome. This is the same load-bearing concern identified by the reader, so agreement is 'agree'.","tokens_in":14042,"tokens_out":10005,"duration_ms":100528,"concrete_test":"Rerun the Table 2 comparisons with equal validation-evaluation budgets: (1) optimize Task Arithmetic and TIES-Merging with the identical Bayesian optimization protocol used for DF-Merge (10 random initial points + 50 EI/UCB iterations) over their coefficient ranges, and (2) evaluate DF-Merge with only the 11-point grid used for the baselines. Compare average test accuracy over the same five seeds, with significance tests. If TA or TIES with 60 evaluations reaches or exceeds DF-Merge, or if DF-Merge with 11 evaluations falls to baseline level, the headline claim is not supported; if DF-Merge still wins under both equal-budget checks, the concern is resolved.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central empirical claim (Table 2) is that DF-Merge outperforms Task Arithmetic, TIES-Merging, and other baselines and narrows the gap to multi-task fine-tuning. The comparison does not control for the number of validation-set evaluations used to select coefficients. In Section 4.1, DF-Merge is run with 10 random initial points plus 50 Bayesian optimization iterations, i.e. 60 evaluations of the validation metric. Task Arithmetic and TIES-Merging are tuned by grid search with step 0.1 over [0,1] and [0.8,1.8] respectively, roughly 11 evaluations; DARE adds only a five-point grid over the drop rate. If the extra ~49 evaluations are what locate a better coefficient, the advantage attributed to DF-Merge may be a search-budget artifact rather than a property of the merging objective. Table 3 shows that the largest component of the gain comes from replacing fixed coefficients with BO-optimized coefficients (GTA+BO vs. Fisher Merging), while the dynamic Fisher weighting contributes only 0.85-1.34 points; this makes the budget confound directly relevant to the headline claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DF-Merge, a model-merging method that unifies model-wise scaling (task arithmetic) and parameter-wise importance weighting (Fisher merging) into a single parameterized objective. A set of per-task coefficients is optimized by Bayesian optimization on held-out validation accuracy, while the Fisher information used for weighting is re-estimated at the coefficient-scaled models. Experiments on T5-base and T5-large across six classification tasks report gains over averaging, Fisher merging, task arithmetic, DARE, and TIES-merging, narrowing the gap to multi-task fine-tuning. The paper also includes ablations, efficiency analyses, and landscape visualizations to support the proposed method.","tokens_in":14295,"tokens_out":6049,"duration_ms":63312,"significance":"If the empirical claims hold, the unified view in Section 2 is a clean and useful conceptual contribution, and the use of Bayesian optimization to select merging coefficients is a practical direction. The algebraic derivations in Section 2 correctly recover averaging, general task arithmetic, and Fisher merging as special cases of Eq. (7), and the paper provides a geometric interpretation that is illuminating. The code is promised to be public, which is helpful for reproducibility. However, the central empirical claim is currently undermined by a validation-evaluation budget confound: DF-Merge is allowed far more evaluations of the validation objective than the grid-search baselines, and the ablations in Table 3 suggest that most of the gain comes from the Bayesian-optimization search itself rather than from the dynamic Fisher weighting. The efficiency and near-optimality analyses are also partly self-referential because they report convergence on the very validation objective being optimized.","major_comments":[{"comment":"The comparison in Table 2 does not control for the number of validation evaluations used to select coefficients. DF-Merge is run with 10 random initial points plus 50 Bayesian optimization iterations (60 evaluations), while Task Arithmetic and TIES-Merging use a grid search with step 0.1 over intervals of length 1.0 (about 11 evaluations) and DARE adds a 5-point grid over its drop rate. If the extra evaluations are what locate a better coefficient, the reported gains in Table 2 may be a search-budget artifact rather than a property of the dynamic Fisher objective. This is a load-bearing issue because Table 3 shows that the largest component of the gain comes from the Bayesian optimization search (removing it costs 4.90–13.71 points), whereas the dynamic Fisher weighting contributes only 0.85–1.34 points. The authors should either run the baselines with a comparable evaluation budget or report DF-Merge at the same budget (e.g., after the first 11 evaluations) to support the superiority claim.","section":"§4.1 / Table 2"},{"comment":"The claim that DF-Merge achieves near-optimal performance in a few iterations is self-referential because the trajectory in Figure 4 is plotted on the validation accuracy objective that Bayesian optimization is explicitly maximizing. The comparison is against the best point found in the same 60-iteration run, not against the global optimum or against test-set performance. To make the efficiency claim meaningful, the authors should report test accuracy at early stopping points (e.g., after 10, 15, or 20 evaluations) and compare with the test performance of the baselines under the same evaluation budget. The current analysis shows that the optimizer converges on its own objective, which is expected behavior, not near-optimality of the merged model on held-out data.","section":"§5.2 / Figure 4"},{"comment":"The phrase \"dynamic Fisher-weighted\" may overstate what Eq. (8) actually does. The Fisher information is re-estimated at the scaled model θ_pre + λ_i τ_i, but the predictive distribution used to compute it is still that of each individual task model, not a distribution conditioned on the merging coefficients in a way that couples tasks. The mechanism is plausible, but the paper does not provide evidence that this re-estimation, rather than the extra flexibility of the coefficients, is responsible for the improvements over GTA. The authors should clarify the exact role of the coefficient-dependent Fisher estimate and ideally ablate it against a version that uses a fixed Fisher estimate at, say, λ_i = 0.5.","section":"§3 / Eq. (8)"}],"minor_comments":[{"comment":"The phrase \"an unified\" should be \"a unified\" in several places, and \"an unified view\" in Section 3 should also be corrected.","section":"Abstract / Section 3"},{"comment":"The x-axis of the optimization trajectory figures is labeled \"number of iterations\" with values up to 60, but the text says the first 10 points are random initial evaluations and that 9 iterations suffice after that. Please clarify whether the axis counts total evaluations or BO iterations, and consistently label the random-initialization region.","section":"Figure 4 / Appendix B"},{"comment":"The symbol f is used both for the merge function and for the black-box objective f_b; this is confusing. Please use distinct notation, for example g for the merge function and f for the objective.","section":"Section 3 / Eq. (7)"},{"comment":"The significance asterisks are defined as \"both DF-Merge (EI) and DF-Merge (UCB) significantly outperform the baseline,\" but the text says improvements are significant for \"almost all baselines.\" Please state the significance test used and whether any multiple-comparison correction was applied, and report which individual comparisons are significant.","section":"Table 2"},{"comment":"The color map in Figure 6 is not labeled with a colorbar; please add one so that the reported accuracy values can be read from the landscape plots.","section":"Section 5.3 / Figure 6"}],"recommendation":"major_revision","confidential_remarks":"The central idea is reasonable, but the manuscript's empirical case would be much stronger if the validation-evaluation budget were matched across methods. The ablations already suggest that the BO search, not the dynamic Fisher weighting, drives most of the gain, so the paper should be careful not to overclaim the contribution of the Fisher component. I also note that the novelty relative to prior Bayesian-optimization-based merging work (Liu et al., 2024) should be sharpened in the related work discussion."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The unified view in Eq. 7 is genuinely useful: Averaging, General Task Arithmetic, and Fisher Merging all fall out as special cases, and the geometric derivation of Fisher Merging is clean. The second thing is more worrying. The headline comparison to baselines does not control for search budget. DF-Merge gets 10 random points plus 50 BO iterations, 60 evaluations of validation accuracy. Task Arithmetic and TIES-Merging get a grid with step 0.1, roughly 11 evaluations. That asymmetry alone could explain a big part of the gap. The ablation in Table 3 shows BO contributes the bulk of the gain and the dynamic Fisher part only adds 0.85 to 1.34 points, so the confound is directly relevant to the central claim.\n\nCredit where it's due. The method is sensible and new: Fisher information estimated at the scaled models, not just at the fine-tuned endpoints, is a nice idea. The BO setup is standard but well executed. The experiments cover T5-base and T5-large over six datasets with significance tests, and the paper is candid about limitations like diagonal Fisher and the need for validation labels.\n\nSoft spots. The budget mismatch is the load-bearing one. The efficiency analysis in Section 5.2 is single-run and self-referential: it shows the BO trajectory approaches its own best-so-far, not a known global optimum. That is a minor point. The main fix is to rerun all baselines with the same number of validation evaluations, or to give the baselines BO as well. If the margin survives that, the paper is in good shape.\n\nWho should read this. Model-merging people will want the unified formulation even if the empirical comparison is conditional. As it stands, the paper deserves peer review, but the reviewer should require a matched-budget comparison and variance reporting before accepting the central claim.","headline":"A clean unification and a sensible new merge method, but the headline empirical comparison is confounded by an unequal validation-search budget.","tokens_in":14811,"tokens_out":4452,"would_cite":true,"duration_ms":41148,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"DF-Merge unifies model-wise scaling and parameter-wise importance weighting in one merging formula, tunes per-task coefficients by Bayesian optimization, and cuts the gap to multi-task fine-tuning to about three points on T5.","keywords":["model merging","task arithmetic","Fisher information","Bayesian optimization","multi-task learning","parameter interference","T5","validation efficiency"],"falsifier":"Run DF-Merge with the same budget as the grid-search baselines, about 11 merge-then-evaluate rounds, on the same six T5-base tasks and check whether it still beats Task Arithmetic by the reported 4.48 points; if the margin collapses to near zero, the dynamic Fisher weighting is not what carries the result.","tokens_in":13878,"feed_emoji":"🧩","tokens_out":6890,"duration_ms":62044,"temperature":0.7,"pith_summary":"The paper tries to show that the two dominant families of model merging, scaling whole task vectors and weighting individual parameters by importance, are special cases of one linear merging formula, and that filling in the free coefficients with Bayesian optimization yields a better multi-task model than either family on its own. The proposed method, DF-Merge, scales each fine-tuned model along its task vector, estimates Fisher information at the scaled position, and merges by Fisher-weighted averaging, with Gaussian-process Bayesian optimization choosing the coefficients from validation-set accuracy. The authors report that this beats strong baselines on T5-base and T5-large across six NLP tasks and closes most of the gap to multi-task fine-tuning. The practical interest is that merging builds a multi-task model without training data or joint training, so a small accuracy gap versus multi-task learning is the price of a dramatic saving in data and compute.","feed_headline":"Merging six models lands within 3.6 points of joint training","feed_subtitle":"Tuning six per-task scaling weights with Fisher information shrinks the gap to full multi-task fine-tuning on T5.","key_machinery":"The central object is the generalized merging operator $f = (\\sum_i C_{\\theta_i})^{-1} (\\sum_i C_{\\theta_i} \\lambda_i \\tau_i) + \\theta_{\\text{pre}}$, where $C_{\\theta_i}$ is a covariance matrix and $\\tau_i = \\theta_i - \\theta_{\\text{pre}}$ is the task vector. Setting $C = I$ recovers Task Arithmetic, model-wise scaling, while setting $C = \\operatorname{diag}(\\widehat{F}_{\\theta_i})$ and $\\lambda_i = 1/M$ recovers Fisher Merging, parameter-wise importance weighting. DF-Merge takes $C_{\\theta_i} = \\operatorname{diag}(\\widehat{F}_{\\theta_i(\\lambda_i)})$, meaning Fisher information is computed at the scaled model $\\theta_{\\text{pre}} + \\lambda_i \\tau_i$, and lets Bayesian optimization choose the $\\lambda_i$ to maximize average validation accuracy. The merge function converts the two prior strategies into one objective, Fisher information imports the low-loss-basin intuition, and Bayesian optimization performs the coefficient search.","core_discovery":"On the paper's own terms, the discovery is that model-wise scaling and parameter-wise importance weighting are not competing merge recipes but two restricted cases of a single formula, and that the unrestricted version, dynamic Fisher-weighted merging, dominates both. DF-Merge assigns each fine-tuned model a coefficient $\\lambda_i$, computes diagonal Fisher information at the interpolated model $\\theta_{\\text{pre}} + \\lambda_i \\tau_i$, and uses Gaussian-process Bayesian optimization, with Expected Improvement or Upper Confidence Bound acquisition, to pick coefficients that maximize average held-out accuracy. On T5-base and T5-large across PAWS, QASC, QuaRTz, Story Cloze, WikiQA and Winogrande, it outperforms all baselines in average accuracy, best baseline 73.66 versus 78.14 for T5-base and 81.86 versus 83.59 for T5-large, and narrows the gap with multi-task fine-tuning to 3.55 and 3.15 points. The paper further claims that near-optimal performance is reached within a few iterations, 9 optimization rounds after 10 random points, and with as little as 5% of each validation set, and that ablations show both Fisher information and Bayesian optimization are necessary components.","pith_inferences":["A controlled comparison that equalizes the validation-evaluation budget, 60 merge-then-evaluate rounds for DF-Merge versus about 11 grid-search steps for the baselines, is not reported; such a comparison could materially reduce the measured margin and is the natural next test of the paper's central claim.","The paper's own diagonal-Fisher assumption treats parameters as independent; extending the merge function to block-diagonal Fisher approximations, a direction the paper mentions, could further close the residual gap to multi-task fine-tuning.","Because Fisher information is computed from the model's predictive distribution rather than from labels, DF-Merge could plausibly be adapted to label-free merging where fine-tuned models pseudo-label test inputs, an extension the paper notes but does not implement.","The coefficient search could in principle transfer to models with different initializations or architectures if an alignment step were inserted, but the paper deliberately restricts itself to the shared-initialization setting."],"forward_implications":["If DF-Merge generalizes as reported, a user with several fine-tuned models sharing an initialization can build a multi-task model from parameter vectors and small validation sets alone, needing no training data and no joint training.","The resulting multi-task model can be optimized directly for non-differentiable metrics such as accuracy, since Bayesian optimization only requires the scalar validation score.","Early stopping is viable: after 10 random initial points, 9 optimization iterations already reach within 0.59 percentage points of the best 60-iteration result on T5-base.","Only a small validation budget is needed: 5% of each validation set suffices to approach full-validation performance and to outpace Task Arithmetic.","The gap to multi-task fine-tuning can shrink to 3.55 points for T5-base and 3.15 points for T5-large, making merging a plausible training-free substitute when a slight accuracy drop is acceptable."],"supporting_citations":[{"why":"Defines task vectors and Task Arithmetic, the model-wise scaling baseline that DF-Merge generalizes and compares against.","marker":"Ilharco et al., 2023"},{"why":"Introduces Fisher-weighted merging, the parameter-wise importance baseline whose diagonal-Fisher estimate DF-Merge reuses and extends.","marker":"Matena and Raffel, 2022"},{"why":"Provides the geometric view of Fisher merging as minimizing a loss-weighted distance, which motivates evaluating Fisher information at scaled coefficients.","marker":"Tam et al., 2024"},{"why":"Supplies the Gaussian-process prior and posterior machinery used for Bayesian optimization of the merging coefficients.","marker":"Williams and Rasmussen, 2006"},{"why":"Supplies the Bayesian-optimization formulation and the Expected Improvement acquisition function used by DF-Merge.","marker":"Frazier, 2018"},{"why":"TIES-Merging is one of the principal baselines whose parameter-interference resolution DF-Merge is compared against.","marker":"Yadav et al., 2024"},{"why":"DARE is a model-wise scaling baseline using drop-and-rescale of task vectors, used for comparison.","marker":"Yu et al., 2024"},{"why":"Provides the Averaging baseline, the simplest merging method that DF-Merge and the other baselines must beat.","marker":"Wortsman et al., 2022"},{"why":"Provides the T5-base and T5-large models on which all experiments are run.","marker":"Raffel et al., 2020"},{"why":"PromptSource supplies the natural-language prompt templates used to format inputs and outputs for the six datasets.","marker":"Bach et al., 2022"}],"fun_headline_variants":["Unified merge formula beats both existing model-merging strategies","Dynamic Fisher merging closes gap to multi-task fine-tuning to 3.5 pts","Bayesian-optimized merging rivals joint training in few iterations","One equation unifies merging; DF-Merge beats all baselines","Fisher-weighted coefficient tuning: near-optimal in few steps"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim of superiority assumes the comparison spends the same validation-evaluation budget: DF-Merge receives 60 coefficient evaluations, 10 random points plus 50 optimization rounds, while Task Arithmetic and TIES-Merging get a grid search of about 11 steps, so much of the gain could come from the larger budget rather than from the dynamic Fisher objective.","fun_headline_variants_meta":{"raw":{"variants":["Unified merge formula beats both existing model-merging strategies","Dynamic Fisher merging closes gap to multi-task fine-tuning to 3.5 pts","Bayesian-optimized merging rivals joint training in few iterations","One equation unifies merging; DF-Merge beats all baselines","Fisher-weighted coefficient tuning: near-optimal in few steps"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000717,"raw_usage":{"total_tokens":3252,"prompt_tokens":1009,"completion_tokens":2243,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":625,"completion_tokens_details":{"reasoning_tokens":2154}},"tokens_in":625,"tokens_out":2243,"duration_ms":17868,"temperature":1.0,"reasoning_tokens":2154,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:03:58.079461+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run DF-Merge with the same budget as the grid-search baselines, about 11 merge-then-evaluate rounds, on the same six T5-base tasks and check whether it still beats Task Arithmetic by the reported 4.48 points; if the margin collapses to near zero, the dynamic Fisher weighting is not what carries the result.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"PromptSource supplies the natural-language prompt templates used to format inputs and outputs for the six datasets."}],"review_version":1}