{"id":"6a5b085f-2ee5-4843-8623-87dc17d03a6c","arxiv_id":"2501.01230","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"DOGE merges fine-tuned models by optimizing a data-free loss-gap proxy with gradient steps projected orthogonal to a shared task subspace, improving average accuracy over previous methods.","lead":"This paper introduces DOGE, a model merging method that frames merging as a constrained optimization problem, minimizing the gap between the merged model and individual task models while retaining shared knowledge. It works without task data and reports accuracy gains over prior merging methods on vision and NLP benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (5)'s linear/NTK proxy is unvalidated and sits in tension with the paper's own λ choice: with near-orthogonal task vectors the proxy's minimizer is near λ=1, yet App. B sets η so average λ≈0.3, so the claimed loss-gap minimization is not established as the mechanism.","rationale":"The reader's weakest assumption was the NTK approximation; I agree partially and sharpen it. The issue is not merely that fine-tuning may leave the NTK regime; it is that the proxy is contradicted by the paper's own hyperparameter choice within the regime they assume. This makes the theoretical story fragile. However, the empirical SOTA claim is supported by a broad benchmark suite and sensible ablations (Table 6 shows each module helps), so I do not move the verdict to reject. The missing error bars and validation-based η are additional concerns, but the proxy inconsistency is the most load-bearing because it attacks the stated objective. A single computational check on released task vectors can settle it. If the check passes, the conditional acceptance stands; if it fails, the paper should be revised to reposition the method as a heuristic and add true-gap validation.","tokens_in":21015,"tokens_out":16564,"duration_ms":176038,"concrete_test":"Run the released ViT-B/32 code to: (1) compute F(λ) in Eq. (5) with Δ=0 over λ∈[0,1.5] and report the minimizer; (2) using a held-out split of each of the 8 tasks, compute the true gap Σ_j(L_j(θ*)-L_j(θ_j))² for TA at λ=0.3, TA at λ=1, the published DOGE TA model, and the unconstrained minimizer of Eq. (5); (3) compute the Spearman correlation between Eq. (5) values and true gaps across these points. If the proxy minimum is near λ=1 while true gaps favor 0.3, or the rank correlation is ≤0, the data-free objective does not represent the loss gap and the paper's central mechanism is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4.1 derives the data-free objective by (i) first-order Taylor expanding L_j around θ0 and (ii) replacing ∇L_j(θ0) with -τ_j/Σα_t under the NTK assumption. Both steps are load-bearing for the claim that DOGE minimizes the gap between the merged model and individual models. The paper never validates either step. The tension is concrete: Fig. 2 reports pairwise cosine similarities mostly 0.01-0.15. For near-orthogonal, equal-norm task vectors and Δ=0, Eq. (5) becomes Σ_j[(1-λ)||τ_j||² - λΣ_{i≠j}⟨τ_j,τ_i⟩]², whose minimizer over λ is close to 1 (cross terms push it slightly below 1 if positive). Appendix B states η is chosen because the calculated average λ was close to 0.3, which is a beneficial scaling coefficient for Task Arithmetic. Thus the operating point of the algorithm (λ≈0.3) is far from the proxy's preferred λ≈1. A defender may say Δ optimization compensates; but that would make Δ responsible for fixing an inaccurate proxy, and the paper provides no check that Eq. (5) tracks the true loss gap. Consequently, the central mechanism is not established: the reported improvements could be driven by the task-aware λ heuristic and the Δ perturbation rather than by solving the constrained optimization in Eq. (2).","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper frames multi-task model merging as a constrained optimization problem: minimize the gap between the merged model and each individually fine-tuned model, subject to a constraint that shared knowledge, represented by a shared subspace of task vectors, is preserved. The authors derive a data-free objective (Eq. (5)) via a first-order Taylor expansion and an NTK-style replacement of the pre-trained gradient by the task vector, then solve it by projected gradient descent with a task-aware, layer-wise merging coefficient. Experiments on CLIP ViT-B/32 and ViT-L/14 across 8, 14, and 20 vision tasks, on Flan-T5 with LoRA on GLUE, and on three 13B LLMs report consistent improvements over Task Arithmetic, Ties-Merging, AdaMerging, and other baselines, with ablations and robustness studies.","tokens_in":21316,"tokens_out":7215,"duration_ms":67245,"significance":"If the mechanism claimed in the paper were established, the work would be valuable: it offers a data-free, plug-and-play component that improves existing merging methods substantially (up to 11.6% over TA on the 8-task vision benchmark), with moderate computational overhead (121 s on ViT-B/32), and the ablations suggest each component contributes. The paper announces code availability and includes sensitivity analyses, robustness to corruptions, and generalization to unseen tasks. However, the central derivation rests on approximations that are not validated; until that is addressed, the theoretical framing remains a heuristic wrapper around an empirical recipe.","major_comments":[{"comment":"The data-free objective is obtained through two load-bearing approximations: the first-order Taylor expansion of L_j around θ0 and the NTK assumption that ∇L_j(θ0) ≈ -τ_j / Σ_t α_t. Neither approximation is validated in the paper, and the NTK replacement is additionally questionable because Adam-style fine-tuning does not make the task vector equal to the sum of raw gradients. The tension is concrete: for the near-orthogonal task vectors reported in Fig. 2 (cosine similarities mostly 0.01--0.15), the minimizer of Eq. (5) over λ (with Δ = 0) is close to 1, whereas App. B sets η so that the average λ is about 0.3. Since Δ is optimized with this fixed λ and is projected to stay orthogonal to the shared subspace, it cannot simply rescale the total vector to the proxy's preferred operating point. The paper therefore does not establish that the reported gains come from minimizing the gap in Eq. (3); they could come from the task-aware λ heuristic and the Δ perturbation alone. I ask for a direct empirical check that Eq. (5) tracks the true per-task loss gap (e.g., compute both on a small held-out subset before and after optimization), and a discussion of the λ discrepancy.","section":"Sec. 4.1, Eq. (5)"},{"comment":"The constraint S_share(θ*, θ0 + λ Σ τ_i) = 0 is never defined as a distance, so the reader cannot verify that the projection in Eq. (7) actually enforces it. More importantly, 'shared knowledge' is identified with the top singular vectors of the task vectors without justification; the claim that updates orthogonal to S_share 'retain shared knowledge' is an assertion, not a derived property. The ablations in Tab. 7 show empirical benefit, but they do not measure shared knowledge itself. Please provide a formal definition of S_share in Eq. (2) and, if possible, a quantitative proxy for shared-knowledge retention (e.g., performance on similar tasks or parameter overlap).","section":"Sec. 4.2, Eq. (2) and Algorithm 1"},{"comment":"The top-30% magnitude mask from Ties-Merging is not present in the derivation of Eq. (5) or in Algorithm 1. This matters because Eq. (5) is an inner product of task vectors, and masking changes every inner product and every gradient. Please state where the mask is applied (before SVD, before Eq. (7), or only at the final output), or remove the mask from the method and show that the results still hold; as written, the optimized objective is not precisely specified.","section":"Sec. 5.1 / App. B"}],"minor_comments":[{"comment":"The claim that the approach 'consistently achieved the highest accuracy across most scenarios' is not fully supported by the table: under impulse noise, DOGE AM's average (65.1) is below AdaMerging's (68.0), and DOGE TA is below AdaMerging on every corruption; please qualify the claim.","section":"App. D, Tab. 11"},{"comment":"The abstract states 'Our code is available here' but the manuscript contains no URL; please provide the actual repository link.","section":"Abstract"},{"comment":"The decomposition τ_j = θ_T − θ_0 = −Σ_t α_t ∇_{θ_t} L_j(θ_t) is written as an equality, but with Adam-style fine-tuning the task vector is not exactly the sum of raw gradients; please present this as an approximation.","section":"Sec. 3.1"},{"comment":"The traditional MTL model is described as an 'upper bound', but in Tab. 1 it is 88.9 while individual models reach 90.8; consider describing it as a reference point or an upper bound for merging methods specifically.","section":"Sec. 5.1"}],"recommendation":"major_revision","confidential_remarks":"The empirical results are broad and the method is simple to use, but the stress-test concern about Eq. (5) is on point: the paper needs a direct validation of the proxy or a reframing of the contribution as an empirical method. If the authors can supply that validation, the paper could be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is an empirically strong model-merging paper, and the method is genuinely new in combination. The central theory, however, is weaker than the experiments, and the stress-test concern is valid: the paper never shows that Eq. (5) is a faithful proxy for the loss gap it claims to minimize.\n\nWhat's good. DOGE is a clean combination of three ideas — a data-free Taylor-expanded gap objective, gradient projection orthogonal to an SVD-based shared subspace, and task-aware norm-based coefficients. The experiments are unusually broad: ViT-B/32 and ViT-L/14 on eight vision tasks, Flan-T5 base/large with LoRA on GLUE, plus an LLM merging study, evaluations on 14/20 tasks, unseen tasks, and corrupted test sets. Ablations show each component has a measurable effect, and the reported compute is modest. Code is promised. That is a solid empirical package.\n\nWhere it gets soft. The derivation of Eq. (5) relies on two unvalidated steps: first-order Taylor expansion of the loss around theta0, and the NTK assumption that grad L_j(theta0) is proportional to -tau_j. Both are load-bearing. The stress-test note makes a sharper point: with the near-orthogonal task vectors measured in Fig. 2, the proxy's own minimizer over lambda sits close to 1, but Appendix B says eta was chosen so the average lambda lands near 0.3 — a value known to work well for Task Arithmetic. So the algorithm operates far from the proxy's preferred regime. If the objective were actually driving the gains, you'd expect the method to favor lambda near 1; instead, the constant eta appears tuned to a known good operating point. That doesn't kill the empirical contribution, but it means the paper has not established that solving Eq. (5) is the mechanism behind the improvements. The lambda heuristic and the Delta perturbation could be doing most of the work.\n\nMinor issues: no error bars or significance tests in the main tables; the sensitivity analysis for eta covers only 0.01-0.09 and is itself reported without variance; the top-30% retention and subspace rank k are heuristic.\n\nBottom line: this deserves a serious referee. It's a useful, well-executed practical method, but the theory needs validation — a direct check of Eq. (5) against the true loss gap using gradients or a small data sample would settle it.","headline":"Solid empirical merging paper with a genuinely new method, but the data-free objective is unvalidated and the reported gains may owe more to the lambda heuristic than to the constrained optimization.","tokens_in":21867,"tokens_out":2724,"would_cite":true,"duration_ms":26664,"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":"The paper frames multi-task model merging as a constrained optimization problem—keep the merged model as close as possible to each expert while preserving shared knowledge—and solves it with adaptive projective gradient descent.","keywords":["model merging","multi-task learning","task vectors","adaptive projective gradient descent","data-free optimization","shared subspace","task arithmetic","LoRA fine-tuning"],"falsifier":"Fine-tune the same expert models with a much larger learning rate or many more steps so they leave the linear regime, then compute Eq. (5)'s objective with the true task data and compare it to the gradient proxy. If the proxy's error grows and DOGE's accuracy advantage over Task Arithmetic or Ties-Merging disappears, the central claim is falsified.","tokens_in":20795,"feed_emoji":"🎯","tokens_out":5043,"duration_ms":40366,"temperature":0.7,"pith_summary":"Merging several fine-tuned expert models into one multi-task model usually means combining their task vectors, and existing methods resolve the resulting conflicts by dropping or orthogonalizing parameters. This paper argues that such pruning throws away task-specific information that is actually needed for performance. Instead, it proposes to minimize the gap between the merged model and each individual expert, subject to a constraint that shared knowledge is retained. The solution is an adaptive projective gradient descent (DOGE) that optimizes a data-free objective in the directions orthogonal to a shared subspace built from all tasks. If the approach holds, model merging can get close to true multi-task training without seeing any task data.","feed_headline":"One algorithm merges models by chasing each expert's performance","feed_subtitle":"A data-free projective gradient method beats Task Arithmetic by up to 11.6 points and AdaMerging by 5.8 across vision and NLP.","key_machinery":"The central object is the task vector τ_i = θ_i − θ_0, the difference between a fine-tuned expert and the pretrained model, interpreted as an accumulated gradient. The argument is carried by three ingredients: (i) a data-free objective that measures, for each task j, ⟨−τ_j, λ ∑_i (τ_i + Δ) − τ_j⟩², obtained by Taylor expansion and the NTK approximation ∇_θ L_j(θ_0) ≈ −τ_j / ∑_t α_t; (ii) a shared subspace S_share built by SVD of the task vectors (the first k left singular vectors of each, deduplicated by another SVD), onto which the gradient is projected so that updates happen only orthogonal to it, preserving shared knowledge; and (iii) a layer-wise merging coefficient λ_i^l = η/‖τ_i^l‖, which treats λ as an adaptive learning rate that balances task-vector magnitudes. The projection step is what converts conflict resolution into a constrained optimization problem rather than a pruning rule.","core_discovery":"The central claim is that task conflicts and shared knowledge should be handled separately: conflicts are resolved by optimizing a modification vector Δ added to each task vector, while shared knowledge is preserved by allowing gradient updates only in directions orthogonal to the subspace spanned by the task vectors' principal components. The paper derives a data-free objective by Taylor-expanding the loss gap between the merged model and the individual models around the pretrained weights, and approximating the pretrained gradient by the negative task vector scaled by the total learning-rate sum (an NTK/linear-regime assumption). Optimizing this objective with gradient descent whose steps are projected away from the shared subspace, plus a task-aware layer-wise merging coefficient λ_i^l = η/‖τ_i^l‖, yields the DOGE algorithm. In experiments across eight vision tasks (ViT-B/32 and ViT-L/14) and eight GLUE tasks (Flan-T5-base/large with LoRA), DOGE improves over Task Arithmetic by up to 11.6 percentage points and over AdaMerging by up to 5.8, and it also transfers to unseen tasks and corrupted test distributions.","pith_inferences":["The NTK approximation used to derive the data-free objective may be the limiting factor; a testable extension is to measure how DOGE's gain degrades as fine-tuning moves away from the linear regime (larger learning rates, more steps, or non-LoRA full fine-tuning).","The shared subspace construction depends on SVD rank choice; a natural extension would be a data-dependent or task-similarity-weighted basis rather than uniform rank per task, especially for tasks with very different intrinsic dimensionality.","The same constrained-gap objective could be applied to heterogeneous models only if task vectors are first aligned to a common space, which the paper notes as a limitation.","DOGE's robustness on corrupted test sets suggests the projection orthogonal to the shared subspace may implicitly regularize the merged model; this could be tested by comparing its feature geometry against the individual experts."],"forward_implications":["If the gap-minimization view is right, the merged model's performance on each task should approach the individual expert's performance, closing much of the gap that sparsification and orthogonality methods leave.","Data-free merging can compete with test-time adaptation methods, meaning no unlabeled test data is needed, which helps privacy and deployment.","The task-aware λ removes grid search over merging coefficients; one global η scales all layers and tasks.","DOGE can be applied on top of existing merging algorithms like Task Arithmetic and AdaMerging, acting as a plug-in rather than a replacement.","The method scales to more tasks (8→14→20) with relatively smaller degradation, suggesting it mitigates negative transfer."],"supporting_citations":[{"why":"Introduces task vectors and Task Arithmetic, the baseline and notation the paper builds on.","marker":"Ilharco et al., 2023"},{"why":"Ties-Merging baseline; also supplies the top-30% magnitude pruning used in DOGE's implementation.","marker":"Yadav et al., 2023"},{"why":"AdaMerging baseline and the test-time adaptation setup DOGE is compared against.","marker":"Yang et al., 2024c"},{"why":"AWD, the orthogonality-promoting method whose information loss motivates the gap objective.","marker":"Xiong et al., 2024"},{"why":"MetaGPT, source of the loss-gap objective (Eq. 3) that DOGE optimizes in data-free form.","marker":"Zhou et al., 2024"},{"why":"Provides the Taylor-expansion/tangent-space view used to turn the loss gap into a data-free objective.","marker":"Ortiz-Jimenez et al., 2023"},{"why":"High-dimensional orthogonality theorem used to explain why task vectors are nearly orthogonal and why forcing orthogonality discards shared knowledge.","marker":"Vershynin, 2018"},{"why":"Gradient projection for multi-task learning, the conceptual basis for projecting gradients in the shared subspace.","marker":"Yu et al., 2020"}],"fun_headline_variants":["Adaptive projective gradient descent merges models with less task conflict","Data-free DOGE merging beats Task Arithmetic by up to 11.6 points","Projective gradient descent for merging: beat AdaMerging by 5.8 points","Multi-task model merging as adaptive projection: no original data needed","Conflicts resolved, shared knowledge kept: new merging algorithm DOGE"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on the assumption that fine-tuning stays in the linear (NTK) regime, so the task vector is exactly proportional to the negative gradient of the pretrained model; if experts are fine-tuned too far, the data-free objective no longer equals the true loss gap and the claimed gains may not persist.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive projective gradient descent merges models with less task conflict","Data-free DOGE merging beats Task Arithmetic by up to 11.6 points","Projective gradient descent for merging: beat AdaMerging by 5.8 points","Multi-task model merging as adaptive projection: no original data needed","Conflicts resolved, shared knowledge kept: new merging algorithm DOGE"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000731,"raw_usage":{"total_tokens":3303,"prompt_tokens":1006,"completion_tokens":2297,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":622,"completion_tokens_details":{"reasoning_tokens":2200}},"tokens_in":622,"tokens_out":2297,"duration_ms":15124,"temperature":1.0,"reasoning_tokens":2200,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:32:05.226885+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fine-tune the same expert models with a much larger learning rate or many more steps so they leave the linear regime, then compute Eq. (5)'s objective with the true task data and compare it to the gradient proxy. If the proxy's error grows and DOGE's accuracy advantage over Task Arithmetic or Ties-Merging disappears, the central claim is falsified.","supporting_citations":[{"cited_title":"selfish” and “catastrophic","cited_arxiv_id":null,"evidence_quote":"Ties-Merging baseline; also supplies the top-30% magnitude pruning used in DOGE's implementation."}],"review_version":1}