{"id":"52e8c6cb-298d-4057-b634-fafb13374d31","arxiv_id":"2507.00016","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"GRFT selects whole rows or columns of weight matrices with the largest squared-gradient sums for fine-tuning, adds L2 regularization, and reports gains over GPS, LoRA, and adapters on FGVC, VTAB, and GLUE.","lead":"This paper proposes GRFT, a parameter-efficient fine-tuning method that updates only entire rows or columns of a model's weight matrices, chosen by the largest sums of squared gradients, plus L2 regularization toward the pre-trained weights. Tests on vision and language benchmarks report state-of-the-art accuracy while updating less than 1.3% of parameters.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The theoretical justification for row/column selection does not follow from Eq. (3.1.4): that constraint is per-column sparsity, whose optimum is GPS-style top-k entries per column, not whole rows, so the top-row-sum rule in Eqs. (3.1.5)-(3.1.6) is unproven as written.","rationale":"The most load-bearing weakness is in the derivation of the central theoretical claim, not in the experimental assumptions. The paper's headline says row/column selection is optimal, but the optimization written as Eq. (3.1.4) has a per-column cardinality constraint. The optimal mask under that constraint is obtained independently per column by keeping the top-k gradient entries; it is a sparse GPS-style mask, and it does not force rows to be selected together. The subsequent row-sum computation in Eq. (3.1.5) and mask in Eq. (3.1.6) implement a different constraint, namely selecting |T| rows with M_{ij}=1 iff i∈T. The top-k row-sum rule is optimal for that row-support constraint, but the paper does not derive it from Eq. (3.1.4); it simply asserts it. This is load-bearing because the stated contribution is precisely the theoretical demonstration. The reader's weakest assumption (the fixed one-step mask over 100 epochs) is also a valid empirical concern, but it is testable only with code and multiple runs; the Eq. (3.1.4) issue is an immediate mathematical inconsistency. Since the empirical results may still be valid and the theorem can likely be repaired by restating the row constraint, I would not move the verdict to REJECT; I would keep the reader's CONDITIONAL verdict, requiring the authors to correct the derivation or qualify the claim.","tokens_in":15087,"tokens_out":7382,"duration_ms":83451,"concrete_test":"Work through the 2x2 counterexample G=[[100,1],[1,100]] with k=1. Compute M_percol from Eq. (3.1.4) by taking the top entry in each column, and compute M_row from Algorithm 1 by taking the top row by sum of squared gradients. Evaluate ||G - G⊙M||_2^2 for both. If the per-column mask has the smaller error, the stated theorem does not imply the algorithm's row mask; the authors must either replace Eq. (3.1.4) with the row-support constraint or withdraw the optimality claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (3.1.4) is presented as the optimization that justifies GRFT: min_M ||G - G⊙M||_2^2 subject to ||M_{·,j}||_0 ≤ k for every column j. For a fixed column, the best feasible mask selects the k entries with the largest squared gradients in that column; this is exactly GPS-style per-neuron sparse selection and does not force selected entries to form whole rows. The row-sum rule used in the algorithm corresponds to a different constraint, namely M_{ij}=1 iff i∈T with |T|=k, and under that constraint the optimum is indeed the top-k rows by Σ_j G_ij^2. But Eq. (3.1.4) does not state or imply that row-support constraint, so the proof as written supports GPS, not GRFT. A concrete counterexample exposes the gap: for G=[[100,1],[1,100]] and k=1, the Eq. (3.1.4) optimum selects the diagonal entries with squared error 10100, while the algorithm's top-row mask selects row 1 with squared error 10001? Under the stated objective the per-column mask is better, so the claimed optimality of row selection is false under the stated constraint. In addition, the derivation in Eq. (3.1.7) uses plain gradient descent, while Algorithm 1 uses Adam on masked gradients; Adam's per-coordinate normalization means the one-step Taylor argument does not directly transfer to the implemented update. These are internal inconsistencies in the central theoretical claim, not merely disagreements with prior work.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes GRFT, a parameter-efficient fine-tuning method that selects entire rows or columns of a pre-trained model's weight matrices based on the sum of squared gradients computed under a supervised contrastive loss, freezes the remaining parameters with a mask, and adds an L2 regularization term pulling updated weights toward the pre-trained initialization. The authors claim a theoretical optimality for selecting rows or columns with the largest squared-gradient sums, and they report accuracy improvements over GPS, LoRA, adapters, and other baselines on FGVC, VTAB-1k, and three GLUE tasks, with substantially reduced parameter counts.","tokens_in":15400,"tokens_out":3182,"duration_ms":39829,"significance":"The empirical direction is useful: structured (row/column) selection is storage- and hardware-friendlier than sparse per-neuron selection, and the ablations in Table 4 give some evidence that row/column selection can match or slightly exceed sparse selection in their setup. The L2 regularization toward pre-trained weights is a sensible and simple mechanism, and the hyperparameter tables are a helpful contribution for reproducibility. However, the paper's central theoretical claim is not established as written: the optimization in Eq. (3.1.4) uses a per-column sparsity constraint that does not imply the row-sum selection rule of Eqs. (3.1.5)-(3.1.6), and the one-step Taylor justification does not cover a mask fixed for 100 training epochs under Adam. The empirical results are therefore currently supported only as a heuristic, and the 'theoretically demonstrate' claim would need to be substantially revised or re-proven.","major_comments":[{"comment":"The optimization problem in Eq. (3.1.4) constrains each column to have at most k nonzeros, i.e., ||M_{.,j}||_0 <= k for every column j. Under this constraint the optimal mask selects, independently in each column, the k entries with the largest squared gradients, which is exactly the GPS-style sparse selection pattern, not whole-row selection. The algorithm's row-sum rule in Eqs. (3.1.5)-(3.1.6) corresponds to a different constraint, namely that all selected entries of a row are either fully masked or fully unmasked. A concrete counterexample exposes the gap: for G = [[100,1],[1,100]] and k=1, the per-column optimum of Eq. (3.1.4) leaves squared error 2, while the top-row mask of Eqs. (3.1.5)-(3.1.6) leaves squared error 10001. Thus the row-selection rule is not the optimum of the stated objective, and the claimed theoretical optimality is not proven as written.","section":"Sec. 3.1, Eq. (3.1.4)"},{"comment":"The Taylor-expansion argument in Eqs. (3.1.1)-(3.1.3) justifies a mask choice for a single gradient descent step from the initial pre-trained parameters. Algorithm 1, however, computes the mask once at initialization using the SCL loss and then fixes it for the entire training run (up to 100 epochs) while optimizing the cross-entropy plus L2 objective with Adam. The paper does not show that the parameters with the largest initial squared gradients remain the most important throughout training, nor that a mask optimal for one step is optimal for the full trajectory. This is a load-bearing assumption because the entire method depends on the frozen mask. An experiment comparing the fixed mask with periodically recomputed masks, or at least with masks computed from mid-training gradients, would be needed to support the claim.","section":"Sec. 3.1, Eqs. (3.1.1)-(3.1.3) and Algorithm 1"},{"comment":"Equation (3.1.7) writes the update as plain masked gradient descent, W_{t+1} - W_t = -eta_t grad L(W_t) \\odot M, but Algorithm 1 uses Adam on the masked gradient, with the coordinate-wise normalization in lines 11-15. Adam's per-parameter scaling changes which coordinates receive effective updates, so the one-step Taylor optimality of a mask under plain gradient descent does not directly transfer to the implemented optimizer. The paper should either provide an analysis for the actual update rule or explicitly frame the theoretical result as a heuristic motivation for the empirical method.","section":"Sec. 3.1, Eq. (3.1.7) vs Algorithm 1"}],"minor_comments":[{"comment":"The dataset descriptions contain errors: NABirds is described as 'a dataset contains 102 flower species with 8,189 images,' which is a description of Oxford Flowers, not NABirds; please correct this and double-check the other dataset statistics.","section":"Sec. 4.2"},{"comment":"The text says each downstream task is trained for '100 iterations' while Table 6 and Algorithm 1 indicate 100 epochs; this wording should be harmonized to avoid confusion.","section":"Sec. 4.1"},{"comment":"Several entries in Tables 1 and 2 are missing spaces or are visually concatenated (e.g., '38.879.7' in Table 2), making the tables hard to read; formatting should be cleaned.","section":"Tables 1 and 2"},{"comment":"The data-subsets procedure selects the mask from the subset with minimal loss, but the paper does not compare this against a random subset or the full dataset; the ablation in Fig. 2(d) shows sensitivity but not that the minimal-loss criterion is the cause of improvement. Please add such a comparison or soften the claim.","section":"Sec. 4.4.3"}],"recommendation":"major_revision","confidential_remarks":"The paper has a clear and practically motivated contribution, but the theory section as written does not prove the stated optimality, and this is the paper's central announced contribution. The empirical results are encouraging, so a major revision that either proves the correct statement or explicitly reframes the selection rule as a heuristic, plus adds experiments on mask stability, could make the paper acceptable. I would also encourage the authors to release the code at revision time, since the hyperparameter tables are otherwise difficult to reproduce."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: GRFT is a modest but plausible win for PEFT. It replaces GPS's per-neuron sparse mask with whole-row or column selection and adds an L2 pull toward the pre-trained weights. The reported numbers are consistent with that story, but the theory section proves a different selection rule than the one the algorithm uses. The evaluation is single-run and heavily per-dataset tuned. Still, the empirical core is worth a referee's time.\n\nWhat's new: structured selection by row/column sums of squared gradients, which cuts mask storage from a full matrix to a list of indices, and the regularizer. The coverage is decent: FGVC, VTAB, and three GLUE tasks on LLaMA-3, with ablations for row vs column vs sparse, norm choice, and the data-subset trick. Gains over GPS and SPT-LoRA are modest but consistent, and parameter counts are low.\n\nThe main soft spot is the proof. Eq. (3.1.4) constrains each column to at most k nonzeros, which is GPS-style per-column sparsity. That does not imply whole-row masks. The stress-test counterexample is correct: for G=[[100,1],[1,100]] and k=1, the per-column optimum picks the diagonal, not a row. The row-sum rule would need a row-support constraint, M_{ij}=1 iff i in T with |T|=k, which is not what's written. So the central claim, as stated, is unproven. Second, the one-step Taylor argument covers gradient descent, but the algorithm runs Adam on masked gradients with a mask fixed for 100 epochs. That gap isn't fatal, but it means the theory doesn't cover the method as executed. Third, the evaluation is single-run, no error bars, no code, and each dataset gets its own row count, lambda, regular layer count, and data-subset count tuned per task. That's a lot of freedom for a state-of-the-art claim.\n\nThe ablations are a genuine plus: each component seems to contribute, and row/column selection consistently beats sparse selection on the FGVC subset they tested. The data-subset trick is ad hoc but transparent.\n\nWho this is for: PEFT researchers who want a GPS variant with smaller masks and structured updates. It's not a breakthrough, but it's a useful data point. I'd send it to review with a clear request: rewrite the theory to match the algorithm, release code and error bars, and be upfront about the per-dataset tuning. If those are fixed, the empirical result stands on its own.\n\nRecommendation: engage as a referee, but treat the theoretical claim as unsupported until rewritten.","headline":"A modest PEFT improvement with a broken proof as written; worth refereeing for the empirical core, but the theory needs a rewrite.","tokens_in":15992,"tokens_out":3910,"would_cite":false,"duration_ms":41401,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"GRFT updates only whole rows or columns of a weight matrix chosen by squared-gradient sums, and the authors report it beats GPS, Adapter, and LoRA while updating as little as 0.30% of parameters on VTAB.","keywords":["parameter-efficient fine-tuning","gradient-based parameter selection","row- and column-wise masks","squared-gradient ranking","L2 regularization","knowledge transfer","ViT","large language models"],"falsifier":"Midway through fine-tuning, recompute the per-row squared-gradient ranking on the same data and compare it with the frozen mask's selected rows; if the agreement is low and switching to the currently top-ranked rows improves validation accuracy, the fixed-mask assumption is false. A control run with masks recomputed every epoch would directly show whether the one-step Taylor-optimal choice stays optimal.","tokens_in":14822,"feed_emoji":"🎯","tokens_out":6533,"duration_ms":75017,"temperature":0.7,"pith_summary":"The paper proposes GRFT, a way to fine-tune large pre-trained models by updating only selected whole rows or columns of each weight matrix, rather than scattered individual weights. The selection rule is to keep the rows or columns with the largest sums of squared gradients, computed once from the pre-trained model under a supervised contrastive loss. The authors argue, through a first-order Taylor approximation of the loss decrease, that these rows or columns give the largest reduction in loss per update, and they add an L2 penalty that pulls the selected weights back toward their pre-trained values to preserve learned knowledge. The reported empirical result is that GRFT beats the sparse-selection GPS baseline and standard PEFT methods such as Adapter and LoRA, while updating only 1.22% of parameters on FGVC and 0.30% on VTAB, and 0.08% on LLaMA3-1B text tasks.","feed_headline":"Whole-row gradient selection fine-tunes with only 0.3% of weights","feed_subtitle":"GRFT cuts mask storage by picking rows/columns via squared-gradient sums and beats sparse selection on FGVC and VTAB.","key_machinery":"The central object is the binary row/column mask $M$ built from the gradient matrix $H = \\nabla L_{\\mathrm{scl}}(W_{\\mathrm{pre}})$. Each row score is $S_i = \\sum_{j=1}^n h_{ij}^2$ (or the analogous column score), and the mask keeps the $k$ rows or columns with the largest scores. The argument-carrying identity is the Taylor approximation $\\Delta L \\approx -\\alpha_t \\|\\nabla L \\odot M\\|^2$, which says the loss decrease is governed by the squared gradient mass retained by the mask; maximizing that mass is why large-gradient rows or columns are chosen. The second machinery piece is the regularized objective $L_R = L_{\\mathrm{cross}} + \\lambda \\sum_{l \\in R} \\|W^l - W^l_{\\mathrm{pre}}\\|^2$, which anchors selected parameters near their pre-trained values.","core_discovery":"GRFT's central claim is that, instead of scattering trainable weights across a matrix, one should update whole rows or columns of the pre-trained weight matrix, choosing the rows or columns whose gradient has the largest squared sum. These gradients are evaluated once, before fine-tuning, using a supervised contrastive loss on the pre-trained model, and a binary mask freezes all other weights. The paper derives this rule from a first-order Taylor expansion of the loss: minimizing the loss change after one gradient step is equivalent to maximizing the inner product of the gradient with its masked version, which favours parameters with the largest squared gradients; aggregating by row or column then selects the largest row or column sums. An L2 regularization term on the last layers, patch embedding, and classification head keeps the updated weights close to their pre-trained values to preserve transfer knowledge. The paper reports that this combination outperforms GPS, Adapter, LoRA, VPT, and SSF on FGVC and VTAB with ViT-B/16, updating 1.22% and 0.30% of parameters respectively, and beats LoRA on GLUE tasks with LLaMA3-1B while updating 0.08%.","pith_inferences":["An untested extension is to recompute the row or column scores periodically during training instead of once at initialization; the paper's one-step argument only covers the first gradient update, so adaptive masks are a natural next test.","The same squared-gradient logic could be fed by a second-order quantity such as the diagonal Fisher information; if the underlying claim is that high-curvature directions matter, such a variant would be a sharper version of the same idea.","Because selection is per layer and independent, GRFT could be combined with per-layer budgets or with LoRA in selected layers, which the paper does not explore.","The data-subset trick of choosing the split with minimal loss for mask computation is only ablated for up to seven subsets; a natural further test is whether this selection generalizes to larger or noisier datasets."],"forward_implications":["On the paper's results, a ViT-B/16 can be adapted to fine-grained classification tasks with only 1.22% of its parameters updated, improving on full fine-tuning's 89.44% average accuracy by reaching 91.33%.","Storing the mask becomes a list of row or column indices instead of a matrix the size of the weights, which removes the main storage drawback of GPS.","Because updates are dense along whole rows or columns, the method avoids sparse-matrix gradient computation and is easier to run on standard hardware.","Adding L2 regularization to the last layers, patch embedding, and classifier head improves accuracy over no norm and over L1 regularization on the FGVC benchmark.","The method transfers to decoder-only language models: on LLaMA3-1B it updates only 0.08% of parameters and outperforms LoRA on the RTE subset of GLUE."],"supporting_citations":[{"why":"Supplies the GPS baseline that GRFT extends, including the per-neuron sparse selection strategy and the reproduced comparison results.","marker":"[49]"},{"why":"Defines the supervised contrastive loss used to compute the gradients on which the mask is built.","marker":"[22]"},{"why":"Provides the LoRA baseline that GRFT compares against and outperforms on vision and text tasks.","marker":"[17]"},{"why":"Provides the Adapter baseline used in the FGVC, VTAB, and GLUE comparisons.","marker":"[15]"},{"why":"Defines the Adam optimizer used for the masked updates in Algorithm 1.","marker":"[23]"},{"why":"Supplies the ViT-B/16 backbone used in the image classification experiments.","marker":"[3]"},{"why":"Supplies the LLaMA3-1B model used in the text classification experiments.","marker":"[8]"},{"why":"Motivates the L2 regularization on the classification head by describing its small, centered uniform initialization.","marker":"[13]"}],"fun_headline_variants":["GRFT updates whole rows by gradient sums to fine-tune with just 0.3% weights","GRFT: squared-gradient rows beat GPS, Adapter, and LoRA with 0.3% params","Whole-row gradient selection fine-tunes state-of-the-art with 0.3% weights","GRFT: pick rows by squared gradients, fine-tune 0.3% weights, beat LoRA","Row/column squared-gradient sums: fine-tune with 0.3% params, outperform GPS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The mask is computed once from the pre-trained model's gradients before training and never changes, on the assumption that the rows or columns giving the largest one-step loss decrease at initialization remain the best parameters to update for the entire fine-tuning run.","fun_headline_variants_meta":{"raw":{"variants":["GRFT updates whole rows by gradient sums to fine-tune with just 0.3% weights","GRFT: squared-gradient rows beat GPS, Adapter, and LoRA with 0.3% params","Whole-row gradient selection fine-tunes state-of-the-art with 0.3% weights","GRFT: pick rows by squared gradients, fine-tune 0.3% weights, beat LoRA","Row/column squared-gradient sums: fine-tune with 0.3% params, outperform GPS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001302,"raw_usage":{"total_tokens":5331,"prompt_tokens":989,"completion_tokens":4342,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":605,"completion_tokens_details":{"reasoning_tokens":4214}},"tokens_in":605,"tokens_out":4342,"duration_ms":36924,"temperature":1.0,"reasoning_tokens":4214,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T00:47:33.244340+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Midway through fine-tuning, recompute the per-row squared-gradient ranking on the same data and compare it with the frozen mask's selected rows; if the agreement is low and switching to the currently top-ranked rows improves validation accuracy, the fixed-mask assumption is false. A control run with masks recomputed every epoch would directly show whether the one-step Taylor-optimal choice stays optimal.","supporting_citations":[{"cited_title":"Zhang, Q","cited_arxiv_id":null,"evidence_quote":"Supplies the GPS baseline that GRFT extends, including the per-neuron sparse selection strategy and the reproduced comparison results."},{"cited_title":"Khosla, P","cited_arxiv_id":null,"evidence_quote":"Defines the supervised contrastive loss used to compute the gradients on which the mask is built."},{"cited_title":"Houlsby, A","cited_arxiv_id":null,"evidence_quote":"Provides the Adapter baseline used in the FGVC, VTAB, and GLUE comparisons."},{"cited_title":"Kingma and J","cited_arxiv_id":null,"evidence_quote":"Defines the Adam optimizer used for the masked updates in Algorithm 1."},{"cited_title":"Dosovitskiy, L","cited_arxiv_id":null,"evidence_quote":"Supplies the ViT-B/16 backbone used in the image classification experiments."},{"cited_title":"Grattafiori and A","cited_arxiv_id":null,"evidence_quote":"Supplies the LLaMA3-1B model used in the text classification experiments."}],"review_version":1}