{"id":"26851121-78be-439c-8ea7-489aea9b86a4","arxiv_id":"2507.10085","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"CRFT selects critical internal representations via attention and saliency scores and fine-tunes only them, improving GSM8K accuracy over ReFT from 29.0% to 32.8% on LLaMA-2-7B.","lead":"A new fine-tuning method for large language models, CRFT, picks out the most influential word positions inside the model using attention patterns, then edits only those positions in a compressed subspace. It reports gains of 3.8 points over the prior ReFT method on the GSM8K math benchmark while using fewer trainable parameters.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's central mechanism—thresholded attention/saliency marks the counterfactually critical positions of Eq. 1—is never directly validated; Fig.","rationale":"The reader's conditional verdict identifies the same weak joint: the operational filters in §2.2 are asserted, not demonstrated, to realize the counterfactual definition in Eq. 1. I agree with that reading and would keep the verdict conditional rather than accept or reject. Credit is due for including two controls: Fig. 4's noise sensitivity and Table 8's random-position interventions. Those controls make the paper more credible than a bare claim, but they do not close the gap: Fig. 4 is about robustness, not answer-flip criticality, and Table 8 is a single-seed training control whose spread (24.5–28.1) overlaps the low end of CRFT variants (29.6–30.4). A secondary concern—the 0.016% parameter count is not derivable from the text unless R is frozen and that is never stated—reinforces the need for a code or checkpoint release, but it is not the main obstacle. The direct overlap test proposed above would settle whether the central mechanism is real; if it fails, the paper still shows a representation-editing recipe that improves over ReFT, but the “critical representation” interpretation and the novelty attribution would need to be withdrawn or substantially softened.","tokens_in":66428,"tokens_out":9481,"duration_ms":118214,"concrete_test":"Take 200 held-out GSM8K examples with LLaMA-2-7B. For each layer and token position, estimate the Eq. 1 critical label by injecting small Gaussian perturbations (e.g., three random directions) and recording whether the final answer flips. Then compute SAF, MAF, and Union threshold sets at the same cardinality and compare their precision/recall/IoU against this flip-based set, using random position sets as the baseline. If the threshold sets are not significantly above chance overlap (or no better than random), the §2.2 identification mechanism is unsupported, and CRFT's gains should be attributed to the low-rank update alone rather than to critical-position selection.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assertion is the identification step: Eqs. 2 and 5 are operational substitutes for Eq. 1, yet no experiment measures their overlap with the counterfactual set. Fig. 4 shows that top-scored positions lose more accuracy under injected noise than bottom-scored positions drawn from the same filter, but noise sensitivity of already-correct examples is not Eq. 1's flip criterion, and no random-position comparison is made at the same cardinality in that figure. Table 8 is the relevant control, and it does show random training-time positions (24.5–28.1) below the best CRFT variant (32.8), but it is single-seed, and the headline uses the best of 12 strategy/mode numbers; several CRFT variants sit at 29.6–30.4, within 0.6–1.5 points of the best random seed (28.1). Since ReFT p7+s7 is 29.0, the marginal gain attributed specifically to “critical” selection is 3.8 points, a gap that could plausibly be seed or strategy variance rather than the information-flow mechanism. Resolving this requires either a direct overlap test of the threshold sets against true flips, or a multi-seed random-position training comparison at identical position count.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes Critical Representation Fine-Tuning (CRFT), a parameter-efficient fine-tuning method that freezes the base transformer and learns low-rank updates (Eq. 6) only for token positions identified as critical by self-referential or multi-referential attention/saliency filters (Eqs. 2–5). The paper reports that on GSM8K with LLaMA-2-7B, CRFT reaches 32.8% accuracy versus 29.0% for ReFT p7+s7 and 14.6% for the base model, with only 0.016% trainable parameters, and reports gains across seven other reasoning benchmarks and three additional base models, together with few-shot extensions and ablations on thresholds, intervention counts, layer choice, and selection criteria.","tokens_in":66552,"tokens_out":4138,"duration_ms":49521,"significance":"If the identification step were validated, this would be a useful contribution: dynamic, interpretable position selection for representation editing, with strong parameter efficiency and broad empirical coverage. The paper is also transparent in providing ablation studies and explicit control experiments (Tables 4–8), and the low parameter count is a genuine strength. However, the central scientific claim that attention/saliency thresholds recover the counterfactual critical set behind Eq. 1 is currently supported only indirectly, and the headline numbers rely on the best of many strategy variants. The contribution is therefore promising but needs a focused validation of the mechanism before the main claim can be accepted.","major_comments":[{"comment":"The load-bearing assertion of the paper is that the threshold-based filters in Eqs. 2 and 5 reproduce the counterfactual critical set M(h) defined in Eq. 1, namely the representations whose perturbation flips the correctness of the model output. This equivalence is never directly measured. The evidence in Section 3.4 and Figure 4 is about noise sensitivity of already-correct examples, which is not the same as the flip criterion in Eq. 1, and no random-position comparison at the same cardinality is included in that figure. Please provide a direct overlap test between the selected positions and the positions that actually flip correctness under perturbation, or justify the proxy with a controlled experiment.","section":"Section 2.2 and Section 3.4"},{"comment":"The random-position training control in Table 8 is the most relevant baseline, but it is single-seed per location and reports a range of 24.5–28.1 accuracy. Several CRFT variants in Table 1 are only slightly above that range (29.6–30.4), the ReFT baseline is 29.0, and the headline 32.8 is the best of twelve strategy/mode values. The marginal gain attributed specifically to 'critical' selection is therefore 3.8 points over ReFT, which could plausibly be seed or strategy variance. Please report multiple seeds with mean and standard deviation for the random-position condition at the same intervention count, and either pre-specify the strategy or report the full distribution of CRFT variants rather than only the best.","section":"Section 3.4, Tables 1 and 8"},{"comment":"The main results in Table 1 use threshold alpha = beta = 0.05, but the ablation in Table 4 shows that alpha = 0.01 gives 33.2 on GSM8K, and Table 11 shows consistent improvements for all strategies at 0.01. Since the paper does not explain why the main tables use 0.05 instead of the better-performing 0.01, the reported configuration is not clearly the tuned one. Please justify the choice of 0.05 or adopt a consistent protocol that avoids selecting hyperparameters and strategy variants on the same benchmark used for the headline claim.","section":"Tables 4, 11, and Section 3.1"},{"comment":"Every CRFT entry in Tables 1 and 2 reports two numbers per strategy, corresponding to two definitions of filtering (previous-layer versus current-layer criticality), and the paper recommends a union strategy without a pre-specified selection rule. With twelve numbers per model on GSM8K alone, the abstract's claim of a 3.8% improvement over ReFT should be tied to a single pre-specified configuration or to a clearly described model-selection procedure; otherwise the headline result is vulnerable to selection over configurations.","section":"Section 3.1 and Tables 1/2"}],"minor_comments":[{"comment":"The notation is inconsistent: Eq. 2 filters based on Info^(l-1)(i,i), while Eqs. 3 and 4 define Info^(l)_SAF(i,i) using attention at layer l; please clarify the layer indexing in both the equations and the surrounding text.","section":"Equations 2 and 3"},{"comment":"The two values per CRFT entry are explained only in Section 3.1, not in the table captions; please state explicitly in each caption that the first value uses previous-layer filtering and the second uses current-layer filtering.","section":"Tables 1 and 2"},{"comment":"The three selection criteria in Table 6 ('order', 'score', 'random') are not precisely defined; for example, it is unclear whether 'random' in Table 6 refers to random positions within the thresholded set or fully random positions, and how it relates to the 'Uniform Random' condition in Table 8.","section":"Section 3.3"},{"comment":"Several generation examples appear to be misaligned with their stated tasks; for instance, the AQuA example shows a ribbon-length instruction above a question about ant shadows, and the model responses do not clearly match the displayed prompt. Please check and correct the qualitative examples.","section":"Appendix C"},{"comment":"Figure 4 would be more informative if it included the random-position noise curve at the same cardinality as the top-5 and last-5 curves, since that is the control needed to support the claim that the selected positions are specifically output-sensitive.","section":"Section 3.4"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the core idea is worth pursuing. My main reservation is validation of the identification mechanism rather than novelty. A direct overlap test between the threshold sets and counterfactual flips, plus multi-seed random-position controls, would resolve the central concern. I have no other editorial reservations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new idea here is straightforward and worth taking seriously: instead of editing fixed positions like ReFT's p7+s7, CRFT selects positions per input using thresholds on self-attention or column-average attention (or saliency variants), then applies the same LoReFT low-rank update. The selection heuristic is genuinely different from ReFT, ACT, and PASTA, and the empirical scope is solid—eight datasets, four models, ablations on thresholds, selection criteria, layer ranges, plus a random-position control. I credit the authors for including Table 8; it is exactly the control that question matters the most, and the best CRFT variant does beat the best random seed by 4.7 points.\n\nThe soft spots are real but fixable. The load-bearing assumption is that thresholded attention/saliency identifies the counterfactual critical set of Eq. 1. No experiment measures the overlap between the two. Fig. 4 shows noise sensitivity of top-scored versus bottom-scored positions, but that is not the flip criterion of Eq. 1, and there is no random-position comparison at the same cardinality in that figure. The headline gain also rests on the best of several strategy/mode combinations; several CRFT variants land at 29.6–30.4, within 1.5 points of the best random seed. That does not kill the paper, but it means the marginal benefit of 'critical' selection over random positions could be smaller than the 3.8-point gap over ReFT suggests.\n\nThe parameter-efficiency claim also deserves a closer look. CRFT's 0.016% versus ReFT's 0.031% appears consistent with intervening in 16 layers instead of 32 (the first half, which Table 7 shows to be best), but the paper does not state this explicitly, so the comparison is hard to interpret. And with no code or data released, none of the numbers are independently checkable yet.\n\nAll of this is proportionate to a reasonable conference submission, not a rejection. The paper is clearly written, the limitations section is honest, and the idea is a legitimate incremental contribution. What it needs is a direct validation of the identification step (e.g., compare threshold-selected positions against true counterfactual flips), multi-seed runs, a clear statement of which layers are used for the parameter count, and a comparison with ACT/PASTA. I would send it to peer review with those requests, and I would read the revision with interest. I would not cite it in my own work yet, mainly because the code and overlap test are missing.","headline":"CRFT is a plausible but under-validated extension of ReFT: dynamic position selection via attention/saliency thresholds is new, yet the paper never directly tests whether those thresholds actually mark the counterfactually critical positions it defines.","tokens_in":67238,"tokens_out":3016,"would_cite":false,"duration_ms":39322,"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":"The paper claims that CRFT, by editing only the hidden states that attention and saliency scores mark as critical, raises LLaMA-2-7B accuracy on GSM8K from 14.6% to 32.8% with 0.016% trainable parameters, beating the fixed-position ReFT…","keywords":["critical representation fine-tuning","chain-of-thought reasoning","parameter-efficient fine-tuning","representation editing","information flow analysis","attention filtering","low-rank subspace intervention","GSM8K"],"falsifier":"On the full benchmark suite, replace the attention and saliency filters with uniformly random positions at the same layer count, update budget, and rank, across at least three seeds. If the CRFT-minus-random margin is within a couple of accuracy points on most datasets—as Table 8 already shows is nearly the case on GSM8K—then the criticality filter is not the driver. A second check would measure the overlap between threshold-flagged positions and the oracle defined in Eq. 1 from input-level perturbations.","tokens_in":66103,"feed_emoji":"🧠","tokens_out":9589,"duration_ms":90186,"temperature":0.7,"pith_summary":"Critical Representation Fine-Tuning (CRFT) claims that a chain-of-thought model can be improved most by editing not all weights and not fixed positions, but the specific hidden representations that carry decisive information between layers. It locates those critical representations by reading the model's own attention and saliency scores, then learns a low-rank correction inside a frozen base model. On GSM8K with LLaMA-2-7B, the method raises accuracy from 14.6% to 32.8%—an 18.2-point gain over the base and 3.8 points over ReFT—while training only 0.016% of the parameters. The same recipe transfers across eight arithmetic and commonsense benchmarks and to few-shot settings, supporting the paper's claim that where an intervention lands matters as much as how many parameters it trains.","feed_headline":"Editing attention-critical hidden states lifts GSM8K 18.2 points","feed_subtitle":"CRFT trains only 0.016% of parameters by locating the token positions attention marks as decisive, beating fixed-position ReFT.","key_machinery":"The load-bearing object is the critical-representation set $M(h)$, defined by counterfactual perturbation in Eq. 1. CRFT operationalizes this set with two filters on the information-flow grid: self-referential filtering keeps positions $i$ whose attention (or saliency) weight on themselves exceeds $\\alpha$, marking representations that consolidate earlier information; multi-referential filtering keeps positions $j$ whose column-average influence on later representations exceeds $\\beta$, marking regulators. The optimization is the low-rank linear intervention of Eq. 6: for each flagged hidden state, the value is moved inside an $r$-dimensional subspace spanned by orthonormal rows $R$ toward a learned projection $Wh+b$, while all other parameters stay frozen.","core_discovery":"The central claim is that the fixed-position convention of ReFT—editing the first and last seven token representations of every layer—is the wrong inductive bias for reasoning. CRFT instead defines a critical representation as one whose small perturbation changes whether the model answers correctly, and proposes that attention self-flow above a threshold (self-referential filtering) or column-average outgoing attention above a threshold (multi-referential filtering), with saliency counterparts, mark those positions. Editing only those positions with the low-rank update $\\Phi(h) = h + R^T(Wh + b - Rh)$ raises LLaMA-2-7B on GSM8K from 14.6% to 32.8%, beating the 29.0% ReFT baseline, while training 0.016% of parameters; the same recipe lifts accuracy across LLaMA-2, LLaMA-3, and Mistral families on arithmetic and commonsense tasks.","pith_inferences":["The criticality filters could be tested against the counterfactual oracle of Eq. 1 directly: if the threshold-selected set has low overlap with perturbation-sensitive positions on held-out layers, the identification step is doing less work than the learnable update; this is my inference, not the paper's claim.","The method suggests a general recipe for representation-level PEFT on other long-generation tasks, such as code or multi-hop QA: compute attention-derived masks once per prompt and learn per-position subspace updates instead of using fixed position schedules.","Because random-position interventions already reach 24.5–28.1 on GSM8K, a decisive follow-up would be to report the random-position gap on all eight benchmarks, not just GSM8K, to establish that the information-flow mask is load-bearing at scale.","The threshold $\\alpha$/ $\\beta$ is a single scalar shared across layers; an inference worth testing is whether per-layer or per-head thresholds, or a learned mask, would beat the union strategy without the equal-count constraint."],"forward_implications":["CRFT beats the fixed-position ReFT baseline on every reported model and most datasets while training half as many parameters at the same rank, so dynamic position selection is a viable replacement for hand-picked positions.","Training 0.016% of parameters on a single GPU for four hours on GSM8K with LLaMA-2-7B makes representation-level chain-of-thought fine-tuning practical where full or LoRA fine-tuning is not.","The few-shot variant, which learns separate update vectors for demonstrations and the question, lifts one-shot GSM8K accuracy from 16.2% to 32.6%, a 16.4-point gain.","Because intervening in the first half of layers gives the best results, early-layer critical representations appear to propagate task-relevant corrections through the whole chain, an advantage a fixed p7+s7 schedule does not exploit.","Attention-map visualization shows CRFT reduces the attention-sink at the initial token and broadens information flow, indicating part of the gain comes from redistributing rather than merely amplifying existing interactions."],"supporting_citations":[{"why":"ReFT is the baseline CRFT extends: it introduces editing fixed first and last seven representations per layer with a low-rank subspace update, the exact setup CRFT replaces with dynamic positions.","marker":"Wu et al., 2024b"},{"why":"pyvene is the intervention library used to run all experiments; the edits in Eq. 6 are implemented on it.","marker":"Wu et al., 2024c"},{"why":"Supplies the information-flow grid view of attention interactions that motivates both self-referential and multi-referential filtering.","marker":"Wang et al., 2023"},{"why":"Defines saliency scores, the gradient-weighted indicator used as an alternative to raw attention in Eq. 4.","marker":"Simonyan, 2013"},{"why":"RAVEL's low-rank subspace interventions are cited as the direct basis for the optimization form in Eq. 6.","marker":"Huang et al., 2024"},{"why":"GSM8K is the benchmark where the headline numbers (14.6%, 29.0%, 32.8%) are measured.","marker":"Cobbe et al., 2021"},{"why":"Documents the attention-sink phenomenon used to interpret CRFT's effect on information flow in Section 3.5.","marker":"Xiao et al., 2023"},{"why":"Supplies the Math10K and Commonsense170K training conventions that define the arithmetic and commonsense experimental scenarios.","marker":"Hu et al., 2023"}],"fun_headline_variants":["Attention flow finds critical states; CRFT lifts GSM8K 18 points","0.016% parameters trained, 18.2-point GSM8K jump via CRFT","Fixed-position ReFT underperforms; CRFT edits only critical states","CRFT: tiny parameter budget, big chain-of-thought reasoning gains","Critical-state fine-tuning boosts reasoning by 18.2 GSM8K points"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the attention or saliency threshold flags exactly the hidden states whose perturbation would flip the model's correctness; if the proxy misses those positions, CRFT is editing positions that random edits would improve almost as much.","fun_headline_variants_meta":{"raw":{"variants":["Attention flow finds critical states; CRFT lifts GSM8K 18 points","0.016% parameters trained, 18.2-point GSM8K jump via CRFT","Fixed-position ReFT underperforms; CRFT edits only critical states","CRFT: tiny parameter budget, big chain-of-thought reasoning gains","Critical-state fine-tuning boosts reasoning by 18.2 GSM8K points"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000496,"raw_usage":{"total_tokens":2459,"prompt_tokens":1001,"completion_tokens":1458,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":617,"completion_tokens_details":{"reasoning_tokens":1355}},"tokens_in":617,"tokens_out":1458,"duration_ms":13369,"temperature":1.0,"reasoning_tokens":1355,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:43:23.051776+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On the full benchmark suite, replace the attention and saliency filters with uniformly random positions at the same layer count, update budget, and rank, across at least three seeds. If the CRFT-minus-random margin is within a couple of accuracy points on most datasets—as Table 8 already shows is nearly the case on GSM8K—then the criticality filter is not the driver. A second check would measure the overlap between threshold-flagged positions and the oracle defined in Eq. 1 from input-level perturbations.","supporting_citations":[],"review_version":1}