{"id":"fc43b95c-f6cd-4a66-bebb-415a8e573afd","arxiv_id":"2501.02009","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A single linear transformation aligns concept representations between different LLMs, so steering vectors transfer across models and even from small to large models.","lead":"Steering vectors, which capture concepts inside one large language model, can be carried into a different model by a simple linear map learned from ordinary sentence representations. The authors test this on three open models and eleven concepts, and report that the map also works for concepts it was not built for and that vectors from a 0.5B model can steer a 7B model.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Behavioral steering after OLS transfer is indirect evidence; the paper never checks whether the transformed source SV actually matches the target's own concept direction, leaving Eq. (3.2)'s geometric claim underdetermined.","rationale":"The reader's weakest assumption was that the OLS map is meaningful only if behavioral steering works, and that successful activation addition could occur for other reasons. My concern is the same soft spot made more precise: the paper's central claim is about representation geometry, but the reported evidence is entirely behavioral. The random-T ablation is a useful control, but it is not matched in norm or orientation, so it cannot falsify the alternative that a large unaligned vector at the chosen layers would also steer behavior. A direct geometric comparison between transformed SVs and the target model's own SVs is the missing experiment that would settle the concern. This does not change the reader's conditional verdict; it sharpens the condition that should be attached to acceptance. The paper has real strengths: a simple and reproducible method, ablations against random T and no-T, and results across eleven concepts. But the interpretation as 'platonic representations' aligned by a linear map should remain conditional until direct geometric evidence is provided. I therefore keep the verdict as CONDITIONAL/UNCHANGED and propose the concrete cosine-similarity test as the decisive check.","tokens_in":22575,"tokens_out":4658,"duration_ms":48713,"concrete_test":"Recompute all RQ1 transfers (Section 4.2) as follows: for each source-target pair, compute the target model's own reference SV on held-out contrastive pairs from the same CAA/RepE dataset, using identical extraction layers. Then compute the normalized alignment between the transformed source SV and the target's own SV, e.g., cosine similarity after mean-centering, and compare it against (a) random T with matched input and output norms, (b) random directions with the same L2 norm as the transformed SV, and (c) T learned from a different concept. If the transformed SV is not substantially closer to the target's own SV than all three controls, the representational-alignment claim of Eq. (3.2) is unsupported, regardless of behavioral outcomes. Report the distribution over all concepts and all six directed transfers.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is geometric: after OLS, Eq. (3.2) asserts that the transformed source SV equals the target model's concept direction. The paper's only support is behavioral: adding beta times the transformed vector changes target outputs, with a random-T ablation. That underdetermines the claim. Activation addition at layer ranges such as 9-27 (Appendix C) is a coarse intervention; a target model may be steerable by many non-aligned directions, especially when beta is hand-tuned per condition, concept, and source-target pair (Tables 5-6). The random-T control is not matched: a matrix with random entries produces a vector of uncontrolled norm and orientation, so failure of random T does not rule out the possibility that any sufficiently large, unaligned vector in a 'steerable' region explains the result. The paper never reports cosine similarity or normalized distance between the transformed source SV and the target model's own SV for the same concept. Without such a direct geometric check, successful behavior transfer could be due to generic target steerability rather than to alignment of concept representations. This is load-bearing because the paper's title, abstract, and Section 6 conclusions are about shared representation geometry, not merely about a steering recipe.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes L-Cross Modulation, a method for transferring steering vectors (SVs) between LLMs by learning a linear map T via ordinary least squares between the hidden-state spaces of a source and a target model. The transformed SV is then added to the target's hidden states with a scaling factor β to modulate its behavior. The authors evaluate on eleven benchmark concepts across three LLMs and report three findings: (1) cross-model SV transfer effectively controls the target; (2) the same T generalizes across concepts; and (3) SVs from a weak model (Qwen2-0.5B) can steer stronger models (e.g., Qwen2-7B) to produce harmful content. Ablations show that a random transformation and direct cross-model addition without T are largely ineffective.","tokens_in":22739,"tokens_out":7828,"duration_ms":72160,"significance":"If the claims hold, this is a valuable contribution to interpretability: it provides evidence for a linear shared geometry of concept representations across LLMs, directly relevant to the Platonic Representation Hypothesis, and it offers a practical recipe for cross-model safety control. Strengths include the use of established CAA/RepE datasets and metrics, the out-of-sample generalization tests (cross-concept and weak-to-strong), and the explicit ablation of T. However, the central geometric claim is currently supported only by indirect behavioral evidence, and the statistical support is incomplete.","major_comments":[{"comment":"The paper's central claim, formalized in Eq. (3.2), is that the transformed source SV equals the target model's own concept direction. The evidence presented is behavioral: adding β times the transformed vector changes target outputs, and a random-T ablation fails. This underdetermines the geometric claim. Random T is not a matched control because it does not preserve the norm or orientation of the transformed vector; with layer ranges as broad as 9–27 (Table 5) and β hand-tuned per condition, concept, and source–target pair (Tables 5–6), many non-aligned directions could plausibly steer the target. The authors should directly measure the alignment between the transformed source SV and the target's own SV for the same concept, e.g., reporting cosine similarity or normalized distance, compared with baselines such as untransformed source SVs and norm-matched random T. Without such a check, the title and Section 6 conclusions about shared underlying structure go beyond what the behavioral experiments establish.","section":"§4.2, Eq. (3.2)"},{"comment":"All headline results are point estimates at manually selected β, with no confidence intervals. Since each evaluation uses 50 items (Appendix B), proportions such as the harmful-output rates in Table 1 have large binomial uncertainty; the aggregate failure counts (4/216 in §4.2, 17/216 in §4.3) similarly lack variance estimates. Without intervals, the reader cannot judge whether the gap between L-Cross Modulation and No Modulation is reliable, nor whether the claimed superiority over Self Modulation in 31/42 and 7/12 cases is within noise. Please report bootstrap confidence intervals or per-item scores for the main comparisons.","section":"§4.1, Tables 1 and 3"},{"comment":"The random-T ablation is not a valid control for the role of T. A matrix with random entries produces a transformed vector with uncontrolled norm and orientation; its failure does not rule out the possibility that any sufficiently large, unaligned vector in the chosen layer range produces the observed behavior. Moreover, the w/o T variant is only tested on the same-dimensionality pair (Llama2 and Llama3.1), leaving the role of T for Qwen2 targets unablated. The authors should use matched random directions (same output norm as the learned T, or random orthogonal matrices) and include all three target models.","section":"§4.2, Table 2"}],"minor_comments":[{"comment":"The OLS problem has no intercept term. The authors should state whether representations were mean-centered; if not, adding a bias term or centering is a standard part of a linear alignment and is likely to improve the fit.","section":"§3, Eq. (3.1)"},{"comment":"t-SNE is a nonlinear dimensionality reduction that preserves local structure; using it to infer global linear relationships such as rotation, scaling, and flipping is not methodologically sound. The quantitative T-similarity measures in Table 4 are more appropriate and should be the primary evidence for the geometric claim.","section":"§4.3, Figure 3"},{"comment":"The weak-to-strong claim in the abstract is supported in the main text only by the harmfulness concept; the additional concepts in Appendix E are shown only as plots. Please include numeric results so that the generality of the claim can be verified.","section":"§4.4, Figure 4"},{"comment":"The manuscript does not include a code availability statement. Since L-Cross Modulation is a simple OLS procedure, releasing the implementation would improve reproducibility.","section":"General"},{"comment":"Typos and wording issues: 'Crorss Modulation' in Table 2, 'adoptd' in Section 2, 'services as a foundation' in the Introduction, and 'L-Corss Modulation' in Appendix D should be corrected.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses an interesting question and the experimental design is mostly sound, but the central geometric interpretation is underdetermined by the current behavioral evidence. The required additions—direct SV alignment measurements, matched random controls, and uncertainty quantification—are feasible within the scope of a revision and would substantially strengthen the paper. I do not see a need for rejection; the flaws are fixable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: solid, workmanlike empirical paper. The real headline is the weak-to-strong transfer: a harmfulness SV from Qwen2-0.5B, mapped through an OLS matrix, steers Qwen2-7B to 88% harmful outputs. That, plus the finding that one T generalizes across eleven concepts, is genuinely new as a package. The method is standard OLS on paired sentence representations—the authors don’t oversell the trick—and the ablations (no T, random T) show the learned T is doing the work. Credit where due: held-out behavioral evaluation, multiple models, honest limitations section that admits beta is manually tuned.\n\nSoft spots. The central geometric claim—Eq. 3.2, that the transformed source SV equals the target’s concept direction—is never directly checked. No cosine similarity or normalized distance between transformed source SV and the target’s own SV for the same concept is reported. The only support is behavioral: add beta times the vector, outputs change, and a random-T control fails. But random T creates a vector with uncontrolled norm and orientation, so its failure doesn’t rule out generic target steerability, especially since beta is hand-tuned per condition and source-target pair (Tables 5-6). A 50-item evaluation with no confidence intervals makes this shakier. Also, only three similar-scale chat models plus one 0.5B are tested, so the 'universal concept geometry' wording goes beyond the data. The paper itself concedes the beta issue but not the missing geometric check.\n\nI don’t think these problems are fatal. The transfer phenomena are probably real, and the weak-to-strong result is practically useful for safety and interpretability. But the Platonic framing is stronger than the evidence. A referee should ask for the direct geometric check and the code (not released). With that, this would be a solid contribution. Without it, it reads as a steering recipe with a philosophical headline.\n\nBottom line: send it to review, with a request for those additions. It deserves referee time. I’d also bring it to a reading group—the gap between behavioral and geometric claims is a good discussion.","headline":"Useful empirical study of linear SV transfer across LLMs; the weak-to-strong result is real, but the geometric claim outruns the behavioral evidence.","tokens_in":23360,"tokens_out":3312,"would_cite":true,"duration_ms":33146,"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":"A single linear map transfers steering-vector control between different LLMs, including from a 0.5B model to a 7B model.","keywords":["steering vectors","cross-model transfer","linear representation hypothesis","LLM interpretability","weak-to-strong transfer","concept alignment","activation steering","Platonic Representation Hypothesis"],"falsifier":"Take a target model whose self-modulation is known to work strongly, learn $T_D$ on a corpus disjoint from the test concept, and sweep $\\beta$ and layers with a transferred vector; if the transferred vector's effect is indistinguishable from a random matrix of the same norm while the target's own vector still steers, then the OLS alignment is not carrying the concept and the claimed geometry is an artifact of activation addition.","tokens_in":22312,"feed_emoji":"🧠","tokens_out":10841,"duration_ms":97253,"temperature":0.7,"pith_summary":"Different large language models, trained on different data, appear to represent the same concept as a direction in their hidden states, and these directions can be aligned from one model to another by a single learned linear map. The paper shows that a steering vector extracted from one model, multiplied by this map, can modulate another model's text generation toward the same concept, across eleven concepts including harmfulness, happiness, fear, fairness, and sycophancy. The same linear map works for many concepts, and steering vectors from a 0.5B model can control a 7B model, suggesting that LLM concept spaces share a roughly linear, common structure rather than being idiosyncratic to each model. If this is right, behavior-control vectors and concept probes could be built once and reused across model families and scales.","feed_headline":"Steering vectors transfer between LLMs with one linear map","feed_subtitle":"Concept controls learned on one model work on another, even from a 0.5B model to a 7B model.","key_machinery":"The load-bearing object is the transformation matrix $T_D$, fitted by ordinary least squares on paired representations from a shared corpus, and applied to steering vectors through Eq. (3.2), $\\bar{\\lambda}_W^{m_t} = \\bar{\\lambda}_W^{m_s} T_D$. Steering vectors are concept directions in hidden-state space, defined either as the mean difference of contrastive text pairs (CAA) or as their first principal component (RepE). $T_D$ does the argument's work: if one map aligns many different concept directions, and does so for concepts not used to fit it, then the two models' concept geometries are related by a single linear change of coordinates. The paper supports that conclusion with the numerical similarity of $T$ matrices fitted on different concepts and with t-SNE visualizations that show the mapped representations behaving like rotated, scaled, or flipped versions of the source representations.","core_discovery":"The paper sets out to show that the concept geometry of one LLM can be transplanted into another by a linear map: a steering vector $\\bar{\\lambda}_W^{m_s}$ for concept $W$ in source model $m_s$ becomes a steering vector for the same concept in target model $m_t$ as $\\bar{\\lambda}_W^{m_t} = \\bar{\\lambda}_W^{m_s} T_D$, where $T_D$ is obtained by ordinary least squares regression of the two models' representations of a shared corpus $D$. The claim is that this single matrix aligns concept directions across models well enough that the transformed vector changes target-model behavior toward the intended concept, that the same $T_D$ generalizes to concepts whose data played no part in fitting it, and that the alignment holds from a 0.5B model to a 7B model. On eleven benchmark concepts across Llama2, Qwen2, and Llama3.1, the paper reports that cross-model modulation is on par with each model's own self-modulation in most cases, and that removing or randomizing $T$ destroys the effect.","pith_inferences":["Editorial extension: because only paired text representations are needed to fit $T_D$, the same procedure should port other linear objects, such as classifier probes or semantic axes, from one model to another; testing on held-out probes would show whether the alignment is a property of geometry rather than of steering alone.","The paper leaves implicit that weak-to-strong transfer turns small open models into control surfaces for larger or closed ones, since a user needs the small model's weights and a few hundred paired sentences from the target, not the target's weights.","A safety consequence the authors do not emphasize: if harmful-direction transfer succeeds this easily, a refusal or safety intervention that works on one family may be bypassable in another family by transferring a small model's harmful vector through $T_D$; this is testable with an alignment evaluation like HarmBench.","The Platonic claim could be quantified by measuring how much of the target model's behavioral variance a single $T_D$ explains across layers, families, and scales; a systematic decrease in residual error with model scale would support the convergence-to-shared-reality reading."],"forward_implications":["If correct, a steering-vector library built once on one open model can be ported to other model families without retraining, because cross-model modulation matches self-modulation in most tested configurations.","Because one transformation matrix per model pair transfers many concepts, concept-specific tuning of the map is unnecessary; only the scaling factor $\\beta$ needs per-concept adjustment.","Weak-to-strong transfer implies that concept diagnostics and behavior controls can be developed on a small, inexpensive model and applied to a larger model from the same family, without modifying the larger model's weights.","The linearity of the transfer reinforces the linear representation hypothesis: concept directions are geometric objects that survive a change of coordinates between models."],"supporting_citations":[{"why":"Defines contrastive activation addition, the steering-vector extraction used for the seven CAA concepts and their evaluation.","marker":"Rimsky et al., 2024"},{"why":"Defines representation engineering, supplying the other steering-vector method and the four RepE concepts, including harmfulness.","marker":"Zou et al., 2023a"},{"why":"States the Platonic Representation Hypothesis that motivates the paper's expectation of shared concept geometry.","marker":"Huh et al., 2024"},{"why":"Formalizes the linear representation hypothesis that concepts correspond to directions in hidden-state space.","marker":"Park et al., 2024"},{"why":"Explains the origin of linear representations in LLMs, grounding why concept directions should survive coordinate changes.","marker":"Jiang et al., 2024"},{"why":"Provides the Llama2-7B backbone used as a source and target model in the transfer experiments.","marker":"Touvron et al., 2023"},{"why":"Provides the Qwen2 backbones, including the 0.5B/7B pair that makes the weak-to-strong result testable.","marker":"Yang et al., 2024"},{"why":"Provides Llama3.1-8B, a third model family for testing transfer across architectures and training dates.","marker":"Dubey et al., 2024"},{"why":"Supplies the HarmBench classifier used to score whether transferred harmfulness vectors actually produce harmful outputs.","marker":"Mazeika et al., 2024"}],"fun_headline_variants":["One linear map transfers concept steering across LLMs","0.5B model's steering vector controls a 7B model","Cross-model concept alignment via a single linear transformation","One matrix aligns LLM concepts: transferable steering vectors"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument rests on the premise that adding a scaled, transformed vector to a target model's hidden states actually steers that model's behavior along the intended concept, so a behavior change after transfer counts as evidence that the two concept directions are aligned.","fun_headline_variants_meta":{"raw":{"variants":["One linear map transfers concept steering across LLMs","0.5B model's steering vector controls a 7B model","Cross-model concept alignment via a single linear transformation","One matrix aligns LLM concepts: transferable steering vectors"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000622,"raw_usage":{"total_tokens":2885,"prompt_tokens":949,"completion_tokens":1936,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":565,"completion_tokens_details":{"reasoning_tokens":1870}},"tokens_in":565,"tokens_out":1936,"duration_ms":12484,"temperature":1.0,"reasoning_tokens":1870,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:32:41.210955+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a target model whose self-modulation is known to work strongly, learn $T_D$ on a corpus disjoint from the test concept, and sweep $\\beta$ and layers with a transferred vector; if the transferred vector's effect is indistinguishable from a random matrix of the same norm while the target's own vector still steers, then the OLS alignment is not carrying the concept and the claimed geometry is an artifact of activation addition.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"States the Platonic Representation Hypothesis that motivates the paper's expectation of shared concept geometry."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Formalizes the linear representation hypothesis that concepts correspond to directions in hidden-state space."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Explains the origin of linear representations in LLMs, grounding why concept directions should survive coordinate changes."}],"review_version":1}