{"id":"98ca6e3a-61a3-46e3-b2d6-09bcad7d3129","arxiv_id":"2608.11797","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In merged language models, task-vector interference is causally carried by the orientation of an internal cross-term, not by its magnitude, and instruction wrappers can hide this interference while the model still carries it.","lead":"This paper studies why combining two fine-tuned language models sometimes causes them to forget one of the skills. It finds that the real problem is not how much internal interference a merge creates, but the direction that interference points in; erasing along that direction removes interference, while equally large changes in other directions make it worse.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The additive counterfactual is shared by the intervention and the output estimand, and the depth-profile rebuttal does not rule out a construction-driven component.","rationale":"The reader's weakest assumption is exactly that both the intervention and the output estimand share the additive reconstruction, so a construction-driven component in D is possible. My stress-test sharpens this: the paper's depth-profile argument, which the reader cites as the main defense, does not actually refute the concern, because regrowth from untouched marginal paths is compatible with the baseline being arbitrary. The coefficient-mismatch control does not close the gap, since it is designed to have near-zero overlap with the erasure direction and therefore does not test the exact additive combination among directions with overlap 1. The Appendix I behavioral failure further weakens the claim that the removed non-additivity is functionally meaningful, although the paper honestly scopes the claim to expressed non-additivity. The paper remains strong in its internal controls, preregistration, numerical-validity audits, and cross-family replication, so I do not recommend rejection; a conditional verdict pending an independent baseline test is appropriate. The reader already issued CONDITIONAL, so no verdict change is needed. The concrete test I propose would settle the baseline question directly and could upgrade the claim to a firmer accept if it passes.","tokens_in":21707,"tokens_out":7608,"duration_ms":86534,"concrete_test":"Run a baseline-independence check: compute h_bar_l for every layer from the four unperturbed forward passes, then run the merged model with every block input clamped to h_bar_l (full-depth additive clamp) and compare the resulting next-token distribution to the logit-space additive prediction p_add used in R. If the clamped output is far from p_add (JSD comparable to the original interference ratio R), the additive reconstruction is not a self-consistent no-interference counterfactual, and D is biased.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The cross-term I_l is defined as the deviation from the additive reconstruction h_bar_l = h_A0 + h_0B - h_00 (Eq. 1), the erasure intervention replaces h_AB with exactly h_bar_l at the patched boundary, and the output estimand R measures non-additivity against the same logit-space additive prediction. Both the target and the outcome are therefore displacements from the same chosen origin. If h_bar_l is not the true no-interference counterfactual, then 'erasing along the cross-term direction' is just moving toward that origin, and D measures proximity to the baseline rather than removal of causally active interference. The paper's main rebuttal is the depth profile: D is near zero at early boundaries and large at late boundaries, in proportion to 1 - rho (Section 5). But this is exactly what a baseline-driven effect would look like when early patches are washed out by later network dynamics: the regrowth measurement shows the network restores the original I_l from the untouched marginal paths, so it cannot distinguish 'the network actively restores true interference' from 'the network's dynamics restore the original deviation from an arbitrary baseline.' The coefficient-mismatch control lies in the same affine span but was constructed to have near-zero overlap with -I_l, so it does not test whether the exact (+1,-1,+1) combination is special among directions with full overlap. Furthermore, the one behavioral endpoint independent of the additive counterfactual (Appendix I) failed to recover, so the interpretation of the removed non-additivity as functional interference is not independently corroborated. If the baseline is biased, the central causal contrast (14x-337x removable interference) could be a property of the chosen affine coordinate system rather than of the network.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies interference in merged language models through a factorial ledger that tracks the layerwise cross-term I_l = h_AB - h_A0 - h_0B + h_00 relative to the additive reconstruction hbar_l = h_A0 + h_0B - h_00. It separates local generation G_l from transport, intervenes on the cross-term by replacing the residual state with h_AB - lambda I_l, and measures expressed interference with an output-side interaction ratio R against the logit-space additive prediction. On Qwen2.5-1.5B, with reduced replications at Llama-3.2-1B and Qwen2.5-7B, the paper reports that transport dominates generation (~65-70%), that erasure along the cross-term direction removes expressed interference dose-dependently while norm-matched controls fail or backfire, that the carried direction is rebuilt by propagation except near the output, and that instruction wrappers amplify internal cross-terms while suppressing their expression. The paper also documents that naive bf16 estimates of local generation are largely quantization roughness, and it reports 46 preregistered predictions with explicit falsifications.","tokens_in":21921,"tokens_out":13429,"duration_ms":140619,"significance":"If the central causal interpretation is accepted, this is a substantial contribution: it is the first activation-level causal intervention on task-vector cross-terms that I am aware of, with unusually careful numerical audits (bitwise determinism nulls, propagated-ULP floors, float32 causal runs), a frozen preregistration chain, controls with disclosed overlaps, and replications across three model points. The bf16 quantization-roughness caution is a valuable standalone methodological warning. The paper is also unusually honest in reporting falsified predictions, including two of three headline expectations. However, the intervention and the primary output estimand share the same additive counterfactual, and the only behavioral endpoint that is independent of that counterfactual (Appendix I) returns a negative result. The paper's broader claims about task-vector interference therefore need either an independent validation of the additive baseline or an explicit narrowing of the claims to the additive-reconstruction definition of interference.","major_comments":[{"comment":"The intervention target and the primary output estimand share the same additive counterfactual. Eq. (1) defines I_l as the deviation of h_AB from hbar_l = h_A0 + h_0B - h_00; the erasure h_AB - lambda I_l is a displacement toward that same hbar_l; and the output estimand R in Eq. (3) measures non-additivity against the logit-space additive prediction l_A0 + l_0B - l_00. D therefore measures, at least in part, whether moving the state toward hbar_l moves the output toward the additive logit prediction. If hbar_l is not the true no-interference counterfactual, D can be construction-driven. The depth-profile rebuttal in Section 5 does not fully rule this out: the regrowth statistic I_post is itself formed against the same hbar-based marginals, so convergence of I_post to I_orig is convergence to the original deviation from that baseline, and the coefficient-mismatch control lies in the same affine span, testing the specialness of the (+1,-1,+1) combination rather than the validity of the span's origin. The one endpoint that does not share the additive counterfactual—the teacher-forced NLL of Appendix I—gives a negative result, so the independent validation is absent. Please either (i) supply an independent test of the baseline, for example a family of alternative references (h_A0+h_0B, h_A0+h_0B-2h_00, or a third-task-derived reference) and show that the dose-response, saturation at lambda=1, and pair contrast are unique to the additive reference; or (ii) explicitly frame the conclusions as being about the additive-reconstruction definition of interference and adjust the abstract and title accordingly.","section":"§3.2–§3.4, Eqs. (1)–(3)"},{"comment":"The 'arithmetic exclusion' is computed from ||G_l|| evaluated at the common reference hbar_l, but in the actual forward pass the state at layer l is not hbar_l, so the effective per-layer injection at that layer is the regeneration operator G_l + M_l of Eq. (4), which the paper itself separates from G_l. The observed ratio ||I_28|| / sum_l ||G_l|| = 2.6 therefore excludes only injection accounts that repeatedly evaluate generation at the reference state; it does not exclude state-dependent generation accounts whose increments are G_l + M_l. Since the transport share is an exact identity only relative to the chosen hbar, this limitation also propagates to the 'transport carries ~69%' claim. Please either recompute the bound with the actual regeneration magnitudes and report that result, or weaken the 'no per-layer injection account survives' wording to what the bound can actually support.","section":"§4.2 and Appendix E"},{"comment":"The headline contrast '14x-337x' is not stable. The 337x value comes from a seed whose D(code+math) is 0.0001, i.e. indistinguishable from zero, and the text acknowledges the near-zero denominator. The robust range from the other seeds is about 14-30x (or 18-52x in unnormalized JSD, again with one seed indistinguishable from zero). Because this contrast is the paper's central quantitative claim, please report the stable range as the headline, state the unstable seed separately, and avoid repeating the 337x figure in the abstract and Section 1 without this qualification.","section":"§5, final paragraph; also abstract and §1"}],"minor_comments":[{"comment":"The text says erasure removes 'roughly 19%' of expressed interference, but with R = 10.33% for code+safety and D = 0.0301 the implied fraction is about 29%; please reconcile the numbers or define the reference R used for the 19% figure.","section":"Abstract and §5"},{"comment":"The caption refers to 'the strongest composition point' without a definition; the text should state that this is the frozen point (1,1) or define the location explicitly.","section":"Figure 1 caption"},{"comment":"The phrase 'norm-matched to the global core-median norm' is not defined; please specify the normalization procedure and whether the median is computed over task vectors, adapters, or something else.","section":"§3.1"},{"comment":"The paper states that all 46 predictions were preregistered before their data, but the P1-P6 memo was written after two pilot cells; since no confirmatory prediction was added after its own outcome data, this is acceptable, but please state the pilot-cell timing in the main text rather than only in the appendix.","section":"§B, P1-P6 memo"},{"comment":"The statement that paired contrasts 'survive' the bf16 rounding floor should be quantified: the claim that the floor is condition-independent and cancels in differences is asserted, but no explicit paired-contrast audit is reported for the main sweep.","section":"§4.1"}],"recommendation":"major_revision","confidential_remarks":"The central evidential weight rests on the claimed frozen preregistration and immutable cell records. Please have the editor request the full freeze log, verdict documents, and code for review; without them, the preregistration claims cannot be independently assessed. The companion measurement paper [Zhu, 2026] supplies several baseline output-side facts, and its status should be clarified because the present paper imports those numbers directly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one; it is more careful than most merging papers and it makes a real empirical claim. The genuinely new pieces are the exact layerwise transport/generation decomposition, activation-level cross-term erasure with four norm-matched controls, and the demonstration that instruction wrappers gate expression while amplifying internal cross-term. The bf16 result—most naive local generation is rounding roughness—is a standalone caution worth citing. I also give credit to the preregistration practice: fourteen main predictions with priors, falsifications reported, replications on a second family and at 7B. That is not theater; it is reproducible work.\n\nThe causal core mostly holds up. The dose-response along the correct direction saturates near lambda=1, the cross-prompt control backfires monotonically, and wrong-pair/coefficient-mismatch controls fail or backfire. The depth profile (early erasure does nothing, late erasure does almost everything, in line with 1-rho) is a good internal control. I am not convinced the shared additive counterfactual is a fatal flaw, but it is the soft spot. Both the erasure target and the output estimand define 'interference' as deviation from the same linear combination h_A0+h_0B-h_00. The depth-profile rebuttal is reasonable but not airtight: a baseline-driven effect could also be washed out early and dominate late if that baseline is not the true no-interference state. The one independent endpoint tried—teacher-forced NLL—passed its validity gate but falsified behavioral recovery; the paper honestly says erasure controls expressed non-additivity, not expert-likeness. That honesty is good, but it means independent corroboration is missing. I would want either a validated independent baseline or a second behavioral endpoint before citing the 14x-337x as a fact. The three-seed outer unit and the missing code URL/commit hash are minor; the two-pair central contrast is worth flagging.\n\nFor model merging and mechanistic interpretability readers, this is a real contribution that deserves serious peer review—not desk rejection. I would send it out, asking the authors to release the artifact and push harder on independent validation. It will also make a good reading-group discussion about counterfactuals and preregistration.","headline":"A careful, preregistered empirical paper that makes a real case for direction over magnitude in task-vector interference, with one shared-counterfactual caveat that keeps me at conditional rather than full accept.","tokens_in":22535,"tokens_out":2653,"would_cite":true,"duration_ms":28584,"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":"In merged language models, task-vector interference is carried and amplified along a stable direction that the forward pass actively rebuilds and the prompt format gates at expression; magnitude is at best a coarse, sometimes inverted…","keywords":["model merging","task arithmetic","cross-term interference","causal intervention","direction specificity","expression gating","instruction templates","quantization roughness"],"falsifier":"Build the cross-term against an independently validated no-interference baseline — for example, a single model trained from the same base on both tasks jointly, or a merge of provably non-interacting adapters — and repeat the erasure dose–response; the claim collapses if removing the cross-term against that baseline no longer removes expressed interference dose-dependently, or if any norm-matched wrong-direction control removes as much as the correct direction. A second direct check: find any layer or condition where an early-depth erasure persists downstream (regrowth ratio well below 1) or where the cross-term fails to reconverge in direction from a structured starting displacement, since the attractor mechanism predicts reconvergence everywhere except where depth runs out.","tokens_in":21445,"feed_emoji":"🧭","tokens_out":16036,"duration_ms":128091,"temperature":0.7,"pith_summary":"This paper claims that when two task vectors are added to a base language model, the functional interference between them is determined not by how much cross-term the network produces but by the orientation of that cross-term and what the forward pass does with it. Tracking an exact layerwise cross-term — the four-corner difference between the merged model's hidden states and the two single-task states plus the base — the paper finds that propagation transports and amplifies the existing term (roughly 65–70% of the layerwise flux, gain above 1 per late block), actively rebuilds it after erasure, and treats the carried direction as an attractor. Erasing along that direction removes expressed interference dose-dependently and saturates near full erasure, while norm-matched wrong-direction controls fail or backfire, and the same erasure finds 13× less removable interference under an instruction wrapper that internally amplifies the cross-term — so wrappers gate expression rather than removing the interference. If the paper is right, merging diagnostics should track the direction that survives propagation, format-wrapped evaluations read the gate rather than the interference, and the apparent ±15% 'universality' of naive bf16 estimates dissolves into quantization roughness.","feed_headline":"Direction, not magnitude, decides merge interference","feed_subtitle":"Erasure along the carried direction removes interference that magnitude metrics cannot see; wrappers hide it.","key_machinery":"The load-bearing object is the layerwise cross-term $I_\\ell = h_\\ell^{AB} - h_\\ell^{A0} - h_\\ell^{0B} + h_\\ell^{00}$ — the four-corner 'factorial ledger' difference between a merged model's residual state at the input of block $\\ell$ and the two single-task states minus the base state — which is exactly the residual of the additive reconstruction $\\bar{h}_\\ell = h_\\ell^{A0} + h_\\ell^{0B} - h_\\ell^{00}$. Three instruments carry the argument. First, an exact decomposition $I_{\\ell+1} = G_\\ell + T_\\ell + M_\\ell$ separates newly generated cross-term from transport of the existing term and measures the per-block gain. Second, cross-term erasure $h_\\ell^{AB} - \\lambda I_\\ell$ at frozen depths, with four norm-matched structural controls (wrong-pair, coefficient-mismatch, cross-prompt, random), makes the direction the only varying quantity; the causal readout is the change $D = R_{\\text{original}} - R_{\\text{patched}}$ in the expressed-interference ratio, with the unpatched main-effect denominator frozen so the dose–response moves for exactly one reason. Third, regrowth and basin tests track the term downstream of erasure, establishing that propagation restores the carried direction in norm and orientation — the attractor property that explains why only late erasures produce durable causal effects.","core_discovery":"At every block of a merged model the paper defines the cross-term $I_\\ell = h_\\ell^{AB} - h_\\ell^{A0} - h_\\ell^{0B} + h_\\ell^{00}$, the exact non-additive residue of merging, and asks what each block generates versus what it carries. The discovery is that the flux is transport-dominated: an exact decomposition $I_{\\ell+1} = G_\\ell + T_\\ell + M_\\ell$ attributes about 69% of the flux to transport of the existing term, with amplification above 1 per late block, and erasing the term early is undone by propagation — it regrows to about 99% of its norm at direction cosine 0.99, and six norm-matched starting displacements all reconverge, so the carried direction behaves as an attractor of the forward pass. Causally, erasing along that direction, $h_\\ell^{AB} - \\lambda I_\\ell$, removes expressed interference dose-dependently and saturates near $\\lambda \\approx 1$ (restoring the additive reconstruction), while wrong-pair, coefficient-mismatch, cross-prompt, and random controls fail or backfire in proportion to their projection on the erasure direction. The same erasure removes roughly 19% of expressed interference on raw prompts but 13× less under an instruction wrapper, even though the wrapper amplifies internal cross-term generation 1.7–1.8×, because the template pins the output distribution and drowns the interaction in the main effect. As a result, task pairs whose local generation magnitudes differ by at most 1.9× differ by 14×–337× in causally removable interference, and the apparent ±15% uniformity of naive bf16 generation turns out to be 75–90% quantization roughness; the paper reports all forty-six predictions as frozen before their data, with falsifications of its own expectations reported as falsifications.","pith_inferences":["If the attractor reading is correct, the cross-term direction is maintained by the marginal single-task paths rather than stored in the merged weights; a testable extension is that the same attractor direction should reappear regardless of coefficient order or composition-grid position, making directional signatures of interference roughly invariant to which task pair is merged first.","The gating result implies that format choice is not a neutral evaluation variable: two evaluations of the same merge can disagree by roughly 20× while internal states remain nearly identical, so comparative claims about merged-model quality should be reported raw and wrapped, or explicitly format-scoped.","Since the causal effect tracks the projection $\\cos(\\delta, -I_\\ell)$ of the displacement on the erasure direction, a cheap held-out predictor may exist in the alignment between the carried cross-term direction and the output readout direction; the paper's own direction features failed, but they were norm-contaminated, so a cleaned alignment feature is a natural next test.","The quantization-roughness result is a caution for the broader literature: layerwise linearity or interference measurements computed at bf16 may be partly flooring artifacts, and re-auditing such estimates in float32 is a cheap decisive check."],"forward_implications":["Erasure-style mitigation must act near the output: early erasures (depths 3–8) are rebuilt by propagation and show $D \\approx 0$, whereas late erasures (depths 20–25) carry the full effect, so removable interference is exactly what the remaining depth cannot reconstruct.","The magnitude family of diagnostics — local generation, cumulative cross-term norm, parameter cosine, and representation bias — is at best a coarse pair-level correlate and is inverted on the format axis; none of them sees the roughly 20× expression collapse under instruction wrappers, so format-wrapped evaluations of merged models read the gate, not the interference.","Pair difficulty in merging is decided by the orientation of the carried cross-term, not its size: pairs within 1.9× in local generation differ by 14×–337× in what erasure can remove, so causally removable interference is the quantity that separates task pairs.","Activation-difference analyses run at training precision can be dominated by quantization roughness: the ±15% bf16 'universality' band is 75–90% weight-rounding artifact, so such estimates need per-estimator precision audits before interpretation.","The directional mechanism transfers across model families and scales — it replicated at all three model points — while magnitude behavior does not, so 'universal' claims built on magnitude should be treated as family-specific."],"supporting_citations":[{"why":"Supplies the task-vector merging operation whose failures this paper intervenes on.","marker":"[Ilharco et al., 2023]"},{"why":"Companion measurement study providing the protocol, adapters, and the output-side expressed-interference estimand with its 20× format collapse.","marker":"[Zhu, 2026]"},{"why":"Defines Cross-Task Linearity, whose layerwise residual is exactly the cross-term $I_\\ell$ that this paper intervenes on.","marker":"[Zhou et al., 2024]"},{"why":"Frames the multi-mediator caveats for activation patching that motivate the norm-matched controls and overlap accounting.","marker":"[Vaidyanathan et al., 2026]"},{"why":"Supplies the representation-bias magnitude metric (SurgeryV2) that the paper measures and finds blind to the gate.","marker":"[Yang et al., 2024]"},{"why":"Documents behavior-level instruction-format fragility that the expression-gating result is the mechanism-level counterpart of.","marker":"[Huang et al., 2026]"},{"why":"Provides the parameter-space direction metric (task singular vectors) that the paper tests and finds weak on held-out pairs.","marker":"[Gargiulo et al., 2025]"},{"why":"Prior parameter-level causal intervention that the activation-level cross-term erasure contrasts with.","marker":"[Kong et al., 2024]"}],"fun_headline_variants":["Direction, not magnitude, drives merge interference","Erase the direction, kill the interference: magnitude fails","The causal lever in model merging is direction, not size","Task-vector interference: it's about direction, not magnitude","Direction is an attractor: erasing it removes merge interference"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the additive reconstruction $\\bar{h}_\\ell = h_\\ell^{A0} + h_\\ell^{0B} - h_\\ell^{00}$ is what a no-interference merge would produce at every layer: the cross-term is defined as the deviation from this linear combination, the erasure restores states to it, and if that counterfactual is wrong the 'direction' being studied is a biased displacement and the causal conclusions could reflect the baseline chosen rather than the network's causal structure.","fun_headline_variants_meta":{"raw":{"variants":["Direction, not magnitude, drives merge interference","Erase the direction, kill the interference: magnitude fails","The causal lever in model merging is direction, not size","Task-vector interference: it's about direction, not magnitude","Direction is an attractor: erasing it removes merge interference"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00044,"raw_usage":{"total_tokens":2401,"prompt_tokens":1283,"completion_tokens":1118,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":899,"completion_tokens_details":{"reasoning_tokens":1038}},"tokens_in":899,"tokens_out":1118,"duration_ms":11319,"temperature":1.0,"reasoning_tokens":1038,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:26:37.240157+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build the cross-term against an independently validated no-interference baseline — for example, a single model trained from the same base on both tasks jointly, or a merge of provably non-interacting adapters — and repeat the erasure dose–response; the claim collapses if removing the cross-term against that baseline no longer removes expressed interference dose-dependently, or if any norm-matched wrong-direction control removes as much as the correct direction. A second direct check: find any layer or condition where an early-depth erasure persists downstream (regrowth ratio well below 1) or where the cross-term fails to reconverge in direction from a structured starting displacement, since the attractor mechanism predicts reconvergence everywhere except where depth runs out.","supporting_citations":[],"review_version":1}