{"id":"514e4aa1-0d59-4368-bd40-281912b3ac92","arxiv_id":"2607.03065","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Subspace-Aligned Rewiring projects RL weight updates onto the base model’s SVD basis, retaining a compact rewiring matrix that preserves reasoning and improves exploration and multi-domain merging.","lead":"RL post-training updates for LLMs can be projected onto the base model’s SVD subspace to keep a tiny “reasoning core” and discard the rest. That post-hoc edit often preserves accuracy, improves multi-sample exploration, and reduces multi-domain interference without retraining.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Rank post-selection and missing uncertainty make the “compact spectral core preserves >99% of RL gains” claim fragile under fixed-budget evaluation.","rationale":"The reader correctly flags that discarding ΔW⊥ is only safe inside an elicitation regime and that boundary cases in §5/App. D limit the claim. That is real, but the paper already scopes those cases. The more load-bearing internal soft spot for the strongest claim as stated is evaluation design: rank is swept until performance is preserved, then that selected rank is reported as evidence of compactness and near-full recovery. Ablations (App. E/F) help show spectral alignment beats pure low-rank or random projection, and multi-scale/multi-setting results are non-trivial, so I do not move to REJECT. I keep CONDITIONAL and agree the paper should not be accepted as-is without tighter rank protocol, uncertainty, and public artifacts. My concern is more about how strongly Table 1/2 support the geometric recovery claim than about whether ΔW⊥ is sometimes necessary knowledge.","tokens_in":18191,"tokens_out":669,"duration_ms":18162,"concrete_test":"Re-evaluate Table 1 and Fig. 2 with a single fixed rank budget (e.g., 1% of spectral rank for every model) chosen before looking at AIME, report mean±std over ≥3 independent sampling seeds (or bootstrap CIs on AVG@32/Pass@k), and include the no-projection control at that same fixed budget. If any model drops >2–3 absolute points below full RL or loses the high-k crossover under fixed rank + uncertainty, the compact-core claim weakens.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central operational claim is that ΔW* = U(U⊤ΔW V)V⊤ (Eq. 5 / Alg. 1) recovers nearly all measured RL reasoning gains inside Sr(W0) with a tiny rewiring matrix M. Table 1 reports the smallest rank found by a per-model rank sweep that already preserves full-RL AIME within evaluation variance (1% for DeepScaleR/OLMo-32B, 10% for POLARIS, 30% for OLMo-7B-Base). That is post-selection on the same benchmarks used to claim preservation, not a fixed a priori budget. Without multi-seed variance, confidence intervals, or a pre-specified rank rule, the “>99% of peak Pass@1 with ~0.58% of parameters” headline can be an artifact of choosing the first rank that matches the target rather than evidence that the spectral core is intrinsically that compact. Appendix D already shows incompleteness outside the elicitation regime (JustRL long training, direct code RL); if the same post-selection is required even inside the claimed regime, the geometric hypothesis in §2.2 is only weakly supported as a general recovery principle.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.5","summary":"The paper proposes Subspace-Aligned Rewiring (SAR), a post-hoc edit of full-parameter outcome-reward RL updates. It decomposes each linear weight update as ΔW = ΔW* + ΔW⊥ relative to the base model’s SVD basis, extracts a compact rewiring matrix M = U⊤ΔWk V (Eq. 5, Alg. 1), and reconstructs ΔW* = U M V⊤. The claim is that the reasoning-effective part of RL is largely concentrated in the pretrained spectral manifold Sr(W0), so SAR can preserve nearly all measured post-training gains with a tiny M (as low as ~0.58% of parameters), improve high-k Pass@k exploration, purify Mix-RL updates, and improve math–code expert merging beyond TA/TIES/DARE and even single-domain experts. Evidence spans 1.5B–32B models (Tables 1–2, Fig. 2), Mix-RL purification (Fig. 3), merging (Table 4), in-house agentic coding (Table 3), and ablations against no-projection, random, diagonal-only, and off-diagonal controls (App. E–F), with scope limits discussed in §5 and App. D.","tokens_in":18555,"tokens_out":1242,"duration_ms":9915,"significance":"If the geometric hypothesis holds in the stated elicitation regime, SAR is a practically useful, training-free editing tool for RL post-training: it compresses reasoning updates, can improve test-time scaling without new rollouts, and offers a spectral filter for multi-domain consolidation and merging. Strengths include a clear operational procedure, multi-scale public-model results, explicit no-projection and structural ablations, and an honest boundary analysis (JustRL long training, direct code RL, dense-critic PPO). The work is significant as an empirical geometry-of-updates paper rather than as a fully settled theory of reasoning; its main contribution is a falsifiable editing recipe with multi-setting support.","major_comments":[{"comment":"Table 1 and §3.1: the headline compactness claim (preserve full-RL AIME with 1%/10%/30% spectral rank; M as low as ~0.58% of parameters) is based on a per-model rank sweep that selects the smallest rank already matching full-RL performance within evaluation variance. That is post-selection on the same benchmarks used to claim preservation. Without a pre-specified rank rule, multi-seed variance, or confidence intervals, the “>99% of peak Pass@1 with ~0.58% parameters” statement is weaker than presented. Please report full rank-sweep curves (or fixed a priori budgets such as 1% for all models) and uncertainty so the geometric recovery claim is not confounded with choosing the first matching rank.","section":null},{"comment":"§2.2–2.3 and App. F: the mechanistic claim that off-diagonal rewiring (Mij) is the geometric substrate of multi-conditional reasoning is only weakly supported. The off-diagonal-only ablation recovers most Pass@1 but loses Pass@32, while diagonal-only fails; this shows both parts matter under the chosen budget, not that off-diagonal entries specifically implement relational composition. The triangle-area story in App. B is illustrative only. Either demote the relational-reasoning interpretation to a hypothesis, or add a more direct test (e.g., controlled interventions on selected Mij blocks with predicted behavioral effects).","section":null},{"comment":"§4.1–4.2 / Fig. 3 / Table 4: the causal claim that residual ΔW⊥ “amplifies cross-domain interference” is inferred from SAR improving coding or merged metrics after projection. That is consistent with filtering harmful residuals, but also with other explanations (regularization, effective low-rank denoising, or lucky rank choice). The no-projection controls help, yet they are still incomplete for the interference story. Please quantify residual mass / domain-specific directions more directly, or state the interference interpretation as a plausible reading rather than established mechanism.","section":null}],"minor_comments":[{"comment":"Abstract and Table 2: clarify that ~0.58% refers to the rewiring matrix M relative to total parameters, not the reconstructed ΔW*, which is larger.","section":null},{"comment":"Algorithm 1 vs. text: the order “top-k of ΔW then project onto base SVD” should be stated once with exact rank definitions for U,V and ΔWk to avoid ambiguity about whether k is shared.","section":null},{"comment":"Table 3: in-house agentic coding results are useful but under-specified (model identity, training delta, variance). Even a short appendix note would help external readers assess transfer.","section":null},{"comment":"Figure 2 / evaluation: report sampling seeds or bootstrap intervals for Pass@k curves; small absolute coverage gains (25/30 vs 26/30 in Table 5) need uncertainty context.","section":null},{"comment":"Related work: the distinction from LoRA/PiSSA/DoRA and from magnitude-based merging is present but could more sharply separate “training parameterization” from “post-hoc spectral filtering of a completed full-RL update.”","section":null}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid empirical systems/geometry contribution and is close to publishable after tightening claims around rank selection and mechanism. I would not reject for being outside consensus; the main risk is overclaiming geometric necessity from post-selected rank matches. Fit for a strong ML venue is good if the revision reports fixed-budget/uncertainty results and softens the relational-rewiring narrative."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful thing here is not a new theory of reasoning. It is a concrete post-hoc edit: take a finished full-parameter RL delta, project it into the base SVD basis as a rewiring matrix M, and keep only that piece. Across 1.5B–32B math models, Mix-RL, expert merging, and an in-house agentic coding stack, that edit preserves most Pass@1, often improves Pass@k, and can beat TA/TIES/DARE and even the best single-domain experts.\n\nWhat is actually new is the operational move and the results that follow from it. SVD compression, LoRA/PiSSA-style spectral adapters, and task-arithmetic merging are all prior art, and the paper cites them. The distinctive claim is that a completed unconstrained RL update already contains a compact, base-aligned rewiring that is more useful than the full delta for exploration and multi-domain transfer. The no-projection, random-basis, diagonal-only, and off-diagonal ablations are the right controls, and they support that spectral alignment is doing real work beyond “just low-rank.” Appendix D is also honest about boundaries: long JustRL runs, direct code RL from a base model, and dense-critic PPO are less projection-compatible.\n\nThe soft spot is real but narrower than a full collapse of the claim. Table 1 reports the smallest rank from a per-model sweep that already matches full-RL AIME within variance. So the “~0.58% of parameters, >99% of peak Pass@1” line is post-selected on the same benchmarks, not a fixed a priori budget with multi-seed CIs. That weakens the geometric slogan more than the method: if you fix a small rank and still get competitive Pass@k and merging gains, the edit remains interesting. Gains are sometimes small in absolute terms, code/artifacts are missing, and “first-principles” is marketing language for an empirical hypothesis. None of that erases the multi-setting pattern.\n\nThis is for people who ship RL post-training, care about test-time scaling after RL, or merge domain experts. I would bring it to reading group, cite the method if I am working in that lane, and send it to peer review. Tighten rank selection, report variance, ship code, and keep claims inside the elicitation regime they already document.","headline":"Useful post-hoc spectral edit of full RL deltas with multi-setting evidence; the >99%/0.58% headline is post-selected, but the operational method and ablations still hold up.","tokens_in":19192,"tokens_out":584,"would_cite":true,"duration_ms":5486,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"The reasoning-effective part of reinforcement-learning updates sits mostly in the base model’s spectral geometry, so projecting those updates onto that subspace preserves gains while improving exploration and multi-domain transfer.","keywords":["reinforcement learning","large language models","spectral subspace","model merging","test-time scaling","reasoning elicitation","post-hoc model editing","parameter geometry"],"falsifier":"Take a strong outcome-reward RL math model and a matched base; apply SAR at the paper’s reported rank and check whether Pass@1 stays within a few points of full RL while Pass@k at large k and multi-domain merge scores fall below the full RL or best single-expert baselines—especially on cases the paper flags as less projection-compatible, such as long-trained reasoning RL or direct code RL from a raw base.","tokens_in":19060,"feed_emoji":"🔀","tokens_out":992,"duration_ms":14314,"temperature":0.7,"pith_summary":"Full-parameter reinforcement learning improves language models on math, code, and related tasks, but the dense updates often narrow exploration and clash when several skills are trained or merged together. This paper argues that the useful part of those updates is largely a rewiring of skills already encoded in the base model’s singular-vector coordinates, not an arbitrary rewrite of the whole weight space. Subspace-Aligned Rewiring extracts that spectral core, discards residual directions, and rebuilds a compact update. Across model sizes, the method keeps nearly all measured post-training accuracy with a tiny fraction of parameters, raises performance under large sampling budgets, cleans mixed-domain training so suppressed skills reappear, and merges domain experts into models that beat prior merge methods and even the best single experts. The practical claim is that a training-free geometric edit can recover and recombine reasoning signal that dense RL had buried.","feed_headline":"Spectral rewiring keeps 99% of RL gains with 0.6% of weights","feed_subtitle":"It also lifts high-k sampling and multi-domain merges beyond full updates and single experts","key_machinery":"Subspace-Aligned Rewiring (SAR): isolate ΔW = W_RL − W_0, take a top-k low-rank piece, project it as U(U⊤ΔW_k V)V⊤ onto the base SVD factors, and add the resulting rewiring matrix M back to the base model. This keeps on-manifold skill recombination and drops orthogonal residual mass.","core_discovery":"Outcome-reward RL updates that improve reasoning are largely recoverable inside the pretrained spectral subspace of the base weights. Projecting the full update onto that subspace yields a compact rewiring among existing singular directions that preserves nearly all Pass@1 gains, improves high-k exploration, and reduces cross-domain interference in mixed training and expert merging.","pith_inferences":["If the useful signal is mostly on-manifold rewiring, future RL optimizers could constrain or regularize updates to stay near the base SVD coordinates during training rather than only cleaning them afterward.","Projection compatibility itself becomes a diagnostic: large reconstruction gaps after SAR may flag when a run is installing new interface knowledge rather than eliciting latent skills.","The same spectral filter might transfer to other dense adaptation steps beyond outcome-reward RL whenever two models share a common pretrained basis.","Storing and shipping only the compact rewiring matrix could become a practical way to distribute multi-skill improvements without full fine-tuned weights."],"forward_implications":["A dense RL checkpoint can be edited after training into a compact spectral core that retains essentially full measured reasoning accuracy with well under 1% of parameters in the rewiring matrix for several strong recipes.","Removing residual off-manifold directions can reverse early Pass@k saturation and expand the set of hard problems solvable by repeated sampling.","Mixed-domain RL updates can be purified so suppressed coding performance rises while math and instruction-following hold steady.","Math and code experts can be merged through spectral filtering so the merged model exceeds both prior merge baselines and the best single-domain expert on primary metrics.","Post-training recipes can treat the rewiring matrix as the editable object for compression, filtering, and composition instead of the full dense delta."],"fun_headline_variants":["Spectral rewiring keeps 99% of RL gains with 0.58% of weights","SAR extracts RL reasoning core via base spectral subspace","Project RL updates onto spectrum: preserve gains, cut interference","Spectral rewiring purifies multi-domain updates and expert merges","Compact spectral rewiring lifts high-k exploration and coding"],"cache_read_input_tokens":128,"weakest_assumption_plain":"When the base model already holds the relevant skills, the update mass that sits outside its spectral geometry can be thrown away without losing essential capability, and is often what suppresses exploration or causes domain clash.","fun_headline_variants_meta":{"raw":{"variants":["Spectral rewiring keeps 99% of RL gains with 0.58% of weights","SAR extracts RL reasoning core via base spectral subspace","Project RL updates onto spectrum: preserve gains, cut interference","Spectral rewiring purifies multi-domain updates and expert merges","Compact spectral rewiring lifts high-k exploration and coding"]},"model":"grok-4.5","effort":"low","cost_usd":0.003572,"raw_usage":{"total_tokens":1188,"prompt_tokens":793,"num_sources_used":0,"completion_tokens":70,"cost_in_usd_ticks":35720000,"prompt_tokens_details":{"text_tokens":793,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":325,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":793,"tokens_out":70,"duration_ms":3267,"temperature":1.0,"reasoning_tokens":325,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T05:07:44.088059+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Take a strong outcome-reward RL math model and a matched base; apply SAR at the paper’s reported rank and check whether Pass@1 stays within a few points of full RL while Pass@k at large k and multi-domain merge scores fall below the full RL or best single-expert baselines—especially on cases the paper flags as less projection-compatible, such as long-trained reasoning RL or direct code RL from a raw base.","supporting_citations":[],"review_version":1}