{"id":"3cb7f1c6-d745-4f2d-958e-4a5ec7d2683c","arxiv_id":"2607.24891","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"RL-S2LU extends learned sequential BP by cascading each selected variable-node update to its second-order neighborhood, yielding large empirical gains over BP and BP-OSD-10 on QLDPC codes.","lead":"A new belief-propagation schedule for quantum LDPC codes updates each chosen qubit and its local check-neighbors, using a previously trained RL order table. On several finite-length codes it beats standard BP and a common BP-plus-OSD baseline at far fewer outer sweeps.","discovery_kind":"extension","skeptic_critique":{"model":"moonshotai/kimi-k3","headline":"No control isolates the learned schedule's contribution: the reported gains may be driven entirely by the deterministic U2 cascade, with the frozen RL-S table acting as an arbitrary (but harmless) anchor ordering.","rationale":"The reader identified the right neighborhood — the frozen QRL table operating under altered residual dynamics (§III: \"uses the same trained table QRL… as RL-S\") — but framed it as a risk that the gains \"would not transfer.\" I disagree with that framing: the central claim is a purely empirical comparison of a fully specified decoder, so a mismatched table cannot make the reported numbers wrong; it can only mean the learning was never the active ingredient. The genuinely load-bearing gap is the absence of any control (random or heuristic anchor + same cascade) that would establish the RL schedule contributes anything under the cascade dynamics. This is a correctness-of-attribution concern that directly bears on the novelty score and the §V conclusion, not a soundness flaw in the stated experiments. I therefore keep the reader's CONDITIONAL verdict: the empirical results are plausible, internally consistent (Algorithm 1, Eqs. (1)–(11) are checkable, complexity accounting in §III.D is honest about the Umax constant factor and serial latency), and the fix is exactly the kind of ablation the reader already conditioned acceptance on. The statistical-rigor gap (no error bars at BLER 1e-7, no released code or Q-table artifacts) reinforces the condition but does not, on its own, rise to reject level for a methods paper of this type.","tokens_in":8729,"tokens_out":5673,"duration_ms":209499,"concrete_test":"On the [[288,12,18]] BB code at p ∈ {0.05, 0.07, 0.09}, run three decoders at T = 10 and T = 100 with identical Monte Carlo budgets (enough trials for ≤10% relative error at the smallest BLER): (i) RL-S2LU as published; (ii) S2LU with anchors drawn uniformly at random from R (Q-table removed); (iii) S2LU with anchors chosen by a non-learned residual heuristic (e.g., max number of unsatisfied adjacent checks). If (ii) or (iii) is within ~0.2 orders of magnitude of (i) at every point, the learned schedule is not load-bearing and the contribution is the cascade alone; if (i) is clearly better, both the attribution and the frozen-table transfer are validated. Optionally add a retrained-under-cascade table as an upper reference.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's contribution is framed as \"learned sequential BP schedules can be strengthened by local propagation without retraining\" (§V), and the decoder's name and novelty rest on the RL component. But the only learned element — the QRL table and greedy anchor rule of (10) — was trained in [19] under single-VN-update dynamics, where each anchor action changes one node's beliefs and residuals. In RL-S2LU, each anchor action triggers up to Umax = 1 + ∆v(∆c−1) VN updates (§III.C–D; ~31 for the BB codes), so the state-transition structure the table was optimized for is substantially altered. Two readings are consistent with the presented results: (a) the learned ranking remains informative under the cascade, or (b) the cascade is doing essentially all the work and almost any deterministic anchor order would produce similar BLER curves. The paper provides no evidence to distinguish these: there is no ablation with a non-learned anchor rule (random anchor, or a simple residual-based heuristic) paired with the same S2LU cascade. This matters for the central claim's meaning, not its literal truth: \"RL-S2LU T=10 beats BP-OSD-10 T=1000\" is an empirical statement that stands regardless of why it works, but if reading (b) holds, the contribution reduces to \"second-order cascades help sequential BP,\" the RL machinery is decorative, and the novelty assessment (already incremental within the authors' RL-scheduling line) drops materially. Note this is sharper than the reader's transfer concern: a poorly matched frozen table would not falsify the numbers — it would reveal that the numbers never depended on the learning at all. A secondary, lesser concern: low-BLER points (down to 1e-7 in Fig. 1) appear without error bars, trial counts, or released artifacts, so the \"order of magnitude gain at small p\" sub-claims are not yet statistically secured.","agreement_with_reader":"partial"},"referee_report":{"model":"moonshotai/kimi-k3","summary":"The manuscript proposes RL-S2LU, a modification of the authors' RL-S sequential BP decoder for CSS QLDPC codes. RL-S uses a Q-table trained offline over residual-syndrome states (Eqs. (8)-(10)) to greedily select anchor variable nodes; RL-S2LU keeps the same frozen table and anchor rule but replaces the single-VN update with a deterministic second-order cascade: after an anchor v* is selected, all VNs sharing a check with v* (the set U2(v*), Eq. (11), of size at most Umax = 1 + ∆v(∆c-1)) are updated in a fixed graph order (Algorithm 1). Simulations on the [[288,12,18]] and [[144,12,12]] bivariate-bicycle codes and the [[180,10]] A5 code show that RL-S2LU with sweep cap T=10 achieves lower block error rate than flooding BP and BP-OSD-10 at T=1000 over the simulated depolarizing range, with further low-p gains at T=100/1000, and typically converges within the first outer sweep (Table II). The message equations (1)-(7), residual state, algorithm, and complexity bounds are clearly specified.","tokens_in":9112,"tokens_out":4218,"duration_ms":222462,"significance":"If the results hold, the paper demonstrates a practically useful fact: a schedule learned under single-VN-update dynamics can be combined at inference time, without retraining, with a deterministic local propagation cascade, yielding large BLER gains while remaining purely local BP (no OSD post-processing). The presentation is a strength: Eqs. (1)-(11) and Algorithm 1 are complete enough to reimplement, the convergence/termination criterion is explicit, and the failure decomposition in Table I (non-convergence vs. logical errors) is informative. The parameter count is small (frozen Q-table, sweep cap T, channel initialization), and the claims are concrete and falsifiable. The contribution is incremental within the authors' RL-scheduling line [15],[18]-[21], and its meaning depends on how much of the gain is attributable to the learned schedule versus the cascade (see Major Comment 1); even in the worst case, the empirical decoder itself appears strong.","major_comments":[{"comment":"§III.C / §IV, Figs. 1-3: there is no ablation isolating the contribution of the learned schedule from that of the deterministic U2 cascade. The Q-table QRL was trained in [19] under single-VN-update dynamics, where each anchor action changes one node's beliefs and residuals; here each action triggers up to Umax = 1+∆v(∆c-1) ~ 31 VN updates for the BB codes (§III.D), so the state-transition structure the table was optimized for is substantially altered. Two readings are consistent with the presented curves: (a) the learned ranking remains informative under the cascade, or (b) the cascade does essentially all the work and almost any anchor order (random, or a simple residual-weight heuristic) paired with the same U2 update would match the reported BLER. The paper's framing — 'learned sequential BP schedules can be strengthened by local propagation without retraining' (§V) — and its name re","section":"§III.C, §IV, Figs. 1-3"},{"comment":"§I, §IV, Fig. 1: the headline comparison 'RL-S2LU with only T=10 decoder sweeps outperforms BP and BP-OSD-10 with T=1000 iterations' conflates unlike units of work. One RL-S2LU sweep performs up to n·Umax local VN updates (§III.D), so T=10 sweeps cost up to ~10·288·31 ≈ 9×10^4 VN updates on the [[288,12,18]] code, versus 1000·288 ≈ 2.9×10^5 VN updates for flooding BP at T=1000 (plus the uncounted order-10 OSD Gaussian-elimination overhead). The claim appears to survive honest accounting, but the paper should state it in terms of measured average local-update counts (or wall-clock equivalents) per decoding, alongside Table II's sweep counts, and note that RL-S2LU's serial latency is worse than flooding BP's by the Umax factor under a fully serial implementation (§III.D acknowledges this only asymptotically).","section":"§I, §IV, Fig. 1, Table II"},{"comment":"§IV: no statistical methodology is reported. Fig. 1 shows BLER down to 10^-7 at p=0.05 and claims 'about one order of magnitude gain over BP-OSD-10 at small values of p,' yet the number of simulated error events/samples per point and confidence intervals are nowhere given, and Table I reports percentages (e.g., 27.0% non-convergence at p=0.05, T=1000) conditioned on error events that must be rare at those BLERs. The simulation protocol (sample counts per p, stopping rule, whether OSD-10 failures were counted identically) should be stated and error bars or sample sizes added to Figs. 1-3 and Table I.","section":"§IV, Fig. 1, Table I"}],"minor_comments":[{"comment":"Eq. (11): U2(v) as defined already contains v (since v ∈ ∂c for every c ∈ ∂v), so the sentence 'U2(v) contains v and all VNs that share at least one adjacent check' is redundant; also, 'second-order' usually denotes distance-2 in graph nomenclature, whereas U2 is the closed distance-2 neighborhood — a clarifying sentence would help.","section":"§III.C, Eq. (11)"},{"comment":"Fig. 1 legend lists RL-S at T=10 but no such curve is discernible, and Fig. 3 omits the RL-S2LU T=100/1000 curves shown in Figs. 1-2, making the cross-code comparison inconsistent. Please make the plotted configurations uniform across the three figures or explain the omissions.","section":"Figs. 1 and 3"},{"comment":"Table II is titled 'average number of outer iterations' while the text uses 'sweeps'; one row (RL-S2LU, T=1000, p=0.08, value 1.3) jumps to 3.2 at p=0.09 and 9.6 at p=0.10, which is worth one sentence of interpretation, since it bears on the latency claims in §III.D.","section":"Table II"},{"comment":"§II.A: the initialization µ = log((1-2p/3)/(2p/3)) assumes the decoder knows the true physical error rate p; please state whether any p-mismatch sensitivity was tested, and note that κP in Eq. (2) embeds the same assumption.","section":"§II.A, Eq. (2)"},{"comment":"Comparison set: BP-OSD-10 is the only strong baseline; a brief note positioning RL-S2LU against other purely-BP improvements (e.g., normalized/offset min-sum variants for degenerate codes, or the cluster-based sequential decoder of the companion work [21]) would clarify where the claimed gain is genuinely new versus inherited from sequential scheduling generally [15].","section":"§IV"},{"comment":"Typesetting artifacts in the author block ('Ari zona', 'Universit y', 'V ahid Nourozi') and a few missing-space artifacts ('VNs', 'U2(v)') should be cleaned up; [20],[21] are cited as arXiv-only 2026 preprints — if [19] is still unpublished, the reproducibility of the inherited Q-table should be addressed (see confidential remarks).","section":"Title page, References"}],"recommendation":"major_revision","confidential_remarks":"The empirical results appear strong and the write-up is technically clean, but two framing issues deserve the editor's attention. First, the contribution sits at the end of a dense chain of self-citations ([15],[18]-[21], several 2026 arXiv preprints by overlapping author sets), and the decoder's only learned component — the Q-table QRL — is taken verbatim from the companion preprint [19] with no retraining, no released table, and no code. The results are therefore not independently reproducible as submitted, and the novelty over [19] reduces to the deterministic U2 cascade if the ablation requested in Major Comment 1 shows the schedule is not load-bearing. Second, if the venue is a short-format conference/letters venue, the requested ablation and work-accounting are feasible within scope; if the journal expects full-length archival treatment, the lack of statistical reporting and the single strong baseline (BP-OSD-10) are thin for that standard. None of this is disqualifying; it bears on how much weight to put on the 'reinforcement-learned' framing in the title."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful takeaway is simple: on three finite-length QLDPC codes, replacing each RL-selected VN update with a deterministic second-order neighborhood cascade (U2) gives lower block error rate and much faster outer-sweep convergence than flooding BP and BP-OSD-10, while staying purely local BP. For the [[288,12,18]] BB code, T=10 already beats BP-OSD-10 at T=1000 across the simulated range; similar pattern on the A5 and shorter BB codes. That is a real engineering result.\n\nWhat is new is the inference-time cascade itself (Algorithm 1, U2/L2 after the greedy anchor). The message equations, residual state, and complexity bounds are written clearly enough to check. Tables I–II and the average-sweep numbers are honest about non-convergence vs logical error and about how quickly the method finishes. Credit where due: they kept the decoder local, avoided algebraic post-processing, and showed the gains on more than one code family.\n\nThe soft spot is real but proportional. The paper reuses the exact QRL table and greedy rule trained under single-VN dynamics, then changes the action to a cascade of size ~Umax. There is no control with a non-learned anchor order (random, residual weight, fixed graph order) paired with the same S2LU cascade. So we cannot tell whether the learned ranking still matters or whether almost any sequential order plus U2 would look similar. That does not falsify the BLER curves; it does mean the framing “learned schedules strengthened by local propagation” is stronger than the evidence. Secondary and smaller: low-p points lack trial counts/error bars and the Q-table is not released, so exact replication is blocked.\n\nThis is for people who build or implement QLDPC decoders and care about finite-length, low-latency local methods. Theory people can skip it. The math and experiments are coherent enough that a serious editor should send it to referees; I would ask for the ablation and basic statistical detail, not a rewrite. Worth engaging if you work on practical QEC decoding; cite the empirical comparison, not the “RL without retraining” slogan until the control exists.","headline":"Solid empirical decoder paper: second-order local cascades on a frozen RL-S schedule beat BP-OSD-10 at far fewer sweeps, but no ablation shows the learned table is doing real work.","tokens_in":10071,"tokens_out":545,"would_cite":true,"duration_ms":11221,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["94B35","81P73"],"pacs":[],"model":"grok-4.5","headline":"A second-order local BP update, driven by a learned schedule, beats heavy BP-OSD on quantum LDPC codes while staying purely local.","keywords":["quantum LDPC codes","belief propagation","reinforcement learning","sequential scheduling","second-order local update","CSS codes","depolarizing channel","BP-OSD"],"falsifier":"Retrain or ablate the Q-table under the actual second-order residual dynamics on the [[288,12,18]] code; if the reported block-error gains over BP-OSD-10 at T=10 vanish or reverse once the schedule is no longer the unmatched RL-S table, the central transfer claim fails.","tokens_in":9804,"feed_emoji":"⚛️","tokens_out":970,"duration_ms":21754,"temperature":0.7,"pith_summary":"Quantum LDPC codes need fast, local decoders, but ordinary belief propagation often stalls because of short cycles and many errors that look the same on the syndrome. Earlier work showed that a reinforcement-learned order for updating variable nodes can help BP converge. This paper keeps that same offline-learned schedule table and, at inference time, expands each chosen update into a small cascade: the selected node plus its neighbors that share a check. The result, RL-S2LU, remains a purely local message-passing decoder with bounded degree cost, yet on several finite-length quantum LDPC codes it corrects more errors with far fewer sweeps than flooding BP or BP with order-10 OSD post-processing. A sympathetic reader cares because high-threshold quantum memory designs need decoders that are both accurate and hardware-local; this shows schedule learning plus a cheap neighborhood cascade can close much of the gap without algebraic post-processing or retraining.","feed_headline":"Local BP cascade beats BP-OSD on quantum LDPC codes","feed_subtitle":"Same learned schedule, second-order neighborhood updates, far fewer sweeps, no algebraic post-processing.","key_machinery":"The second-order neighborhood U2(v): after the learned policy picks an anchor v, the decoder runs the quaternary sequential VN update on an ordered traversal of v and all variables that share at least one adjacent stabilizer check with v, while only the anchor is removed from the without-replacement schedule set.","core_discovery":"RL-S2LU reuses the trained RL-S Q-table and greedy anchor rule, but replaces each selected variable-node update with a deterministic second-order local cascade over that node and the variable nodes sharing an adjacent X- or Z-check. On the tested bivariate-bicycle and A5 codes, this purely BP decoder with small sweep caps outperforms conventional flooding BP and BP-OSD-10 run with far more iterations, and typically converges within the first outer sweep in the low-error regime.","pith_inferences":["If the unmatched Q-table already works this well, a schedule trained explicitly on second-order residual transitions might unlock still lower error floors or fewer sweeps.","The same cascade-after-learned-anchor idea may transfer to other sparse quantum or classical codes where flooding stalls on short cycles, without needing OSD hardware.","Hardware implementations could treat each anchor’s U2 neighborhood as a small parallel tile, trading local wiring for fewer global iterations in quantum memory controllers."],"forward_implications":["Learned sequential BP for QLDPC can be strengthened by local cascade propagation without retraining or OSD.","On the [[288,12,18]] BB code, T=10 RL-S2LU sweeps already beat BP and BP-OSD-10 at T=1000 over the simulated depolarizing range.","Raising the sweep cap further cuts non-convergence failures and improves the low-p block error rate while average outer sweeps stay near one in the low-error regime.","For bounded-degree QLDPC families the extra work stays O(Tn) with a larger constant, and the cascade is locally parallelizable.","On shorter codes the remaining failures become mostly logical rather than non-convergence, pointing to a logical-error-limited regime under pure BP."],"fun_headline_variants":["RL-S2LU local cascade beats BP-OSD-10 on quantum LDPC","Second-order BP updates cut errors without OSD post-processing","Same RL schedule, local 2-hop cascade, fewer sweeps than BP-OSD","RL-S2LU: purely local BP tops flooding and BP-OSD-10","Learned schedule plus second-order cascade lifts QLDPC BP"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The offline-trained schedule table still picks good anchors when each action suddenly updates a whole local neighborhood and changes residual states in ways the original training never saw.","fun_headline_variants_meta":{"raw":{"variants":["RL-S2LU local cascade beats BP-OSD-10 on quantum LDPC","Second-order BP updates cut errors without OSD post-processing","Same RL schedule, local 2-hop cascade, fewer sweeps than BP-OSD","RL-S2LU: purely local BP tops flooding and BP-OSD-10","Learned schedule plus second-order cascade lifts QLDPC BP"]},"model":"grok-4.5","effort":"low","cost_usd":0.002201,"raw_usage":{"total_tokens":898,"prompt_tokens":688,"num_sources_used":0,"completion_tokens":85,"cost_in_usd_ticks":22008000,"prompt_tokens_details":{"text_tokens":688,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":125,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":688,"tokens_out":85,"duration_ms":3283,"temperature":1.0,"reasoning_tokens":125,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T12:47:26.578941+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Retrain or ablate the Q-table under the actual second-order residual dynamics on the [[288,12,18]] code; if the reported block-error gains over BP-OSD-10 at T=10 vanish or reverse once the schedule is no longer the unmatched RL-S table, the central transfer claim fails.","supporting_citations":[],"review_version":1}