{"id":"dd06eb94-dd51-477c-8115-0d8a756482c6","arxiv_id":"2608.04872","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A-SR is an agentic LLM framework that improves symbolic regression success rates through role-conditioned evidence routing, protocol selection, and online role-policy adaptation.","lead":"A framework called A-SR routes symbolic regression proposals through four specialist LLM roles, selects coordination protocols, adapts role policies online, and routes memory by search state. On LLM-SRBench scientific domains it reports raising solved-task accuracy from 25.79% to 48.30% over the prior best LLM-guided baseline, and winning 7 of 8 real-world ID/OOD metrics.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper never specifies the numeric values of λ_v, λ_b, λ_i, λ_p in Eq. (2) or the decision rule of SelectProtocol, so the claimed improvement cannot be reproduced or attributed to the online role-policy mechanism.","rationale":"The paper's strongest claim is a performance number, but the scientific contribution is the mechanism. My concern targets the mechanism: the two adaptive pieces named in the claim—protocol selection and online role-policy adaptation—are not fully specified. Eq. (2) defines the reward with abstract λ's; Eq. (1) defines the protocol choice with an abstract SelectProtocol; no numeric values or thresholds are given anywhere in the manuscript or appendices. The Limitations section's statement that the protocol selector 'may require recalibration' is consistent with the selector being tuned for the evaluated benchmark rather than a principled transferable rule. The ablation evidence is thin: the online-vs-static gap in Table 3 is 2.22 percentage points (1 task out of 45), and without seeds or a sensitivity sweep this could be sampling noise. The paper does present useful diagnostics (validity, role usage, memory routing) and its component ablations are the right kind of evidence; I am not claiming the results are fabricated. But as published, a reader cannot implement A-SR, run the ablation, or verify that the 48.30% Acc@0.01 is attributable to the claimed control shift rather than to hidden configuration choices. The condition for acceptance should be release of exact hyperparameters and code plus multi-seed sensitivity results.","tokens_in":24262,"tokens_out":9863,"duration_ms":103567,"concrete_test":"Release the exact hyperparameter configuration—λ_v, λ_b, λ_i, λ_p, B0, and the SelectProtocol thresholds—along with code, and rerun the 45-task ablation with 5 seeds and a sensitivity sweep over λ ∈ {0.5×, 1×, 1.5×} and B0 ∈ {40, 80, 160}. If the A-SR-online minus A-SR-Static Acc@0.01 gap is not consistently positive across the sweep and larger than seed noise, the attribution of the headline gain to online role-policy adaptation fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline numerical claim is accompanied by a mechanism claim: gains come from shifting control to role-conditioned evidence views, with online role-policy adaptation playing a key role. The mechanism is defined by Eq. (2)–(5), but the paper only states λ_v, λ_b, λ_i, λ_p are 'fixed across tasks' (§3.3) and never reports their values or the actual profile-to-protocol mapping in Eq. (1). The four protocols are described as archetypes, but the thresholds that turn (ρ_rel, ρ_prod) into π⋆ are not given. Consequently, the method as written is a family of methods parameterized by unspecified constants; no independent implementation can reproduce the reported 25.79%→48.30% or 24.58%→38.29% improvements. The scarcity is consequential: the key ablation contrast between A-SR online (31.11%) and A-SR-Static (28.89%) in Table 3 is a 1-task difference on 45 tasks, and without λ values one cannot run the sensitivity analysis needed to know if online adaptation matters. The paper's own Limitations section concedes the protocol selector 'may require recalibration' for other domains, which underscores that the selector is hand-configured rather than derived. This does not disprove the empirical result, but it makes the central mechanism claim unverifiable from the paper alone.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents A-SR, an agentic LLM-guided symbolic regression framework that replaces a unified proposal-evaluation loop with role-conditioned evidence views: four roles (Generator, Analyst, Simplifier, Reviewer) coordinated by a hierarchical controller with protocol selection, online role-utility adaptation, and state-routed process memory. The framework self-evolves within a run without updating LLM parameters, and a LoRA-distilled variant (A-SR-LoRA) uses recorded trajectories as a role-conditioned proposal prior. The authors report large average Acc@0.01 improvements over Deliberate Evolution on LLM-SRBench (25.79% to 48.30% with Llama3.1-8B-Instruct; 24.58% to 38.29% with Qwen3-4B-Instruct-2507 for A-SR-LoRA) and best ID/OOD NMSE on 7 of 8 real-world LLM-SR tasks. The appendices provide implementation details, ablations, OOD tables, process diagnostics, and formula-level case studies.","tokens_in":24752,"tokens_out":6938,"duration_ms":63646,"significance":"The empirical headline claims are internally consistent: the 48.30% average matches the four LSR-Synth Acc@0.01 values for A-SR in Table 1, and the 7-of-8 claim matches Table 2. The framing—shifting control from expression edits to role–memory-view pairs—is a conceptually useful reframing for LLM-guided symbolic regression, and the two-timescale self-evolution (test-time adaptation plus offline LoRA distillation) is a plausible contribution. The paper also includes strengths that are not always present in this literature: explicit caveats about benchmark memorization (Appendix C), a synthetic distillation corpus explicitly not built from benchmark labels, process-level diagnostics (Figures 4, 7, 8), and formula-level case studies (Table 4, Tables 14–15). However, the core mechanism—online role-policy adaptation and protocol selection—is under-specified, and all headline results are point estimates from stochastic LLM sampling with no variance information. As a result, the central attribution claim is not yet verifiable from the manuscript alone.","major_comments":[{"comment":"The online role-policy mechanism at the center of the paper's contribution is not reproducible. The weights λ_v, λ_b, λ_i, λ_p in Eq. (2) are stated to be 'fixed across tasks' but their numerical values are never given; the smoothing rate η, the adaptation strength α_{π*}, the gate g_{π*,t}(r), and the protocol-induced base scores S^{π*}(r) in Eq. (4) are also unspecified. Eq. (1) defines π* = SelectProtocol(ρ_rel, ρ_prod) but the manuscript never states the decision rule, e.g., the thresholds on r_invalid, r_param, Δ_invalid, n_best, τ_stag that map a profile to one of the four protocols. Without these constants and rules, no independent implementation can reproduce the reported improvements (25.79%→48.30%, 24.58%→38.29%) or attribute them to online adaptation rather than to the hand-chosen defaults. The Limitations section (§6) concedes that the protocol selector 'may require recalibration for substantially different scientific domains,' which confirms it is hand-configured. Please provide the complete parameter settings and the exact profile-to-protocol mapping for all four protocols, or release code that unambiguously encodes them.","section":"§3.3, Eq. (2)-(5); §3.2, Eq. (1)"},{"comment":"The ablation evidence for the central mechanism claim is statistically inconclusive. A-SR online achieves Val Acc 31.11% versus A-SR-Static 28.89%, a difference of one task on the 45-task subset, and fixed role rotation 24.44%. All numbers in Tables 1, 3, 10, 11, and 12 are point estimates from stochastic LLM sampling (temperature 0.8, per Tables 8/9), with no error bars, repeated seeds, or significance tests reported anywhere. With a one-task difference, the contrast between online and static adaptation cannot be distinguished from sampling noise, so the paper's statement that 'online role-policy adaptation improves solved-task reliability' is not supported by the reported evidence. Please report multi-seed or bootstrap intervals for at least the ablation table and the headline average Acc@0.01 values.","section":"§4.5, Table 3"},{"comment":"The manuscript does not distinguish between baselines the authors re-ran under matched budgets and seeds and values copied from prior publications. For the real-world tasks, Section 4.1 states 'published baseline values are taken from LLM-SR when available,' and DE is not re-run because it is not open-sourced; for LLM-SRBench, DE numbers are presumably taken from Pang et al. 2026, but this is not stated per cell. Since the headline claims are comparative (e.g., 'best ID/OOD NMSE on 7 of 8'), the lack of provenance and run-to-run variability makes the comparisons unverifiable. Please mark which numbers are reproduced and which are quoted, and add variability estimates for the reproduced A-SR runs.","section":"§4.1, §4.3, Tables 1-2"}],"minor_comments":[{"comment":"A-SR-LoRA's OOD NMSE on Physics (4.319e3) is more than two orders of magnitude worse than A-SR-Static (2.34e1) and worse than DE (1.97e3); the main-text sentence 'A-SR variants improve solved-task extrapolation reliability on Material, Chemistry, and Biology' should acknowledge this degradation rather than implying uniform improvement.","section":"Appendix Table 10"},{"comment":"The 'representative run' is a single trajectory; please state how the run was selected (e.g., median seed) so the reader can gauge how typical the shown dynamics are.","section":"§4.4, Figures 4 and 8"},{"comment":"Eq. (1) is introduced before the four protocols are defined in the following paragraph; consider moving the protocol descriptions before Eq. (1) or defining SelectProtocol explicitly to avoid the appearance of a placeholder.","section":"§3.2, Eq. (1)"},{"comment":"The teacher model for the distillation corpus is referred to as 'GPT-5.5'; if this denotes a specific model version, please provide a citation or clarify the version naming, since this affects the reproducibility of the distillation corpus.","section":"Appendix F"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's headline numbers appear internally consistent, and the paper includes unusually thorough appendices and caveats. The central unresolved issue is that the mechanism claimed to produce the gains is under-specified (no λ values, no SelectProtocol mapping) and the key ablation contrast is within one task with no variance estimates. I believe these are fixable within the manuscript's scope—the authors can supply the missing constants, the decision rules, or code, and add seed-based uncertainty—so I recommend major revision rather than rejection. I would also encourage the authors to release code, as the current reproducibility posture is the main obstacle to acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth taking seriously. It proposes a real shift in control for LLM-guided symbolic regression — from edit operators to role-conditioned evidence views — and reports large gains: 25.79% to 48.30% Acc@0.01 on LSR-Synth with Llama3.1-8B, and 7 of 8 best ID/OOD NMSE on the real-world tasks. The numbers in the tables are internally consistent, and the framing is genuinely new relative to DE: the unit of control is the role–memory-view pair, not the expression edit. The distillation corpus is built on a synthetic meta-SR task bank with GPT-5.5, explicitly not on benchmark validation or OOD labels, so the circularity concern is largely addressed. The process diagnostics are a good idea and the limitations section is honest.\n\nThe soft spots are real but not fatal. The paper never specifies the values of λ_v, λ_b, λ_i, λ_p in Equation (2), and the SelectProtocol mapping from reliability/productivity profiles to the four protocols is described qualitatively, not as a concrete rule. That means the method as written is a family of methods; no independent team can reproduce the reported gains without guessing. This matters more than usual because the paper's mechanism claim rests on online role-policy adaptation, yet the key ablation contrast is 31.11% vs. 28.89% on a 45-task subset — a one-task difference. Add the absence of multi-seed error bars and the reliance on published numbers for DE, and the headline result is plausible but not yet verified. These are addressable: code release, five seeds, and a table of the missing constants would turn this into a checkable contribution.\n\nThe paper is coherent on its own terms and the authors are not overclaiming in the limitations. This is a serious empirical methods paper for the LLM-guided SR community. It deserves peer review, not a desk reject, but I would not cite the exact numbers until the code and hyperparameters are out. My recommendation: send it out, and make code release and a sensitivity analysis on the λ weights explicit conditions for acceptance.","headline":"A plausible new control abstraction for LLM-guided symbolic regression with a strong but under-specified headline result — deserves review if the authors ship code and numbers.","tokens_in":25168,"tokens_out":1652,"would_cite":false,"duration_ms":19744,"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":"LLM-guided equation search doubles its solved-task rate by routing evaluator feedback to role-specialized agents.","keywords":["symbolic regression","LLM agents","role-conditioned prompting","process memory routing","coordination protocols","self-evolving search","trajectory distillation","scientific equation discovery"],"falsifier":"A direct test would be to run A-SR on LLM-SRBench's LSR-Synth domains with a different profiling budget (say B0=20 or B0=200) or with per-domain-tuned reward weights, and check whether the Acc@0.01 improvement over DE persists; if the margin collapses, the reported gain is tied to the hand-coded coordination rule rather than to the role-conditioned evidence-view principle. A second test: hold out entire scientific domains, re-derive the protocol-selector thresholds only on the held-in domains, and see if A-SR still beats DE on the held-out ones.","tokens_in":24053,"feed_emoji":"🧮","tokens_out":5779,"duration_ms":49630,"temperature":0.7,"pith_summary":"The paper argues that LLM-guided symbolic regression fails not because the model lacks ideas, but because a single prompt and a scalar score cannot tell the next proposal what went wrong. A-SR replaces that unified loop with a coordinator that routes evaluator feedback to four role-specialized agents — Generator, Analyst, Simplifier, Reviewer — each seeing a different memory view, and selects among four coordination protocols based on an early profile of the search. The claim is that this shift of control from expression edits to role-conditioned evidence views is what drives the headline gains: Acc@0.01 on the four LSR-Synth scientific domains rises from 25.79% to 48.30% with Llama3.1-8B, and the LoRA-distilled variant raises Qwen3-4B from 24.58% to 38.29%. If true, it means two small open models can be made to solve scientific equation recovery at roughly double the rate of the strongest prior agentic baseline, with no parameter updates during search.","feed_headline":"Agentic routing doubles solved-rate in symbolic regression","feed_subtitle":"A-SR lifts LLM-SRBench Acc@0.01 from 25.79% to 48.30% on Llama3.1-8B by routing failures to role-specialized agents.","key_machinery":"The central object is the role-conditioned evidence view: a prompt context composed of the active role, routed process memory, recent evaluator feedback, and best candidate. Four roles share one LLM backbone — Generator (new structures), Analyst (missing terms), Simplifier (compression), Reviewer (validity and stability). A protocol selector chooses from four coordination archetypes after profiling the first 80 evaluations; an online role policy updates role utilities from an evaluator-derived reward; and a memory router exposes elite formulas, failure traces, or motif memory depending on the inferred process state. A-SR-LoRA adds an offline path: recorded trajectories are distilled into role-specific LoRA modules over an open-weight backbone, keeping the same coordination loop.","core_discovery":"A-SR's central claim is a performance statement plus a control-structure statement. On LLM-SRBench's four LSR-Synth scientific domains, the system raises average Acc@0.01 over the strongest comparable baseline from 25.79% to 48.30% when built on Llama3.1-8B-Instruct, and the distilled A-SR-LoRA raises the Qwen3-4B-Instruct result from 24.58% to 38.29%; on four real-world tasks it takes the best ID/OOD NMSE on seven of eight reported metrics. The paper argues the improvement comes from making the role-conditioned evidence view the unit of control: evaluator feedback is turned into reliability and productivity profiles that select a coordination protocol, update role-level utilities, and route elite motifs, failure traces, and validity diagnostics to different agents, so the next proposal sees the evidence matching its current failure mode. Ablations against fixed role rotation and against removing memory routing or protocol selection are used to support the claim that coordination, not role prompting alone, is what carries the gains.","pith_inferences":["The same role-conditioned evidence-view control could apply to other LLM program-search domains (e.g., code repair or theorem proving) where failures are heterogeneous, though the protocol archetypes would need re-deriving per domain.","The claimed gains likely depend on the early profiling budget B0=80 and on the fixed reward weights; a sensitivity sweep over these would reveal whether the method's margin over DE is robust or tuned.","The paper's evidence that role usage stays non-collapsed suggests the coordinator is solving a multi-armed bandit over roles; connecting it to bandit guarantees could give a principled regret bound for the test-time adaptation.","A-SR-LoRA's distillation corpus is teacher-generated on synthetic tasks; a direct test would be whether the adapters transfer to unseen experimental datasets beyond the four reported real-world tasks."],"forward_implications":["Scientific equation discovery with 8B-or-smaller open models becomes a practical target: the same coordination loop roughly doubles solved-task rate on LLM-SRBench's scientific domains without finetuning the backbone.","Small-model users can buy further accuracy by distilling recorded search trajectories into role-conditioned LoRA adapters, as A-SR-LoRA does with Qwen3-4B.","Because the coordinator is defined by explicit protocols, rewards, and routing rules, the search becomes auditable: one can see which role acted, which memory it saw, and which failure mode changed.","The separation of static, online, and distilled variants suggests deployment choices: broad expression recovery, reliability under shifting search states, and cheap open-source inference can be traded off.","Treating process traces, not just candidate populations, as search state opens a path toward learned controllers trained on meta-SR task banks."],"supporting_citations":[{"why":"LLM-SRBench provides the LSR-Synth scientific domains and Acc@0.01 success metric that carry the headline numbers.","marker":"Shojaee et al. 2025b"},{"why":"LLM-SR supplies the executable-program formulation of symbolic regression and the four real-world scientific discovery tasks.","marker":"Shojaee et al. 2025a"},{"why":"Deliberate Evolution is the closest agentic baseline; its reported results define the 25.79% and 24.58% baselines that A-SR claims to improve.","marker":"Pang et al. 2026"},{"why":"DSR is one of the neural symbolic regression baselines compared on the real-world tasks.","marker":"Petersen et al. 2021"},{"why":"uDSR is a unified deep symbolic regression baseline compared on the real-world tasks.","marker":"Landajuela et al. 2022"},{"why":"PySR serves as an evolutionary symbolic regression baseline in the real-world comparisons.","marker":"Cranmer 2023"},{"why":"Supplies the BFGS quasi-Newton optimizer used by the evaluator to fit continuous parameters in all A-SR variants.","marker":"Fletcher 2013"},{"why":"vLLM serves the open-source LLM backbones and is part of the infrastructure for the benchmark runs.","marker":"Kwon et al. 2023"}],"fun_headline_variants":["A-SR doubles symbolic regression solved-rate via role-aware agents","From 26% to 48%: agentic routing doubles sym-reg accuracy","Role-conditioned agents lift symbolic regression success from 26% to 48%","A-SR: self-evolving agents double equation discovery rate"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The hand-coded protocol selector and the fixed reward weights in the role-utility update are assumed to transfer across scientific domains, and the first 80 evaluated candidates are assumed to be enough to profile the search; if those assumptions fail for a new domain, the reported gains over the baselines would not generalize.","fun_headline_variants_meta":{"raw":{"variants":["A-SR doubles symbolic regression solved-rate via role-aware agents","From 26% to 48%: agentic routing doubles sym-reg accuracy","Role-conditioned agents lift symbolic regression success from 26% to 48%","A-SR: self-evolving agents double equation discovery rate"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000884,"raw_usage":{"total_tokens":3873,"prompt_tokens":1056,"completion_tokens":2817,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":672,"completion_tokens_details":{"reasoning_tokens":2739}},"tokens_in":672,"tokens_out":2817,"duration_ms":21288,"temperature":1.0,"reasoning_tokens":2739,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T17:24:01.279936+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct test would be to run A-SR on LLM-SRBench's LSR-Synth domains with a different profiling budget (say B0=20 or B0=200) or with per-domain-tuned reward weights, and check whether the Acc@0.01 improvement over DE persists; if the margin collapses, the reported gain is tied to the hand-coded coordination rule rather than to the role-conditioned evidence-view principle. A second test: hold out entire scientific domains, re-derive the protocol-selector thresholds only on the held-in domains, and see if A-SR still beats DE on the held-out ones.","supporting_citations":[{"cited_title":"Nathan and Aravena, Ignacio and Mulcahy, Garrett and Petersen, Brenden , title =","cited_arxiv_id":null,"evidence_quote":"uDSR is a unified deep symbolic regression baseline compared on the real-world tasks."},{"cited_title":", journal =","cited_arxiv_id":null,"evidence_quote":"PySR serves as an evolutionary symbolic regression baseline in the real-world comparisons."}],"review_version":2}