Collaborative Principle Evolution via Evidence Transfer for Scientific Discovery

1 INTRODUCTION

• Existing LLM-based AI Scientists use hypothesis-driven loops but operate alone, while principle-aware methods maintain a context-specific evidence stream per cycle.Naively scaling principle optimization can make principles overconfident or noisy when evidence is duplicated, context-shifted, or awaiting replication.Source: §1 · p. 1
• Parallel branches must provide complementary coverage, use transfers compatible with their source context, and save more wall-clock time than screening costs.Source: §1 · p. 2
• COEVOLVE collects, deduplicates, discounts, scores, and routes branch-level evidence for target-branch posterior updates.Its transfer loop aims to maximize information gained from each branch while preserving branch autonomy.Source: §1 · p. 2
• Principle co-evolution couples independent branches through a shared pool of tested evidence, allowing likelihood updates without forming a global posterior.Branches explore different sub-domains over a shared principle space.Source: §1 · p. 2
• 66.5% mean solution quality versus 57.0% for PiEvo, with COEVOLVE alone above the published SOTA anchor on all five autoresearch tasks.COEVOLVE completed the same evaluation budget 1.80× faster than PiEvo on GPT-5.6-Terra.Source: §1 · p. 2
• The introduction presents principle co-evolution and COEVOLVE as a framework for widening parallel scientific exploration through evidence transfer.The evaluation covers six scientific-discovery tasks and five autoresearch tasks.Source: §1 · p. 2

2 RELATED WORK

• The review situates COEVOLVE among agentic-science systems and contrasts its parallel evidence sharing with PiEvo's single evidence stream (Pu et al., 2026).Source: §2 · p. 2
• Multi-agent discovery systems coordinate roles, plans, or reasoning, but communication remains prompt-level and leaves cross-agent record eligibility and weight unspecified.Source: §2 · pp. 2–3
• Parallel-search primitives manage information flow, yet experiment-level imports may be dependent or require replication; COEVOLVE imports gated, discounted observations.Source: §2 · p. 3

3.1 PROBLEM SETUP AND NOTATIONS

• Each branch tests hypotheses and maintains its own posterior over a shared principle universe; tested pairs form its local evidence.Source: §3.1 · p. 3
• The coordination core adds evidence exchange without changing the branch-level loop, publishing locally tested pairs as candidate imports.Source: §3.1 · p. 3

3.2 THEORETICAL FRAMEWORK

• A record’s value is the target-posterior entropy reduction it induces, net of transfer cost, measuring information the target does not already have.Source: §3.2 · p. 3
• The router admits candidates only when lower-confidence net value exceeds a margin, then ranks survivors by certified value per transfer cost, subject to quota and redundancy caps.Source: §3.2 · p. 4
• Cross-branch observations enter through an explicit source-to-target likelihood discounted for context heterogeneity, with each accepted import contributing one factor to the target posterior.Source: §3.2 · pp. 4–5
• With a finite principle universe and positive prior, linearly growing discounted log-likelihood contrast yields exponential posterior concentration; calibrated value estimates let the gate bound below-margin admissions.Source: §3.2 · p. 5
• Exact enumeration certifies the numerical update, not Gaussian Process misspecification or residual context shift, so the gate remains a conservative heuristic rather than a deployed guarantee.Source: §3.2 · p. 5
• Branches keep their posterior and search history private by construction, while privacy-preserving variants for sensitive shared evidence remain future work.Source: §3.2 · p. 5

4.1 EXPERIMENT SETUP

• The evaluation covers six scientific benchmarks, compares COEVOLVE with vanilla multi-agent, autonomous-agent, and principle-guided baselines, and uses two backbones, three seeds, and a 72-query budget.COEVOLVE uses three branches by default, with 24 queries per branch.Source: §4.1 · pp. 5–6

4.2 EVALUATION METRICS

• SQ measures the best normalized outcome, APD the spread of valid hypotheses, and AUOC how early strong running-best values arrive; Table 2 compares exploration and exploitation.The pooled branch trajectories are used to score multi-branch COEVOLVE runs.Source: §4.2 · p. 6, Table 2 · p. 7

4.3 PERFORMANCE ANALYSIS

• COEVOLVE achieves the highest average SQ on both backbones (63.9%–69.1%) and the best average APD and AUOC on both, leading the exploration–exploitation balance.Its average SQ represents an 8%–20% relative gain over InternAgent-1.5 and an 11%–23% gain over PiEvo.Source: Table 1 · p. 6, §4.3 · p. 7, Table 2 · p. 7

4.4 EFFICIENCY ANALYSIS

• 1.80× wall-clock speedup comes with a 1.22× token premium and a 0.97× per-token conversion rate; token-normalized AUOC favors COEVOLVE on four of six tasks.The efficiency analysis also reports end-to-end time, token-normalized AUOC, equal-time quality gap, and Pareto optimality.Source: Figure 4 · p. 7, §4.4 · p. 8

4.5 CASE STUDY ON AUTONOMOUS RESEARCH HARNESS

• COEVOLVE alone keeps all five autoresearch task means above their SOTA anchors, raising the cross-task average from PiEvo’s +5.8 to +16.7; the coordination core adds +10.9 points beyond stage guidance.Stage guidance adds +0.4 percentage points; the reported case-study setup uses five tasks and a 72-evaluation budget.Source: §4.5 · p. 8, Table 3 · p. 8

4.6 ABLATION STUDY

• Sharing improves best-of-seed SQ over Isolated on all six tasks; discounting matters most, while branch-count and routing optima vary by task and setting.Removing discounting costs 19.0 SQ, while the preferred branch count differs across MBO, AMP, and TMC.Source: §4.6 · p. 9

5 CONCLUSION

• 66.5% mean solution quality versus 57.0% for PiEvo; COEVOLVE keeps branch-level posteriors separate while routing gated, discounted evidence.The coordination core couples branches through observations rather than a shared posterior.Source: §5 · p. 10
• 1.80× wall-clock speedup versus PiEvo, alongside the reported mean solution-quality advantage.Source: §5 · p. 10
• COEVOLVE is the only system above the published SOTA anchor on each of five representative auto-research tasks.Source: §5 · p. 10

A FORMAL ASSUMPTIONS AND GUARANTEES

• Before entropy saturation, complementary branch information and per-branch information-rate and activity floors yield a coverage rate proportional to branch count, discounted by redundancy and idle rounds.The result requires Assumptions 2–3; the proof does not require independence across rounds or branches.Source: A FORMAL ASSUMPTIONS AND GUARANTEES · p. 14, §B.1 · p. 16
• Under calibrated discounted-contrast and finite-likelihood assumptions, posterior mass on the true principle converges exponentially fast in effective samples, including fractional-weight imports.Effective samples count local observations at weight 1 and imports at their discount weight.Source: A FORMAL ASSUMPTIONS AND GUARANTEES · pp. 14–15, §B.2 · p. 17
• With calibrated value-estimate error radii, the probability of accepting any import whose net value is at or below η is bounded by the summed candidate-specific failure budgets.The guarantee is only as strong as the calibration of the radius used by the gate.Source: A FORMAL ASSUMPTIONS AND GUARANTEES · p. 15
• If active branches have positive discovery hazards and discover independently conditional on history, the discovery-time tail decays exponentially at the combined hazard rate.For small, comparable per-branch hazards, the expected time to first discovery shrinks roughly by a factor of K.Source: A FORMAL ASSUMPTIONS AND GUARANTEES · p. 15

B.1 PROOF OF PARALLEL MUTUAL-INFORMATION COVERAGE

• The parallel-coverage proof telescopes round-level information and lower-bounds active rounds; it uses no independence assumption across rounds or branches.The per-round information floor is consistent only before the prior entropy is saturated; afterward the rate must be re-derived from residual entropy.Source: §B.1 · pp. 16–17

B.2 PROOF OF BRANCH CONCENTRATION UNDER DISCOUNTED IMPORTS

• The concentration proof uses posterior odds and a simultaneous contrast bound; the effective evidence count sums full local weights and fractional import weights.The stated bound may be uninformative until the effective evidence count clears its crossover.Source: §B.2 · pp. 17–18

B.3 PROOF OF NEGATIVE-TRANSFER CONTROL

• Conditioning on each candidate when it is gated makes the calibration bound applicable even when the candidate stream is adaptive.The argument uses the calibrated-estimate assumption at this step.Source: §B.3 · p. 18
• When a candidate’s true net value is at or below η, a calibrated estimate within its error radius makes the gate reject it; a union bound sums failure probabilities across the realized stream.The resulting control depends on the allocated per-candidate budgets and the calibration radius.Source: §B.3 · p. 18

B.4 PROOF OF PARALLEL DISCOVERY UNDER HAZARDS

• Conditional independence of active branches’ discovery events lets the proof multiply their non-discovery probabilities and derive a combined hazard bound.The independence assumption excludes a common discovery failure mode beyond observed history.Source: §B.4 · p. 19
• With a common small hazard λ, the expected discovery time is bounded approximately by 1/(Kλ); perfectly coupled branches would provide no such speedup.Source: §B.4 · p. 19

Theorem A.1

• 1.03×–2.85× faster completion of the shared evaluation budget across all six tasks, with a +8.3 SQ average equal-time lead and best average APD on both backbones.The passage reports mean speedup of 1.80× and APD values of 52.0 and 58.1.Source: C THEOREM–EXPERIMENT ALIGNMENT · p. 20

Theorem A.2

• The shared arm’s best-of-seed SQ exceeds Isolated on all six tasks, while removing discounting costs 19.0 SQ, the largest knockout effect.Accepted imports are reported to yield up to +43.3 SQ points on TMC.Source: C THEOREM–EXPERIMENT ALIGNMENT · p. 20

Theorem A.3

• Removing the gate admits 137 imports rather than 42 and more than doubles outcome standard deviation from 4.6 to 11.1, while mean SQ shifts by only −2.1.The reported pattern is consistent with protection against rare harmful imports rather than a large mean shift.Source: C THEOREM–EXPERIMENT ALIGNMENT · p. 20

Theorem A.4

• On SPO, COEVOLVE sustains 15.3%–30.0% while systems without principle branching score 0.0%; at fixed budget, the branch-count response peaks at K=3 on MBO.The evidence ties the discovery advantage to hazard diversity rather than branch count alone.Source: C THEOREM–EXPERIMENT ALIGNMENT · p. 20

• Source trust discounts branches that mispredict their measurements, while context compatibility and independent replication affect transfer weight and cost.Context shift is the only state-dependent transfer cost and makes less-compatible evidence both more discounted and more expensive; missing estimates fail closed at zero.Source: D IMPLEMENTATION DETAILS OF THE… · p. 21
• The value estimate measures expected target-posterior entropy change after a candidate import, weighted by the source outcome’s empirical-rank relevance.The core evaluates the finite principle universe by cloning the target posterior and applying the evidence at weight α; the value estimate changes this calculation through relevance weighting, cost constants, and exact enumeration.Source: D IMPLEMENTATION DETAILS OF THE… · p. 21
• Routing drops near-duplicate candidates within each branch’s admitted set using a token-Jaccard cap, retaining the highest-ranked candidate.This approximate per-round routing filter is distinct from exact-hash deduplication in the evidence pool; the default cap is Rmax=0.3, while Rmax=1 disables the approximate cap.Source: D IMPLEMENTATION DETAILS OF THE… · p. 21
• The core logs accepted and rejected candidates, discount components, duplication, replication, predictive-density checks, entropy changes, and coordination time.Rejected records remain in the pool without altering target posteriors.Source: D IMPLEMENTATION DETAILS OF THE… · p. 21
• The defaults include a relevance floor of 0.1, a −25 predictive-density rejection threshold, and a per-candidate confidence schedule with total δ=0.05.Constants are fixed across tasks, backbones, and ablations unless explicitly varied; all runs use three fixed seeds per cell, and the per-task principle universe, prior, and GP outcome models follow PiEvo unchanged.Source: D IMPLEMENTATION DETAILS OF THE… · p. 21, Table 4 · p. 22
• Candidates pass the safe-value gate, are ranked within a target’s routing quota, and enter its posterior as likelihood factors raised to the transfer weight.The loop then monitors diversity and audit diagnostics for the next round; under Gaussian predictive models, the discounted update contributes a corresponding term to the target log posterior.Source: D IMPLEMENTATION DETAILS OF THE… · pp. 21–22

E ABLATION OF HYPERPARAMETERS IN COEVOLVE

• MBO peaks at K=3, AMP is flat, and TMC reaches a plateau matching or exceeding PiEvo from K=3 onward as branch count increases.The K=5 comparison uses unequal per-branch budgets of {15, 15, 14, 14, 14}, preserving the total budget of 72.Source: E ABLATION OF HYPERPARAMETERS IN… · p. 22, Figure 8 · p. 22
• In the one-at-a-time sensitivity analysis, best-of-seed SQ peaks at the default redundancy cap and routing quota, plateaus for λ from 1 to 2, and shows no monotone response to η.Source: E ABLATION OF HYPERPARAMETERS IN… · p. 22, Figure 9 · p. 23

F ABLATION OF EVIDENCE TRANSFER IN COEVOLVE

• On AMP, shared COEVOLVE reaches 37.6 ± 2.6 SQ, above Independent at 32.3 ± 0.6 and Isolated at 29.7 ± 2.0 (Welch’s t, p<0.05).The Independent–Isolated difference is within seed noise, whereas the shared arm remains clearly best.Source: F ABLATION OF EVIDENCE TRANSFER IN… · p. 24, Table 5 · p. 24
• On NHO, all arms saturate at 94.4–95.0 SQ, and Independent nominally matches COEVOLVE within noise.The passage characterizes NHO as a seven-dimensional continuous search space with a smooth surrogate and little complementary coverage left to transfer.Source: F ABLATION OF EVIDENCE TRANSFER IN… · p. 24, Table 5 · p. 24
• On NHO, COEVOLVE reaches the identical g-factor ceiling of 1.90 but converges 1.5× faster than Independent: 120 versus 184 minutes.The same speed-oriented signature appears on the Terra backbone as a +10.5 equal-time gap in Figure 4(c).Source: F ABLATION OF EVIDENCE TRANSFER IN… · p. 24
• Disabling discounting or redundancy control degrades portfolio and worst-branch quality; disabling the VoI gate admits over 3× as many imports and raises variance.With the gate disabled, two of three seeds degrade, consistent with protection against rare harmful imports rather than an average-case quality effect.Source: F ABLATION OF EVIDENCE TRANSFER IN… · p. 24, Table 6 · p. 25
• Table 7’s pooled-best uplift is a window-level association, not a causal transfer estimate; its inert rate measures immediate running-best changes, and TMC and Promoter have only 2 and 1 accepted imports.The table also reports evidence-flow, deduplication, and budget-splitting quantities; uplift is value-selected and need not agree with the branch-level inert rate.Source: Table 7 · p. 25, F ABLATION OF EVIDENCE TRANSFER IN… · p. 25

G STATISTICAL ANALYSIS

• Experiments use three seeds per cell, so headline comparisons rely on aggregate paired tests over the 18 Terra task–seed pairs rather than individual per-task tests alone.Per-task tests are reported for completeness.Source: G STATISTICAL ANALYSIS · p. 26
• Across 18 Terra task–seed pairs, COEVOLVE’s paired SQ gain is positive in 15 of 17 non-tied pairs (sign test p=0.002), and wall-clock speedup exceeds 1× in 17 of 18 pairs (p=1.5 × 10−4).The equal-time gap is positive in 15 of 17 non-tied pairs (p<0.01; Wilcoxon p=8 × 10−4); the table pools all 18 task–seed pairs.Source: G STATISTICAL ANALYSIS · p. 26, Table 8 · p. 26
• Only 4 of 12 task–backbone pairs reach p<0.05 against PiEvo, and only SPO (Gemma) and NHO (Terra) survive Bonferroni correction.The authors therefore state the closed-world claim as best average SQ with the aggregate paired test, not per-task superiority on every task; tests use rounded summary statistics with n=3 per cell.Source: G STATISTICAL ANALYSIS · p. 26, Table 9 · p. 26
• On all five autoresearch tasks, COEVOLVE’s mean improvement is significantly above the anchor, but pairwise comparisons against individual reference arms are underpowered at three seeds.The reported interval argument is that COEVOLVE’s worst case matches or exceeds every other arm’s best case on all five tasks.Source: G STATISTICAL ANALYSIS · p. 26

H.1 TASKS AND BASELINES / H.2 MEASUREMENTS

• COEVOLVE spends 1.55× PiEvo’s billable tokens on average, while ALDE uses less than 1× as its branches converge early and exhaust the budget sooner.The five tasks require method artifacts and use published SOTA anchors with sealed graders; the grader reports per-instance improvement relative to each anchor.Source: §H.1 · p. 27, §H.2 · p. 28, Table 10 · p. 28

H.3 EFFICIENCY IN THE HARNESS REGIME

• COEVOLVE’s equal-time quality gap over PiEvo is positive on all five tasks, averaging +12.3 percentage points and never falling below the budget-end gap.All fifteen COEVOLVE runs reach PiEvo’s mean final quality; the self-TTT ratio is 0.9/1.2/0.8/1.3/1.9× on ALDE/Deconv/InvScat/D2D/MolEdit, respectively.Source: Figure 11 · p. 28, §H.3 · p. 28, Table 11 · p. 29

H.4 TRAJECTORY PATTERN

• COEVOLVE’s AUOC is best on ALDE (+0.006), Deconv (0.212), and InvScat (−0.090), ties PiEvo on D2D, and trails PiEvo on MolEdit.It leads at the later stage on all five tasks, but not throughout; on D2D, Arbor is best at 0.1447.Source: §H.4 · p. 28, Figure 12 · p. 29

H.5 TASK EXPLORATIVENESS ANALYSIS

• COEVOLVE’s margin over the runner-up rises with task explorativeness: +0.1/+2.8 points on D2D/MolEdit, +4.2 on ALDE, and +30.0/+17.2 on Deconv/InvScat.The four reference arms are negative on InvScat, while COEVOLVE is the unique positive arm there and remains positive across all five tasks.Source: §H.5 · p. 29

I.1 DESIGN PRINCIPLES

• The benchmark is designed to make tasks searchable rather than memorizable, gate scores on admissible physical properties, and normalize quality using fixed domain-defined reference scales.Gate rejections consume evaluations and score 0.0; the scale bounds hold by construction for four tasks and empirically with wide margin for MBO and SPO.Source: §I.1 · pp. 31–32, Table 12 · p. 32

I.2 NANOHELIX OPTICAL-CHIRALITY OPTIMIZATION (NHO)

• NHO is a seven-dimensional coupled structure–environment optimization whose simulator-defined optimum lies on a narrow manifold requiring aligned excitation.Its parameters cover four helix properties and three excitation properties; the optimum is simulator-defined and appears in no publication.Source: §I.2 · p. 32

I.3 MOLECULAR BIO-ACTIVITY OPTIMIZATION (MBO)

• MBO maximizes a molecular regressor’s predicted pChEMBL activity, with a PAINS filter blocking assay-interference motifs that could inflate predicted scores without genuine binding.Each pChEMBL unit corresponds to an order of magnitude in potency.Source: §I.3 · p. 33

I.4 ATYPICAL ANTIMICROBIAL-PEPTIDE DESIGN (AMP)

• AMP maximizes the macrel classifier’s confidence over 12–50-residue peptide sequences to probe its decision boundary away from the classifier’s saturation region.Source: §I.4 · p. 34
• AMP reverses the textbook AMP profile: candidates must be acidic and moderately hydrophobic, so success requires finding alternative classifier-responsive features rather than relying on prior knowledge.Candidates have net charge ≤0 at pH 7 and hydrophobic fraction in [0.30, 0.60], with repeat and diversity constraints against degenerate sequences.Source: §I.4 · p. 34

I.5 PROMOTER EXPRESSION OPTIMIZATION (PROMOTER)

• The motif-free promoter landscape spans ∼7.7–14.7, requiring discovery of non-canonical expression drivers after banning yeast GRF motifs and GC-box cores.The task scores 50-nucleotide sequences with a yeast-trained LegNet surrogate; candidate constraints also prevent repetitive or degenerate sequences.Source: §I.5 · pp. 34–35

I.6 TRANSITION-METAL-COMPLEX POLARIZABILITY OPTIMIZATION (TMC)

• TMC searches 82,800 valid combinations of four distinct ligands from a 49-ligand pool, requiring exactly two anionic and two neutral ligands for charge neutrality.The objective is to maximize polarizability; the task frames this as a combinatorial search with a smooth but subtle surrogate response.Source: §I.6 · p. 35

Superconductor Critical-Temperature Optimization

• SPO searches copper-oxide formulas for the highest possible critical temperature, with room temperature (298.15 K) as the stated target.The task considers element-first, ratio-second formulas and specifies no environmental conditions.Source: §I.7 · pp. 36–37
• The search spans La-Sr-Cu-O, La-Ba-Cu-O, and Nd-Ce-Cu-O families, including genuine two-site co-doping.Co-doping may combine a rare-earth site with Cu or two rare earths; ratios are given to two decimal places.Source: §I.7 · pp. 36–37
• Candidates matching specified textbook superconductor backbones or violating formula constraints score 0.0.Banned backbones include Y-Ba-Cu, Bi-Sr-Ca-Cu, and Hg- or Tl-bearing Ba-Ca-Cu; formulas also need at least four distinct elements and no more than two decimal digits in ratios.Source: §I.7 · pp. 36–37
• SPO presents a bimodal landscape, with surrogate-scored basins near 27–35 K and 80–95 K; early exploration determines which basin a trajectory locks onto.The lower basin is conventional La-based, while the higher basin is electron-doped T′-phase.Source: §I.7 · p. 36