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Epi: Towards a Persistent, Self-Improving Agent for Autonomous Research

Yue Huang, Zhangchen Xu, Xiaonan Luo, Zheyuan Liu, Lichi Li, Yiping Wang, Peiyang Song, Eric Gabriel Ramos, Enze Xie, Olexandr Isayev, Paul Liang, Nouha Dziri, Huan Sun, Jianfeng Gao, Ying Liu, Misha Sra, Xiangliang Zhang, Alex Pentland, Zichen Chen

arXiv:2610.24944v1cs.CLcs.AI

TL;DR

Autonomous research agents face the challenge of sustaining investigations and learning across model sessions. Épi combines persistent memory, branching and review with fixed verification; its campaigns produce record-setting mathematical results and Épi-turbo outperforms Codex on FrontierOR tasks at lower model cost.

  • Problem

    Autonomous research investigations can span more than one model session, requiring continuity, reusable experimental lessons and ways to preserve and compare alternatives.

    Source: §1 · pp. 1–2

  • Method

    Épi uses persistent research state, hierarchical memory, versioned branches and independent review, with candidates evaluated under a fixed ruler and verifier.

    Source: §1 · p. 2, §2.2 · p. 3

  • Results

    Épi produced 120 record-setting results, while Épi-turbo scored 5.4% higher than Codex on 30 FrontierOR tasks at 64% of its model cost.

    Source: §1 · p. 2, §9 · p. 16

  • Takeaways & Limitations

    Persistent records and explicit constructions and proof arguments support inspection of the research process and further scientific work.

    Source: §9 · p. 16

    Model weights were fixed in the reported campaigns.

    Source: §2.2 · p. 3

Abstract

from arXiv · show

We present \'{E}pi, an autonomous research agent that sustains investigations across model sessions and evolves its methods through accumulated experience. \'{E}pi combines persistent research history, hierarchical memory, branching and independent review to maintain research continuity, learn from experiments, and explore and revisit alternative approaches. Its experiments run across session boundaries, and a fixed verifier evaluates their outputs. \'{E}pi produced 120 record-setting results, comprising 20 numerical bound records across 12 families and 100 construction records across eight families. These include an approximately 84-fold narrower interval for the $n$-queens constant and a more than 3.6-million-fold narrower rigorous interval for the quartic Feigenbaum attractor dimension. Exact dual certificates establish that the Cohn-Elkies linear-programming bound cannot be sharp in dimensions 10 and 11. Beyond numerical improvements, \'{E}pi gives a computer-assisted proof of Tuza's conjecture for split graphs with an eight-vertex clique part and at most three triangle-active neighborhood types, with arbitrary multiplicities. We extend this research process to algorithmic coding with \'{E}pi-turbo, a lightweight configuration that develops executable solvers for tasks including vehicle routing, scheduling and production planning. On 30 FrontierOR tasks, \'{E}pi-turbo achieves a 5.4% higher total benchmark score than Codex at 64% of its model cost, using the same underlying model and reasoning effort. \'{E}pi is designed to support human understanding by connecting computational results to explicit methods and mathematical arguments that researchers can examine and build upon.

1 Introduction

Autonomous investigations must preserve research state and evidence-linked lessons across sessions while exploring and revisiting alternatives. Épi combines persistent memory, branching, independent review and fixed verification, producing mathematical records and extending the process to algorithmic coding.

Research challenges

  • Long investigations require continuity of experiments and decision rationale, retrieval of evidence-linked lessons, and preservation of alternatives for comparison and backtracking.These needs arise because research decisions span sessions and ongoing experiments generate new evidence.Source: §1 · pp. 1–2

Épi

  • Épi sustains investigations with hierarchical memory, versioned branches, independent review and persistent execution across model sessions.Branches share feasibility checks, an objective and comparison value; verified findings can establish references for later campaigns.Source: §1 · p. 2

Algorithmic coding

  • On 30 FrontierOR tasks, Épi-turbo scored 5.4% higher than Codex at 64% of its model cost, using the same model and reasoning effort.The tasks include routing, scheduling, production planning and graph optimization.Source: §1 · p. 2

Contributions

  • The collection reports 120 record-setting results: 100 improved constructions and 20 numerical bounds, each improving a documented literature or registry reference for the same problem and normalization.It gives an approximately 84-fold narrower interval for the n-queens constant and a more than 3.6-million-fold narrower rigorous interval for the quartic Feigenbaum attractor dimension; exact certificates show the Cohn–Elkies bound is not sharp in dimensions 10 and 11. It proves Tuza’s conjecture for split graphs with an eight-vertex clique part and at most three triangle-active neighborhood types, with arbitrary multiplicities.Source: §1 · p. 2

Human understanding

  • Épi preserves implementations, artifacts and notes so researchers can inspect method development and assess evidence supporting computational findings.The paper also connects outputs to explicit constructions, certificates and mathematical arguments.Source: §1 · p. 2

2 Research Setting

The research setting specifies how candidate outputs are checked and compared, then defines how investigations persist across bounded model sessions.

2.1 Problems and Evidence

  • A task’s ruler specifies submission format, feasibility, objective, normalization and comparison value, while improvement is measured against a reference with a prespecified gain floor.Records retain comparison values and sources; theorem claims require a proof connecting checked objects to the full claim.Source: §2.1 · p. 3

2.2 Campaigns and Sessions

  • A campaign is a complete investigation that can span sessions, with saved research state and running experiments resumed by later sessions.The reported campaigns keep model weights fixed; methods adapt through feedback, retrieved memory and independent review.Source: §2.2 · p. 3

3 The Épi Research Loop

Épi’s research loop compares evolving methods under consistent task rules, while persistent records and feedback support branching, memory, review and later inspection.

3.1 Evolving Research Environments

  • Before search, Épi establishes a common evaluation rule by checking scorer reproduction, input validation, configuration, feasibility checks and the gain criterion.The shared rule gives branches a consistent basis for comparing methods.Source: §3.1 · pp. 3–4
  • Verification requirements match claim types, and verified findings can update later campaigns’ references, task formulations and evidence requirements.Computer-assisted theorems require finite checks plus a mathematical reduction; numerical certification may require exact arithmetic or controlled error.Source: §3.1 · p. 4

3.2 Self-improving Research Agents

  • Versioned branches preserve implementations, tests and evidence, letting Épi compare alternatives under one ruler and resume from earlier work.Abandoned branches retain reasons for abandonment and remain available for inspection.Source: §3.2 · pp. 4–5
  • Hierarchical memory separates current-investigation context from reusable experience, including lessons and documented dead ends retrieved to guide later experiments.Handover notes and referenced files let later sessions recover relevant state without replaying the full history.Source: §3.2 · p. 5
  • A separate review model assesses whether evidence supports the agent’s interpretation of progress, while an isolated verifier checks candidate validity and gain.The review is recorded for subsequent sessions and experiment selection.Source: §3.2 · p. 5
  • Persistent records of alternatives, outcomes and assessments let researchers compare branches, inspect evidence behind changes and revisit implementations.Lessons summarize reusable findings and link to code and experimental artifacts.Source: §3.2 · p. 5

4 Experimental Results

The reported collection comprises numerical-bound and construction records, counted by distinct final instances or parameter settings and compared under consistent conventions.

4.1 Setup and Counting

  • 120 record-setting results comprise 20 numerical bounds across 12 families and 100 constructions across eight families; Tuza’s theorem extension is separate from that count.One final result counts per distinct instance or parameter setting; intermediate improvements do not add records.Source: §4.1 · pp. 5–6

4.2 Construction Records

  • 97 of the 100 construction records concern geometric packing; the other three cover vehicle routing, a signed-maximum inequality variant and a Zhang–Zagier construction.Figure 2 groups final records by collection and family; repeated improvements to one setting count once.Source: §4.2 · p. 6, Figure 2 · p. 6

4.3 Numerical Bound Records

  • The numerical-record overview covers 20 records across 12 families, with improving directions indicated and interval widths reduced in rounded form.Precise bounds are provided in the appendix and Table 2.Source: §4.3 · p. 6, Table 1 · p. 7

5 Case Studies

The case studies apply Épi to refine constructions, certify numerical bounds, optimize a hardness formulation, and prove a new case of Tuza’s conjecture. Their results range from improved records to a computer-assisted theorem for split graphs.

5.1 Refining a Published Packing

  • The 34-unit-pentagon packing reduces the enclosing triangle’s side length from approximately 12.9814 to 12.9756, a 0.0445% reduction.Épi jointly refines pentagon centers and orientations while checking containment and overlap.Source: §5.1 · p. 7

5.2 Separating the Cohn–Elkies Bound from Packing Density

  • In dimensions 10 and 11, dual lower bounds exceed packing upper bounds by approximately 0.35% and 1.92%, showing exact Cohn–Elkies optimization cannot attain the true density.The table and figure use center-density normalization; the separation implies additional constraints or a different bounding method are needed for a sharp bound.Source: §5.2 · pp. 8–9, Figure 4 · p. 9, Table 2 · p. 9

5.3 Narrowing the Interval for the n-Queens Constant

  • The n-queens constant’s interval narrows by approximately 84-fold, from 3.30 × 10^-7 to approximately 3.94 × 10^-9.Rational feasibility checks and directed rounding support the refined bounds, with each endpoint having a retained witness.Source: §5.3 · pp. 9–10

5.4 Optimizing a Formulation: MAX-4-CUT

  • For MAX-4-CUT, Épi optimizes edge weights in Nagda et al.’s fixed gadget framework through a linear program with coloring constraints.The released weighted edge list and finite checks verify the resulting hardness ratio exactly.Source: §5.4 · p. 10

5.5 A Finite Construction for the Spencer Constant

  • An 8 × 8 matrix with discrepancy exactly five raises the Spencer constant’s record lower bound from 7/8.Enumerating all 256 sign assignments verifies the matrix’s discrepancy.Source: §5.5 · p. 10

5.6 Certifying Near-Optimal Water-Network Design

  • For waterund36, the certified lower bound comes within approximately 10^-5 of the same known feasible value, closing more than 99.999% of the MINLPLib gap.A relaxation containing every feasible network and exact rational inequalities extend the certificate to the original nonlinear problem.Source: §5.6 · p. 11, Figure 6 · p. 11

5.7 From Numerical Optimization to Proof: Tuza’s Conjecture

  • Épi proves τ△(G) ≤ 2ν△(G) for split graphs with an eight-vertex clique part and at most three triangle-active neighborhood types, without restricting their multiplicities.The extension covers three types with unrestricted overlaps, whose triangles can compete for the same clique edges.Source: §5.7 · p. 12
  • The proof checks 872 three-type profiles, including exact cover and packing certificates for 560 profiles, then extends the result to arbitrary multiplicities.An independent checker verifies witnesses and the complete profile enumeration; Zeng’s truncation lemma connects these finite checks to the infinite family.Source: §5.7 · p. 12

6 Épi-turbo: Fast, Low-cost Algorithm Design

Épi-turbo adapts Épi’s persistent, branch-based research process for low-budget algorithm design, testing executable solvers under a fixed evaluator. On 30 FrontierOR tasks, it scores higher overall than Codex while using less model cost.

6.1 Purpose and Design

  • Épi-turbo designs, implements, and tests solvers for new instances, retaining verified research state and branch-specific code and evidence across sessions.Its sessions continue the best method, record state and next steps before ending, and stop when further sessions do not improve the best verified score; the maximum call cost is reserved within budget, and independent review and extra validation are off.Source: §6.1 · pp. 12–13

6.2 Benchmark and Protocol

  • The benchmark tests standalone programs on unseen instances, compares quality and runtime against references, and excludes tasks with unreliable reference values.The selected 30 tasks were new to both systems; held-out evaluation uses four instances per task, each with a one-hour limit, and the study reports no statistical significance because there is one run per system per task.Source: §6.2 · p. 13

6.3 Results

  • Épi-turbo scores 53.96 against Codex’s 51.21 on 30 FrontierOR tasks while using 64% of Codex’s model cost.The same model and reasoning effort are used; each system receives a $20 budget per task, with one run per task and system.Source: §6.3 · p. 13, Table 3 · p. 14
  • Épi-turbo has the higher score on 18 tasks, with total gains of 4.54 versus total losses of 1.79; it costs less on 27 tasks.Figure 7 displays task-level score differences, model costs, and held-out runtimes.Source: §6.3 · p. 13, Figure 7 · p. 14
  • On the 13-task hard split, Épi-turbo scores 10% higher and wins on 9 tasks; the two systems are close on ranks 51–70.Across all 30 tasks, Épi-turbo has both the higher score and lower model cost on 15.Source: §6.3 · p. 13, Table 4 · p. 14
  • The higher score comes mainly from speed: median held-out runtime is 2.9 seconds for Épi-turbo versus 9.3 seconds for Codex.No Épi-turbo held-out run exceeds 30 minutes, while Codex exceeds 30 minutes on 17 of 120 runs across 7 tasks; long runs can improve solutions but decrease the speed term.Source: §6.3 · p. 13

6.4 Selected Cases

  • Selected cases show complementary gains: both score terms improve in clique interdiction, production planning crosses the 1% band, maximum clique matches references, and vehicle-routing runs are faster.The ten largest score-difference cases span vehicle routing, scheduling, production planning, facility location, clustering, and graph optimization; Table 5 reports held-out scores, quality, and speed.Source: §6.4 · pp. 13–15

7 Related work

Related systems explore alternatives, preserve research state, or evaluate executable outputs in different ways. Épi combines persistent state and branches while keeping its model weights fixed and its verifier fixed within a campaign.

7 Related work

  • AI Scientist-v2 uses agentic tree search for experimental alternatives, while Co-Scientist uses critique and InternAgent-1.5 coordinates generation with verification [Yamada et al., 2025; Feng et al., 2026].AIRA2 addresses asynchronous experiments with a consistent evaluation protocol; Épi keeps its verifier fixed as its approach changes [Hambardzumyan et al., 2026].Source: §7 · pp. 15–16
  • Kosmos connects literature search and data analysis; ScienceFlow preserves resumable executable states, while AgentRxiv and AutoKD pass knowledge between investigations [Mitchener et al., 2025; Zhao et al., 2026; Ge et al., 2026].Épi retains both campaign state and reusable lessons, with branches preserving alternative histories.Source: §7 · p. 16
  • FunSearch and AlphaEvolve guide program generation by measured performance, while SimpleTES, Dream-RSI, and TTT-Discover use other search-history or model-adaptation strategies [Romera-Paredes et al., 2024; Novikov et al., 2025; Ye et al., 2026; Zheng et al., 2026; Yuksekgonakgül et al., 2026].Épi keeps model weights fixed and uses stored lessons and branch histories; its investigations can also find certificates or prove statements.Source: §7 · p. 16

8 Autonomous Research for Human Understanding

Épi aims to connect autonomous research with human understanding by making methods and supporting evidence inspectable. Its case studies connect computational artifacts to explicit formulations and arguments that researchers can examine and extend.

8 Autonomous Research for Human Understanding

  • Épi retains implementations, experiments, and assessments so researchers can examine how methods develop and understand results through explicit formulations and arguments.The cited examples include the Cohn–Elkies separation, a reusable MAX-4-CUT gadget-weight procedure, and finite certificates for a statement about an infinite graph family.Source: §8 · p. 16

9 Conclusion

Épi’s campaigns produced 120 record-setting results, with released constructions and certificates supporting checkable mathematical findings. The appendix reports improvements across numerical bounds and constructions, including rigorous intervals, exact certificates, and a proof for a bounded class of split graphs.

9 Conclusion; A Mathematical Results and Supporting Evidence

  • Épi’s collection contains 120 record-setting results, and its released constructions and certificates provide checkable evidence for the reported advances.The records comprise 100 improved constructions and 20 numerical bounds across 12 numerical families, as detailed in the appendix.Source: §9 · p. 16, A Mathematical Results and Supporting… · p. 20

A.1 Relevant Variables of Boolean Functions

  • The record bound on Wellens’ D∞ decreases from 4.3935 to 4.3654674227, supported by exact infeasibility certificates and rational feasibility witnesses for degrees 1 through 48.D∞ controls the number of relevant variables relative to Boolean-function degree.Source: §A.1 · p. 20

A.2 Cohn–Elkies Linear Programming

  • The Cohn–Elkies program’s optimum is separated from three-point packing upper bounds in dimensions 10 and 11 by final dual-vector lower bounds.The bounds use Li’s discrete reduction.Source: §A.2 · p. 20

A.3 Spencer Discrepancy Constant

  • The explicit 8 × 8 discrepancy-five matrix improves the universal-constant lower bound to 5/8 ≈ 1.767767 from 7/17 ≈ 1.697749.Exhausting all 256 sign assignments verifies the matrix’s discrepancy.Source: §A.3 · p. 20

A.4 Dimer Entropy in Three Dimensions

  • The record upper bound on cubic-lattice perfect-matching entropy decreases from 0.452130 to 0.452010.Positive integer vectors satisfy the transfer-operator inequalities; the resulting logarithm is approximately 0.452009597554483, and the stated bound is rounded upward.Source: §A.4 · p. 20

A.5 The n-Queens Constant

  • Approximately 84 times narrower, the n-queens constant interval is supported by retained lower and upper witnesses and rational feasibility checks.The witnesses have resolutions 65,536 and 4,096, respectively.Source: §A.5 · p. 20

A.9 Additive Combinatorics: Bh[g] Sets; A.11 Quantum-Capacity Thresholds

  • Épi improves all five Bh[g] coefficients, and its 40-qubit states improve reported independent X–Z and Two-Pauli thresholds of approximately 0.118371 and 0.118067.Separate interval spectral calculations verify positive coherent information for both states, establishing positive quantum capacity at the stated noise parameters.Source: §A.9 · p. 21, Table 6 · p. 21, §A.11 · p. 22

A.10 Quartic Feigenbaum Attractor Dimension

  • More than 3.6 million times narrower, the new quartic Feigenbaum attractor dimension interval has width 2.130433 × 10^-9.A separate implementation checks the pressure inequalities throughout the domain.Source: §A.10 · p. 21

A.12 Water-Network Design: Waterund36

For waterund36, a certificate establishes a global lower bound by ruling out networks at or below an exact rational cutoff. The resulting gap to the known feasible value is about 0.00001001.

A.12 Water-Network Design: Waterund36

  • The waterund36 certificate excludes objective values at or below an exact rational cutoff, leaving a gap of about 0.00001001 to the known feasible value 662.8070384.The comparison lower bound is 655.5441707; the proof lifts feasible networks into a bounded relaxation and derives incompatible bounds under the cutoff assumption.Source: §A.12 · p. 22

A.13 Tuza’s Conjecture: Proof for Three Neighborhood Types

Theorem 1 is proved for split graphs with an eight-vertex clique part and at most three triangle-active neighborhood types, with arbitrary multiplicities. A finite reduction and checked certificates cover the remaining neighborhood profiles.

A.13 Tuza’s Conjecture: Proof for Three Neighborhood Types

  • A neighborhood profile is a triple of active neighborhoods considered up to relabeling the clique part and permuting the three types.Independent vertices with fewer than two clique neighbors are discarded because they occur in no triangle.Source: §A.13 · p. 22
  • Truncating each neighborhood type to 28 copies preserves both triangle-cover and triangle-packing numbers, extending the finite result to arbitrary multiplicities.Every triangle uses a clique edge, so a packing uses at most 28 triangles; all 28 clique edges suffice for covers.Source: §A.13 · p. 22
  • The remaining 560 profiles with three distinct active neighborhood types are covered by exact certificates containing 18,444 integer boxes.An independent enumeration found 872 profiles; 35 have nested neighborhoods and 277 satisfy Zeng’s maximum-cut criterion, while cases with at most two types follow from Zeng’s theorem.Source: §A.13 · p. 22
  • A separate checker verified every certificate box’s triangle cover, edge-disjoint packing, cardinality inequality, and multiplicity-vector coverage; all 560 profiles and 18,444 boxes passed.The certificates cover the remaining profiles, and truncation extends the conclusion to arbitrary multiplicities, proving Theorem 1.Source: §A.13 · p. 23

B Additional Construction Results

The additional construction results include a refined 34-pentagon enclosing triangle and constructions for vehicle routing and signed autocorrelation. The comparisons use task-specific objective conventions and archived references where stated.

B Additional Construction Results

  • The 34-pentagon enclosing triangle side length decreases from 12.98141 to 12.97563735803487.Released coordinates retain the construction at full precision.Source: B Additional Construction Results · p. 23
  • The vehicle-routing construction serves 1,047 customers in 238 routes with vehicle capacity 128.Its objective uses the instance’s rounded Euclidean distances, and the route list determines customer coverage, capacity feasibility, and total length.Source: B Additional Construction Results · p. 23, Table 7 · p. 23
  • Under the signed-maximum objective, the released autocorrelation construction improves the archived reference by approximately 7.65 × 10^-4.For signed constructions, the signed-maximum and maximum-absolute-value variants can differ.Source: B Additional Construction Results · p. 23
  • The c82 Zhang–Zagier construction has an accompanying Arb-based numerical certificate for its objective.The comparison uses the archived reference from maaxgrin (2026).Source: B Additional Construction Results · p. 23

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