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

AI summary

Overview

Research area: Autonomous AI research agents, LLM-driven scientific discovery, and algorithmic code generation (cs.CL / NLP, with mathematical optimization).

Technical level: Intermediate. Readers should be comfortable with optimization bounds, certificates and dual witnesses, and with the basic mechanics of LLM agents (contexts, sessions, tool use). The system architecture itself is described in plain terms.

Scope: A technical report introducing Épi, an agent that carries a research program across multiple model sessions via persistent memory, branching and independent review, and that produces 120 record-setting mathematical results plus a low-cost variant, Épi-turbo, benchmarked on 30 operations-research coding tasks.

What This Paper Is About

Most AI research agents can only work within a single model session, so a long investigation outlives the agent's memory and forces it to restart. The authors build Épi to keep a research program alive across sessions: it stores code, artifacts and notes persistently, keeps a hierarchy of lessons and dead ends, develops competing approaches on separate versioned branches, and has a different model independently review its progress.

The claim is validated on problems whose outputs can be mechanically checked — numerical bounds, geometric constructions and a computer-assisted theorem — where Épi reports 120 results that beat documented literature or registry references. The authors also show the same loop transfers to algorithmic coding, where a lightweight configuration called Épi-turbo beats Codex on 30 FrontierOR tasks at 64% of its model cost.

Key Contributions

1. An integrated persistent research agent. Épi combines hierarchical memory (short-term working context plus long-term lessons and recorded dead ends), versioned branches with backtracking, and independent review by a different model, all running on the Breadboard execution infrastructure that keeps jobs and state alive across session boundaries.

2. A verification protocol with a "fixed ruler" and a gain floor. Before search begins, each task fixes the submission format, feasibility conditions, objective, normalization and comparison value, plus a positive gain floor δ; a candidate is accepted only if the verifier returns V(x)=1 and the improvement Δ(x) ≥ δ. The environment is allowed to evolve between campaigns, but every branch within a campaign is judged by the same rule.

3. 120 record-setting results traceable to literature or registry references. 20 numerical bound records across 12 families and 100 construction records across eight families (97 of the constructions are geometric packings), plus a Tuza's-conjecture extension that brings the report to 21 families but is excluded from the record count.

4. A transferable agent configuration for algorithm design. Épi-turbo keeps Épi's verifier, persistence, branching and memory but changes budget discipline (per-call cost reservation, continuous sessions, stopping when sessions stop improving), reaching a 5.4% higher total benchmark score than Codex on 30 FrontierOR tasks at 64% of the model cost.

Main Findings

• Headline record count: 120 record-setting results — 20 numerical bound records across 12 families and 100 construction records across eight families — with one final result counted per distinct instance or parameter setting, and intermediate improvements not counted. Comparisons are against references available as of September 16, 2026.

• n-queens constant: The interval for α narrows from [1.944000752, 1.944001082] (width 3.30×10⁻⁷) to 1.9440010223327 ≤ α ≤ 1.9440010262694 (width approximately 3.94×10⁻⁹), roughly an 84-fold reduction.

• Quartic Feigenbaum attractor dimension: The rigorous interval width drops from 7.80×10⁻³ to 2.13×10⁻⁹, a more than 3.6-million-fold narrowing, backed by a full-domain interval proof.

• Cohn–Elkies bound is not sharp in dimensions 10 and 11: New exact dual lower bounds (0.058044329039, 0.056433853144, 0.057731808202, 0.066440082613 for dimensions 9, 10, 11, 13) exceed the known packing upper bounds 0.05623600 (d=10) and 0.05664550 (d=11), giving relative separations of approximately 0.35% and 1.92%. This shows that even exact optimization of the Cohn–Elkies linear program cannot recover the true packing density in those dimensions.

• Spencer constant: An explicit 8×8 matrix with entries in {−1, 0, 1} whose discrepancy is exactly five — verified by exhausting all 256 sign assignments, giving row-maximum norms of five or seven — raises the lower bound from 7/√17 to 5/√8.

• A computer-assisted theorem: Épi proves Tuza's conjecture (τ△(G) ≤ 2ν△(G)) for split graphs with an eight-vertex clique part and at most three triangle-active neighborhood types, with arbitrary multiplicities. Of 872 three-type profiles, 35 are nested and 277 further satisfy Zeng's maximum-cut criterion; Épi constructs exact cover and packing certificates for the remaining 560 profiles using 18,444 multiplicity boxes, and Zeng's truncation lemma extends the checks to arbitrary multiplicities. This goes beyond prior work covering |C|=8 with at most two types.

• Beyond the headline records: Other improvements include Wellens' D∞ (4.393500 → 4.365467), dimer entropy (0.452130 → 0.452010), Ramsey c₄,₅ (0.007932 → 0.007865, via a 1,024-vertex graph), MAX-4-CUT (195581/198140 ≈ 0.987085 → 84931/86101 ≈ 0.986411), Klarner λ (4.52380 → 4.29569), quantum noise bounds (0.118371 → 0.118067 and 0.1198803 → 0.1193415), and the waterund36 MINLPLib lower bound (655.544171 → 662.807028, leaving a gap of 1.001×10⁻⁵ and closing more than 99.999% of the gap).

• A concrete packing refinement: For 34 unit-side regular pentagons in an equilateral triangle, Épi starts from a published side length of approximately 12.9814 and reaches approximately 12.9756, a 0.0445% reduction.

• Épi-turbo vs. Codex: On 30 FrontierOR tasks new to both systems, with both using GPT-6-Astra at the same reasoning effort and a $20 model budget per task, Épi-turbo scores 53.96 versus 51.21, wins on 18 tasks to 12, costs $7.30 versus $11.35 on average, and takes a median 22 minutes versus 37 minutes. Gains (4.54 total) outweigh losses (1.79), and Épi-turbo is cheaper on 27 of the 30 tasks.

• Where the score comes from: The mean quality term is nearly tied (1.030 vs. 1.032), while the mean speed term favors Épi-turbo (0.784 vs. 0.675). Median held-out runtime is 2.9 seconds versus 9.3 seconds, and Codex exceeded 30 minutes on 17 of 120 held-out runs across 7 tasks while no Épi-turbo run did.

• Honest caveats: On direct per-instance objective comparison Codex produces the better solution more often (61 instances to 18, with 40 ties out of 119 comparable), and Épi-turbo is more than 1% worse on 29 instances versus 10; it also produced 1 infeasible solution in 120 held-out runs versus 0.

Methodology in Plain English

Set up the measuring stick first. For each problem, a curator supplies the question and source material; the agent picks the methods. Before any search, the team verifies that the scoring script reproduces the published reference result, checks input validation, and locks in the feasibility checks, objective, normalization and a minimum meaningful improvement (the gain floor). This prevents the agent from "winning" through convention changes or rounding artifacts.

Keep the state outside the model. Because a model session has a bounded context, Épi stores code, artifacts and detailed research notes in a persistent filesystem, and keeps a separate memory store of reusable lessons and documented dead ends. At each session boundary the agent writes a handover note identifying current state and next steps; the next session gets relevant memory records plus file references rather than a full replay of history.

Branch like a programmer. Each approach lives on a versioned branch with its own implementation, tests and notes. The agent can fork from an earlier commit, compare branches under the same ruler, return to an abandoned branch when new findings make it useful, and record why a branch was dropped.

Get a second opinion. A different model reviews the score trajectory, attempted approaches, retrieved findings, baseline and resource use, and judges whether the agent's interpretation of progress is justified. This is kept separate from the verifier, which only checks validity and gain.

Require checkable evidence. Constructive claims need coordinates or objects the verifier can check; rigorous bounds need exact arithmetic, outward rounding, or a dual certificate; theorems need both finite checks and a mathematical argument explaining why those finite checks establish the full statement. For Tuza, this means separating 872 profile checks (18,444 multiplicity boxes) from the lemma that lifts them to arbitrary multiplicities.

Make the coding variant frugal. Épi-turbo tells the agent the complete score formula (including that the speed term only counts within 1% of the reference), that final scoring uses unseen instances, and that every model call costs money. It reserves each call's maximum price before spending, saves a budget slice for the end, runs one continuous session where possible, and stops when extra sessions stop improving the best verified score. Independent review and extra validation were switched off because their cost exceeded their benefit on short tasks.

Why This Matters

For research: The paper reframes agent self-improvement as something that happens through accumulated, inspectable experimental experience rather than through retrained weights — the authors keep model weights fixed throughout the reported campaigns. The fixed-ruler protocol also gives a template for making agent-discovered results comparable to published ones, and the Cohn–Elkies separation is a genuine statement about a method's structural limits, not just a better constant.

Real-world applications (drawn from the FrontierOR tasks and the mathematical campaigns):

• Logistics and vehicle routing — the benchmark and case studies include vehicle-routing tasks where both systems beat reference values by 5% to 17%.
• Manufacturing and production planning — production-planning and cooperative crane scheduling tasks appear among the ten largest score differences, with Épi-turbo programs running 2 to 7 times faster than Codex's.
• Process and network design — the waterund36 water-network case shows certified near-optimality for nonlinear flow and concentration constraints, of the kind used in industrial utility planning.
• Geometry-constrained engineering — 97 of the 100 construction records are geometric packings (pentagons in triangles, circles in semicircles, quadrants and octagons), the same class of problem as component layout and material nesting.
• Network and graph optimization — maximum clique and clique interdiction tasks, plus Ramsey-type constructions, connect to scheduling, clustering and facility location.

Industry relevance: The Épi-turbo result is the commercially pointed one: higher benchmark score at 64% of the model cost and roughly 40% lower median research time (22 vs. 37 minutes) means agentic optimization is becoming cost-competitive with general coding agents on operations-research problems, using the same underlying model. Persistence across sessions is also an infrastructure requirement — the authors rely on Breadboard for isolated environments, long-running jobs and recoverable state — which matters to anyone deploying agents on multi-hour workloads.

Future Directions

1. Extend the Tuza result beyond three neighborhood types. The proof covers at most three triangle-active neighborhood types with an eight-vertex clique part; going to more types or larger clique parts raises the number of profiles and multiplicity boxes that must be certified, and the paper leaves open how far the enumeration approach scales.

2. Push the Cohn–Elkies separation further. The paper shows the linear program cannot be sharp in dimensions 10 and 11, and states that a sharp bound requires additional constraints or a different bounding method — an obvious next campaign is to add those constraints and see whether the gap closes. Whether dimensions 9 and 13 can also be separated is not established here, since only 10 and 11 have new lower bounds crossing known packing upper bounds.

3. Strengthen the empirical case for Épi-turbo. The comparison used one run per task per system on 30 tasks, and the authors explicitly state they do not report statistical significance; the task set was also filtered to exclude unreliable reference values. Multi-run evaluation, the remaining FrontierOR tasks (the benchmark has 180), and reinstating the review and validation components at larger budgets are natural follow-ups.

4. Broaden beyond checkable mathematics and coding. Every reported result has a mechanical verifier — coordinates, dual certificates, exact arithmetic, or finite profile checks. How the loop behaves when outputs are only partially checkable, and how human researchers should audit an ever-growing library of branches and certificates, are open questions the paper raises without resolving.

Target Audience

Researchers and engineers building LLM-based agents for scientific or engineering automation; practitioners of global optimization, sphere packing and extremal combinatorics who want to know what an agent can contribute to their subfield and how to check the claims; and technical leaders evaluating agent tools for operations-research and solver development, for whom the Épi-turbo cost and runtime comparisons against Codex are the most directly actionable content. Readers wanting step-by-step reproduction should note that the record tables, precise bounds and certificates are deferred to the paper's appendices and to the released results repository (Epi Team, 2026).

Authors’ abstract

We present Épi, an autonomous research agent that sustains investigations across model sessions and evolves its methods through accumulated experience. Épi 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. Épi 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, Épi 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 Épi-turbo, a lightweight configuration that develops executable solvers for tasks including vehicle routing, scheduling and production planning. On 30 FrontierOR tasks, Épi-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. Épi is designed to support human understanding by connecting computational results to explicit methods and mathematical arguments that researchers can examine and build upon.