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

cs.CLOct 18, 2026

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

Authors: Yue Huang, Zhangchen Xu, Xiaonan Luo, Zheyuan Liu, Lichi Li, Yiping Wang, Peiyang Song, Eric Gabriel Ramos,

Organizations: Bake AI · University of Notre Dame · University of Washington · Carnegie Mellon University ·

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.

Figures & tables

Figure 1: Épi’s research architecture. The agent develops methods on versioned branches and retrieves saved history and cross-case lessons. An independent model reviews the evidence. The environment checks each candidate under a fixed ruler and gain floor. The execution infrastructure supports experiments, persistent storage and isolated verifier execution across sessions. Section 2 defines the acceptance rule.

Figure 2: The 120 records, grouped by collection and family. Each dot is one final record. Multiple parameter settings within a family count separately; repeated improvements to the same setting count once. The Tuza theorem extension is shown separately.

Quantity	Previous bound	Épi	Evidence
Wellens’ $D_{\infty}$ $\downarrow$	$4.393500$	$4.365467$	Rational witnesses
CE dual bounds $\uparrow$	$1/20,\;1/24,$ $1/24,\;1/28$	Table 2 : $d=9,10,11,13$	Exact dual certificates
Spencer constant $\uparrow$	$7/\sqrt{17}$	$5/\sqrt{8}$	All 256 sign assignments
Dimer entropy $\downarrow$	$0.452130$	$0.452010$	Integer transfer inequalities
$n$ -queens interval width	$3.30\!\times\!10^{-7}$	$3.94\!\times\!10^{-9}$	Rational and interval checks
Ramsey $c_{4,5}$ $\downarrow$	$0.007932$	$0.007865$	A 1,024-vertex graph

Table 1: Twenty numerical records across 12 families. Arrows indicate the improving direction. Interval widths are reduced. This overview uses rounded decimals. Precise bounds appear in the appendix and Table 2 .

Figure 3: Nine final record constructions. The three pentagon arrangements use unit-side pentagons; circle packings use a unit-radius semicircle or quadrant, or a unit-circumradius octagon. Percentages compare the final artifact with its archived reference. Triangle side length decreases; circle radius increases.

Dimension	Earlier dual bound	Épi dual bound $L_{d}$	Packing upper bound $U_{d}$
9	$1/20$	$0.058044329039$
10	$1/24$	$0.056433853144$	$0.05623600$
11	$1/24$	$0.057731808202$	$0.05664550$
13	$1/28$	$0.066440082613$

Table 2: New lower bounds on the optimal Cohn–Elkies bound in dimensions 9, 10, 11, and 13, rounded downward. The packing upper bounds are converted from Table 1.1 of Cohn et al. (2022) to center density and rounded upward. All values use center-density normalization.

Figure 4: Left: paired markers compare the earlier and improved dual lower bounds on the Cohn–Elkies optimum in each dimension. Right: in dimensions 10 and 11, the new lower bounds exceed known upper bounds on actual packing density. The displayed values use center density, and the relative gaps are

L_{d}/U_{d}-1

Figure 5: Two new mathematical records. Left: the interval for the $n$ -queens constant is approximately 84 times narrower. Right: an explicit $8\times 8$ matrix with discrepancy five gives the Spencer lower bound $5/\sqrt{8}$ . The matrix entries are $-1$ , $0$ , and $1$ .

Figure 6: Two improvements in certified uncertainty. The horizontal axes show interval or bound-gap width on logarithmic scales. Left: the rigorous enclosure for the quartic Feigenbaum attractor dimension becomes over 3.6 million times narrower. Right: the waterund36 gap to the same known feasible value decreases from about

7.263

1.001\times 10^{-5}

Measure	Épi-turbo	Codex
Total benchmark score	$53.96$	$51.21$
Tasks with the higher score	$18$	$12$
Mean quality term	$1.030$	$1.032$
Mean speed term	$0.784$	$0.675$
Instances with the better solution (119 comparable, 40 ties)	$18$	$61$
Instances more than 1% worse than the other system	$29$	$10$

Table 3: Épi-turbo and Codex on 30 FrontierOR tasks that were new to both systems. Both systems use GPT-6-Astra and a model budget of $20 per task. All scores are for the held-out instances. The instance counts compare the objective values of the two programs directly.

Figure 7: Épi-turbo and Codex on 30 FrontierOR tasks. A: The score difference for each task, in order of size. Épi-turbo has the higher score on 18 tasks, and its gains are larger than its losses. B: The model cost for each task. Each point below the dashed line is a task where Épi-turbo costs less. C: The runtime of each held-out run on a logarithmic scale, with the medians as vertical bars.

Group	Tasks	Total score	Higher score	Model cost
Hard split	13	$22.33$ / $20.30$	$9$ / $4$	$95 /$ 152
Ranks 51–70	17	$31.64$ / $30.91$	$9$ / $8$	$124 /$ 188
All tasks	30	$53.96$ / $51.21$	$18$ / $12$	$219 /$ 341

Table 4: Results by task group. The hard split is the official set of the 50 hardest FrontierOR tasks. Each pair of values gives Épi-turbo first and Codex second.

Task	Score	Quality term	Speed term	Model cost
Hyperplane clustering amaldi2013	$2.162$ / $1.283$	$1.163$ / $1.282$	$0.999$ / $0.001$	$2.59 /$ 4.86
Clique interdiction furini2021	$2.090$ / $1.256$	$1.091$ / $0.841$	$0.999$ / $0.415$	$3.82 /$ 6.47
Vehicle routing with node costs he2020	$2.094$ / $1.353$	$1.098$ / $1.108$	$0.995$ / $0.245$	$3.42 /$ 13.90
Maximum clique furini2019	$1.987$ / $1.487$	$1.000$ / $0.988$	$0.987$ / $0.500$	$5.78 /$ 11.58
Cooperative crane scheduling kress2019	$1.853$ / $1.572$	$1.103$ / $1.074$	$0.750$ / $0.498$	$4.78 /$ 3.90
Process configuration and production planning delage2022	$2.023$ / $1.759$	$1.024$ / $1.012$	$0.999$ / $0.747$	$7.32 /$ 13.04

Table 5: The ten FrontierOR coding tasks with the largest score difference in favor of Épi-turbo, sorted by the difference. Task names identify the optimization problem solved by each generated program; benchmark IDs appear below them. Scores, quality and speed are measured on held-out instances. Each pair gives Épi-turbo first and Codex second.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

$h$	Published coefficient	Épi coefficient
3	$14.3$	$14.287390218082$
4	$71.49$	$70.289552594834$
5	$413.07$	$408.104453996958$
6	$2774.16$	$2749.492485514635$
7	$21294.74$	$21149.189776156220$

Appendix

Table 6: Improved upper-bound coefficients for

B_{h}[g]

sets.

Problem	Archived reference	Épi
Vehicle routing, XL-n1048-k237	$380107$	$380092$
Autocorrelation (signed maximum)	$1.4515718639$	$1.4508066395$
Zhang–Zagier, $c_{82}$	$0.2536331090$	$0.2535744749$

Appendix

Table 7: Non-packing construction results in the construction collection.

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