Paper deep dive

Humanize MLE Agents: Multi-Agent Session Alternation Beyond Single-Agent Limits

Changye Li, Zijian Zhang, Muheng Li, Yiduo Pang, Tingjun Wu, Menghan Li, Yitong Liu, Hongkai Guo, Mengchi Chen, Chenyu He, Kaisheng Ma, Wei Xu, Song Han, Sihao Liu, Ligeng Zhu

Year: 2026Venue: arXiv preprintArea: cs.AIType: PreprintEmbeddings: 105

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%

Last extracted: 10/12/2026, 7:26:24 AM

Summary

The paper introduces Humanize MLE Agents (HMA), a multi-agent workflow that alternates between two LLM-based agents on a shared workspace to overcome 'long-horizon deceleration' and 'harness staleness' observed in single-agent Machine Learning Engineering (MLE). By modeling sessions as a context-reset semi-Markov decision process (CR-SMDP) and capping each session at k experiments, HMA achieves state-of-the-art performance on MLE-bench, outperforming single-agent baselines with significantly lower time budgets.

Entities (6)

Humanize MLE Agents · method · 98%MLE-bench · dataset · 95%Context-Reset Semi-Markov Decision Process · mathematicalmodel · 92%Harness staleness · phenomenon · 90%Long-horizon deceleration · phenomenon · 90%Kaggle · platform · 85%

Relation Signals (5)

Humanize MLE Agents → evaluatedon → MLE-bench

confidence 95% · Across 75 Kaggle tasks in MLE-bench, HMA reaches a state-of-the-art any-medal rate of 78.2%

Humanize MLE Agents → outperforms → single-agent baselines

confidence 95% · HMA reaches a state-of-the-art any-medal rate of 78.2%, exceeding the strongest open-source baseline by 8.0 points

Humanize MLE Agents → uses → Context-Reset Semi-Markov Decision Process

confidence 92% · We model these alternating agent sessions as a context-reset semi-Markov decision process (CR-SMDP)

Humanize MLE Agents → addresses → Long-horizon deceleration

confidence 90% · These findings suggest that their benefits may not persist across versions, which motivates a workflow-level approach... Humanize MLE Agents (HMA)

Humanize MLE Agents → addresses → Harness staleness

confidence 90% · harness staleness... motivates workflow-level coordination across agent sessions

Cypher Suggestions (0)

No Cypher suggestions yet.

Abstract

Abstract:Existing LLM-based agent approaches for long-horizon machine learning engineering (MLE) often use context engineering, implemented through custom harnesses that manage tools, skills, and accumulated experience. However, we find that as single-session execution lengthens, the agent's reasoning intensity declines alongside slowing progress, summarized as long-horizon deceleration, and the benefits of these custom harnesses vanish as the underlying model improves, summarized as harness staleness. These findings suggest that their benefits may not persist across versions, which motivates a workflow-level approach in which agents build on one another's work across sessions. We model these alternating agent sessions as a context-reset semi-Markov decision process (CR-SMDP) and establish sufficient conditions for alternation to exceed single-agent reference limits, derive an explicit experiment-budget bound, and characterize when session caps preserve this advantage. Guided by this analysis, we introduce Humanize MLE Agents (HMA), which alternates two agents on a shared workspace, limits each session to at most k experiments and resets the context between sessions, without additional task-specific harness or prior knowledge supplements. Across 75 Kaggle tasks in MLE-bench, HMA reaches a state-of-the-art any-medal rate of 78.2%, exceeding the strongest open-source baseline by 8.0 points with a quarter of its time budget. Moreover, among six configurations spanning five heterogeneous agent pairs, HMA improves any-medal rate over the constituent baselines by 6.4 points on average, demonstrating cross-pair generality. A supplementary case on kernel optimization reaches 878 cycles, within 1.6% of the community leaderboard leader, demonstrating applicability beyond MLE.

PDF

Open source PDF →Open local PDF →

Trouble viewing inline? Open PDF directly →

Full Text

101,503 characters extracted from source content.

Expand or collapse full text

Humanize MLE Agents: Multi-Agent Session Alternation Beyond Single-Agent Limits Changye Li Affiliation: Tsinghua University Zijian Zhang Affiliation: Tsinghua University Affiliation: NVIDIA Muheng Li Affiliation: Tsinghua University Yiduo Pang Affiliation: Zhejiang University Tingjun Wu Affiliation: Tsinghua University Menghan Li Affiliation: Tsinghua University Yitong Liu Affiliation: Tsinghua University Hongkai Guo Affiliation: Tsinghua University Mengchi Chen Affiliation: Tsinghua University Chenyu He Affiliation: Zhejiang University Kaisheng Ma Affiliation: Tsinghua University Wei Xu Affiliation: Tsinghua University Song Han Affiliation: NVIDIA Affiliation: MIT Sihao Liu Affiliation: NVIDIA Ligeng Zhu Affiliation: NVIDIA Abstract Existing LLM-based agent approaches for long-horizon machine learning engineering (MLE) often use context engineering, implemented through custom harnesses that manage tools, skills, and accumulated experience. However, we find that as single-session execution lengthens, the agent’s reasoning intensity declines alongside slowing progress, summarized as long-horizon deceleration, and the benefits of these custom harnesses vanish as the underlying model improves, summarized as harness staleness. These findings suggest that their benefits may not persist across versions, which motivates a workflow-level approach in which agents build on one another’s work across sessions. We model these alternating agent sessions as a context-reset semi-Markov decision process (CR-SMDP) and establish sufficient conditions for alternation to exceed single-agent reference limits, derive an explicit experiment-budget bound, and characterize when session caps preserve this advantage. Guided by this analysis, we introduce Humanize MLE Agents (HMA), which alternates two agents on a shared workspace, limits each session to at most k experiments and resets the context between sessions, without additional task-specific harness or prior knowledge supplements. Across 75 Kaggle tasks in MLE-bench, HMA reaches a state-of-the-art any-medal rate of 78.2%, exceeding the strongest open-source baseline by 8.08.0 points with a quarter of its time budget. Moreover, among six configurations spanning five heterogeneous agent pairs, HMA improves any-medal rate over the constituent baselines by 6.46.4 points on average, demonstrating cross-pair generality. A supplementary case on kernel optimization reaches 878 cycles, within 1.6% of the community leaderboard leader, demonstrating applicability beyond MLE. Code: https://github.com/humanfia/hma 1 Introduction LLM-based agents tackle machine learning engineering (MLE) through repeated experiments: writing training code, running it, and evaluating candidate solutions (Chan et al., 2025; Toledo et al., 2025; Karpathy, 2026). For long-horizon tasks, producing a working solution is only the beginning: the agent must keep finding ways to improve it. As further gains become harder to find, the agent is expected to spend more tokens reasoning about the limitations of the current solution and deciding the next action. In our experiment across six models, however, mean output tokens per response—a proxy for reasoning intensity—decline over time as score gains diminish (Figure 2). We refer to this phenomenon as long-horizon deceleration and analyze its implications for prior agent design. Existing approaches often seek to sustain improvement through context engineering, supplying Markdown instructions, skills, and accumulated knowledge to guide an agent’s next steps (Zhu et al., 2026; Du et al., 2026; Karpathy, 2026; Rajasekaran et al., 2025). However, guidance that helps one model need not help its successor. For example, OpenAI recommends rewriting AGENTS.md, skills, and task prompts when upgrading models (Provencher, 2026), while Anthropic advises removing instructions for checks that newer models can already perform on their own (Anthropic, 2026c). As model capabilities improve, guidance that once compensated for their limitations can thus become redundant or counterproductive. We observe a related pattern in our comparison of three custom MLE harnesses—systems that manage a model’s tools, context, and execution loop (Zhu et al., 2026; Du et al., 2026; Zhao et al., 2026). Nevertheless, our comparison shows that the relative benefits of specialized harnesses diminish or reverse as the base model improves, even under longer execution budgets (Table 2). We refer to this decline in relative performance as harness staleness, which indicates the limitations of custom harness design. These limitations motivate workflow-level coordination across agent sessions, each defined as an agent’s execution from context initialization to termination. In MLE, code, trained models, and evaluated candidates persist in a shared workspace, allowing successive agents to build on prior work (Zhao et al., 2026; Young, 2025). This persistence enables complementary roles: the agent that discovers a useful candidate need not be the one best suited to refine it, and subsequent changes can provide a new starting point when the first agent returns. We therefore ask: Can structured alternation convert complementary agent capabilities into a consistent advantage over the best single agent under a matched budget? Figure 1: HMA overview. (A) Declining output tokens per response accompany diminishing score gains, indicating decelerating single-agent exploration; harness gains can vanish or reverse as models improve. (B) HMA alternates native agents after at most k experiments, resetting context while preserving shared work and candidates for final review. The motor analogy illustrates options A and B alternately energizing shared state XiX_i toward the final result E E. The CR-SMDP view captures how complementary options can extend exploration beyond single-agent limits. To address this question, we represent alternating agent sessions as a context-reset semi-Markov decision process (CR-SMDP). We establish sufficient conditions and derive experiment-budget bounds under which alternation exceeds single-agent reference limits, and identify when fixed-k interruption retains this advantage (Sections 3.1–3.3). Building on these results, we introduce Humanize MLE Agents (HMA), which coordinates two native agents—complete model—harness pairs using official harnesses—through a shared workspace (Figure 1). Each session is capped at k experiments; after each handoff, the other agent continues with the shared work and a reset context. The workflow leaves each agent’s tools, context management, and execution loop unchanged (Bolin, 2026; Anthropic, 2026b), and provides no task-specific knowledge at initialization. Because coordination depends on completed experiments and persistent task artifacts, application to other iterative optimization tasks is a natural question. In summary, our contributions are: • We identify single-agent limitations and show how HMA sustains exploration. We characterize long-horizon deceleration across six models and harness staleness across three custom MLE harnesses in Sections 2. In contrast, from the early to the late phase of execution, HMA retains 86.4% of its mean output tokens per response, compared with 60.7% for matched single-agent baselines, indicating more persistent exploration across sessions. • Alternation and workflow design extend single-agent limits. Our CR-SMDP analysis establishes sufficient conditions and experiment-budget bounds for exceeding single-agent reference limits (Theorem 3.3), and characterizes when fixed-k interruption preserves this advantage Theorem 3.5). Algorithm 1 instantiates these principles with context reset, alternating agents, and final review of candidates (Sections 3.1–3.4). • HMA achieves state-of-the-art any-medal performance with cross-pair generality. On MLE-bench, HMA achieves a state-of-the-art any-medal rate of 78.2%, exceeding the strongest published open-source workflow by 8.0 points. Across the six heterogeneous agent-pair configurations, HMA improves the any-medal rate over the constituent baselines by 6.4 points on average, with gains in every configuration (Sections 4.2). We also explore applicability beyond MLE-bench through a supplementary 48-hour kernel-optimization case study (Section 4.5). 2 Motivation: Limits of Single-Agent Exploration Figure 2: Single-session exploration decelerates over time. Each curve reports mean output tokens per recorded model response for one /goal configuration, pooling responses across 75 tasks and repeats. Across configurations, mean response length falls by 29.8%–45.0% from hours 0–2 to hours 3–5, indicating slower single-session exploration over time. Table 1: Specialized harnesses become less effective as the backbone improves. We report medal rates on the 16-task MLE-bench subset, compared on DeepSeek-V4-Flash with DeepSeek-V4.1-Flash. The DeepSeek Harness row is the native baseline. Bold and underlined entries indicate the largest and second-largest rates within each model column. With the weaker backbone, some specialized harnesses match or exceed the native baseline, whereas the stronger backbone consistently favors the native harness. This gap persists despite the longer execution budgets of the specialized workflows, showing the empirical pattern we name harness staleness. Harness Time (h) DeepSeek-V4-Flash Medals (%) DeepSeek-V4.1-Flash Medals (%) DeepSeek Harness 6 16.7 77.1 ScienceFlow 24 25.0 +8.3 68.8 −8.3-8.3 ML-Master 2.0 24 6.3 −10.4-10.4 37.5 −39.6-39.6 MLEvolve 12 18.8 +2.1 50.0 −27.1-27.1 In this section, we investigate two limitations of single-agent MLE workflows: diminishing exploration over extended execution and limited transfer of harness improvements across model versions. These observations motivate HMA, which coordinates alternating agents from different providers to extend exploration beyond the capabilities of an individual model–harness system. Long-horizon deceleration. We examine six single-session configurations under /goal mode. Figure 2 reports mean output tokens per response in a trailing 30-minute window, used as a proxy for the agent’s reasoning intensity. Across configurations, response length decreases by 29.8%–45.0% from hours 0–2 to hours 3–5. Together with the rapid saturation of prefix gains in Figure 3, this reveals diminishing returns from continued single-agent exploration; detailed measurement definitions and supporting statistics are given in Appendix D.1. Harness staleness. To counter diminishing single-agent exploration, existing harnesses introduce planning, review, and context engineering (Young, 2025; Rajasekaran et al., 2025). With task-specific cold-start knowledge disabled for fairness, our comparison of recent MLE harnesses (Zhu et al., 2026; Du et al., 2026; Zhao et al., 2026) reveals harness staleness: their benefits relative to the official harness diminish as the backbone improves (Table 2). The stronger performance of the official harness is consistent with a possible benefit from model–harness alignment acquired during training. This motivates treating each agent as an integrated model–harness system and studying how agents from different providers collaborate through workflow-level coordination. We present detailed configurations and results in Appendix D.2. 3 Method In this section, we formulate Humanize MLE Agents (HMA) as a context-reset semi-MDP (Section 3.1), derive conditions and experiment budgets for alternation to exceed single-agent reference limits (Section 3.2), analyze fixed-k interruption and empirical cap selection (Section 3.3), and present the complete HMA workflow (Section 3.4). 3.1 HMA Preliminaries Workflow policy and task state. A multi-agent workflow that alternates between agent sessions is governed by a fixed policy over options μ (Sutton et al., 1999). Without loss of generality, we consider two agents, A and B, working on a shared task. The state x=(W,E,c(u))x=(W,E,c^(u)) comprises the shared workspace W, retained result E, and context c(u)c^(u) of the active agent u∈A,Bu∈\A,B\. Session i of the workflow, executed by agent u, is modeled as an option oi(u)=(ℐi(u),πi(u),βi(u))o_i^(u)=(I_i^(u), _i^(u), _i^(u)), with initiation set ℐi(u):=x:μ⁡(oi(u)∣x)>0I_i^(u):=\x:μ(o_i^(u) x)>0\, internal policy πi(u) _i^(u), and termination rule βi(u) _i^(u). Termination creates an option boundary, where μ selects the next option. Task initialization and result quality. For a general MLE task, N is the total experiment budget of the workflow; each primitive step completes one experiment and updates (W,E)(W,E) within an option. The initial state x0=(W0,E0,∅)∼ν0x_0=(W_0,E_0, ) _0 is drawn from the task-state distribution ν0 _0, with workspace W0W_0, empty result E0E_0, and empty context. Let EnE_n be the result retained after n experiments, with normalized quality q⁡(x):=q⁡(E)∈[0,1]q(x):=q(E)∈[0,1]. Expected quality and target-success probability are Perfμ⁡(N):=μ,ν0q(EN)Perf_μ(N):=E_μ, _0q(E_N) and pμ(N,τ):=Prμ,ν0⁡(q⁡(EN)≥τ)p_μ(N;τ):= _μ, _0(q(E_N)≥τ) for τ∈[0,1]τ∈[0,1]. Workflow trajectory, rewards, and values. The trajectory is (x0,o0(u0),x1,o1(u1),…)(x_0,o_0^(u_0),x_1,o_1^(u_1),…), where session i starts at xix_i and selects oi(ui)∼μ(⋅∣xi)o_i^(u_i) μ(· x_i) with ui∈A,Bu_i∈\A,B\. The option kernel is P(u)(x,x′):=Pr⁡(xi+1=x′∣xi=x,ui=u)P^(u)(x,x ):= (x_i+1=x x_i=x,u_i=u). With a discount factor γ=1γ=1 and reward rn+1:=q⁡(En+1)−q⁡(En)r_n+1:=q(E_n+1)-q(E_n). Let r¯(u)(x) r^(u)(x) be the expected option reward from x. Values Vμ(x)V^μ(x) and Qμ(x,oi(u))Q^μ(x,o_i^(u)) are expected future quality increments, with QμQ^μ executing oi(u)o_i^(u) first. The semi-MDP Bellman recursion (Bradtke and Duff, 1994; Dietterich, 2000) gives Qμ(x,oi(u))=r¯(u)(x)+∑x′P(u)(x,x′)Vμ(x′),Vμ(x)=∑uμ⁡(oi(u)∣x)Qμ(x,oi(u)).Q^μ(x,o_i^(u))= r^(u)(x)+Σ _x P^(u)(x,x )V^μ(x ), V^μ(x)=Σ _uμ(o_i^(u) x)Q^μ(x,o_i^(u)). (1) Context-Reset SMDP. The HMA workflow is formulated as a context-reset SMDP (CR-SMDP), whose option boundaries preserve (W,E)(W,E) and reset context to ∅ . For integer cap k≥1k≥ 1, remaining experiment budget t, and natural duration Ti(u)(xi)T_i^(u)(x_i) measured in experiments, option i completes di(u)=min⁡Ti(u)(xi),k,td_i^(u)= \T_i^(u)(x_i),k,t\ experiments before natural termination, fixed-k interruption, or budget exhaustion. If Ti(u)(xi)>kT_i^(u)(x_i)>k almost surely and t≥kt≥ k, then βi(u)(ℓ)=ℓ≥k _i^(u)( )=1_\ ≥ k\ and di=kd_i=k, where ℓ counts completed experiments within the option. Further formulation details and early natural termination analysis appear in Appendix A.1. 3.2 Alternation Beyond Single-Agent Limits For u∈A,Bu∈\A,B\, let (u) B^(u) be a finite set of single-agent workflow variants of u with ordinary or specified stronger harnesses. Define the reference workflow family A,B:=(A)∪(B) B_A,B:= B^(A)∪ B^(B). All workflows initialize from x0∼ν0x_0 _0 and satisfy the following retention assumption. Assumption 3.1 (Retention of the best result). q⁡(En+1)≥q⁡(En)q(E_n+1)≥ q(E_n) for all n. We adopt the fixed-k termination rule from Section 3.1. For simplicity, assume the alternating policy μk=(A,B,u0,k) _k=(A,B,u_0,k) starts with u0∈argmaxu∈A,B⁡Perf(A,B,u,k)(N)u_0∈ *arg\,max_u∈\A,B\Perf_(A,B,u,k)(N), where A¯=B A=B and B¯=A B=A. With option kernels Pk(u)P_k^(u), including context reset, define the cycle kernel and reference ceiling: Mμk=Pk(u0)Pk(u¯0),U∗:=max⁡limN→∞b∈A,B⁡Perfb⁡(N).M_ _k=P_k^(u_0)P_k^( u_0), U_*:= _b∈ B_A,B _N→∞Perf_b(N). (2) On each task, let refX_ref and μkaltX_ _k^alt contain states whose shared components (W,E)(W,E) are reachable by the references and alternation, respectively. For τ>U∗τ>U_*, the target set :=x∈μkalt∖ref:q⁡(x)≥τT:=\x _ _k^alt _ref:q(x)≥τ\ contains high-quality states beyond reference reachability; the next assumption requires persistent cooperative access to them. Assumption 3.2 (Cooperative access and use). Fix μk _k and τ∈(U∗,1]τ∈(U_*,1]. In cycle m, agents u and u¯ u start at x2mx_2m and x2m+1x_2m+1, respectively. There exist constants α,β∈(0,1]α,β∈(0,1] such that, for every m with Prμk⁡(q⁡(x2m)<τ)>0 _ _k(q(x_2m)<τ)>0, Prμk(x2m+1∈G∣q(x2m)<τ)≥α,G:=x:q(x)<τ,∑x′∈Pk(u¯)(x,x′)≥β. _ _k(x_2m+1∈ G q(x_2m)<τ)≥α, G:=\x:q(x)<τ,\ Σ _x P_k^( u)(x,x )≥β\. (3) Here α bounds u’s access to states useful to u¯ u, and β bounds u¯ u’s probability of reaching T. Theorem 3.3 (Joint alternation exceeds the reference limits). Under Assumptions 3.1 and 3.2, let a=αβa=αβ and F0=Prμk⁡(q⁡(x0)<τ)F_0= _ _k(q(x_0)<τ). For finite k and integers m≥0m≥ 0, Perfμk⁡(2km)≥τ⁡[1−F0(1−a)m],Uμk:=limN→∞Perfμk⁡(N)≥τ>U∗.Perf_ _k(2km)≥τ[1-F_0(1-a)^m], U_ _k:= _N→∞Perf_ _k(N)≥τ>U_*. (4) Proof sketch. With Fm=Prμk⁡(q⁡(x2m)<τ)F_m= _ _k(q(x_2m)<τ), persistent access and quality preservation give Fm+1≤(1−a)FmF_m+1≤(1-a)F_m. Iteration and q≥0q≥ 0 imply the bound; monotone convergence gives the limit. ∎ Corollary 3.4 (Experiment budget). Under Theorem 3.3, with F0=1F_0=1, fixed p0∈(0,1)p_0∈(0,1), and 0<a≪10<a 1, a sufficient budget for pμk(N,τ)≥p0p_ _k(N;τ)≥ p_0 has the leading form Nsuff(k,p0,τ)=2kalog⁡11−p0[1+O⁡(a)].N_suff(k,p_0,τ)= 2ka 11-p_0\, [1+O(a) ]. (5) Taking p0=(U∗+η)/τp_0=(U_*+η)/τ, 0<η<τ−U∗0<η<τ-U_* guarantees mean quality U∗+ηU_*+η. The budget form also applies to a single agent with a uniform conditional success probability of at least a>0a>0. Appendix A.2 gives the proofs, exact budgets, and startup analysis. 3.3 Fixed-k Interruption and Empirical Choice In this section, we study when fixed-k interruption maintains the advantage in Theorem 3.3 and motivate short caps empirically. We use Natural-Termination Alternation (NTA), μ∞:=(A,B,u0,∞) _∞:=(A,B,u_0,∞), as the reference without fixed-k interruption, with di(u)=min⁡Ti(u)(xi),td_i^(u)= \T_i^(u)(x_i),t\. Let xi,ℓx_i, be the state after ℓ experiments within option i, with entry xi,0=xix_i,0=x_i and final state xi,−1:=xi,di(ui)x_i,-1:=x_i,d_i^(u_i) before context reset. At a boundary, xi+1,0=f⁡(xi,−1)x_i+1,0=f(x_i,-1), where f⁡(W,E,c):=(W,E,∅)f(W,E,c):=(W,E, ). We define Aμ∞(xi,−1):=Vμ∞(xi+1,0)−Qμ∞(xi,−1,oi(ui))A _∞(x_i,-1):=V _∞(x_i+1,0)-Q _∞(x_i,-1,o_i^(u_i)). Here Qμ∞Q _∞ continues the current option, whereas Vμ∞V _∞ starts the reset option; the interruption theorem (Sutton et al., 1999, Theorem 2) gives nondegradation when Aμ∞(xi,−1)≥0A _∞(x_i,-1)≥ 0. For the capped policy μk _k, define the interrupted option indices μk(N):=i≥0:∑j=0idj(uj)<N,di(ui)=k<Ti(ui)(xi,0)J_ _k(N):=\i≥ 0: _j=0^id_j^(u_j)<N, \ d_i^(u_i)=k<T_i^(u_i)(x_i,0)\. The expected net gain and NTA margin are μk(N):=μk∑i∈μk(N)Aμ∞(xi,−1)A_ _k(N):=E_ _k _i _ _k(N)A _∞(x_i,-1) and Δμ∞(N):=Perfμ∞⁡(N)−U∗ _ _∞(N):=Perf_ _∞(N)-U_*. Theorem 3.5 (Expected advantage under fixed-k interruption). For the optimal initial agent u0u_0, a sufficient condition to exceed U∗U_* is Δμ∞(N)+μk(N)>0⟹Perfμk⁡(N)>U∗. _ _∞(N)+A_ _k(N)>0 _ _k(N)>U_*. (6) Proof sketch. Telescoping the option-level Bellman recursion gives Perfμk⁡(N)−Perfμ∞⁡(N)=μk(N)Perf_ _k(N)-Perf_ _∞(N)=A_ _k(N). Substitution proves the claim; see Appendix A.3. ∎ Corollary 3.6 (Upper bound on the required cap). Suppose Δμ∞(N)>0 _ _∞(N)>0 and interruption losses decay geometrically with k, then some finite 1≤k≤k01≤ k≤ k_0 satisfies Perfμk⁡(N)>U∗Perf_ _k(N)>U_*. Empirically selected cap range: k≤5k≤ 5. Figure 3 compares six goal and five NTA configurations on n=75n=75 MLE-bench tasks (Chan et al., 2025). The prefix curves show that k=5k=5 preserves most observed gains with fewer within-option experiments, motivating candidate caps k≤5k≤ 5. Detailed analysis are presented in Appendix A.3; statistical and empirical details are provided in Appendix B. Figure 3: Short prefixes retain most observed gains. The horizontal axis reports the mean percentage of within-option experiments retained by the first k experiments, and the vertical axis reports the corresponding percentage of observed gains retained. Faint curves represent individual configurations, the dark curve averages gain retention equally across configurations, and guides mark k=1,3,5k=1,3,5. Across the eleven configurations, k=5k=5 retains 97.83% of observed gains with a mean within-option experiment retention of 73.77%, supporting candidate caps k≤5k≤ 5. Algorithm 1 HMA with Fixed-k Interruption Require: Workflow μk=(A,B,u0,k) _k=(A,B,u_0,k); task distribution ν0 _0; total time ttotalt_total; final review time trevt_rev. Ensure: Final candidate E E. 1: Stage 1: Workflow Initialization 2: x0=(W0,E0,∅)∼ν0x_0=(W_0,E_0, ) _0. 3: tend←ttotalt_end← t_total; ts←tend−trevt_s← t_end-t_rev. 4: i←0i← 0; u←u0u← u_0; ℰ←∅E← . 5: Stage 2: Alternate Options 6: while t<tst<t_s do 7: ℓ←0 ← 0; xi,0←xix_i,0← x_i. 8: while βi(u)(ℓ,t,k)=0 _i^(u)( ,t;k)=0 do 9: xi,ℓ+1←πi(u)(xi,ℓ)x_i, +1← _i^(u)(x_i, ). 10: Append (Ei,ℓ+1,u)(E_i, +1,u) to ℰE. 11: ℓ←ℓ+1 ← +1. 12: end while 13: xi+1←f⁡(xi,−1)x_i+1← f(x_i,-1). 14: i←i+1i← i+1; u←u¯u← u. 15: end while 16: Stage 3: Final Review 17: E^←E−1 E← E_-1. 18: if |ℰ|≥2∧t<tend ≥ 2 t<t_end then 19: E^←Review(u¯−1)(ℰ,E−1,tend) E← Review^( u_-1)(E,E_-1,t_end). 20: end if 21: return E E. 3.4 HMA Workflow Overview In this section, we describe the implementation of the HMA workflow, including alternating agent execution and final review, as summarized in Algorithm 1. Agent Execution. Algorithm 1 implements μk=(A,B,u0,k) _k=(A,B,u_0,k) from x0∼ν0x_0 _0. Here t is elapsed time, tend=ttotalt_end=t_total is the final deadline, and ts=tend−trevt_s=t_end-t_rev ends exploration. Agent u executes πi(u) _i^(u) until βi(u)(ℓ,t;k)=ℓ≥minTi(u)(xi),k∨t≥ts=1 _i^(u)( ,t;k)=1\ ≥ \T_i^(u)(x_i),k\\ \ t≥ t_s\=1. Then xi,−1=xi,ℓx_i,-1=x_i, and xi+1=f⁡(xi,−1)x_i+1=f(x_i,-1) reset context for agent u¯ u. Final review. The archive ℰE stores evaluated candidates and their authors in order; (E−1,u−1)(E_-1,u_-1) is the latest pair. We reserve the final trevt_rev for the other agent u¯−1 u_-1 to review the archive and select E^←Review(u¯−1)(ℰ,E−1,tend) E← Review^( u_-1)(E,E_-1,t_end), with E−1E_-1 as the fallback. This cross-agent check seeks agreement on the best archived candidate without test-set scores, approximating the result-retention objective of Assumption 3.1 at final selection. 4 Experiment 4.1 Experiment Setup Implementation details. We implement HMA on Humanize (Liu et al., 2026), following Algorithm 1 with GPT, Kimi, GLM, DeepSeek, and Claude agents, each using their native harness and max reasoning effort. For MLE-bench, each task run uses one NVIDIA A10 GPU and a six-hour budget: agents alternate under k=5k=5, reset context at each handoff, and reserve the final 15 minutes for final review. Exact model–harness mappings, hardware, baseline configurations, and framework details are given in Appendix C. Benchmark. Our main evaluation uses MLE-bench (Chan et al., 2025), comprising 75 Kaggle competitions requiring agents to develop machine learning solutions. We report the percentage of tasks earning any medal (All) or a gold medal (Gold), supplemented by complexity-specific and leaderboard-based metrics in Table 2. Test-set scores are unavailable to agents and used only for offline evaluation. Section 4.5 supplements this evaluation with an exploratory application to kernel optimization. 4.2 Main Comparison Table 2: HMA exceeds the stronger constituent agent in overall medal rate. All performance metrics are percentages. Lite, Medium, and High report medal rates by task complexity. Med+ measures the percentage outperforming the human leaderboard median; Mean Percentile averages leaderboard percentiles across tasks. Avg. of Single averages the two constituent six-hour goal baselines, and signed gains measure HMA’s improvement over this average in percentage points. HMA starts with the first listed model. Bold and underlined medal rates mark the best and second-best results. Statistical details and available HMA standard deviations appear in Appendix C.3. Workflow Time (h) Medal Rate (%) Overall Metrics (%) Mean Percentile (%) Lite (22) Medium (38) High (15) All (75) Gold Med+ Single-Agent Baselines with Native Harnesses (/goal) Claude Opus 5 6 80.3 ± 1.5 78.1 ± 2.3 46.7 ± 0.0 72.4 ± 1.6 50.7 ± 0.8 85.3 ± 1.3 84.8 ± 0.6 GPT-5.6-sol 6 80.3 ± 1.5 69.3 ± 2.3 46.7 ± 6.7 68.0 ± 1.3 47.6 ± 2.5 81.3 ± 0.8 81.3 ± 1.3 GLM-5.3 6 77.3 ± 0.0 57.0 ± 0.9 40.0 ± 0.0 59.6 ± 0.4 38.2 ± 2.2 75.1 ± 1.2 75.7 ± 0.9 DeepSeek-V4.1-Flash 6 77.3 ± 2.6 61.4 ± 6.3 37.8 ± 2.2 61.3 ± 4.1 37.8 ± 0.9 74.2 ± 2.4 74.7 ± 2.3 Kimi K3 6 77.3 ± 2.6 45.6 ± 2.3 42.2 ± 2.2 54.2 ± 1.6 34.7 ± 1.3 73.3 ± 2.3 73.8 ± 1.6 DeepSeek-V4-Flash 6 54.5 ± 6.9 24.6 ± 1.8 24.4 ± 5.9 33.3 ± 3.5 15.6 ± 1.6 50.2 ± 3.2 51.8 ± 2.8 Open-Source Agent Baselines ScienceFlow DeepSeek-V4-Flash-Preview 24 80.3 ± 1.5 74.6 ± 0.9 44.4 ± 2.2 70.2 ± 1.2 – – – MLEvolve Gemini-3.1-Pro-preview 12 80.3 ± 1.5 64.0 ± 0.9 46.7 ± 0.0 65.3 ± 0.8 34.7 ± 0.0 76.0 ± 2.3 – ML-Master 2.0 DeepSeek-V3.2-Speciale 24 75.8 ± 1.5 50.9 ± 3.5 42.2 ± 2.2 56.4 ± 2.5 19.6 ± 0.9 63.1 ± 1.2 – HMA (Ours) Claude Opus 5 ↔ GPT-5.6-sol Avg. of Single 6 80.3 ± 1.1 73.7 ± 1.6 46.7 ± 3.3 70.2 ± 1.0 49.1 ± 1.3 83.3 ± 0.8 83.0 ± 0.7 HMA (ours) 6 84.8 ++4.5 80.7 ++7.0 62.2 ++15.6 78.2 ++8.0 53.8 ++4.7 90.7 ++7.3 89.0 ++5.9 GPT-5.6-sol ↔ Claude Opus 5 Avg. of Single 6 80.3 ± 1.1 73.7 ± 1.6 46.7 ± 3.3 70.2 ± 1.0 49.1 ± 1.3 83.3 ± 0.8 83.0 ± 0.7 HMA (ours) 6 86.4 ++6.1 76.3 ++2.6 46.7 ++0.0 73.3 ++3.1 50.7 ++1.6 85.3 ++2.0 85.4 ++2.3 GPT-5.6-sol ↔ DeepSeek-V4.1-Flash Avg. of Single 6 78.8 ± 1.5 65.4 ± 3.4 42.2 ± 3.5 64.7 ± 2.1 42.7 ± 1.3 77.8 ± 1.2 78.0 ± 1.3 HMA (ours) 6 81.8 ++3.0 76.3 ++10.9 46.7 ++4.5 72.0 ++7.3 50.7 ++8.0 85.3 ++7.6 84.4 ++6.4 GPT-5.6-sol ↔ Kimi K3 Avg. of Single 6 78.8 ± 1.5 57.5 ± 1.6 44.4 ± 3.5 61.1 ± 1.0 41.1 ± 1.4 77.3 ± 1.2 77.6 ± 1.0 HMA (ours) 6 81.8 ++3.0 71.1 ++13.6 53.3 ++8.9 70.7 ++9.6 50.7 ++9.6 85.3 ++8.0 83.9 ++6.4 GPT-5.6-sol ↔ GLM-5.3 Avg. of Single 6 78.8 ± 0.8 63.2 ± 1.2 43.3 ± 3.3 63.8 ± 0.7 42.9 ± 1.7 78.2 ± 0.7 78.5 ± 0.8 HMA (ours) 6 77.3 −1.5-1.5 73.7 ++10.5 46.7 ++3.4 69.3 ++5.6 50.7 ++7.8 82.7 ++4.4 81.5 ++2.9 DeepSeek-V4.1-Flash ↔ Kimi K3 Avg. of Single 6 77.3 ± 1.9 53.5 ± 3.4 40.0 ± 1.6 57.8 ± 2.2 36.2 ± 0.8 73.8 ± 1.6 74.3 ± 1.4 HMA (ours) 6 77.3 ++0.0 63.2 ++9.6 40.0 ++0.0 62.7 ++4.9 38.7 ++2.4 80.0 ++6.2 78.1 ++3.8 HMA outperforms single-agent and specialized workflow baselines. Table 2 compares HMA with single agents using native harnesses, evaluated in our experiments, and specialized workflows using results reported in their original papers (Zhu et al., 2026; Du et al., 2026; Zhao et al., 2026). Opus-first HMA achieves 78.2% overall medals, exceeding our strongest single-agent baseline at 72.4% and the highest published workflow baseline at 70.2%. HMA and our single-agent baselines share a six-hour budget, whereas the published workflows use 12–24 hours. HMA achieves these gains without task-specific knowledge bases or additional prompt engineering, while retaining the agents’ existing internal harnesses. HMA improves heterogeneous agent pairs across capability levels. Across five model pairs with constituent medal rates of 54.2%–72.4%, all six HMA configurations improve overall medal rate over the stronger constituent, and Gold, Med+, and mean percentile over constituent averages. For Opus–GPT, both starting orders retain the advantage, reaching 78.2% and 73.3% medals versus the stronger constituent’s 72.4%, indicating that the observed advantage is not tied to a single favorable initial agent. 4.3 Experiment Analysis and Ablation Study Figure 4: HMA sustains response length and continued improvement. (a) Mean output tokens per response and (b) medal rate, both plotted against active runtime. Bold red and dashed blue curves report weighted means for HMA and its matched constituent goal references, respectively; each HMA configuration receives equal weight, and each goal reference is the equally weighted mean of its two constituent agents. Faint curves show individual configurations. HMA sustains exploration and continued improvement. The response-level curve in Figure 4 (a) uses the same 30-minute trailing window. From hours 0–2 to hours 3–5, HMA retains 86.4% of its mean output tokens per response, versus 60.7% for matched goal references. In Figure 4 (b), the six HMA configurations reach 42.7%–60.0% medals within two hours and continue improving through six hours, contrasting with the single-agent deceleration in Section 2. Final review improves historical any-medal retention. Holding exploration fixed, final review changes 8.9% of selections and increases any-medal outcomes from 311 to 319, with no losses relative to the pre-review candidate. Among the 450 task runs, 330 produce at least one medal-winning exploration candidate; final selection retains a medal in 319 of these runs (96.7%), compared with 311 (94.2%) before final review. These results quantify how terminal review supports the best-result retention objective in Assumption 3.1. Additional analyses and ablations. Appendix E details the weighting and aggregation used to construct the mean curves in Figure 4, together with trajectory construction and task-level comparisons. Appendix F further examines starting-order effects, model time allocation, and partner participation (Appendix F.1); the interruption-parameter ablations(Appendix F.2); natural termination and the fixed-duration approximation (Appendix F.3); and final review’s effects on final selection and historical any-medal retention (Appendix F.4). 4.4 Case Study Figure 5: HMA GPT–Opus alternation sustains improvement on INGV. (a) Test MAE across 27 experiments, using a logarithmic axis with a linear inset. (b) Mean output tokens per response for each experiment. Blue and purple regions identify GPT and Opus; dotted lines mark handoffs, and horizontal lines show reference scores. On INGV Volcanic Eruption Prediction, GPT and Opus improve the historical best MAE in five of six post-handoff options (Figure 5). Their final MAE of 34,234 is 46.5% below the best of six constituent goal runs. Mean response length also increases on four of five returns to a previously used model, illustrating continued refinement of shared task state alongside renewed output. Appendix G provides detailed measurements and additional cross-model cases. 4.5 Exploratory Application Beyond MLE-bench Figure 6: HMA Opus–GPT alternation on AOPT. (a) Best accepted cycle count over 48 hours, using a broken vertical axis (upper: logarithmic; lower: linear) to resolve later improvements. (b) Mean output tokens per response for each experiment with available transcripts; gaps indicate missing records. Blue and purple regions identify GPT and Opus; dotted lines mark option boundaries. The preceding case illustrates continued refinement within MLE. We next explore the workflow on Anthropic’s Original Performance Take-Home (AOPT) (Anthropic, 2026a), a kernel-optimization task measured in simulated execution cycles. Claude Opus 5.5 and GPT-6-astra alternate with a cap of three accepted submissions per session (cap 3). The selected 48-hour run reaches 878 cycles at 34 hours 33 minutes and retains this score in its final candidate. Figure 6 pairs the performance trajectory with response-length traces, following the presentation in Figure 5. For context, 878 cycles matches the 10th-ranked score on the Paradigm community leaderboard as of October 8, 2026 (Paradigm, 2026), just 14 cycles (1.62%) above the leading score of 864 cycles. The leaderboard uses a separate nine-seed judge, so this is a comparison of reported scores rather than a verified leaderboard placement. This single-run case provides preliminary evidence of the workflow’s applicability to kernel optimization beyond MLE-bench over a longer horizon. 5 Related Work MLE agents and harness-level systems. MLE-bench evaluates autonomous agents on Kaggle competitions (Chan et al., 2025). Recent MLE systems improve individual agents through search, reflection, memory, branch reuse, recoverable workspaces, or task-conditioned interfaces (Toledo et al., 2025; Chen et al., 2026; Du et al., 2026; Zhu et al., 2026; Zhao et al., 2026; Yu et al., 2026; Zhang et al., 2026; Ye et al., 2026). These methods modify how one model acts within its harness. HMA instead leaves each native model–harness pair unchanged and coordinates complete agents at the workflow level. Multi-agent and long-horizon workflows. Prior workflows sustain long-horizon execution through reusable experience, reflection, tree search, workflow search, communication, role assignment, checkpointing, or independent review (Shinn et al., 2023; Zhao et al., 2024; Zhou et al., 2024; Zhang et al., 2025; Wu et al., 2024; Qian et al., 2024; Li et al., 2025). Recent handoff studies examine candidate transfer, learned control exchange, and the quality cost of continuing another model’s trajectory (Luo et al., 2026; Li et al., 2026; Ganz et al., 2026). HMA studies fixed-cap alternation of complete native agents on one shared workspace, with a context reset at every handoff. Options and semi-MDPs. Semi-Markov decision processes model actions with variable duration, while options represent such actions through an internal policy and termination rule (Bradtke and Duff, 1994; Dietterich, 2000). The interruption theorem characterizes when terminating an option early preserves or improves continuation value (Sutton et al., 1999); subsequent work studies learned and off-policy termination (Bacon et al., 2017; Harutyunyan et al., 2018). HMA models each agent session as an option and applies this framework to fixed-cap alternation with context reset. 6 Conclusion HMA alternates native agents, resetting context while preserving shared task state. Our CR-SMDP analysis gives sufficient conditions and budget bounds for exceeding single-agent reference limits and conditions for preserving this advantage under fixed-cap interruption. Across six MLE-bench configurations, HMA outperforms the stronger constituent in medal rate under equal six-hour budgets, reaching 78.2% at best. A supplementary AOPT case illustrates application to kernel optimization over 48 hours; establishing comparative gains beyond MLE-bench remains future work. Together, these results motivate further study of workflow-level coordination for sustained exploration across iterative optimization tasks. Acknowledgments We thank Zijian Huang, Chengxing, Jing Xiong, Zhengkai Lin, Boshi Zhang, Yan Hu, Dongyun Zou, and Chang Liu for their participation in the early exploration of this project and their contributions to workflow design and experiments. AI use statement In this work, we used generative AI tools for language polishing, grammar checking, and generating portions of the code. The research ideas, methodology, experimental design, and interpretation of results were developed by the authors. We reviewed all AI-assisted text to ensure that it accurately conveyed our intended meaning. LLM-generated code was verified and tested for correctness by two authors. We take full responsibility for the final content of this work, including all text, claims, and artifacts produced with the assistance of generative AI. References Anthropic (2026a) Anthropic Anthropic’s Original Performance Take-Home. Note: GitHub repositoryAccessed October 8, 2026 External Links: Link Cited by: §4.5. Anthropic (2026b) Anthropic How Claude Code works. Note: Claude Code documentationDocumentation version updated September 26, 2026. Accessed September 26, 2026 External Links: Link Cited by: §B.2, §C.2, §1. Anthropic (2026c) Anthropic Prompting Claude Opus 5. Note: Claude Platform documentationAccessed September 25, 2026 External Links: Link Cited by: §1. Bacon et al. (2017) P. Bacon, J. Harb, and D. Precup The Option-Critic architecture. Proceedings of the AAAI Conference on Artificial Intelligence 31 (1). External Links: ISSN 2159-5399, Link, Document Cited by: §5. Bolin (2026) M. Bolin Unrolling the Codex agent loop. Note: OpenAI EngineeringPublished January 23, 2026. Accessed September 21, 2026 External Links: Link Cited by: §B.2, §C.2, §1. Bradtke and Duff (1994) S. Bradtke and M. Duff Reinforcement learning methods for continuous-time Markov decision problems. In Advances in Neural Information Processing Systems, G. Tesauro, D. Touretzky, and T. Leen (Eds.), Vol. 7, p. . External Links: Link Cited by: Definition A.2, §3.1, §5. Chan et al. (2025) J. S. Chan, N. Chowdhury, O. Jaffe, J. Aung, D. Sherburn, E. Mays, G. Starace, K. Liu, L. Maksin, T. Patwardhan, L. Weng, and A. Mądry MLE-bench: evaluating machine learning agents on machine learning engineering. External Links: 2410.07095, Link Cited by: §D.2, §1, §3.3, §4.1, §5. Chen et al. (2026) J. Chen, B. D. Mishra, J. Nam, R. Meng, T. Pfister, and J. Yoon MARS: modular agent with reflective search for automated AI research. External Links: 2602.02660, Link Cited by: §5. DeepSeek-AI (2026) DeepSeek-AI DeepSeek Harness: everything is a plugin. GitHub. Note: https://github.com/deepseek-ai/deepseek-harness Cited by: §B.2, §C.2. Dietterich (2000) T. G. Dietterich Hierarchical reinforcement learning with the MAXQ value function decomposition. Journal of Artificial Intelligence Research 13, p. 227–303. External Links: ISSN 1076-9757, Link, Document Cited by: Definition A.1, §3.1, §5. Du et al. (2026) S. Du, X. Yan, J. Shi, Z. Cao, S. Feng, Z. Liang, B. Sun, T. Peng, Y. Zhou, X. Li, J. Zhou, L. He, B. Zhang, and L. Bai MLEvolve: a self-evolving framework for automated machine learning algorithm discovery. External Links: 2606.06473, Link Cited by: §C.2, §D.2, §1, §2, §4.2, §5. Ganz et al. (2026) R. Ganz, M. S. Nacson, A. Kalyanpur, and R. Litman The handoff tax: continuing non-native trajectories in LLM agents. External Links: 2608.24358, Link Cited by: §5. Garivier and Cappé (2011) A. Garivier and O. Cappé The KL-UCB algorithm for bounded stochastic bandits and beyond. In Proceedings of the 24th Annual Conference on Learning Theory, S. M. Kakade and U. von Luxburg (Eds.), Proceedings of Machine Learning Research, Vol. 19, Budapest, Hungary, p. 359–376. External Links: Link Cited by: §B.1. Harutyunyan et al. (2018) A. Harutyunyan, P. Vrancx, P. Bacon, D. Precup, and A. Nowé Learning with options that terminate off-policy. Proceedings of the AAAI Conference on Artificial Intelligence 32 (1). External Links: ISSN 2159-5399, Link, Document Cited by: §5. Karpathy (2026) A. Karpathy Autoresearch: AI agents running research on single-GPU nanochat training automatically. Note: GitHubReleased March 2026. Accessed September 25, 2026 External Links: Link Cited by: §1, §1. Li et al. (2026) J. Li, E. Zhang, D. Zhou, E. Chen, and Y. Yan Learning to hand off: provably convergent workflow learning under interface constraints. External Links: 2605.19140, Link Cited by: §5. Li et al. (2025) Y. Li, S. Ping, X. Chen, X. Qi, Z. Wang, Y. Luo, and X. Zhang AgentGit: a version control framework for reliable and scalable LLM-powered multi-agent systems. External Links: 2511.00628, Link Cited by: §5. Liu et al. (2026) S. Liu, L. Zhu, Z. Zhang, D. Zou, Z. Zhang, C. Li, S. Bian, S. Han, and T. Nowatzki Humanize: judgement engineering for agentic coding. External Links: 2610.08900, Link Cited by: §C.1, §4.1. Luo et al. (2026) S. Luo, Y. Huang, G. Deng, H. Wang, H. Luo, L. Li, Z. Hu, J. Feng, and Q. Liu Relay, don’t route: adaptive population handoff for cost-efficient LLM-driven evolution. External Links: 2608.05651, Link Cited by: §5. Moonshot AI (2026) Moonshot AI Kimi Code CLI. Note: GitHubOfficial open-source software. Accessed September 21, 2026 External Links: Link Cited by: §B.2, §C.2. Paradigm (2026) Paradigm Anthropic Take-Home Challenge: Community Leaderboard. Note: Paradigm PuzzlesAccessed October 8, 2026 External Links: Link Cited by: §4.5. Provencher (2026) E. Provencher Rethinking skills and prompts for GPT-6 Astra. Note: OpenAI Developers BlogAccessed September 25, 2026 External Links: Link Cited by: §1. Qian et al. (2024) C. Qian, W. Liu, H. Liu, N. Chen, Y. Dang, J. Li, C. Yang, W. Chen, Y. Su, X. Cong, J. Xu, D. Li, Z. Liu, and M. Sun ChatDev: communicative agents for software development. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), L. Ku, A. Martins, and V. Srikumar (Eds.), Bangkok, Thailand, p. 15174–15186. External Links: Link, Document Cited by: §5. Rajasekaran et al. (2025) P. Rajasekaran, E. Dixon, C. Ryan, and J. Hadfield Effective context engineering for AI agents. Note: Anthropic EngineeringPublished September 29, 2025. Accessed September 21, 2026 External Links: Link Cited by: §1, §2. Shinn et al. (2023) N. Shinn, F. Cassano, A. Gopinath, K. Narasimhan, and S. Yao Reflexion: language agents with verbal reinforcement learning. In Advances in Neural Information Processing Systems, A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, and S. Levine (Eds.), Vol. 36, p. 8634–8652. External Links: Document, Link Cited by: §5. Sutton et al. (1999) R. S. Sutton, D. Precup, and S. Singh Between MDPs and semi-MDPs: a framework for temporal abstraction in reinforcement learning. Artificial Intelligence 112 (1-2), p. 181–211. External Links: ISSN 0004-3702, Link, Document Cited by: §A.3, Definition A.2, §3.1, §3.3, §5. Toledo et al. (2025) E. Toledo, K. Hambardzumyan, M. Josifoski, R. Hazra, N. Baldwin, A. Audran-Reiss, M. Kuchnik, D. Magka, M. Jiang, A. M. Lupidi, A. Lupu, R. Raileanu, K. Niu, T. Shavrina, J. Gagnon-Audet, M. Shvartsman, S. Sodhani, A. H. Miller, A. Charnalia, D. Dunfield, C. Wu, P. Stenetorp, N. Cancedda, J. N. Foerster, and Y. Bachrach AI research agents for machine learning: search, exploration, and generalization in MLE-bench. External Links: 2507.02554, Link Cited by: §1, §5. Wu et al. (2024) Q. Wu, G. Bansal, J. Zhang, Y. Wu, B. Li, E. Zhu, L. Jiang, X. Zhang, S. Zhang, J. Liu, A. H. Awadallah, R. W. White, D. Burger, and C. Wang AutoGen: enabling next-gen LLM applications via multi-agent conversations. In First Conference on Language Modeling, External Links: Link Cited by: §5. Ye et al. (2026) Z. Ye, Y. Huang, H. Jin, B. Hou, J. Shao, Z. Yu, J. Chen, M. Cowan, S. Cao, S. Xing, H. Chen, V. Grover, T. Chen, and L. Ceze CAKE: compiler-agent co-design for frontier kernel evolution. External Links: 2608.12629, Link Cited by: §5. Young (2025) J. Young Effective harnesses for long-running agents. Note: Anthropic EngineeringPublished November 26, 2025. Accessed September 21, 2026 External Links: Link Cited by: §1, §2. Yu et al. (2026) Z. Yu, Y. Wu, Z. Yin, K. Chen, Z. Zhao, M. Wang, S. Yan, and L. Yang Recursive experiential-working memory evolution for long-horizon agent harnesses. External Links: 2608.24876, Link Cited by: §5. Zhang et al. (2026) G. Zhang, L. Lu, F. Xie, K. Zhu, J. Wang, Z. Xie, Z. Yu, Z. Liu, Z. Sun, Q. Li, Y. Liao, H. Chang, X. Hu, Q. Ren, W. Zhou, C. Hu, Y. Deng, and S. Yan JIT-Agent: scaling harness intelligence via just-in-time harness evolution. External Links: 2608.25593, Link Cited by: §5. Zhang et al. (2025) J. Zhang, J. Xiang, Z. Yu, F. Teng, X. Chen, J. Chen, M. Zhuge, X. Cheng, S. Hong, J. Wang, B. Zheng, B. Liu, Y. Luo, and C. Wu AFlow: automating agentic workflow generation. In The Thirteenth International Conference on Learning Representations, External Links: Link Cited by: §5. Zhao et al. (2024) A. Zhao, D. Huang, Q. Xu, M. Lin, Y. Liu, and G. Huang ExpeL: LLM agents are experiential learners. Proceedings of the AAAI Conference on Artificial Intelligence 38 (17), p. 19632–19642. External Links: ISSN 2159-5399, Link, Document Cited by: §5. Zhao et al. (2026) M. Zhao, J. Dong, K. Xu, Z. Hasan, C. Fan, S. Jiang, S. Mao, Y. Ling, L. Zou, T. Zhou, Y. H. Chan, W. Zhang, Z. Zhou, G. Huang, H. Li, W. Cun, Z. Chen, M. Yuan, and Y. Geng ScienceFlow: a long-horizon agent for ML research, scientific discovery and beyond. External Links: 2608.14354, Link Cited by: §C.2, §D.2, Appendix G, §1, §1, §2, §4.2, §5. Zhou et al. (2024) A. Zhou, K. Yan, M. Shlapentokh-Rothman, H. Wang, and Y. Wang Language agent tree search unifies reasoning, acting, and planning in language models. In Proceedings of the 41st International Conference on Machine Learning, R. Salakhutdinov, Z. Kolter, K. Heller, A. Weller, N. Oliver, J. Scarlett, and F. Berkenkamp (Eds.), Proceedings of Machine Learning Research, Vol. 235, p. 62138–62160. External Links: Link Cited by: §5. Zhu et al. (2026) X. Zhu, Y. Cai, Z. Liu, B. Zheng, C. Wang, R. Ye, Y. Zhang, L. Zhang, W. E, S. Chen, and Y. Wang Toward ultra-long-horizon agentic science: cognitive accumulation for machine learning engineering. External Links: 2601.10402, Link Cited by: §C.2, §D.2, §1, §2, §4.2, §5. Appendix Contents Appendix A Theoretical Details and Proofs We organize the formal supplement in the same order as the Method section: Appendix A.1 defines the finite-budget CR-SMDP and exact performance curves; Appendix A.2 proves the cooperative alternation guarantee and budget bound; Appendix A.3 handles NTA, fixed-k interruption, and sufficient-cap conditions. A.1 Model Details and Exact Performance We supplement Section 3.1 with finite-budget definitions, the general option recursion, and exact performance expressions used in the alternation proof. Definition A.1 (State and finite budget). The state from Section 3.1 implicitly includes agent identity, option age, and any scheduling history needed for the Markov property (Dietterich, 2000, Section 3.2). For session oi(ui)o_i^(u_i) at xix_i, let nin_i be the completed experiment count and tit_i the remaining budget. Then ni:=∑h=0i−1dh,ti:=N−ni,di=min⁡Ti(ui)(xi),k,ti.n_i:= _h=0^i-1d_h, t_i:=N-n_i, d_i= \T_i^(u_i)(x_i),k,t_i\. (7) Here n0=0n_0=0, and Ti(u)(xi)T_i^(u)(x_i) is the positive, almost-surely finite natural duration, which may depend on the entry state. Thus early natural termination and a final partial option are included; k=∞k=∞ gives NTA. Values track the remaining budget, vanish when it is exhausted, and no option starts at ti=0t_i=0. Definition A.2 (Option rewards and transitions). For γ∈(0,1]γ∈(0,1] and the experiment rewards in Section 3.1, define r¯(u)(x):=[∑ℓ=0di−1γℓrni+ℓ+1|xi=x,ui=u]. r^(u)(x):=E\! [ _ =0^d_i-1γ r_n_i+ +1\; |\;x_i=x,\ u_i=u ]. (8) Let Φk,t(u)(x′,d∣x) _k,t^(u)(x ,d x) be the joint law of duration and next option-entry state, including context reset, and Pk,t(u)(x,x′):=∑dΦk,t(u)(x′,d∣x)P_k,t^(u)(x,x ):= _d _k,t^(u)(x ,d x). The complete-option kernel is Pk(u):=Pk,∞(u)P_k^(u):=P_k,∞^(u); finite t truncates the same option. Suppressing fixed k,tk,t, the general semi-MDP recursion (Sutton et al., 1999; Bradtke and Duff, 1994) is Qμ(x,oi(u))=r¯(u)(x)+∑d,x′γdΦ(u)(x′,d∣x)Vμ(x′).Q^μ(x,o_i^(u))= r^(u)(x)+ _d,x γ^d ^(u)(x ,d x)V^μ(x ). (9) At γ=1γ=1, this reduces to equation 1, and total reward is q⁡(EN)−q⁡(E0)q(E_N)-q(E_0). Proposition A.3 (Exact performance expressions). Let μP_μ be the one-experiment kernel under μ on the augmented state, including option boundaries, and Sτ:=x:q⁡(x)≥τS_τ:=\x:q(x)≥τ\. After workflow termination, retain the terminal state. Then pμ(N,τ)=ν0μNSτ,Perfμ⁡(N)=ν0μNq,p_μ(N;τ)= _0P_μ^N1_S_τ, _μ(N)= _0P_μ^Nq, (10) where Sτ1_S_τ indicates target attainment. These expressions give the probability of reaching SτS_τ and the expected final quality, respectively, with Perfμ⁡(N)≥τpμ(N,τ)Perf_μ(N)≥τ p_μ(N;τ). Proof of Proposition A.3. The endpoint law is ν0μN _0P_μ^N; applying it to Sτ1_S_τ and q gives equation 10. Taking expectations of q≥τSτq≥ 1_S_τ yields the inequality. ∎ A.2 Alternation Guarantee and Experiment Budget We follow Section 3.2: cooperative access yields a failure recursion, which proves the alternation guarantee and the experiment budget; we then discuss startup effects. Definition A.4 (Reference ceiling and cycle budget). For the reference family in Section 3.2, bounded quality and Assumption 3.1 give U∗:=maxb∈A,B⁡Ub,Ub:=limN→∞Perfb⁡(N)=b,ν0[limN→∞q⁡(EN)].U_*:= _b∈ B_A,BU_b, U_b:= _N→∞Perf_b(N)=E_b, _0\! [ _N→∞q(E_N) ]. (11) Fix μk _k and τ>U∗τ>U_*. Write u for the first agent in each cycle: cycle m executes o2m(u)o_2m^(u) followed by o2m+1(u¯)o_2m+1^( u), with kernel MμkM_ _k. Before total-budget truncation, the experiments used by m cycles are Cμk,m:=∑i=02m−1min⁡Ti(ui)(xi),kC_ _k,m:= _i=0^2m-1 \T_i^(u_i)(x_i),k\, so Cμk,m≤2kmC_ _k,m≤ 2km for finite k. Write Fm:=Prμk⁡(q⁡(x2m)<τ)F_m:= _ _k(q(x_2m)<τ), where Prμk _ _k and μkE_ _k include the initial draw from ν0 _0. Lemma A.5 (Cooperative success and failure recursion). Under Assumptions 3.1 and 3.2, each cycle has conditional success probability at least a:=αβa:=αβ whenever Fm>0F_m>0, and Fm+1≤(1−a)FmF_m+1≤(1-a)F_m for all m≥0m≥ 0. Proof of Lemma A.5. The u-option enters G with conditional probability at least α, and the u¯ u-option reaches ⊆SτT S_τ from each x∈Gx∈ G with probability at least β. By the Markov property, for Fm>0F_m>0, Prμk⁡(x2m+2∈Sτ∣x2m∉Sτ)≥βPrμk(x2m+1∈G∣x2m∉Sτ)≥αβ=a. _ _k(x_2m+2∈ S_τ x_2m∉ S_τ)≥β _ _k(x_2m+1∈ G x_2m∉ S_τ)≥αβ=a. (12) Quality retention makes SτS_τ absorbing, so Fm+1≤Fm(1−a)F_m+1≤ F_m(1-a). If Fm=0F_m=0, it also gives Fm+1=0F_m+1=0. ∎ Theorem A.6 (Joint alternation exceeds the reference limits; Theorem 3.3 restated). Under Assumptions 3.1 and 3.2, take a=αβa=αβ as a lower bound on conditional success per cycle, and F0=Prμk⁡(q⁡(x0)<τ)F_0= _ _k(q(x_0)<τ). For finite k, Perfμk⁡(2km)≥τ⁡[1−F0(1−a)m],Uμk:=limN→∞Perfμk⁡(N)≥τ>U∗.Perf_ _k(2km)≥τ[1-F_0(1-a)^m], U_ _k:= _N→∞Perf_ _k(N)≥τ>U_*. (13) Proof of Theorem A.6. Iterating Lemma A.5 gives Fm≤F0(1−a)mF_m≤ F_0(1-a)^m. Since Cμk,m≤2kmC_ _k,m≤ 2km, quality retention and Proposition A.3 yield Perfμk⁡(2km)≥τpμk(2km,τ)≥τ⁡(1−Fm)≥τ⁡[1−F0(1−a)m].Perf_ _k(2km)≥τ p_ _k(2km;τ)≥τ(1-F_m)≥τ[1-F_0(1-a)^m]. (14) Bounded monotone convergence ensures that UμkU_ _k exists; letting m→∞m→∞ gives Uμk≥τ>U∗U_ _k≥τ>U_*. The same proof permits early natural termination when Assumption 3.2 holds for the resulting kernels, since Cμk,m≤2kmC_ _k,m≤ 2km still holds. ∎ Corollary A.7 (Experiment budget; Corollary 3.4 restated). Under the theorem’s conditions, let F0=1F_0=1 and fix p0∈(0,1)p_0∈(0,1). For 0<a≪10<a 1, a sufficient budget for pμk(N,τ)≥p0p_ _k(N;τ)≥ p_0 has the leading form Nsuff(k,p0,τ)=2kalog⁡11−p0[1+O⁡(a)].N_suff(k,p_0,τ)= 2ka 11-p_0\, [1+O(a) ]. (15) Proof of Corollary A.7. For 0<a<10<a<1, the bound pμk(2km,τ)≥1−(1−a)mp_ _k(2km;τ)≥ 1-(1-a)^m reaches p0p_0 once m≥log⁡(1/(1−p0))/[−log⁡(1−a)]m≥ (1/(1-p_0))/[- (1-a)]. Hence the exact rounded sufficient budget is Nsuff(k,p0,τ)=2k⌈log⁡(1/(1−p0))−log⁡(1−a)⌉.N_suff(k,p_0,τ)=2k (1/(1-p_0))- (1-a) . (16) Using −log⁡(1−a)=a+O⁡(a2)- (1-a)=a+O(a^2) and a rounding error below 2k2k gives (2k/a)log⁡(1/(1−p0))+O⁡(k)(2k/a) (1/(1-p_0))+O(k), equivalent to equation 15 for fixed p0p_0. Finally, p0=(U∗+η)/τp_0=(U_*+η)/τ, 0<η<τ−U∗0<η<τ-U_*, gives Perfμk⁡(N)≥U∗+ηPerf_ _k(N)≥ U_*+η by Proposition A.3. ∎ Startup and initial-agent effects. Startup denotes the early cycles before cooperative progress stabilizes. The initial agent can affect access to G and finite-budget quality. If the two starts later have similar conditional success rates, their subsequent budget scales 2k/a2k/a are similar, while their startup progress can still differ. A.3 Interruption Guarantee and Sufficient Caps We expand Section 3.3. Corollary A.8 extends the alternation guarantee to NTA. We define interruption advantages in Definition A.9 and compare the workflows through option-level Bellman recursions. Theorem A.10 compares fixed-k interruption with NTA; Corollaries A.11–A.12 give a finite candidate condition and the explicit cap bound underlying Corollary 3.6. Corollary A.8 (Natural termination and quality limits). For Natural-Termination Alternation (NTA), use μ∞=(A,B,u0,∞) _∞=(A,B,u_0,∞). Under Assumptions 3.1 and 3.2 and almost-surely finite option durations, let Mτ:=infm≥0:q⁡(x2m)≥τM_τ:= \m≥ 0:q(x_2m)≥τ\. Then Cμ∞,Mτ<∞C_ _∞,M_τ<∞ almost surely and Uμ∞≥τ>U∗U_ _∞≥τ>U_*. If NTA and a finite cap satisfy access for every τ∈(U∗,U†)τ∈(U_*,U ), where U†∈(U∗,1]U ∈(U_*,1] bounds both reachable quality spaces, then Uμk=Uμ∞=U†U_ _k=U_ _∞=U . Proof of Corollary A.8. Applying equation 12 to NTA gives Prμ∞⁡(Mτ>m)≤F0(1−a)m→0 _ _∞(M_τ>m)≤ F_0(1-a)^m→ 0, with a=αβa=αβ. Thus MτM_τ and the sum of its option durations are almost surely finite. Monotone quality yields Uμ∞≥τU_ _∞≥τ. Combining this argument with Theorem A.6 for every τ∈(U∗,U†)τ∈(U_*,U ) and using the common upper bound gives equality for both limits. ∎ Definition A.9 (Interruption advantage and reference margin). Fix μk=(A,B,u0,k) _k=(A,B,u_0,k) and N. The workflows μk _k and μ∞=(A,B,u0,∞) _∞=(A,B,u_0,∞) share internal policies and boundary updates and differ only in option termination. Following Section 3.3, xi,0=xix_i,0=x_i is option i’s entry, xi,−1=xi,di(ui)x_i,-1=x_i,d_i^(u_i) its endpoint before reset, and xi+1,0=f⁡(xi,−1)x_i+1,0=f(x_i,-1) the next entry, with q⁡(xi+1,0)=q⁡(xi,−1)q(x_i+1,0)=q(x_i,-1). At an added cap interruption, NTA would continue from xi,−1x_i,-1 with the current context. Ending the option instead gives advantage Aμ∞(xi,−1):=Vμ∞(xi+1,0)−Qμ∞(xi,−1,oi(ui))A _∞(x_i,-1):=V _∞(x_i+1,0)-Q _∞(x_i,-1,o_i^(u_i)). Both values use NTA with the same remaining experiment budget; the next entry activates the other agent with empty context. The interruption contribution is zero at natural termination or budget exhaustion. The added interruptions are indexed by μk(N):=i≥0:∑j=0idj(uj)<N,di(ui)=k<Ti(ui)(xi,0).J_ _k(N):= \i≥ 0: _j=0^id_j^(u_j)<N,\ d_i^(u_i)=k<T_i^(u_i)(x_i,0) \. Thus natural termination takes precedence when it coincides with the cap. The expected net gain is μk(N):=μk∑i∈μk(N)Aμ∞(xi,−1)A_ _k(N):=E_ _k _i _ _k(N)A _∞(x_i,-1), and the NTA margin is Δμ∞(N):=Perfμ∞⁡(N)−U∗ _ _∞(N):=Perf_ _∞(N)-U_*. Theorem A.10 (Expected advantage under fixed-k interruption; Theorem 3.5 restated). For the selected initial agent u0u_0, a sufficient condition to exceed U∗U_* is Δμ∞(N)+μk(N)>0⟹Perfμk⁡(N)>U∗. _ _∞(N)+A_ _k(N)>0 _ _k(N)>U_*. (17) Proof of Theorem A.10. Let M be the number of options executed under μk _k within budget N, with xM,0x_M,0 terminal, and let ιi:=i∈μk(N) _i:=1_\i _ _k(N)\. For each i<Mi<M, the option-level Bellman recursion (Sutton et al., 1999, proof of Theorem 2) gives μk[q⁡(xi+1,0)−q⁡(xi,0)+Vμ∞(xi+1,0)∣xi,0]−Vμ∞(xi,0) _ _k\! [q(x_i+1,0)-q(x_i,0)+V _∞(x_i+1,0) x_i,0 ]-V _∞(x_i,0) (18) =μk[ιiAμ∞(xi,−1)∣xi,0]. =E_ _k\! [ _iA _∞(x_i,-1) x_i,0 ]. Since Vμ∞(xM,0)=0V _∞(x_M,0)=0 and x0,0=x0∼ν0x_0,0=x_0 _0, summing telescopes: Perfμk⁡(N)−Perfμ∞⁡(N) _ _k(N)-Perf_ _∞(N) =μk[q⁡(xM,0)−q⁡(x0,0)−Vμ∞(x0,0)] =E_ _k\! [q(x_M,0)-q(x_0,0)-V _∞(x_0,0) ] (19) =μk∑i∈μk(N)Aμ∞(xi,−1)=μk(N). =E_ _k _i _ _k(N)A _∞(x_i,-1)=A_ _k(N). Thus Perfμk⁡(N)−U∗=Δμ∞(N)+μk(N)Perf_ _k(N)-U_*= _ _∞(N)+A_ _k(N), which proves equation 17. ∎ Initial-agent dependence of interruption gains. The kernels Pk(A)Pk(B)P_k^(A)P_k^(B) and Pk(B)Pk(A)P_k^(B)P_k^(A) can induce different early task states, changing both Δμ∞(N) _ _∞(N) and μk(N)A_ _k(N). Consequently, the preferred initial agent can depend on k and N; the associated startup budget effects are discussed in Appendix A.2. Corollary A.11 (A sufficient cap in a finite candidate range). Fix A,B,u0,NA,B,u_0,N with Δμ∞(N)>0 _ _∞(N)>0 and integer K≥1K≥ 1. For each candidate cap 1≤k≤K1≤ k≤ K, let μk=(A,B,u0,k) _k=(A,B,u_0,k) and suppose there is εμk≥0 _ _k≥ 0 with μk(N)≥−εμkμk|μk(N)|A_ _k(N)≥- _ _kE_ _k|J_ _k(N)|. Then min1≤k≤K⁡⌊N/k⌋εμk<Δμ∞(N)⟹∃ 1≤k≤K:Perfμk⁡(N)>U∗. _1≤ k≤ K N/k _ _k< _ _∞(N) ∃\,1≤ k≤ K:Perf_ _k(N)>U_*. (20) Proof of Corollary A.11. Each added interruption uses a distinct block of k experiments, so |μk(N)|≤⌊N/k⌋|J_ _k(N)|≤ N/k and μk(N)≥−⌊N/k⌋εμkA_ _k(N)≥- N/k _ _k. Choose a minimizing cap in equation 20 and apply Theorem A.10. ∎ Corollary A.12 (Explicit cap under geometric loss decay; quantitative form of Corollary 3.6). Fix A,B,u0,NA,B,u_0,N with Δμ∞(N)>0 _ _∞(N)>0. Under the expected loss condition of Corollary A.11, assume εμk≤Cρk _ _k≤ Cρ^k for every μk=(A,B,u0,k) _k=(A,B,u_0,k), k≥1k≥ 1, with constants C>0C>0 and 0<ρ<10<ρ<1. The policy μk0:=(A,B,u0,k0) _k_0:=(A,B,u_0,k_0) with the following cap preserves at least half the NTA margin: k0 k_0 :=max⁡1,⌈log⁡(2NC/Δμ∞(N))−log⁡ρ⌉, := \! \1, (2NC/ _ _∞(N))- ρ \, (21) Perfμk0⁡(N) _ _k_0(N) ≥U∗+12Δμ∞(N)>U∗. ≥ U_*+ 12 _ _∞(N)>U_*. Proof of Corollary A.12. The expected loss is at most ⌊N/k⌋Cρk≤NCρk N/k Cρ^k≤ NCρ^k. The choice of k0k_0 makes this at most Δμ∞(N)/2 _ _∞(N)/2; substitution in equation 19 proves the claim. Taking k=k0k=k_0 for the selected initial agent gives a sufficient cap in [1,k0][1,k_0], proving Corollary 3.6. Uniform C,ρC,ρ and a positive margin lower bound across budgets give k0=O⁡(log⁡N)k_0=O( N). ∎ Appendix B Prefix Retention and Empirical Cap Selection We quantify the observed gains retained by short prefixes and provide the simultaneous confidence construction used to motivate candidate caps in Section 3.3. Executed fixed-k outcomes are analyzed separately in Appendix F. B.1 Retention Statistics and Confidence Bounds We establish the statistical guarantee supporting Section 3.3. Definition B.1 specifies task-level prefix retention, Assumption B.2 states the sampling condition, and Proposition B.3 gives simultaneous 1−δ1-δ lower confidence bounds. Definition B.1 (Observed prefix gain). For policy μ and task j, define μ,j:=i:oi(ui) is recorded on task j under μ.O_μ,j:=\i:o_i^(u_i) is recorded on task j under μ\. For each session index i∈μ,ji _μ,j, let lil_i be its recorded experiment count and qi(d)q_i(d) its best quality after d experiments, with entry quality at d=0d=0. For integer k≥0k≥ 0, define gi(k)=qi(min⁡k,li)−qi(0),ζμ,j(k)=∑i∈μ,jgi(k)∑i∈μ,jgi(li).g_i(k)=q_i( \k,l_i\)-q_i(0), _μ,j(k)= _i _μ,jg_i(k) _i _μ,jg_i(l_i). (22) The ratio is defined for positive total gain; nμn_μ counts these tasks. Assumption B.2 (Independent task observations). For each prespecified policy μ, cap k, and statistic, let Yj∈[0,1]Y_j∈[0,1] be ζμ,j(k) _μ,j(k) or ζμ,j(k)≥0.91_\ _μ,j(k)≥ 0.9\. Conditional on defined ratios, assume independence across the nμn_μ tasks. Dependence across configurations and caps is allowed. Proposition B.3 (Simultaneous lower confidence bounds). Under Assumption B.2, set Y¯=nμ−1∑jYj Y=n_μ^-1 _jY_j and μY=nμ−1∑jYj _Y=n_μ^-1 _jEY_j. For McmpM_cmp prespecified comparisons and δ∈(0,1)δ∈(0,1), define μ¯Y≤Y¯ μ_Y≤ Y by nμdKL(Y¯∥μ¯Y)=log(Mcmp/δ),n_μd_KL( Y\| μ_Y)= (M_cmp/δ), (23) with μ¯Y=0 μ_Y=0 when Y¯=0 Y=0. Then Pr⁡(μ¯Y≤μY for all comparisons)≥1−δ ( μ_Y≤ _Y for all comparisons)≥ 1-δ. Proof of Proposition B.3. The exponential-moment bound (Garivier and Cappé, 2011, Lemma 9), Jensen’s inequality, and Chernoff optimization give Pr(Y¯≥z)≤e−nμdKL(z∥μY) ( Y≥ z)≤ e^-n_μd_KL(z\| _Y) for μY<z≤1 _Y<z≤ 1. Inverting at failure level δ/Mcmpδ/M_cmp gives equation 23; a union bound over the comparisons proves the claim. ∎ B.2 Configurations and Observed Prefix Results This subsection documents the MLE-bench configurations and results supporting empirical cap selection in Section 3.3 and Figure 3. Table 3 lists six goal and five NTA configurations, all using max reasoning effort. A goal task run is one continuous session; NTA alternates at natural termination, starting with the first listed model. Harness documentation is provided by Bolin (2026); Anthropic (2026b); Moonshot AI (2026); DeepSeek-AI (2026). Table 3: Model and harness composition of the eleven MLE-bench prefix-analysis configurations. NTA arrows specify the starting order of the repeating pair. Family Model(s), in starting order Harness(es), same order Goal GPT-5.6-sol Codex Goal Kimi K3 Kimi Code Goal GLM-5.3 Claude Code Goal DeepSeek-V4-Flash DeepSeek Harness Goal DeepSeek-V4.1-Flash DeepSeek Harness Goal Claude Opus 5 Claude Code NTA GPT-5.6-sol → Kimi K3 Codex → Kimi Code NTA Kimi K3 → GPT-5.6-sol Kimi Code → Codex NTA GLM-5.3 → DeepSeek-V4-Flash Claude Code → DeepSeek Harness NTA DeepSeek-V4.1-Flash → GLM-5.3 DeepSeek Harness → Claude Code NTA Claude Opus 5 → GPT-5.6-sol Claude Code → Codex For MLE-bench, we use q=1−(position−1)/(leaderboardsize)q=1-(position-1)/(leaderboard\ size) on 75 tasks, including 75 measured Opus goal runs. Each goal task run is one option; NTA follows recorded boundaries, giving 1,065 options. At each k, Figure 3 plots the mean of min⁡k,li/li \k,l_i\/l_i across options horizontally and gain retention averaged across tasks within each configuration, then equally across configurations vertically, both as percentages. Individual curves use each configuration’s data, starting at (0,0)(0,0) and ending at (100,100)(100,100) at its maximum option length. At k=1,3,5k=1,3,5, mean gain retention is 63.15%, 93.35%, and 97.83%, with experiment fractions 24.76%, 54.88%, and 73.77%. At k=5k=5, individual configurations retain 96.11%–99.20% (Opus: 98.74%), motivating candidates 1≤k≤51≤ k≤ 5. For eleven configurations, fifty caps (k=1,…,50k=1,…,50), and two statistics, Mcmp=1100M_cmp=1100. At δ=0.05δ=0.05 and k=5k=5, 87.84%–98.67% of tasks retain at least 90% of gains; Appendix B.1 gives simultaneous lower bounds of 65.08%–83.30%. Appendix C Experimental Setup and Reproducibility We collect the execution environment, agent configurations, baseline settings, evaluation rules, and repeat protocol used throughout the experiments. Empirical findings are separated into Appendices D–G. C.1 Humanize and Execution Environment Terminology. A configuration specifies the agent or agent pair, starting order, cap, and budget. A task run is one complete execution on one task; a repeat evaluates the full task suite. Each agent session is modeled as an option, with experiments counted within it; a model response is one recorded output from a model call. Framework. We implement the workflow on Humanize (Liu et al., 2026), which coordinates agent execution in a shared workspace, fixed-k interruption, and final review as specified in Algorithm 1. The model harness supplies the internal agent policy; the workflow controls option boundaries and preserves shared task workspace. HMA uses k=5k=5 and ttotal=21600t_total=21600 seconds per task, including trev=900t_rev=900 seconds reserved for the other agent’s final review. Thus exploration ends at ts=20700t_s=20700 seconds. Hardware. Our execution environment exposes 30 vCPUs backed by an Intel Xeon Platinum 8358 processor, 220 GiB RAM, and one NVIDIA A10 GPU. The GPU reports 24 GiB of available device memory. These resources are shared by the two alternating agents within a single task run. C.2 Agent and Baseline Configurations Agents. Table 4 lists the full model names and native harnesses. In analyses and figures, GPT, Kimi, GLM, and Opus abbreviate GPT-5.6-sol, Kimi K3, GLM-5.3, and Claude Opus 5; DeepSeek-V4 and DeepSeek-V4.1 abbreviate the corresponding Flash models. DeepSeek alone denotes the version specified for the configuration. All agents in our runs use max reasoning effort. Codex, Claude Code, Kimi Code, and DeepSeek Harness provide the model execution interfaces (DeepSeek-AI, 2026; Bolin, 2026; Anthropic, 2026b; Moonshot AI, 2026). Appendix B.2 separately lists the goal and NTA configurations used for prefix analysis. Table 4: Model–harness mappings and reasoning effort for our runs. Model Harness Reasoning effort GPT-5.6-sol Codex max Kimi K3 Kimi Code max GLM-5.3 Claude Code max DeepSeek-V4-Flash DeepSeek Harness max DeepSeek-V4.1-Flash DeepSeek Harness max Claude Opus 5 Claude Code max Comparison baselines. We include ScienceFlow, MLEvolve, and ML-Master 2.0 using their reported results (Zhao et al., 2026; Du et al., 2026; Zhu et al., 2026). Table 5 records their original configurations; the max reasoning setting applies to our runs, while these published results retain their reported inference settings. Table 5: Configurations of the three comparison baselines, as reported in their original papers. Resource allocations and time budgets differ across methods. Baseline Model and time budget Execution resources Key configuration ScienceFlow DeepSeek-V4-Flash-Preview; 24 h 16–32 logical CPU cores, 256 GB RAM, at most 2 GPUs Recoverable workspaces, ESTRA re-anchoring, and resource-aware execution control. MLEvolve Gemini-3.1-Pro-preview; 12 h 21 vCPUs, 234 GB RAM, 1 NVIDIA H200 Temperature 1.0; 500 expansion steps; 3 parallel branches and 3 initial drafts. ML-Master 2.0 DeepSeek-V3.2-Speciale; DeepSeek-V3.2 (thinking) for context promotion; 24 h 36 AMD EPYC vCPUs and 2 RTX 4090 GPUs per agent; 1008 GB RAM and 1 TB SSD shared across 4 tasks Hierarchical cognitive caching; prior wisdom initialized from 407 Kaggle competitions excluding MLE-bench. C.3 Evaluation Protocol and Repeats Evaluation metrics. Lite, Medium, High, and All denote the 22-, 38-, 15-, and 75-task sets, respectively. Lite, Medium, and High report medal percentages within each complexity group; All reports the medal percentage over the full 75-task suite. For repeated evaluations, rates are calculated from per-repeat medal counts before averaging. Table 2 reports all performance metrics to one decimal place. Within a model pair, Avg. of Single averages the two constituent goal means with equal weight; HMA gains are computed against this mean before rounding. Gold is the percentage of tasks attaining a gold medal. Med+ is the percentage outperforming the human leaderboard median. Mean percentile averages the task-level leaderboard percentile over the evaluated suite, using the rank convention in Appendix B.2. All metrics use the workflow’s returned candidate; for HMA this is the final review selection or its fallback in Algorithm 1. Test-set scores are computed offline. Repeated evaluations. Each configuration is evaluated in three independent repeats over the fixed 75-task suite. Reported values average the three repeats; published baseline uncertainties retain their original definitions. Appendix D Additional Evidence for the Motivation We provide the detailed evidence behind the two motivation claims in Section 2: response-length decay in uninterrupted runs and harness staleness across model versions. D.1 Declining Response Length in Single-Agent Runs Configurations. We document Figure 2 using the six configurations in Table 4. The /goal protocol runs one agent until natural termination or exhaustion of six hours of active runtime, without model alternation or fixed-cap interruption. Each of the six configurations is evaluated on 75 tasks with three independent repeats and max reasoning effort. Recorded cohorts and prompt policies are retained. Response-level moving average. Figure 2 reports mean output tokens per recorded model response. At one-minute active-runtime checkpoints, we divide the sum of provider-reported output tokens by the number of responses in the preceding 30 minutes, pooling the 75 tasks and repeats within each configuration. Near the origin, the window uses the elapsed prefix; windows without responses are undefined. This response-weighted statistic excludes tool-return text, input tokens, and coordinator output, while retaining model responses that request tools. Early versus late responses. Table 6 compares responses in hours 0–2 and 3–5 using raw event totals divided by response counts in each interval. All six configurations show a reduction of 29.8%–45.0%; these interval statistics are computed before temporal smoothing. Table 6: Mean output tokens per recorded response. Change is relative to hours 0–2. The same task suite and repeats are used as in Figure 2. Model Hours 0–2 tokens/response Hours 3–5 tokens/response Change (%) GPT-5.6-sol 336.5 213.6 −36.5-36.5 Claude Opus 5 1008.3 554.8 −45.0-45.0 GLM-5.3 658.4 388.5 −41.0-41.0 DeepSeek-V4.1-Flash 1137.5 696.1 −38.8-38.8 Kimi K3 585.7 390.2 −33.4-33.4 DeepSeek-V4-Flash 682.2 479.2 −29.8-29.8 D.2 Harness Staleness across Model Versions Comparison setup. We compare ML-Master 2.0 (Zhu et al., 2026), MLEvolve (Du et al., 2026), and ScienceFlow (Zhao et al., 2026) with the official DeepSeek Harness on a 16-task MLE-bench subset (Chan et al., 2025), using DeepSeek-V4-Flash and DeepSeek-V4.1-Flash. We retain the research harnesses’ original workflow designs and experimental settings while disabling task-specific cold-start knowledge wherever present. Execution budgets are reported in Table 2. DeepSeek Harness runs each model under /goal with max reasoning effort for six hours; its reported medal rate is averaged over three repeats. Result accounting. Medal rates use all 16 tasks as the denominator. The disqualified ScienceFlow run on Chaii with DeepSeek-V4.1-Flash is counted as no medal because its checkpoint had seen the test answers. Table 2 reports medal rates and percentage-point differences from the corresponding DeepSeek Harness baseline. Table 7 provides the task-level outcomes. These 16-task DeepSeek Harness references are distinct from the full 75-task results in Table 2. Table 7: Task-level outcomes for the harness comparison. DeepSeek Harness entries report the number of runs earning a medal out of three; its medal total is the mean count. The last row divides each medal total by 16, matching Table 2. Other columns report medal classes from the retained run: G, S, and B denote gold, silver, and bronze; — denotes no medal, × denotes the disqualified ScienceFlow V4.1 Chaii run. V4 and V4.1 denote DeepSeek-V4-Flash and DeepSeek-V4.1-Flash. When a run did not nominate a final artifact, the recorded score-independent rule selects its latest eligible submission. Workflow DeepSeek Harness ScienceFlow ML-Master 2.0 MLEvolve Task V4 V4.1 V4 V4.1 V4 V4.1 V4 V4.1 3D Object Detection 1/3 2/3 S G — S — — APTOS Blindness Detection 0/3 3/3 S B — G — S Toxic Comment Classification 0/3 3/3 — G — — B S Leaf Classification 1/3 3/3 S S — — B G Billion Word Imputation 0/3 3/3 — G — — — — Cdiscount Image Classification 0/3 1/3 — — — — — — Chaii Question Answering 0/3 1/3 — × — — — — Freesound Audio Tagging 1/3 1/3 — — — — — S iMet 0/3 1/3 — S — — — — iWildCam 2/3 3/3 — G — S G S Kuzushiji Recognition 2/3 3/3 B — — G — — Learning Agency Essay Scoring 0/3 3/3 — G — G — — LMSYS Chatbot Arena 0/3 2/3 — S — — — — PetFinder Pawpularity 0/3 3/3 — G — S — S Tweet Sentiment Extraction 0/3 2/3 — S — — — S US Patent Phrase Matching 1/3 3/3 — — S — — S Medals 2.7 12.3 4 11 1 6 3 8 Medal rate (%) 16.7 77.1 25.0 68.8 6.3 37.5 18.8 50.0 Appendix E Additional Main-Comparison Analyses We supplement the main comparison with the aggregation rules, response and performance trajectories, matched constituent weighting, and task-level comparisons used for Figure 4. Analysis configurations. We analyze the five participating goal models and six HMA configurations in Table 2, using the protocol in Appendix C. The trajectory aggregation and matched constituent construction follow the definitions below. The separate scheduling ablations appear in Appendix F. Performance and response trajectories. At each active-runtime checkpoint, we aggregate the medal status of the latest accepted candidate on each task, assigning zero before a valid submission. Final points use the returned candidate under the recorded selection rule. Scores use the corrected answer keys. Receipt processing at the nominal deadline is included in the final point. Figure 4 (a) uses the response-level statistic in Appendix D.1: at each one-minute checkpoint, total actor output tokens in the preceding 30-minute trailing window are divided by the number of recorded responses, pooling tasks and repeats within each configuration and including HMA’s final review. Near the origin, the window uses the elapsed prefix; empty windows are undefined. Figure 4 (b) retains the unsmoothed medal-rate trajectory. Token counts measure output volume across different tokenizers, not a common monetary or computational cost. Neither panel extrapolates trajectories or uses best-so-far score selection. Matched group-average curves. Figure 4 assigns weight 1/61/6 to each HMA configuration. For configuration j with constituent models Aj,BjA_j,B_j, its goal reference is (YAjgoal(t)+YBjgoal(t))/2(Y_A_j^goal(t)+Y_B_j^goal(t))/2, where Y denotes mean output tokens per response or medal rate, computed within each configuration as above. We average these six references at each common runtime checkpoint. The resulting matched model weights are reported in Table 9; the same weights are used for Goal and HMA, so each model contributes equally to both references. DeepSeek-V4-Flash is excluded because it appears in none of the six HMA configurations. This matches the mean-of-constituents reference used for the gains in Table 2; the weights describe configuration composition rather than measured execution-time shares. Both panels use active runtime horizontally, with mean output tokens per response in (a) computed over a 30-minute trailing window and mean medal rate in (b). Faint curves retain the participating configurations. For the early/late comparison, we divide raw output-token totals by response counts separately in hours 0–2 and 3–5 within each configuration, then apply the same group weights. The resulting means are 610.9 and 527.6 tokens per response for HMA, and 650.3 and 394.9 for goal, retaining 86.4% and 60.7%, respectively; these interval statistics are computed before temporal smoothing. Table 8: Matched workflow weights. The matched weight is used for both Goal and HMA, so every model contributes equally to both references. Model Matched weight GPT 5/125/12 Opus 1/61/6 DeepSeek-V4.1 1/61/6 Kimi 1/61/6 GLM 1/121/12 Table 9: Early and final medals. Any-medal rates are reported at two hours and at the six-hour endpoint for each HMA order. Order 2h 6h Opus/GPT 57.3 78.2 GPT/Opus 58.7 73.3 GPT/DeepSeek-V4.1 54.7 72.0 GPT/Kimi 60.0 70.7 GPT/GLM 50.7 69.3 DeepSeek-V4.1/Kimi 42.7 62.7 Early progress and task-level gains. Table 9 reports the any-medal rates at two hours and at the six-hour endpoint. The six HMA configurations attain 57.3%, 58.7%, 54.7%, 60.0%, 50.7%, and 42.7% medals at two hours, with corresponding final rates of 78.2%, 73.3%, 72.0%, 70.7%, 69.3%, and 62.7%. Across matched GPT goal comparisons, GPT–Kimi HMA gains medals on 5, 4, and 6 tasks and loses them on 4, 3, and 2, yielding net gains of 1, 1, and 4. These successful tasks remain within the evaluated goal-task union, characterizing gains achieved within the six-hour budget. Appendix F Ablation Studies We supplement Section 4.3 with starting-order effects, executed fixed-k comparisons, natural-termination statistics, and a selection-only final review audit. We discuss order before cap size because model exposure within a finite time budget depends on both. F.1 Starting-Order Effects We compare GPT-first and Kimi-first alternation under NTA and HMA with k=5k=5, then relate the endpoint differences to model-session time and partner participation. Configurations. Each configuration covers the same 75 tasks with a six-hour budget and max reasoning effort. The additional Kimi-first HMA run records 283 exploration options: among the 75 initial options, 52 reach the cap, 22 end naturally, and one reaches the deadline. The GPT-first k=5k=5 run records 277 exploration options, with 66 initial cap closures and nine natural exits. Corrected answer keys give 42/75 medals for Kimi-first NTA, including three corrected outcomes. For the Kimi-first HMA archive, the terminal window is 21,700 seconds; all accepted candidates arrive within 21,600 seconds and its six-hour medal count matches the returned result. Final quality and finite-budget exposure. Figure 7(a) compares both GPT–Kimi starting orders under the six-hour budget. NTA reaches 77.3% and 56.0% medals with GPT and Kimi first, respectively; HMA with k=5k=5 reaches 70.7% and 66.7%, narrowing the observed gap from 21.3 to 4.0 percentage points. The six-hour horizon limits sustained participation by both agents under NTA: by 5.75 hours, the second agent has produced a recorded response on only 19/75 GPT-first tasks and 47/75 Kimi-first tasks. Under NTA, the nominal first model occupies about 81–83% of the budget. Because the GPT goal baseline is stronger than the Kimi baseline (68.0% versus 54.2%), the longer uninterrupted GPT exposure in the GPT-first archive is associated with the higher NTA result. GPT-first HMA instead allocates 51.1% to GPT and 46.3% to Kimi, whereas Kimi-first HMA still allocates 81.3% to Kimi and only 16.2% to GPT. These finite-budget differences accord with the startup effects in Appendix A.2; improvement from interruption remains conditional on continuation advantage (Theorem 3.5). Figure 7: Fixed-cap interruption: starting-order and cap ablations. Both panels use the same 75-task, six-hour GPT-5.6-sol–Kimi K3 suite. (a) Starting-order comparison: NTA and HMA with k=5k=5; the cap narrows the observed order gap. (b) GPT-first HMA with k∈1,3,5k∈\1,3,5\; the new A10 runs produce 49/75 and 50/75 medals at k=1k=1 and k=3k=3, while the existing k=5k=5 run produces 53/75. Values are final medal rates, with counts shown in the cap panel. Model time allocation. We reconstruct occupied model-session intervals from native session and controller logs over the first six hours. Native creation and completion records determine session endpoints. For an interrupted session without a completion record, we use the next session or option start, or the active attempt’s end, whichever occurs first. Intervals are intersected with active-runtime windows; pause gaps and auxiliary subagent sessions are excluded, and final review is attributed to its executing model. If wj(u)w_j^(u) is the resulting model-u duration on task j, its mean budget share is 100∑j=175wj(u)/(75⋅21600)100 _j=1^75w_j^(u)/(75· 21600). All returns to a model are accumulated. Unallocated time averages 0.07% and 0.15% for GPT-first and Kimi-first NTA, and 2.63% and 2.49% for the corresponding HMA runs. These shares include tool execution and waiting within sessions. Recorded starting-order exceptions. Workflow labels retain the archived nominal configurations. In the GPT-first NTA archive, seven of 75 tasks have Kimi as the earliest recorded native session; the other NTA configuration and both HMA runs match their nominal initial models on all 75 tasks. Runtime attribution follows the recorded model, and all tasks remain included. Thus the historical NTA groups are configuration comparisons rather than perfectly controlled starting-order interventions. Designated-partner participation. We measure participation from the first recorded response by the nominal second agent (Kimi in the GPT-first configuration and GPT in the Kimi-first configuration), excluding turn-review sessions. This measures observable access to search, rather than an exact controller launch time. Tasks with no such response are right-censored at six hours; counts retain all 75 tasks in the denominator. Table 10 reports these response-based timing statistics separately from the session-duration estimates above. With GPT first, the second agent’s mean within-task share of output tokens before hour 5.75 rises from 13.0% under NTA to 36.1% under HMA. A cap limits experiments per option; it does not impose a fixed wall-clock duration on an experiment. Table 10: The cap advances access to the second agent. All counts are out of 75 tasks and exclude final review. By the six-hour deadline, 22 GPT-first NTA tasks and 18 Kimi-first NTA tasks still have no recorded response from the second agent. Tasks with a second-agent response Median first response (h) Final medals (%) Workflow By 3 h By 5 h By 5.75 h GPT → Kimi NTA 17 18 19 5.97 77.3 Kimi → GPT NTA 15 27 47 5.56 56.0 GPT → Kimi HMA 55 69 75 1.89 70.7 F.2 Effects of the Fixed Interruption Cap We hold GPT as the initial agent and compare executed HMA policies with k∈1,3,5k∈\1,3,5\, complementing the observed-prefix analysis in Appendix B. Configurations and results. Each cap contributes one repeat over 75 tasks with the same model pair, max reasoning effort, and nominal six-hour budget including final review. The k=1k=1 and k=3k=3 archives use a 21,700-second terminal window. Table 11 reports the final medal counts and rates, also plotted in Figure 7(b). These cap configurations and the reverse-order configuration are used for scheduling ablations; the main comparison retains its six configurations. Table 11: k=5k=5 gives the highest medal rate among the tested finite caps. GPT-first HMA alternates GPT-5.6-sol and Kimi K3 on the same 75 tasks under the nominal six-hour budget. Cap k Medals / 75 Medal rate (%) 1 49 65.3 3 50 66.7 5 53 70.7 Empirical selection within the candidate range. The prefix statistics in Appendix B motivate candidates 1≤k≤51≤ k≤ 5. Among the executed GPT-first runs, k=1,3,5k=1,3,5 yield 65.3%, 66.7%, and 70.7% medals, respectively, against the GPT goal mean of 68.0%. These results support selecting k=5k=5 within the tested finite caps for this order and horizon. Theorem 3.5 gives the corresponding conditional advantage criterion; the prefix statistics guide candidate selection without directly estimating its continuation values. Interaction with time and starting order. A larger cap permits longer uninterrupted experiment blocks before handoff, while the six-hour deadline limits the partner’s subsequent search. Given GPT’s stronger standalone performance, the GPT-first cap trend and higher GPT-first NTA result are consistent with a benefit from preserving more continuous GPT search. Conversely, k=5k=5 improves the Kimi-first result and reduces sensitivity to the initial agent. The limited horizon can therefore leave the pair’s complementary capabilities incompletely exploited, making cap size and initial-agent choice jointly relevant. The recorded starting-order exceptions in Appendix F.1 delimit this interpretation. F.3 Natural Termination before the Cap We report option-closure outcomes from terminal controller receipts and evaluator ledgers for the six main-table HMA configurations. One complete repeat per configuration, using the first Opus-first GPT repeat, yields 450 task runs with the same answer keys and final-candidate rule as Table 2. Option closure. Table 12 separates the first option from later options and distinguishes reaching five accepted experiments, natural termination before five, and closure at the exploration deadline. Final review sessions are excluded. Initial options contain 57 natural exits among 446 closures before the deadline (12.8%); later options contain 598 among 992 (60.3%). Across all options, 655/1,438 closures before the deadline are natural (45.5%). Of the 655 natural exits, 248 produce no accepted experiment. These are retained in the audit. One GPT–DeepSeek deadline receipt omits the cap field following a controller timeout; its accepted count is zero, and the recorded standing submission agrees with the adopted fallback. All 1,888 recorded option counts are at most five. Table 12: Observed option-closure reasons at k=5k=5. Each configuration has 75 initial options. Natural-exit percentages exclude deadline closures because the latter censor whether an option would reach the cap or terminate naturally. The first listed model starts each workflow. Initial option Later options Configuration Cap Natural Deadline Cap Natural Deadline Opus → GPT 61 13 1 56 121 74 GPT → Opus 72 2 1 89 69 74 GPT → DeepSeek-V4.1 71 4 0 88 132 75 GPT → Kimi 66 9 0 56 71 75 GPT → GLM 54 19 2 71 36 73 DeepSeek-V4.1 → Kimi 65 10 0 34 169 75 All configurations 389 57 4 394 598 446 F.4 Final Review and Historical Any-Medal Retention We evaluate retention of historically attained any-medal outcomes on the same 450 task runs as Appendix F.3, supplementing the mechanism in Section 3.4. Selection-only comparison. We hold each recorded exploration trajectory fixed and compare the returned candidate with the candidate standing immediately before final review. The reserved final review time is not reallocated to search, so this measures the effect of final selection rather than a rerun with a longer exploration budget. Historical any-medal retention. For each task run, historical any-medal status is one if any accepted exploration candidate earns bronze or better, and zero otherwise. We compute this status from offline evaluator records before final review; repeated receipts for a reviewed candidate add no new historical outcome. Historical any-medal retention is the fraction of historically medal-positive task runs whose selected candidate earns a medal. Table 13 compares this fraction before and after final review. Of 450 task runs, 330 produce a medal-winning candidate; final review raises retained medals from 311/330 (94.2%) to 319/330 (96.7%), recovering eight medals without losing any held immediately before final review. Table 13: Final review improves retention of historical any-medal outcomes. Each configuration contains 75 task runs. Historical counts runs with at least one medal-winning exploration candidate; retention divides selected medal counts by Historical. Before and after refer to the standing candidate and final review’s returned candidate. Missed counts historical medal outcomes not retained after final review. Configuration Changed Historical any medal Selected medals before → after Retention (%) before → after Missed after Opus → GPT 4 59 58→5858→ 58 98.3→98.398.3→ 98.3 1 GPT → Opus 6 57 55→5555→ 55 96.5→96.596.5→ 96.5 2 GPT → DeepSeek-V4.1 11 56 51→5451→ 54 91.1→96.491.1→ 96.4 2 GPT → Kimi 6 54 52→5352→ 53 96.3→98.196.3→ 98.1 1 GPT → GLM 9 54 48→5248→ 52 88.9→96.388.9→ 96.3 2 DeepSeek-V4.1 → Kimi 4 50 47→4747→ 47 94.0→94.094.0→ 94.0 3 All configurations 40 330 311→319311→ 319 94.2→96.794.2→ 96.7 11 Across all 450 runs, the returned candidate matches the historical any-medal status in 439 (97.6%), including 120 runs that never produce a medal. The conditional retention rate of 96.7% excludes these 120 runs. Final review changes 40 selections (8.9%); 311/319 final medals (97.5%) were already held before final review. Thirty-five GLM-pair final reviews are silent and one DeepSeek-pair final review fails; their recorded fallback candidates remain included. This audit measures historical any-medal retention at final selection. Medal recovery and remaining misses. On MBM-01 with GPT–DeepSeek-V4.1, the first GPT option reaches 0.84671 without a medal, and DeepSeek reaches bronze at 0.85445. The returning GPT replaces the standing result with 0.75795; final review restores the archived DeepSeek candidate and recovers the medal. On MBM-20 with GPT–GLM, GPT produces a gold-medal candidate at 0.84835, but the final GLM candidate scores 0.25403; final review restores 0.84835. In aggregate, final review reduces missed historical medals from 19 to 11, supporting its role in retaining search outcomes at final selection. Appendix G Case Studies of Heterogeneous Alternation We examine four model pairs across five model families: GPT–Opus, GPT–DeepSeek, GLM–Kimi, and DeepSeek–Kimi. The INGV case in Section 4.4 is followed by examples from text prediction, image regression, and satellite positioning. Selection and measurement. We selected task runs with inspectable artifacts, controller logs, evaluator receipts, and native response records. GPT–Opus, GPT–DeepSeek, and DeepSeek–Kimi occur in the main comparison; GLM–Kimi is an additional combination using the same k=5k=5 workflow. Following the trajectory analysis of Zhao et al. (2026), we align each accepted candidate with its producing option using controller counts and receipt times. Test scores are evaluated offline and were hidden from the agents; all accepted scores, including regressions, are plotted. Goal references use three runs per constituent. The appendix figures compare disjoint first- and last-20-response windows; options with fewer than 40 responses show their counts instead. Final review is excluded from token statistics and preserves the standing candidate in all four cases. Response renewal is compared within the same model, since tokenizers and policies differ. These cases illustrate observed mechanisms rather than estimating their average causal effect. G.1 INGV Volcanic Eruption Prediction Repeated refinement. On INGV (MBH-07), GPT and Opus complete seven exploration options with 5, 5, 5, 2, 5, 1, and 4 accepted experiments and 77, 263, 251, 59, 110, 49, and 48 responses, respectively. Options 1, 2, 3, and 5 reach the cap; options 4 and 6 end naturally, and option 7 reaches the deadline. Their best MAEs are 1,123,915, 41,214, 39,061, 39,878, 37,422, 36,934, and 34,234: five of the six post-handoff options improve the historical best, while the fourth option regresses. Shared features and cached predictions support successive refinements. The trace records GPT reusing and pruning Opus’s retrieval features, Opus adding consistency constraints for paired windows, GPT introducing an uncertainty-based residual gate, Opus refining its calibration, and GPT enforcing joint temporal feasibility. Score comparisons and plot conventions. After the first Opus session reaches 41,214 MAE, subsequent alternation lowers it to 34,234, a further 16.9% improvement and 46.5% below the best of six constituent goal runs (63,991). Native MAE resolves progress beyond the already-gold goal results. Figure 5(a) retains all 27 accepted scores, including regressions, without smoothing; it uses a logarithmic axis with a linear inset for late options. Horizontal lines mark the gold threshold (3,971,366), the minimum MAE in MLE-bench’s 621-entry reference leaderboard (3,438,191), and the best constituent goal endpoint. Blue and purple regions identify GPT and Opus, and dotted vertical lines mark handoffs. Response measurement and renewal. In Figure 5(b), each point averages output tokens per response from the preceding accepted submission or option start to the current acceptance. The 27 intervals contain 826 responses, excluding 31 trailing responses; final review is excluded. Comparing the first experiment after each return with the same model’s preceding last experiment, mean response length increases on four of five returns by a factor of 1.6–3.6; the final Opus return has a ratio of 0.94. G.2 Google QUEST Q&A Labeling: GPT–DeepSeek Repeated reuse of text-model predictions. On Google QUEST Q&A Labeling (MBM-10), GPT-5.6-sol and DeepSeek-V4.1-Flash complete seven options, five of which produce 23 accepted candidates. GPT initializes sparse-text and encoder models; DeepSeek completes additional DeBERTa fits and combines their saved predictions. Subsequent sessions reuse these artifacts for target-specific blending, calibration, and larger-encoder refinement. The first five options achieve best Spearman correlations of 0.45664, 0.47124, 0.48741, 0.50381, and 0.50760. The returned candidate scores 0.50747, versus 0.47252 for the best of six constituent goal runs (Figure 8). At the first returns, GPT’s mean response length rises from 168.9 to 529.1 tokens and DeepSeek’s from 647.2 to 1060.9; GPT’s next return instead falls from 616.7 to 339.2. The final two options produce no accepted experiment, so neither response renewal nor useful progress occurs at every handoff. Figure 8: GPT–DeepSeek refinement on Google QUEST. (a) All 23 accepted scores, including regressions. Shading identifies the active model; reference lines mark the best constituent goal endpoint and gold threshold. (b) First- and last-20-response means per option. Options 6 and 7 have only 17 and 5 responses and no accepted experiments; their response counts replace overlapping windows. Final review retains the standing candidate and is excluded from token statistics. G.3 PetFinder Pawpularity: GLM–Kimi Extending a shared prediction pool. On PetFinder Pawpularity (MBM-27), GLM-5.3 builds CLIP and DINOv2 feature caches, regressors, and calibrated predictions before Kimi K3 takes over at 2.40 hours. Kimi reuses the out-of-fold predictions in a constrained stack and adds concatenated-feature ridge and MLP members, improving the best test RMSE from 16.87437 to 16.78333. Returning GLM explores further combinations and reaches 16.77953; the returned candidate scores 16.85639 and earns gold (Figure 9). Neither constituent earns a medal in its three goal runs. The three productive options contain 5, 5, and 3 experiments; the final Kimi option adds none. GLM’s returning first 20 responses average 724.5 tokens, compared with 503.8 in its preceding option’s last 20. The final score regression remains visible: artifact reuse improves the search trajectory without ensuring that the returned candidate is its best. Figure 9: GLM–Kimi cooperation on Pawpularity. (a) Every accepted test RMSE, with a linear inset resolving the late candidates. The dotted and dashed lines show the best of six constituent goal endpoints and the gold threshold. (b) Response-length windows for the three productive options; the last option has only 12 responses. The final candidate remains below the gold threshold despite regressing from the best observed RMSE. G.4 Google Smartphone Decimeter: DeepSeek–Kimi Late correction after an unsuccessful refinement. On the Google Smartphone Decimeter Challenge 2022 (MBH-12), DeepSeek-V4.1-Flash builds a GNSS fusion pipeline with Doppler constraints and robust optimization, reaching 4.33091 mean haversine error. Kimi K3 improves it to 4.28914, but DeepSeek’s next option leaves a worse candidate at 5.35529. Returning at 5.08 hours, Kimi retains the shared solver, checks the mean-error objective, and replaces straight-line extrapolation through an end-of-log outage with a direction-matched route from public training trajectories. Its accepted candidate reaches 2.77310 and earns bronze, a 42.1% reduction from the best of six constituent goal endpoints (4.78536), none of which earns a medal (Figure 10). Kimi’s first 20 returning responses average 847.9 tokens, below the preceding Kimi option’s last-20 mean of 1010.0. This late quality gain therefore does not require a response-length rebound. Figure 10: DeepSeek–Kimi correction in smartphone positioning. (a) All ten accepted mean-haversine scores. The fourth option repairs the late outage and crosses the bronze threshold after the third option regresses. The dotted line is the best constituent goal endpoint. (b) First- and last-20-response means; the final DeepSeek option contains nine responses and no accepted experiment. Final review retains Kimi’s repaired candidate.

Instant research discovery