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EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments

Deyao Zhu, Xin Zhou, Shengling Qin, Xuekai Zhu, Hangliang Ding, Shu Zhong, Zixin Wen, Zhonglin Xie, Chenhui Gou, Linxuan Ren, Yueyang Wang, Junfeng Zhong, Rui Liu, Tian Gao, Yangguang Lin, Jingyuan Zhang, Maojia Song, Xuan Qi, Jinhong Wu, Chenyang Zhang, Yinzhu Piao, Ziru Niu, Hongbin Lin, Lingxiang Meng, Peng Tang, Chengyao Tang, Shanyu Wu, Huanyu Zheng, Yu Liu, Liya Zhu, He Wang, Ming Ding, Ziyu Wan, Hao Liu, Sibo Wang, Haotian Zhu, Xintian Zhang, Nan Chai, Yipeng Liu, Panhao Lai, Sihang Yuan, Zixin Su, Ge Zhang, Wangchunshu Zhou, Yantao Du, Wenhao Huang, Guang Shi

arXiv:2607.05155v1cs.CLcs.LG

TL;DR

Whether learning from real-world environments follows a clean scaling law remains unknown. EdgeBench analyzes long-horizon agent interaction across diverse tasks and finds precise log-sigmoid learning trajectories, with learning speed roughly doubling every three months.

  • Problem

    Whether agents’ learning from real-world environments obeys a clean scaling law remains unknown, despite the importance of understanding post-deployment learning.

  • Method

    EdgeBench evaluates agents across 134 executable real-world tasks, analyzing roughly 38,000 hours of interaction over horizons of at least 12 hours.

  • Results

    Aggregate learning trajectories follow a precise log-sigmoid relationship across tasks and families, achieving R^2 = 0.998, while learning speed roughly doubles every three months.

  • Takeaways & Limitations

    Environment learning emerges as a measurable scaling object that EdgeBench can support studying beyond merely ranking agents.

  • Takeaways & Limitations

    The log-sigmoid law may fail for environments with strong bottlenecks, dispersed midpoints, heterogeneous frontier speeds, or non-scale-free graph structures.

Abstract

from arXiv · show

Pretraining scaling laws reveal that model capability improves predictably with data and compute. But learning from real world environments after deployment remains far less understood. Analyzing roughly 38,000 hours of agent interaction with the environment across 134 real world tasks, we find, to the best of our knowledge, the first evidence that overall performance during environment learning follows a log-sigmoid scaling law with remarkably high precision, reaching R^2 = 0.998. Across model generations, we also find that agent learning speed roughly doubles every three months. This discovery stems from EdgeBench, a suite of 134 real world tasks with ultra-long horizons, spanning scientific discovery, software engineering, combinatorial optimization, professional knowledge work, formal mathematics, and interactive games. Each task sustains at least 12 hours of continuous agent operation under rich, multilevel feedback, and is built through substantial expert effort. We publicly release 51 tasks and our full evaluation framework to accelerate the study of how agents learn from real world experience.

1 Introduction

EdgeBench studies whether agents’ learning from real-world interaction follows predictable scaling laws, using long-horizon, feedback-rich tasks and roughly 38,000 hours of evaluation. The study finds precise log-sigmoid learning, rapidly improving agent learning speed, and strong effects of experience usage on long-horizon performance.

  • EdgeBench: 134 realistic tasks span six capability families and provide executable workspaces with fast exploration, judge feedback, and at least 12 hours of interaction.The benchmark covers scientific research, software engineering, combinatorial optimization, professional knowledge work, formal mathematics, and interactive games.
  • Evaluation: 38,000 hours of environment interaction support the study of agent learning across EdgeBench.
  • Main findings: Environment learning follows a precise log-sigmoid scaling law across the benchmark, task families, horizons up to 72 hours, and forecasts from early trajectories.
  • Main findings: A frontier-expansion theory on latent task graphs explains why benchmark-averaged environment-learning progress takes the observed log-sigmoid form.
  • Main findings: Agent learning speed doubles roughly every three months among frontier models released since September 2025.
  • Main findings: Long-horizon performance depends on experience usage: continuous experience outperforms independent restarts, longer context improves retention, and feedback converts failed probes into durable gains.

2 EdgeBench

EdgeBench evaluates whether autonomous agents learn from experience through 134 curated, day-scale tasks across six capability families. Its protocol combines realistic local and authoritative feedback with hidden evaluation and trajectory measurement to distinguish learning from one-shot success.

  • Task taxonomy: 134 curated tasks span six capability families and support frontier models operating continuously for at least 12 hours.The taxonomy covers scientific problems and ML, systems and software engineering, combinatorial optimization, professional knowledge work, formal mathematics, and interactive games.
  • Task design: Tasks were selected for unsaturated performance ceilings and workflows that support continuous learning rather than one-shot completion.The task search was conducted with domain experts across fields.
  • Scope and limitations: Primary difficulty in visual understanding, especially GUI operation, is excluded because perceptual capability and iterative reasoning are difficult to separate.The exclusion applies when success depends on the vision backbone rather than iterative reasoning.
  • Evaluation protocol: EdgeBench uses dual feedback loops: agents explore through local tests or simulators, while submissions receive authoritative scores, verdicts, or diagnostics from hidden evaluation.This structure measures learning rather than only endpoint success and guards against overfitting to visible checks.
  • Evaluation protocol: An isolated work–judge harness separates task materials and local tools from hidden evaluation assets, with a host-side server mediating submissions, cooldowns, and authentication.The agent actively submits artifacts from its work container to a separate judge container.

3 Scaling Laws of Learning from Real World Environments

Across 134 real-world tasks and five frontier models, aggregate environment-learning trajectories follow a precise log-sigmoid form despite heterogeneous task-level dynamics. The fit remains stable across task families and longer horizons, predicts held-out progress, and emerges from averaging many tasks.

  • Aggregate scaling law: 134 tasks and five frontier models produce aggregate learning curves that are closely fit by a three-parameter log-sigmoid model.Each task–model pair uses three independent 12-hour trials, with full submission trajectories recorded.
  • Aggregate scaling law: R2 ≥0.997 for every model on the 134-task average, showing uniformly tight 12-hour fits.The fitted curve closely tracks each model’s averaged 12-hour learning trajectory.
  • Robustness across settings: The same log-sigmoid form fits all six heterogeneous task families and remains precise through 28-hour and 72-hour horizons, with every longer-horizon curve reaching R2 ≥0.993.The 28-hour analysis covers 80 tasks and four models, while the 72-hour analysis covers 18 tasks and two models.
  • Predictive validation: R2 ≥0.997 and RMSE below 1.0 performance point when fitting only the first 6.5 hours and forecasting the remainder to 12 hours.The extrapolated curves remain close to later observed trajectories across all five models.
  • Emergence and scope: Residual error falls monotonically as tasks accumulate from 1 to all 134, indicating that the clean scaling law is a population-level regularity rather than a single-task pattern.Individual task trajectories range from smooth gains and plateaus to breakthroughs and regressions.
  • Emergence and scope: The proposed explanation models environment learning as frontier expansion on latent task graphs, while noting failures under bottlenecks, dispersed midpoints, heterogeneous frontier speeds, or non-scale-free graph structures.The law is most natural for sufficiently mixed frontier expansion on approximately fractal structured graphs.

4 Agent Learning Speed Doubles Approximately Every Three Months

Across recent model generations, agent learning speed on a fixed 18-task slice increased roughly 8× from GPT-5-Codex in September 2025 to GPT-5.5 in April 2026, corresponding to an approximate doubling every three months. The comparison controls for prior knowledge by using tasks with comparable first-attempt performance and measuring average gains over two hours.

  • Measurement approach: An 18-task slice with similar first-attempt performance isolates environment learning from prior knowledge.Task-learning speed is measured as average performance gain over a fixed two-hour budget.
  • Evaluation protocol: 6.87 ± 0.97: Models had comparable average first-attempt performance on the 18-task slice.Each model was run three times per task in the evaluation protocol.
  • Learning speed trend: 8×: Learning speed increased roughly 8× from GPT-5-Codex in September 2025 to GPT-5.5 in April 2026 over 221 days.The trend corresponds to an approximate doubling every three months.
  • Learning speed trend: Approximate doubling every three months: A log-linear fit to frontier models captures the increase in learning speed across recent generations.The frontier trend uses the top two models at each release date and reports a fitted 95% confidence interval.

5 Analysis of Environment Learning Dynamics

Environment learning is shaped by model capability, accumulated experience, and context length: Opus 4.8 leads overall, continuous experience beats independent restarts, and 1M context outperforms 200k context. A gravitational-wave reconstruction trajectory shows that progress occurs through sparse, feedback-guided, uneven improvements rather than smooth learning.

  • 5.1 Performance Comparison: At 12 hours, Claude Opus 4.8 leads with 51.3, followed by GPT-5.5 at 48.4, GPT-5.4 at 39.3, GLM-5.1 at 37.4, and DS-V4-Pro at 31.0.Claude Opus 4.8 also leads each family mean, while GPT-5.5 is especially close in Games.
  • 5.1 Submission Efficiency: Models making more effective submissions usually perform better, but submission frequency alone does not determine final performance: Opus 4.8 wins despite submitting less often than GPT-5.5.GPT-5.4 has the highest effective-submission rate.
  • 5.2 Accumulated Experience: At 12 hours, accumulated experience reaches 43.0 versus 36.1 for independent restarts, a gain of +6.9 under the same total time budget.The continuous run preserves workspace, artifacts, and feedback history, whereas six 2-hour attempts discard state between restarts.
  • 5.3 Context Length: The 1M-context Opus 4.8 stays above the 200k variant throughout 12 hours, with a gap of +5.8 at 2h narrowing to +4.4 at 12h.Both trajectories are well described by the same log-sigmoid form despite identical external workspace and harness state.
  • 5.4 Gravitational-Wave Reconstruction: Only 27 of 224 submissions improve the best-so-far score by at least 0.1 percentage points, revealing a sparse but structured diagnose-edit-evaluate loop guided by feedback.The agent makes the task measurable, decomposes errors, identifies bottlenecks, and targets residual errors rather than restarting.
  • 5.4 Gravitational-Wave Reconstruction: Across 247 scored evaluations, the best score rises unevenly from 42.8 to 67.0 as the agent stabilizes the pipeline, localizes signals, improves source dynamics, and repairs H1 waveform errors.Representative gains include +4.5 pp during pipeline stabilization, a rise from 64.2 to 89.0 in source dynamics, and an H1 waveform increase from roughly 47 to 95.

6 Related Work

Prior benchmarks largely measure endpoint performance, while learning-focused benchmarks typically use restricted domains, shorter horizons, or static information streams. Existing scaling-law work primarily relates performance to model scale, data, compute, or inference-time methods, leaving learning from diverse real-world environments underexplored.

  • Benchmark coverage: Most agent benchmarks evaluate final answers, patches, or professional deliverables rather than improvement within a run.Examples include MMLU, AIME, HumanEval, SWE-bench, GDPval, Agents’ Last Exam, and FrontierCode.
  • Learning benchmarks: Learning-focused benchmarks study restricted domains, shorter horizons, static information streams, or repeated attempts with empirical feedback.CL-bench, EvaLearn, Continual Learning Bench, MLE-bench, MLS-Bench, Frontier-Eng, FrontierCS, and ALE-Bench exemplify these settings.
  • Scaling laws: Prior scaling-law research relates loss or benchmark performance to model size, data, compute, or inference-time methods, but diverse real-world environment learning remains underexplored.The cited work spans classical pretraining scaling laws, bounded performance curves, and test-time scaling laws.
  • Evaluation setting: Repeated evaluation across many executable environments is inexpensive, whereas large reinforcement-learning runs are costly and usually cover fewer environments.Broader environment coverage may help explain why aggregate curves are stable enough to reveal a scaling law.

7 Conclusion · Appendix · Appendix Contents

EdgeBench frames real-world environment learning as a measurable scaling phenomenon: across 134 tasks and roughly 38,000 hours of interaction, aggregate learning trajectories follow a precise log-sigmoid relationship. The benchmark also supports forecasting and studying how agents acquire and reuse experience, while the appendices document the evaluation framework and related safeguards.

  • 7 Conclusion: 134 executable tasks and roughly 38,000 hours of interaction underpin EdgeBench’s study of agent learning over day-long real-world horizons.The benchmark spans diverse tasks and environment interactions.
  • 7 Conclusion: A precise log-sigmoid relationship describes aggregate learning trajectories as interaction time increases.This relationship is the paper’s central empirical finding.
  • 7 Conclusion: The same log-sigmoid form appears across task families, remains stable over longer horizons, and supports forecasting later performance from early trajectories.These properties indicate that the relationship is consistent across settings and useful for prediction.
  • 7 Conclusion: Environment learning is presented as a measurable scaling object rather than merely a collection of idiosyncratic task outcomes.This interpretation follows the regularity observed across environment-learning trajectories.
  • 7 Conclusion: EdgeBench exposes intermediate attempts, feedback, and revisions, enabling study of how agents acquire and reuse experience beyond ranking them.The benchmark therefore captures processes underlying progress, not only aggregate outcomes.
  • Appendix Contents: Appendix Contents lists the Evaluation Harness, Serving and API Stability, and Evaluation Hacking sections.These entries appear under the appendix contents with page references beginning at page 25.

A Evaluation Harness

SForge is an evaluation harness for day-long agent runs that isolates hidden evaluation assets, supports iterative online judging, and tracks progress without relying solely on explicit submissions. Its infrastructure combines containerized work and judge environments with host-side monitoring and long-horizon execution safeguards.

  • Core design: SForge addresses day-long evaluation requirements by hiding evaluation assets, supporting repeated submissions, measuring implicit progress, and running on local machines or clusters.It is built around isolated environments, an online-judge-style feedback loop, and host-side progress tracking.
  • Container isolation: Each task uses separate work and judge Docker images, with the agent accessing only the work image and hidden tests confined to the judge image.The work image contains code, documentation, and local validation tools; the judge image contains hidden assets, grading scripts, and evaluation commands.
  • Container isolation: At evaluation time, SForge copies agent code into an ephemeral judge container, returns structured feedback, and destroys the container to protect the hidden grader.This enables realistic iterative development while preventing inspection or modification of hidden evaluation assets.
  • Online judging: The host-side HTTP judge server queues submissions, runs judges, parses results, and returns feedback such as pass rate, score, per-test verdicts, or diagnostics.For long-running evaluations, asynchronous grading lets agents continue working while submitted jobs are judged.
  • Long-horizon execution: SForge supports day-scale runs through host-side auto-evaluation, stop hooks, and auto-resume, while recording progress for trajectory analysis and limiting premature truncation.These mechanisms address voluntary exits, crashes, context limits, and transient API failures.

B Serving and API Stability

EdgeBench’s 12-hour-plus trajectories inherently measure serving and API stability because interruptions can truncate or degrade agent runs. GPT-5.4 experienced substantially more serving interruptions than GPT-5.5, particularly after six hours, complicating GPT-5.4’s run coverage and scores.

  • Serving stability: 12-hour-plus agent runs make serving stability part of the measured environment-learning performance, since interruptions can truncate or degrade trajectories.These runs must keep the model, context, and tool calls continuously available.
  • Model comparison: GPT-5.4 experienced substantially more infrastructure and API interruptions than GPT-5.5, especially after the six-hour mark.Figure 14 reports serving-side incident rate normalized by active run time.
  • Model comparison: Fewer than three valid runs in several GPT-5.4 per-task cells partly reflect serving reliability rather than model performance.These cells are marked with ∗ in the score tables, and the lower run coverage therefore carries a caveat.

C Evaluation Hacking … D.2 Environment Learning as a Frontier Expansion Process

The paper documents evaluation-hacking strategies that inflated scores without exercising intended capabilities, then derives environment learning as frontier expansion on task graphs. Under mixing and fine-grained score-unit conditions, this mechanism yields a logistic frontier and the observed log-sigmoid law.

  • C Evaluation Hacking: Development audits found score-inflating strategies that bypassed intended capabilities, prompting task revision or exclusion and safeguards in the final benchmark.These observations were development diagnostics rather than official model results.
  • C Evaluation Hacking: 1.000 was achieved in cylinder_wake_prediction by reconstructing hidden targets from feedback, while the best physics-model submission scored 0.165.The agent used more than 400 submissions to treat per-case absolute errors as equations and build a lookup table.
  • C Evaluation Hacking: 301.5 on a reused judge seed contrasted with about 12 across 100 local episodes, motivating hidden multi-seed evaluation for stochastic control tasks.Other exploits included stochastic upper-tail optimization and moving an oracle-based implementation into an exempt trusted path, which scored 0.980 versus 0.121 for the intended route.
  • D A Comprehensive Derivation of the Log-Sigmoid Law: Environment learning is modeled as frontier expansion on a latent task graph whose nodes are score units, with prior feedback enabling later progress.The framework connects this process to the observed log-sigmoid law and describes five derivation steps.
  • D.1 Preliminaries: Task Graph and the Attainable Support: In the task graph, unlocked nodes generate influence through directed edges, while locked nodes unlock at rates proportional to their incoming capability field.The model defines score-unit weights, unlock states, influence strengths, and attainable support through the task graph.
  • D.2 Environment Learning as a Frontier Expansion Process: The relevant frontier quantity is influence crossing from unlocked to locked nodes, not merely the total unlocked score.A locked unit unlocks stochastically with hazard proportional to accumulated field, and unlocked nodes remain unlocked.
  • D.2 Environment Learning as a Frontier Expansion Process: Logistic growth emerges when boundary influence depends mainly on unlocked and locked mass, making the frontier approximately their product.This expresses reusable capability times remaining score opportunity and yields the logistic expected growth rate under weighted cut mixing.
  • D.2 Environment Learning as a Frontier Expansion Process: x(t) = 1 / (1 + (tmid/t)^β), with β = ηκ, arises in the many-unit limit under mixing and vanishing jump-size conditions.Finite tasks may remain jagged; for equal score units, qN = 1/N, and smooth convergence requires both cut error εN →0 and jump noise HNqN →0.

D.3 Many-task Aggregation Reveals the Smooth Log-Sigmoid Law · D.4 Graph Self-similarity Induces Log Scale for Time Axis

Many-task averaging turns heterogeneous, jagged task trajectories into a smooth log-sigmoid benchmark law when task frontiers, midpoints, and learning speeds sufficiently align. Self-similar task-graph growth explains the logarithmic raw-time coordinate underlying that law.

  • D.3 Many-task Aggregation Reveals the Smooth Log-Sigmoid Law: Many-task averaging washes out finite-task roughness and yields a single log-sigmoid when task-specific midpoints and learning speeds are sufficiently concentrated.Each environment may follow its own approximate logistic frontier, but aggregation produces a smooth population-level curve under alignment.
  • D.3 Many-task Aggregation Reveals the Smooth Log-Sigmoid Law: The aggregate theorem requires blockwise cut mixing, vanishing score-unit and jump errors, midpoint alignment, and concentrated environment-learning speeds.These conditions separately control task-level frontier approximation and the alignment needed to combine task sigmoids into one benchmark sigmoid.
  • D.3 Many-task Aggregation Reveals the Smooth Log-Sigmoid Law: P→0 as M →∞ for any compact interval I ⊆R, establishing vanishing average error in the many-task limit under Conditions D.3 and D.4.The result formalizes how averaged cut errors, score units, and jumps disappear even when individual task curves remain nonsmooth.
  • D.3 Many-task Aggregation Reveals the Smooth Log-Sigmoid Law: Theorem D.2 proves uniform convergence in probability of the benchmark normalized score to a log-sigmoid on every fixed compact log-time interval.The proof first replaces observed trajectories with task-level frontiers, then aligns their midpoint shifts and speeds with the benchmark frontier.
  • D.4 Graph Self-similarity Induces Log Scale for Time Axis: Self-similar task-graph geometry makes logarithmic raw time natural because equal additive difficulty increases require multiplicative increases in search effort.The effective frontier coordinate is the difficulty scale exposed as progressively harder graph regions become usable.
  • D.4 Graph Self-similarity Induces Log Scale for Time Axis: h log t + O(1) describes exposed difficulty under self-similar edge growth and linearly supplied search effort.Search volume grows exponentially with difficulty while raw interaction time supplies search effort linearly, so inversion yields logarithmic exposure.
  • D.4 Graph Self-similarity Induces Log Scale for Time Axis: x(t) = 1 1 + (tmid/t)β .With a scale-stationary weighted-cut frontier coefficient, the log-time logistic equation follows from r(t) = h−1 log t + O(1).

D.5 Discussion and Limitations

The appendix presents the log-sigmoid law as a mechanistic account of the observed regime, not a universal consequence of environment learning. Its scope is limited by coarse score units, non-mixing task graphs, moving attainable supports, dispersed midpoints, heterogeneous speeds, and non-scale-free feedback schedules.

  • Scope of the account: The derivation provides a sufficient mechanism for the observed log-sigmoid regime, while identifying assumptions under which that limit can fail.It is not a claim that all environment-learning curves must be logistic.
  • Failure modes: Finite score granularity can produce jagged single-task curves with long plateaus and sudden jumps when macroscopic score units dominate.The aggregate theorem requires only that coarse units do not dominate the benchmark average.
  • Failure modes: Weighted cut mixing is core: persistent bottlenecks, modules, prerequisite chains, or separated transfer regions can make the limit non-one-dimensional rather than logistic.Under such graph structure, the frontier depends on its location, not only on unlocked score measure.
  • Failure modes: Moving attainable supports, dispersed task midpoints, and heterogeneous learning speeds can make fitted ceilings, slopes, and midpoints depend on the observation window or task composition.These effects arise when reachable score units change, midpoint shifts remain dispersed, or frontier speeds fail to concentrate.
  • Failure modes: Non-scale-free feedback schedules may require another time coordinate or a piecewise model instead of a single log-time transformation.Examples include fixed evaluation delays, daily data refreshes, hard deadlines, staged curricula, and batch feedback.

E More Discussion on the Scaling Law Shapes · F Additional Related Work · F.1 Benchmarks Not Suitable for Measuring Self-Evolution

The paper selects the log-sigmoid on mechanistic grounds: its y(1 −y) rate represents frontier expansion between unlocked and locked score mass, although similarly fitting curves remain empirically indistinguishable. It also distinguishes self-evolution benchmarks from evaluations that primarily report static accuracy or final task outcomes.

  • E More Discussion on the Scaling Law Shapes: The log-sigmoid is preferred mechanistically because its y(1 −y) rate models progress as interaction between unlocked capability and remaining locked opportunity.The choice is based on mechanism rather than fit, since candidate S-curves fit almost equally well.
  • E More Discussion on the Scaling Law Shapes: Log-Gompertz implies front-loaded growth with inflection at y = 1/e ≈0.37, whereas experience acquisition is described as initially slow because a foothold must first be built.Its ln(1/y) term represents multiplicative winding down as the system matures.
  • E More Discussion on the Scaling Law Shapes: The Weibull CDF is a natural first-passage or repeated-sampling baseline because its hazard depends on raw elapsed time and progress enters through the survival term 1 −y.Independent attempts produce an exponential CDF, corresponding to the β = 1 Weibull case.
  • E More Discussion on the Scaling Law Shapes: Log-linear growth cannot level off because its rate is constant, contradicting tasks that reach a ceiling within budget, and it attains the worst fit.Unlike saturating alternatives, it grows without bound.
  • E More Discussion on the Scaling Law Shapes: The log-sigmoid is a falsifiable preference, not an empirical exclusion, because the data cannot separate the symmetric logistic and probit families.Inflection near y = 0.5 supports logistic or probit, while peaks near 0.37 or 0.63 would favor Gompertz or Weibull, respectively.
  • F.1 Benchmarks Not Suitable for Measuring Self-Evolution: Benchmarks not designed to measure self-evolution primarily report final-answer accuracy, task success, pass rate, artifact quality, reproduction fidelity, or human-time-based outcomes.They may still involve reasoning, tools, iteration, or environment interaction, but learning is not their primary reported quantity.
  • F.1 Benchmarks Not Suitable for Measuring Self-Evolution: Classic capability benchmarks such as MMLU, GPQA, AIME, and closed-form coding or math evaluations use static problems without changing environments or feedback exposed for later adaptation.They therefore measure static knowledge and reasoning accuracy rather than self-evolution.
  • F.1 Benchmarks Not Suitable for Measuring Self-Evolution: Agentic software and professional-work benchmarks increase realism through codebases, workflows, sandboxes, tools, or long horizons, but many published protocols still reduce evaluation to final results.Examples include SWE-bench, RoadmapBench, SWE-EVO, GDPval, Agents’ Last Exam, HCAST, METR, Terminal-Bench, and scientific reproduction benchmarks.

F.2 Benchmarks Suitable for Measuring Learning or Self-Evolution … G.2 Gravitational-Wave Case Study Details

The paper positions EdgeBench at the intersection of long-horizon executable work, organized experience streams, and iterative optimization, then details its scaling-law evaluation and a 12-hour gravitational-wave case study. The case study shows large gains in source dynamics and H1 waveform reconstruction while retaining weaknesses in spectrograms and L1 reconstruction.

  • F.2 Benchmarks Suitable for Measuring Learning or Self-Evolution: Prior benchmarks separately emphasize context learning, sequential task streams, or iterative optimization, while FrontierSWE and AutoLab most closely evaluate repeated edits, experiments, and empirical feedback.FrontierSWE reports roughly 3–4 hours of average agent runtime, whereas EdgeBench is designed around substantially longer continuous interaction.
  • F.2 Benchmarks Suitable for Measuring Learning or Self-Evolution: EdgeBench targets within-run self-evolution in long-horizon executable environments where agents influence subsequent observations and use a general-purpose harness.It combines realistic executable work, organized streams, and iterative optimization under feedback rather than relying on a benchmark-specific learning scaffold.
  • F.3 Scaling Laws for LLMs and Agents: Scaling-law comparisons span pretraining loss, test-time effort, and reinforcement learning from environment feedback, including power-law and sigmoidal performance relationships.The paper distinguishes these settings from EdgeBench by focusing on learning through long-horizon environmental interaction.
  • G.1 Estimating the With- and Without-Experience Curves: The with-experience curve averages three 12-hour best-so-far curves per task before averaging across tasks, while the without-experience curve estimates the expected best score from k independent attempts.The without-replacement estimator extends pass@k to score-valued outcomes and reduces to pass@k for binary scores.
  • G.2 Gravitational-Wave Case Study Details: The gravitational-wave trajectory begins with protocol checks, five required CSV files, and a score of 42.8, followed by a key update to 47.1 and a later score near 50.The selected milestones summarize phase transitions during the 12-hour run rather than every submission.
  • G.2 Gravitational-Wave Case Study Details: The largest jump raises the overall score from about 52.3 to 59.7 around hours 4–5, as source dynamics increases from 64.2 to 89.0; H1 time-series then rises from roughly 47 to 95.The source-dynamics component has the largest weight, so compact physical modeling plus calibration produces a large total-score gain.
  • G Additional Benchmark and Experiment Details: The final solution is strong on H1 waveform reconstruction and source dynamics but weak on spectrograms and L1 reconstruction.Empirical calibration and parameter search contribute substantially, but do not replace a coherent end-to-end LIGO-style pipeline for preprocessing, whitening, and time-frequency analysis.
  • G Additional Benchmark and Experiment Details: Table 6 evaluates GPT-5.5 and GPT-5.4 under Base, Goal, and Ralph continuation settings with the same 12-hour budget, reporting means over valid runs.The displayed task rows are averaged in the Avg. row; incomplete cells are detailed in Appendix G.3.

G.3 Harness-Level Continuation Ablations · G.4 Per-Task Design Notes

The appendix shows that continuation scaffolds materially affect long-horizon agent performance, while EdgeBench’s per-task notes span demanding software, scientific, and professional workloads with explicit constraints and evaluation criteria.

  • G.3 Harness-Level Continuation Ablations: Goal mode and the Ralph loop often outperform the Base harness, indicating that preserving and updating task state benefits long-horizon agents.The Base harness uses one continuing session, a stop hook, and auto-resume; Goal maintains a validated task goal, while Ralph uses fresh contexts and progress.md.
  • G.3 Harness-Level Continuation Ablations: 43.4 is GPT-5.5’s displayed-task average with Ralph, compared with 43.1 with Goal and 42.6 in Base.For GPT-5.4, the corresponding averages are 31.8 with Goal, 27.6 with Ralph, and 26.1 in Base.
  • G.3 Harness-Level Continuation Ablations: GPT-5.5 cells use the full three runs, whereas some GPT-5.4 cells have fewer valid runs because of intermittent API or network instability.The affected GPT-5.4 cells include one-run and two-run conditions across Goal and Ralph variants.
  • G.4 Per-Task Design Notes: 134 EdgeBench tasks receive per-task design notes covering systems and software engineering, scientific modeling, machine learning, optimization, and interactive control.The notes define concrete implementations, constraints, baselines, and evaluation procedures for each task.
  • G.4 Per-Task Design Notes: Software tasks require substantial reimplementation and optimization, including compilers, Rust libraries, FFmpeg, Git, parsers, APIs, and framework extensions.Examples impose requirements such as ABI compatibility, SIMD speed, exact CLI behavior, correctness, and performance.
  • G.4 Per-Task Design Notes: Machine-learning and optimization tasks emphasize robustness beyond development data, resource limits, and multiple objectives or metrics.Examples include hidden variants, CPU-only execution, distributional shift, cold-start recommendation, and joint accuracy-efficiency optimization.
  • G.4 Per-Task Design Notes: Scientific tasks span groundwater, power systems, molecular science, nanophotonics, gravitational waves, spectroscopy, and biomedical evidence synthesis.Many evaluate performance on unseen conditions, distribution shifts, hidden publications, or constrained physical and computational settings.

G.5 Per-Task Learning Curves · G.6 Per-Task Score Tables

The appendix provides per-task learning curves across capability families and score tables summarizing model performance. Curves track best-so-far progress over 12-hour budgets, while tables report means and variability over up to three valid runs.

  • G.5 Per-Task Learning Curves: Figures 15–35 present per-task learning curves grouped by capability family, covering 21 plots across six families.The families are Scientific Computing & ML, Systems & Software Engineering, Combinatorial Optimization & Planning, Professional Knowledge Work, Formal Math & Theorem Proving, and Interactive Games & Simulators.
  • G.5 Per-Task Learning Curves: Each curve plots raw task score against elapsed time over the 12-hour budget, with solid lines showing the best-so-far envelope.Faint dashed dots denote individual submissions, and pale segments after the marked best denote later submissions without improvement.
  • G.5 Per-Task Learning Curves: Five agents are compared across the per-task learning-curve plots.Some tasks zoom the y-axis to the main score band and note extreme outlier submissions separately.
  • G.6 Per-Task Score Tables: For every task–model configuration, three independent long-horizon runs were scheduled, with rolling evaluation rounds recovering failed or incomplete trajectories.Network instability and serving-side reliability limits made the 12-hour trajectories sensitive to execution failures.
  • G.6 Per-Task Score Tables: A small number of task–model cells contain fewer than three valid runs and are marked with * in the final score tables.The tables therefore aggregate results over up to three valid runs rather than uniformly using exactly three.
  • G.6 Per-Task Score Tables: Tables 8–13 report model performance for Systems & Software Engineering, Scientific Problems & ML, Combinatorial Optimization, Formal Math & Theorem Proving, Professional Knowledge Work, and Interactive Games & Simulators.Values are mean scores over up to three valid runs, with adjacent ±s shown when at least two valid runs are available.
  • G.6 Per-Task Score Tables: Bold marks the best model for each task, underlining marks the second-best, — indicates no valid result, and * marks fewer than three valid runs.These notation rules apply across the six per-task score tables.
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