| AlphaGeometry | Google DeepMind (2024) | Proofs · Proof-state search | Transformer language model trained from scratch on synthetic theorems and proofs | Symbolic deduction engine (DD + AR) | Formal proof / check | In the paper's evaluation on a test set of 30 olympiad-level geometry problems (IMO-AG-30), AlphaGeometry solves 25, versus ten for the earlier Wu's method baseline and 18 for the strongest baseline (DD + AR + human-designed heuristics). Symbolic deduction with algebra (DD + AR) alone solves 14. | Source ↗ |
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| FunSearch | Google DeepMind (2023) | Mathematics · Program evolution | Pretrained LLM, frozen (Codey, a PaLM 2 based code model, used without fine-tuning) | Program evaluator in a sandbox | Empirical benchmark | On the cap set problem, FunSearch found a cap set of size 512 in 8 dimensions, larger than any previously known, and raised the lower bound on the asymptotic cap set capacity to 2.2202 (previous best 2.2180). On online bin packing it evolved heuristics that beat first fit and best fit on the OR-Library sets OR1-OR4 and on Weibull instances. | Source ↗ |
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| AlphaProof | Google DeepMind (2025) | Proofs · Proof-state search | AlphaZero-inspired agent trained on millions of auto-formalized problems | Lean proof assistant | Formal proof / check | At IMO 2024 the system with AlphaProof as its core engine solved three of the five non-geometry problems, including the hardest one; combined with AlphaGeometry 2 this reached a score equivalent to a silver medallist, with multi-day computation. | Source ↗ |
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| AlphaTensor | Google DeepMind (2022) | Mathematics · Offline solver discovery | Custom transformer-based torso, policy and value network trained with reinforcement learning and synthetic demonstrations (not an LLM) | Exact algebraic tensor-rank verifier and Monte Carlo Tree Search, plus target GPU/TPU runtime benchmarker | Formal proof / check | In Nature (2022), AlphaTensor discovered a 4x4 matrix multiplication algorithm using 47 multiplications in modulo-2 arithmetic (Z_2), beating Strassen's 1969 construction of 49 in that field, and improved the best known rank across more than 70 matrix sizes up to 5x5. By adding hardware runtime to the reward, it also found algorithms 10% to 20% faster than human and compiler baselines on NVIDIA V100 GPUs and Google TPU v2. | Source ↗ |
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| AlphaDev | Google DeepMind (2023) | Engineering · Offline solver discovery | AlphaZero-style transformer and MLP policy-value network trained via reinforcement learning (not an LLM) | exhaustive permutation verifier for correctness, and latency measured on real CPUs or estimated by a learned latency model, inside Monte Carlo Tree Search | Formal proof / check | In Nature (2023), AlphaDev discovered new x86 assembly sorting routines for small fixed and variable sequence lengths, cutting one instruction from sort3 (17 vs 18 instructions) and speeding up sort3 through sort5 by up to 70% and 250,000-element sorting by about 1.7%. The routines were merged into the LLVM libc++ standard sorting library. | Source ↗ |
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| AlphaEvolve | Google DeepMind (2025) | Mathematics · Program evolution | Gemini 2.0 Flash and Gemini 2.0 Pro ensemble, frozen | Automated evaluators (exact for many math constructions, simulators or benchmarks for engineering tasks) | Empirical benchmark | Applied to over 50 open math problems, AlphaEvolve matched the best known construction in about 75% of cases and found a better one in about 20%, including a kissing-number configuration of 593 spheres in 11 dimensions (previous record 592). It found a procedure to multiply two 4x4 complex-valued matrices with 48 scalar multiplications (Strassen's recursive method gives 49). At Google it recovered on average 0.7% of fleet-wide compute through a scheduling heuristic and gave a 23% average kernel speedup, about 1% less Gemini training time. Deployment figures as reported by Google DeepMind. | Source ↗ |
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| RFdiffusion | University of Washington (Institute for Protein Design) (2023) | Chemistry · Oracle-trained generation | SE(3)-equivariant diffusion model fine-tuned from RoseTTAFold structure-prediction weights, coupled with ProteinMPNN graph neural network sequence design (not an LLM) | AlphaFold2 structural self-consistency and interface pAE filtering, plus wet-lab biolayer interferometry, circular dichroism and cryo-EM | Empirical benchmark | In Nature (2023), RFdiffusion designed de novo protein binders across five therapeutic and viral targets with an experimental hit rate of roughly 19% when testing 95 designs per target (two to three orders of magnitude higher than classical Rosetta binder design), and a cryo-EM structure of a designed Influenza HA binder (PDB: 8SK7) matched the design model at atomic accuracy (1.45 A backbone RMSD). | Source ↗ |
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| GNoME (Graph Networks for Materials Exploration) | Google DeepMind (2023) | Materials · Active-learning generation | Message-passing Graph Neural Networks (GNoME) paired with structural and compositional candidate pipelines (not an LLM) | Density Functional Theory (DFT, VASP) structural relaxation and convex-hull phase stability evaluation | Physics simulation | In Nature (2023), GNoME identified 2.2 million crystal structures below the previous convex hull of known materials, including 381,000 structures on the updated convex hull (nearly an order of magnitude more than the roughly 48,000 stable inorganic crystals previously catalogued). Active learning raised the DFT stability hit rate from under 10% to over 80% for compositional pipeline candidates and from 6% to 33% for structural candidates. | Source ↗ |
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| MatterGen | Microsoft Research (2025) | Materials · Oracle-trained generation | Equivariant score-based diffusion model over atom types, coordinates and periodic lattices with fine-tuned adapter modules (not an LLM) | MatterSim pre-relaxation and Density Functional Theory (DFT) convex-hull and property evaluation, plus X-ray diffraction and nanoindentation on the synthesized sample | Physics simulation | In Nature (2025), MatterGen more than doubled the fraction of generated inorganic structures that are both novel and thermodynamically stable (within 0.1 eV/atom of the DFT convex hull) compared with prior generative baselines, and reduced root-mean-square atomic displacement during DFT relaxation by more than 50%. In a targeted high-bulk-modulus search, the authors synthesized a generated compound (TaCr2O6) in the lab whose measured bulk modulus (169 GPa) matched the target within 20%. | Source ↗ |
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| AutoVerus | Microsoft Research, University of Illinois Urbana-Champaign, Columbia University and UC Irvine (2024) | Code verification · Verifier-guided repair | GPT-4o (frozen), orchestrated as a network of specialized agents | Verus verifier (SMT-based) | Formal proof / check | Proves 137 of 150 tasks (91.3%) on Verus-Bench, with at most 3 tries per task and GPT-4o; 122 were proved on the first attempt. A baseline that repeatedly calls GPT-4o for up to 10 minutes proved 67 of 150. More than half were done in under 30 seconds or 3 LLM calls. | Source ↗ |
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| OptiMUS (Optimization Modeling Using Solvers and LLMs) | Stanford University (2024) | Optimization · Formalize and solve | GPT-4 (frozen), structured across formulator, programmer and evaluator agents with a connection graph | Gurobi Mixed-Integer Linear Programming (MILP) solver plus automated execution checks | Formal proof / check | At ICML 2024, OptiMUS solved 78.8% of NL4OPT (vs 64.2% for Chain-of-Experts), 66.7% of ComplexOR (vs 38.1%), and 72.0% of the authors' graduate-level NLP4LP benchmark (vs 53.1%). Removing the solver-guided debugging loop in ablations dropped NLP4LP accuracy from 71.6% to 58.2%. | Source ↗ |
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| LLM-Modulo Framework | Arizona State University (2024) | Optimization · Verifier-guided repair | GPT-4-Turbo and GPT-3.5-Turbo (frozen) | External symbolic verifiers (VAL for PDDL) and programmatic hard-constraint and commonsense critics | Formal proof / check | Proposed at ICML 2024 (arXiv:2402.01817) and evaluated on the TravelPlanner benchmark (arXiv:2405.20625), pairing GPT-4-Turbo with external programmatic constraint critics in a bi-directional loop raised the final all-constraints pass rate from 4.4% (direct prompting) to 20.6% (a 4.6x gain), and raised GPT-3.5-Turbo from 0% to 5.0%. | Source ↗ |
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| LLM+P (Large Language Models + Classical Planners) | University of Texas at Austin and Sony AI (2023) | Robotics · Formalize and solve | GPT-4 (frozen) with in-context PDDL problem examples | Fast Downward classical symbolic planner | Formal proof / check | Across seven standard International Planning Competition (IPC) domains including Blocksworld, Barman, Floortile, Grippers, Storage, Termes and Tyreworld (20 tasks per domain), LLM+P with GPT-4 and in-context examples solved the majority of tasks with valid, cost-minimizing plans, whereas direct GPT-4 plan generation failed on almost all tasks in Barman, Floortile, Storage and Termes. | Source ↗ |
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| REINVENT 4 (with DockStream docking) | AstraZeneca (Molecular AI) (2024) | Chemistry · Oracle-trained generation | RNN and transformer SMILES generators (priors pretrained, then fine-tuned by transfer and reinforcement learning) | Scoring function with docking (Vina, rDock, Glide, GOLD via DockStream) and RDKit property checks | Physics simulation | In the paper's demonstration on PDK1 (PDB 2XCH), 50 epochs of staged learning with batch size 128 produced 119 hits out of 6,400 generated molecules (1.9%), where a hit means a docking score of -8 kcal/mol or better and QED of 0.7 or higher; the hits spanned 103 generic scaffolds. | Source ↗ |
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| Eureka | NVIDIA, UPenn, Caltech, UT Austin (2023) | Robotics · Program evolution | GPT-4 (gpt-4-0314), frozen | RL training in Isaac Gym with a ground-truth task fitness function | Empirical benchmark | Across 29 open-source RL environments with 10 robot morphologies, in simulation, the abstract reports Eureka outperforming expert human-written rewards on 83% of tasks, with an average normalized improvement of 52%. It also used its rewards in a curriculum to get a simulated Shadow Hand to perform pen spinning. | Source ↗ |
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| AlphaGeometry2 | Google DeepMind (2025) | Proofs · Proof-state search | Gemini-architecture language model trained on synthetic data | Symbolic deduction engine | Formal proof / check | Solves 42 of 50 IMO geometry problems from 2000 to 2024 (IMO-AG-50); the paper states an overall solving rate of 84% on geometry problems from the last 25 years versus 54% for the original, and says AG2 surpasses an average gold medalist. The formal language now covers 88% of those problems, up from 66%. | Source ↗ |
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| DeepSeek-Prover-V1.5 with RMaxTS | DeepSeek (2024) | Proofs · Proof-state search | DeepSeek-Prover-V1.5 (DeepSeekMath-Base fine-tuned for Lean 4) | Lean 4 proof assistant | Formal proof / check | With RL plus RMaxTS at a sample budget of 32 x 6400 (mixture of two guiding prompts) it reaches 63.5% on miniF2F-test; on the ProofNet test set it reaches 25.3% at a budget of 4 x 6400. The paper calls both new state of the art at publication. | Source ↗ |
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| Seed-Prover | ByteDance Seed (AI4Math team) (2025) | Proofs · Verifier-guided repair | Lemma-style whole-proof language model | Lean proof assistant | Formal proof / check | The abstract reports 78.1% of formalized past IMO problems proved, MiniF2F saturated, above 50% on PutnamBench, and 5 of 6 IMO 2025 problems fully proved; a separate Seed-Geometry engine handles geometry. | Source ↗ |
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| ATLANTIS (Team Atlanta, AIxCC winner) | Team Atlanta (2025) | Security · Verifier-guided repair | Several commercial LLMs used by agents (models vary by module) | Fuzzers, sanitizers, PoV replay and project tests | Empirical benchmark | Won the DARPA AIxCC final at DEF CON 33 (August 2025) with 392.76 points; the team's paper reports 43 of 70 vulnerabilities found. DARPA's overall figures (all teams): 54 of 63 synthetic vulnerabilities found and 43 patched, 18 real-world bugs found, about $152 average per task. | Source ↗ |
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| LLM-SR | Virginia Tech, Carnegie Mellon University and Allen Institute for AI (2025) | Science · Program evolution | Frozen LLM (GPT-3.5-turbo, Mixtral-8x7B) | Numerical fit to data scored by error | Empirical benchmark | Across four problems (two oscillators, E. coli growth, aluminum stress-strain) with about 2.5K iterations, LLM-SR beat symbolic regression baselines on normalized MSE, most clearly out of domain: for E. coli growth 0.0037 against 1.0141 for the best baseline. | Source ↗ |
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| EoH (Evolution of Heuristics) | City University of Hong Kong, Huawei Noah's Ark Lab, Southern University of Science and Technology (2024) | Optimization · Program evolution | Pretrained LLM, frozen (GPT-3.5-turbo in main runs; Gemini Pro, CodeLlama, DeepSeek compared) | Benchmark evaluation of the heuristic code | Empirical benchmark | On online bin packing, EoH with about 2,000 LLM queries (GPT-3.5-turbo) averaged a 1.18% gap to the lower bound over six test sets, against 2.23% for FunSearch (which the paper says needs around 1 million queries), 4.13% for best fit and 4.51% for first fit. It also reached the best-known tour on three TSPLib instances (pr124, kroA150, u159) and led on Taillard flow-shop sets. | Source ↗ |
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| DrEureka | University of Pennsylvania, NVIDIA and UT Austin (2024) | Robotics · Program evolution | GPT-4, frozen | Physics simulation with RL training and a reward-aware physics prior | Empirical benchmark | On a real quadruped forward-locomotion test (2 m/s target, 5 m track), the best DrEureka policy reached 1.83 m/s and 5.00 m versus 1.32 m/s and 4.17 m for the human-designed setup. The robot also walked atop a real yoga ball for 15.4 seconds on average. | Source ↗ |
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| ReProver (LeanDojo) | LeanDojo team (Kaiyu Yang et al.) (2023) | Proofs · Proof-state search | Retrieval-augmented transformer tactic generator, trained on LeanDojo data | Lean proof assistant via LeanDojo | Formal proof / check | On the LeanDojo Benchmark test set, pass@1 is 51.2% (random split) and 26.3% (novel_premises split) with retrieval, versus 47.6% and 23.2% without retrieval and 29.0% and 7.4% for zero-shot GPT-4. Also 26.5% on miniF2F and 13.8% on ProofNet (pass@1, 10 minute wall-time limit per theorem). | Source ↗ |
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| AlphaVerus | Carnegie Mellon University (2024) | Code verification · Verifier-guided repair | Llama 3.1 70B (frozen, no fine-tuning) | Verus verifier with a misalignment filter | Formal proof / check | With Llama 3.1 70B and no model fine-tuning, verified-code generation reaches 32.9% on HumanEval-Verus and 65.7% on MBPP-verified (pass@256), versus 27.1% and 35.9% for GPT-4o and 11.8% and 26.9% for Llama 3.1 70B. | Source ↗ |
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| Goedel-Prover | Princeton Language and Intelligence (Princeton University), with Tsinghua University, Amazon, Meta FAIR and Numina (2025) | Proofs · Oracle-trained generation | DeepSeek-Prover-V1.5-Base fine-tuned over successive rounds | Lean compiler | Formal proof / check | Goedel-Prover-SFT reaches 57.6% Pass@32 on miniF2F, 7.6 points above DeepSeek-Prover-V1.5-RL; the paper's abstract reports over 60% Pass@32 after RL including DPO, 7 PutnamBench problems at Pass@512, and proofs for 29.7K Lean Workbook problems versus 15.7K for prior provers. | Source ↗ |
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| BFS-Prover | ByteDance Seed (2025) | Proofs · Proof-state search | 7B policy language model (open-sourced as BFS-Prover-V1-7B) | Lean 4 compiler via LeanDojo | Formal proof / check | Reaches 72.95% on the miniF2F test set as an accumulative score; the single-run figure is 70.83% +/- 0.89 at a budget of 2048 x 2 x 600 (Lean 4.7.0). The authors say this shows plain best-first search can compete when scaled. | Source ↗ |
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| ChemSpaceAL | Yale University (Batista group) (2024) | Chemistry · Active-learning generation | GPT-style transformer trained on SMILES strings, fine-tuned each iteration | Docking (DiffDock) with an interaction-based scoring function; cluster-based sampling | Surrogate oracle | In the paper's computational study on c-Abl kinase, the model learned to generate molecules similar to FDA-approved inhibitors without being shown them and reproduced two exactly (imatinib and bosutinib after five iterations). The method was also applied to the HNH domain of Cas9, which has no commercial small-molecule inhibitors. | Source ↗ |
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| OSS-Fuzz-Gen (LLM fuzz target generation) | Google (OSS-Fuzz) (2023) | Security · Verifier-guided repair | Google LLMs (model not named on the page) | OSS-Fuzz build tooling; calling the function, start-up crashes and coverage are reported metrics | Empirical benchmark | Google's page reports 14 of 31 tested OSS-Fuzz projects compiled new targets and increased coverage (gains 0 to 31%; tinyxml2 line coverage 38% to 69%), and a similar target in OpenSSL rediscovered CVE-2022-3602. | Source ↗ |
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| ShinkaEvolve | Sakana AI (2025) | Optimization · Program evolution | LLM ensemble, frozen (claude-sonnet-4, o4-mini, gpt-4.1 family; gpt-5-nano for meta and novelty) | Task evaluators plus an embedding-similarity filter and UCB1 bandit | Empirical benchmark | ShinkaEvolve found a circle-packing (n=26) solution with sum of radii 2.63598 under its relaxed verifier, beating AlphaEvolve's reported solution within 150 program evaluations. It also improved ALE-Agent solutions on ALE-Bench by about 2.3% on average over 10 tasks, designed an AIME agent scaffold (gpt-4.1-nano, 7 LLM calls), and found a new mixture-of-experts load-balancing loss. | Source ↗ |
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| ReEvo (Reflective Evolution) | Peking University, KAIST, Southeast University, Singapore Management University (AI4CO) (2024) | Optimization · Program evolution | Pretrained LLMs, frozen (GPT-3.5 Turbo, GPT-4 Turbo, Llama 3 70B compared) | Objective evaluation on problem instances | Empirical benchmark | Across six combinatorial problems (TSP, CVRP, OP, MKP, BPP, DPP), with a budget of 100 heuristic evaluations and GPT-3.5 Turbo, ReEvo beats EoH on sample efficiency in five problems, and designed heuristics improved neural solvers, for example POMO's TSP1000 gap from about 52% to 29%. Its genetic algorithm for decap placement scored 12.98 vs 12.41 for the expert-designed one. | Source ↗ |
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| OpenEvolve | algorithmicsuperintelligence (open-source community project) (2025) | Optimization · Program evolution | Pluggable LLM ensemble, frozen (any OpenAI-compatible API or supported CLI) | User-defined evaluator (tests, benchmarks, profilers) | Empirical benchmark | The project reports 2-3x speedups on GPU kernels (MLX Metal) and a circle packing for n=26 that its README calls state of the art, plus sorting and signal-processing examples. These are the project's own claims; the README gives no numeric circle-packing score. | Source ↗ |
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| Self-Harness | Shanghai Artificial Intelligence Laboratory (2026) | ML systems · Verifier-guided repair | Fixed base LLM (MiniMax M2.5, Qwen3.5-35B-A3B or GLM-5), no weight updates | Benchmark task verifiers and a pass-count acceptance rule | Empirical benchmark | The paper reports that for three base models (MiniMax M2.5, Qwen3.5-35B-A3B, GLM-5) across three benchmarks (Terminal-Bench-2.0, SWE-bench Verified, AppWorld) every final harness improves both held-in and held-out pass rates, with relative gains of up to 132%. On Terminal-Bench-2.0 held-out, MiniMax M2.5 went 40.5% to 61.9% and Qwen3.5-35B-A3B 23.8% to 38.1%. | Source ↗ |
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| Active learning for conditional crystal inverse design | The University of Hong Kong (2025) | Materials · Active-learning generation | Con-CDVAE conditional crystal variational autoencoder, fine-tuned each iteration | CGCNN pre-filter, MACE-MP-0 molecular dynamics, DFT (via APEX workflows) | Physics simulation | For a 350 GPa bulk modulus target, in a range sparse in the training data, three active learning iterations lowered the mean absolute percentage error of generated crystals from about 0.4 to 0.2 (CGCNN-evaluated). DFT bulk moduli of new structures averaged 343.54 GPa (standard deviation 27.20) after the first iteration and 356.52 GPa (standard deviation 18.61) after the second. | Source ↗ |
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| Darwin Godel Machine | Sakana AI and University of British Columbia (Jeff Clune lab) (2025) | ML systems · Program evolution | Frozen foundation model (Claude 3.5 Sonnet for self-modification; Claude 3.5 Sonnet or o3-mini for evaluation) | Benchmark test suites run in a sandbox | Empirical benchmark | Over 80 iterations, the best agent rose from 20.0% to 50.0% on SWE-bench (Verified) and from 14.2% to 30.7% on Polyglot (abstract figures; the paper's Section 4.4 gives 14.0% as the Polyglot start). | Source ↗ |
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| ESM3 | EvolutionaryScale (2025) | Chemistry · Oracle-trained generation | ESM3 98B multimodal masked protein model | 3D structural consistency verifier and wet-lab fluorescence assay | Physics simulation | Generated esmGFP, a glowing fluorescent protein sharing only 58% sequence identity with the closest known fluorescent protein (~500 million years of evolutionary divergence). | Source ↗ |
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| Mind Evolution | Google DeepMind, University of California, San Diego (2025) | Optimization · Program evolution | Gemini 1.5 Flash / Pro evolutionary operators | Programmatic constraint checker and island genetic algorithm | Formal proof / check | Solved >95% of TravelPlanner and Natural Plan multi-constraint benchmarks with Gemini 1.5 Flash, surpassing Best-of-N and sequential Reflexion by wide margins. | Source ↗ |
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| robust-kbench pipeline (Sakana AI) | Sakana AI (2025) | ML systems · Program evolution | Frozen LLM ensemble (o3, o4-mini, Claude Sonnet 3.7, GPT-4.1) | Compiler, numeric check against PyTorch, GPU timing and profilers; LLM verifiers as filter | Empirical benchmark | On 200 Level 1 and 2 KernelBench tasks the average speedup was 3.13x, falling to 1.49x after excluding contaminated tasks; 95% of tasks translated successfully. On twelve robust-kbench tasks forward kernels reached up to 2.5x over PyTorch eager. | Source ↗ |
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| T3 Planner | Jia Li et al. (2025) | Robotics · Verifier-guided repair | Pretrained LLMs (GPT-4o, DeepSeek-reasoner, Gemini-2.5-Pro), plus a distilled Qwen3-4B | Signal Temporal Logic robustness computation and simulation of the generated controller | Formal proof / check | In simulated household, chip-design and navigation scenarios, success rates with GPT-4o were 91.65%, 91.60% and 83.69%, against 56.67%, 61.29% and 50.00% for AutoTAMP with GPT-4o. The authors claim a 30 to 40% improvement. | Source ↗ |
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| ADAS (Automated Design of Agentic Systems) | University of British Columbia, Vector Institute (2024) | ML systems · Program evolution | GPT-4 meta-agent | Sandboxed Python execution and validation benchmark evaluator | Empirical benchmark | Discovered agent architectures that outperform hand-designed baselines by up to 13.6 percentage points on ARC logic tasks and transfer across foundation models. | Source ↗ |
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| AlphaFold 3 | Google DeepMind, Isomorphic Labs (2024) | Chemistry · Oracle-trained generation | Pairformer + 3D all-atom diffusion network | Ranking formula of pTM and ipTM with clash, disorder and chirality terms | Physics simulation | Achieved 76.4% PoseBusters accuracy on protein-ligand complexes, far surpassing classical physics-based docking tools. | Source ↗ |
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| Chain-of-Experts | Zhejiang University, Huawei Noah's Ark Lab (2024) | Optimization · Formalize and solve | GPT-4 multi-role formulation agents | Gurobi / PuLP mixed-integer programming solver | Formal proof / check | Reported to significantly outperform state-of-the-art LLM-based approaches on the LPWP and ComplexOR operations research benchmarks. | Source ↗ |
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| ChatAFL | Nanyang Technological University, University of Melbourne (2024) | Security · Verifier-guided repair | LLM protocol grammar and seed mutator | Coverage-guided stateful greybox fuzzer and address sanitizers | Empirical benchmark | Covered 47.6% more state transitions and 29.6% more code branches than AFLNet across nine network protocol implementations, discovering 9 previously unknown vulnerabilities. | Source ↗ |
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| ChemCrow | EPFL, University of Rochester (2024) | Chemistry · Verifier-guided repair | GPT-4 chemical synthesis planner | RDKit, RXN4Chemistry retrosynthesis engine, and robotic wet-lab execution | Physics simulation | Autonomously planned and executed wet-lab syntheses of an insect repellent, three organocatalysts, and a novel chromophore. | Source ↗ |
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| CrystaLLM | University of Bristol, University College London (2024) | Materials · Verifier-guided repair | Autoregressive CIF transformer (CrystaLLM) | CIF validity checks and a learned formation-energy network (ALIGNN); DFT on finished structures | Physics simulation | Rediscovered unseen experimental crystal structures and identified novel stable inorganic phases validated by ab initio DFT. | Source ↗ |
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| CrystalTextLLM | New York University, Meta AI (2024) | Materials · Verifier-guided repair | Fine-tuned LLaMA-2 70B on CIF crystal strings | Pymatgen validator, M3GNet potential, and VASP DFT solver | Physics simulation | Nearly 90% of sampled structures pass geometric and charge-neutrality checks, and a high fraction relax to metastable or stable states in DFT. | Source ↗ |
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| DafnyBench Verifier Repair | Massachusetts Institute of Technology (2024) | Code verification · Verifier-guided repair | Claude 3 Opus / GPT-4o invariant synthesizer | Dafny formal verifier | Formal proof / check | Verified 68% of the 782 ground-truth formal verification programs in DafnyBench via multi-turn compiler feedback. | Source ↗ |
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| DiffSBDD | EPFL, University of Oxford (2024) | Chemistry · Oracle-trained generation | SE(3)-equivariant 3D pocket-conditioned diffusion network | RDKit chemical validator and QuickVina2 / AutoDock Vina physics docking oracle | Physics simulation | Generated pocket-specific 3D ligands with stronger Vina binding scores and drug-likeness than autoregressive 3D baselines on CrossDocked2020. | Source ↗ |
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| Fuzz4All | University of Illinois Urbana-Champaign, ETH Zurich (2024) | Security · Program evolution | StarCoder + GPT-4 autoprompting distiller | Compiler/SMT crash and output-check oracle | Empirical benchmark | Achieved 36.8% higher line coverage than language-specific fuzzers across 9 systems in 6 languages and found 98 bugs (64 confirmed previously unknown). | Source ↗ |
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| InternLM2-StepProver | Shanghai Artificial Intelligence Laboratory (2024) | Proofs · Proof-state search | InternLM2-StepProver 8B tactic and critic models | Lean 4 (executes each proposed tactic) and critic-guided best-first tree search | Formal proof / check | Reached 65.9% pass@64 on miniF2F-test and 54.5% on ProofNet, and proved 177 PutnamBench problems in Lean 4. | Source ↗ |
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| LaSR (Library-Augmented Symbolic Regression) | Cornell University, Massachusetts Institute of Technology (2024) | Science · Program evolution | LLM symbolic concept and mutation generator | PySR genetic programming and BFGS numerical optimizer | Empirical benchmark | Recovered significantly more exact ground-truth physical laws on the Feynman Symbolic Regression Benchmark than standalone PySR or LLM-only baselines. | Source ↗ |
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| Lean-STaR | Stanford University, Tsinghua University (2024) | Proofs · Proof-state search | InternLM2-Math-Base 7B with thought-tactic policy | Lean theorem prover and best-first search tree | Formal proof / check | Improved miniF2F-test pass@64 in Lean from 30.8% to 46.3%, outperforming tactic-only search baselines. | Source ↗ |
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| LLAMBO | University of Cambridge, Huawei Noah's Ark Lab (2024) | Optimization · Active-learning generation | GPT-3.5 in-context surrogate and candidate sampler | Expected Improvement acquisition ranker and black-box objective evaluator | Empirical benchmark | Outperformed Gaussian Process and Random Forest Bayesian Optimization baselines in the low-trial regime across 25 Bayesmark tasks. | Source ↗ |
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| LLMorpheus | Northeastern University (2024) | Security · Verifier-guided repair | Code-generating LLM mutant operator | Compiler and automated mutation-testing execution engine | Empirical benchmark | On 13 real-world JavaScript packages, produced mutants resembling real bugs that StrykerJS, a state-of-the-art mutation testing tool, cannot produce. | Source ↗ |
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| Orb Universal Interatomic Potential | Orbital Materials (2024) | Materials · Active-learning generation | Graph network interatomic potential, initialised from a denoising diffusion pretraining phase | None in the loop: the potential predicts energy, forces and stress, and it is not a generative search | Physics simulation | Topped the Matbench Discovery leaderboard for predicting stable inorganic crystals at 3-6x higher relaxation speed than prior equivariant potentials. | Source ↗ |
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| ORLM (Operations Research Language Model) | Cardinal Operations, Tsinghua University (2024) | Optimization · Formalize and solve | Fine-tuned Mistral-7B / LLaMA-3 ORLM | COPT mixed-integer and linear programming solver | Formal proof / check | Outperformed GPT-4 across NL4Opt, MAMO, and IndustryOR benchmarks using a 7B open-weight model paired with the COPT solver. | Source ↗ |
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| SyntheMol | Stanford University, McMaster University (2024) | Chemistry · Proof-state search | Chemprop GNN value oracle + reaction-template MCTS | SMARTS chemical reaction validator, MCTS, and wet-lab MIC assay | Physics simulation | Searched a combinatorial space of 30 billion synthesizable molecules to discover 6 structurally novel compounds with potent wet-lab antibacterial activity against A. baumannii. | Source ↗ |
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| TamGen | Microsoft Research (2024) | Chemistry · Oracle-trained generation | 3D geometric pocket encoder + chemical GPT decoder | Molecular docking engine and wet-lab IC50 enzymatic assay | Physics simulation | Designed novel Mycobacterium tuberculosis ClpP inhibitors validated in wet-lab assays with strong enzymatic inhibition (IC50 = 0.9 uM). | Source ↗ |
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| Baldur | University of Massachusetts Amherst, Google (2023) | Proofs · Verifier-guided repair | Minerva-based proof generation and repair LLMs | Isabelle/HOL proof assistant and Sledgehammer ATP | Formal proof / check | Proved 47.9% of theorems in the Isabelle Archive of Formal Proofs benchmark (65.7% when combined with Thor Sledgehammer). | Source ↗ |
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| Chroma | Generate Biomedicines (2023) | Chemistry · Oracle-trained generation | Polymer-graph SE(3) diffusion model | Geometric symmetry projectors, refolding filters, and X-ray crystallography | Physics simulation | Designed 310 proteins across point-group symmetries, programmable shapes, and protein classes, with crystallographic structures matching design to 1.0-1.4 Angstrom backbone RMSD. | Source ↗ |
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| Clover (Closed-Loop Verifiable Code Generation) | Stanford University (2023) | Code verification · Verifier-guided repair | GPT-4 Dafny code and specification generator | Dafny compiler and Z3 SMT solver | Formal proof / check | Accepted 87% of correct Dafny programs while rejecting all of adversarial incorrect synthesis candidates on the CloverBench suite. | Source ↗ |
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| Coscientist | Carnegie Mellon University (2023) | Chemistry · Verifier-guided repair | GPT-4 experimental planner and protocol synthesizer | Opentrons robotic execution validator and UV-vis spectrophotometer | Physics simulation | Autonomously executed Suzuki-Miyaura and Sonogashira cross-coupling reactions on cloud lab hardware and ran an optimization study that selected conditions against previously collected, fully mapped yield datasets. | Source ↗ |
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| DiffCSP | Tsinghua University, Renmin University of China (2023) | Materials · Oracle-trained generation | Periodic E(3)-equivariant joint diffusion network | Space-group symmetry validator and DFT energy evaluator | Physics simulation | Outperformed USPEX evolutionary crystal search and CDVAE on MP-20 and Perov-5 crystal structure prediction at a fraction of the compute time. | Source ↗ |
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| EvoPrompt | Tsinghua University, Microsoft Research (2023) | Optimization · Program evolution | GPT-3.5 / Alpaca evolutionary crossover operator | Genetic Algorithm / Differential Evolution controller and benchmark evaluator | Empirical benchmark | Outperformed human-engineered and gradient-free prompt baselines by up to 25% across 31 NLP and reasoning datasets. | Source ↗ |
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| OPRO (Optimization by PROmpting) | Google DeepMind (2023) | Optimization · Program evolution | PaLM 2 / GPT-4 optimizer model | Exact objective function evaluator and sorted trajectory buffer | Empirical benchmark | Discovered prompts that boosted GSM8K accuracy by up to 8 percentage points over human baselines and solved small-scale TSP and linear regression trajectories. | Source ↗ |
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| Promptbreeder | Google DeepMind (2023) | Optimization · Program evolution | PaLM 2L self-referential evolutionary mutator | Tournament genetic algorithm and benchmark fitness evaluator | Empirical benchmark | Outperformed Chain-of-Thought, Plan-and-Solve, and OPRO across arithmetic, commonsense, and hate-speech classification benchmarks. | Source ↗ |
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| Self-Debugging with Execution Feedback | Google DeepMind, University of California, Berkeley (2023) | Code verification · Verifier-guided repair | Codex / PaLM-2 / StarCoder | Interpreter runtime and unit-test execution oracle | Empirical benchmark | Improved pass@1 by up to 12 percentage points across TransCoder C++-to-Python translation, Spider text-to-SQL, and MBPP Python synthesis. | Source ↗ |
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| TitanFuzz | University of Illinois Urbana-Champaign (2023) | Security · Program evolution | Codex seed generator + InCoder span mutator | Dataflow/branch coverage analyzer and differential execution oracle | Empirical benchmark | Achieved 50.84% (PyTorch) and 30.38% (TensorFlow) higher code coverage than state-of-the-art DL fuzzers and detected 65 bugs (41 confirmed previously unknown). | Source ↗ |
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| TPSR (Transformer-based Planning for Symbolic Regression) | Virginia Tech, Meta AI (2023) | Science · Proof-state search | Pre-trained symbolic regression transformer (E2E) | Monte Carlo Tree Search and BFGS numerical optimizer | Empirical benchmark | Significantly improved symbolic equation recovery and extrapolation R^2 on SRBench and Feynman physics datasets over beam search or sampling. | Source ↗ |
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| Voyager | NVIDIA, California Institute of Technology (2023) | Robotics · Program evolution | GPT-4 code generator and curriculum planner | Mineflayer simulator runtime and a GPT-4 critic (self-verification) | Empirical benchmark | Unlocked 3.3x more unique items, traveled 2.3x longer distances, and reached key tech-tree milestones up to 15.3x faster than prior agent baselines. | Source ↗ |
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| AlphaCode | Google DeepMind (2022) | Code verification · Verifier-guided repair | 41B encoder-decoder code transformer | Sandboxed test execution and input-output equivalence clustering | Empirical benchmark | Placed in the top 54.3% of human participants across 10 recent Codeforces competitions, the first AI system to reach competitive human rank. | Source ↗ |
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| CDVAE (Crystal Diffusion Variational Autoencoder) | Massachusetts Institute of Technology (2022) | Materials · Oracle-trained generation | Periodic SE(3)-equivariant diffusion VAE | Crystallographic validity checker and a learned energy model | Physics simulation | Generated valid periodic crystal structures across carbon, perovskite, and Materials Project benchmarks with high structural and compositional validity. | Source ↗ |
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| Code as Policies | Google Research (2022) | Robotics · Formalize and solve | Codex / PaLM code-generation model | Shapely computational geometry library and classical robot motion controller | Empirical benchmark | Executed spatial-geometric manipulation, drawing, and tabletop rearrangement tasks on physical Franka Panda and UR5e robot arms without task-specific training. | Source ↗ |
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| CodeT | Microsoft Research (2022) | Code verification · Verifier-guided repair | Codex / InCoder code generator | Sandboxed execution matrix and RANSAC bipartite consensus solver | Empirical benchmark | Raised pass@1 on HumanEval to 65.8% (+18.8 points over Codex greedy decoding) and improved MBPP and APPS accuracy by over 15 points. | Source ↗ |
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| Draft, Sketch, and Prove (DSP) | Meta AI, Peking University (2022) | Proofs · Proof-state search | Minerva / Codex formal sketch generator | Isabelle/HOL kernel and Sledgehammer automated theorem provers | Formal proof / check | Solved 39.3% of miniF2F test theorems in Isabelle/HOL, a more than 10 percentage point jump over prior direct tactic-generation baselines. | Source ↗ |
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| HyperTree Proof Search (HTPS) | Meta AI (2022) | Proofs · Proof-state search | Online-trained encoder-decoder tactic and value transformers | Lean / Metamath kernel and PUCT AND-OR hypergraph search | Formal proof / check | Solved 82.6% of Metamath set.mm test theorems and 41.0% of miniF2F-curriculum theorems in Lean, discovering shorter proofs than human ground truth. | Source ↗ |
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| Pocket2Mol | Peking University (2022) | Chemistry · Oracle-trained generation | E(3)-equivariant autoregressive 3D GNN | QVina docking score, used to evaluate finished molecules | Physics simulation | Generated drug-like 3D molecules with more realistic torsion angles and stronger Vina binding scores than 3D voxel baselines on CrossDocked2020. | Source ↗ |
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| ProteinMPNN | University of Washington (2022) | Chemistry · Oracle-trained generation | ProteinMPNN 3D message-passing neural network | The model log probability for ranking; AlphaFold2 refolding and X-ray crystallography / cryo-EM as measures of whether designs fold | Physics simulation | Achieved 52.4% native sequence recovery (vs. 32.9% for Rosetta) and rescued previously failed de novo protein cyclic oligomers, nanoparticles, and binders in wet-lab crystallography. | Source ↗ |
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| SayCan | Google Research, Everyday Robots (2022) | Robotics · Formalize and solve | PaLM 540B semantic skill proposer | RL Bellman value-function affordance critics and physical robot controller | Empirical benchmark | Executed 101 real-world mobile manipulation tasks in an office kitchen with 84% planning rate and 74% physical execution success. | Source ↗ |
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| Synchromesh | Microsoft Research (2022) | Code verification · Verifier-guided repair | Codex / GPT-3 with constrained token masking | Incremental CFG parser and static type/scope completion engine | Formal proof / check | Eliminated syntax, type, and scope errors across SQL, Vega-Lite visualization specs, and calendar DSLs while boosting execution accuracy. | Source ↗ |
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| PICARD | Element AI, ServiceNow Research (2021) | Code verification · Proof-state search | T5-3B sequence-to-sequence model | Incremental monadic SQL parser and relational schema type-checker | Formal proof / check | Boosted T5-3B exact-match and execution accuracy on Spider and CoSQL benchmarks by 4-7 percentage points and eliminated 98% of syntax and schema errors. | Source ↗ |
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| A-CEoH (Algorithmic Contextual EoH) | Karlsruhe Institute of Technology and TU Dortmund University (2026) | Optimization · Program evolution | Pretrained LLMs, frozen (Qwen2.5-Coder:32b, GPT-4o, Gemma2:27b) | A* runs on instances (solved or not, plan quality, time) | Empirical benchmark | For unit-load pre-marshalling, Qwen2.5-Coder:32b-generated heuristics solved 30 of 30 held-out instances (seeds 10-39) against 27 of 30 for the "Optimal A*" baseline. For the sliding puzzle they solved 10 of 10 on seeds 0-9 against 5 of 10 for Hybrid A* and for "Optimal A*". | Source ↗ |
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| CoupleEvo | Karlsruhe Institute of Technology (2026) | Optimization · Program evolution | Qwen3-coder:30b, frozen | Evaluation on coupled-problem instances | Empirical benchmark | On two coupled problems (inventory routing, and multi-robot multi-bay pre-marshalling) with Qwen3-coder:30b, the sequential and iterative strategies converged more stably than the integrated one. On inventory routing the mean relative gap was 0.0429 (sequential), 0.0433 (iterative), 0.0537 (integrated). | Source ↗ |
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| ReEvo-designed memetic algorithm for secure fluid antenna systems | Harbin Institute of Technology, Shenzhen (2026) | Engineering · Program evolution | Pretrained LLM (DeepSeek Reasoner) inside the ReEvo reflective-evolution framework | Wireless channel simulation with secure WMMSE beamforming scoring each port subset | Empirical benchmark | At equal generation counts (100 generations), the evolved memetic algorithm reached 11.423 bit/s/Hz at 1 W (7.6% over a conventional GA) and 23.611 bit/s/Hz at 5 W (8.2% over a conventional GA), and about 4 to 6% above the two LLM-assisted GA baselines. | Source ↗ |
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| T-GADE | Osaka Metropolitan University (2026) | Optimization · Program evolution | Pretrained LLM, frozen (also used as a self-repair model, HoxLM) | Bin packing evaluation and free-energy survival selection | Empirical benchmark | In a preregistered seed-paired comparison at 400 total LLM calls on online bin packing, the HoxLM configuration won 9 of 10 runs against EoH, with a median sealed excess of 0.836% against 3.912%. | Source ↗ |
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| AlphaEvolve at scale on 67 math problems (Georgiev, Gomez-Serrano, Tao, Wagner) | Google DeepMind, Brown University, Institute for Advanced Study and UCLA (Georgiev, Gomez-Serrano, Tao, Wagner) (2025) | Mathematics · Program evolution | Gemini-based AlphaEvolve (frozen), with Deep Think and AlphaProof for proof steps | Deterministic evaluator scoring the construction; some results later proven by hand or in Lean (one simple Kakeya case) | Empirical benchmark | The paper reports 67 problems across analysis, combinatorics, geometry and number theory. AlphaEvolve rediscovered the best known solutions in most cases and found improved ones in several, for example an autocorrelation upper bound reduced from 1.5708 to 1.5032 and a finite field Kakeya construction of size 1/4 p^3 + 7/8 p^2 - 1/8 for primes p = 1 mod 4. | Source ↗ |
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| CALM (Co-evolution of Algorithms and Language Model) | City University of Hong Kong, Southeast University, University of Victoria, Hon Hai Research Institute (2025) | Optimization · Program evolution | Qwen2.5-7B-Instruct, INT4, fine-tuned with GRPO (about 1.15% of weights) | Benchmark evaluation of heuristic quality | Empirical benchmark | A Qwen2.5-7B-Instruct model (INT4, on a single 24GB GPU) with GRPO fine-tuning reached an average 0.71% gap on online bin packing, against 0.89% for MCTS-AHD and 2.40% for Best Fit, and beat the best listed competitor on CVRP (3.95% vs 4.70%) and OP (12.58% vs 16.34%) at N=200 in the paper's tables. | Source ↗ |
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| CEoH (Contextual Evolution of Heuristics) | Karlsruhe Institute of Technology and TU Dortmund University (2025) | Optimization · Program evolution | Pretrained LLMs, frozen (Gemma2:27b, Qwen2.5-Coder:32b, DeepSeekV3:685b, GPT-4o) | Instance evaluation of heuristic inside a tree search | Empirical benchmark | For unit-load pre-marshalling, Qwen2.5-Coder:32b with CEoH reached a fitness of 12.5% (best overall), against 14.3% for the best EoH run (GPT-4o 2024-08-06). The "Optimal A*" baseline scored about 8.1%. CEoH outperformed EoH for Gemma2:27b, Qwen2.5-Coder:32b and DeepSeekV3:685b. | Source ↗ |
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| CogFunSearch | Google DeepMind with Janelia Research Campus, Rockefeller University, Max Planck Institute for Biological Cybernetics, Princeton University, UCL and Columbia University (2025) | Science · Program evolution | Pretrained LLM, frozen (inherited from FunSearch) | Held-out predictive score of each program on behavioral data | Empirical benchmark | In a bioRxiv preprint, on rat choices in a 2-armed drifting bandit task (data from Miller et al. 2021), CogFunSearch reliably found programs that beat the best existing cognitive model the authors compared against, both when improving supplied programs and when starting from scratch. | Source ↗ |
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| FunBO | Google DeepMind (2025) | Optimization · Program evolution | Code-generating LLM inside an island evolutionary loop | Gaussian Process Bayesian Optimization benchmark evaluator | Empirical benchmark | Discovered acquisition functions that outperform Expected Improvement (EI) and Upper Confidence Bound (UCB) on unseen black-box optimization and HPO benchmarks. | Source ↗ |
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| InvDesFlow-AL | Renmin University of China (2025) | Materials · Active-learning generation | Diffusion model on atom types, lattice and fractional coordinates (EGNN) | DPA-2 relaxation, committee scoring, Bohrium Ehull query, DFT for the superconductor task | Physics simulation | Generated average formation energy fell over five iterations (means -1.14, -2.03, -2.93, -3.56, -3.77; units not stated in the text). The authors report 1,598,551 materials with Ehull below 50 meV, and Li2AuH6 as a conventional superconductor with a transition temperature of about 140 K from first-principles electron-phonon calculations. Crystal structure prediction RMSE is 0.0423 angstrom, reported as a 32.96% improvement over existing generative models. | Source ↗ |
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| AFlow (Automating Agentic Workflow Generation) | DeepWisdom, Hong Kong University of Science and Technology (2024) | ML systems · Program evolution | Claude 3.5 Sonnet / GPT-4o mutation operator | Monte Carlo Tree Search and benchmark execution evaluator | Empirical benchmark | Outperforms hand-crafted and automated workflow baselines by 5.7% average across six coding and math benchmarks while enabling smaller models to beat GPT-4o. | Source ↗ |
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| FlowMM | Meta AI (2024) | Materials · Oracle-trained generation | Riemannian flow-matching crystal network | Crystallographic manifold constraints and VASP DFT evaluator | Physics simulation | Achieved state-of-the-art thermodynamic stability and 3x faster integration steps than diffusion baselines on MP-20 and MPTS-52. | Source ↗ |
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| HSEvo | Hanoi University of Science and Technology and George Mason University (2024) | Optimization · Program evolution | Pretrained LLM, frozen | Benchmark evaluation of heuristic code and diversity metrics | Empirical benchmark | The authors propose two diversity metrics and use them to compare FunSearch, EoH and ReEvo. They report EoH has higher diversity but unstable scores, ReEvo has good scores but poor diversity, and that HSEvo reaches high diversity and good objective scores while staying cost-effective. | Source ↗ |
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| Lean Copilot | California Institute of Technology (2024) | Proofs · Proof-state search | ReProver / ByT5 tactic and premise models | Lean 4 kernel and best-first proof search | Formal proof / check | Automates proof goals directly inside Lean 4 workflows with 3.8x faster tactic inference than Python RPC bridges. | Source ↗ |
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| AlphaCode 2 | Google DeepMind (2023) | Code verification · Verifier-guided repair | Fine-tuned Gemini Pro | Sandboxed C++ execution filter and behavioral clustering engine | Empirical benchmark | Solved 43% of Codeforces Division 1+2 problems and ranked at the 85th percentile of human competitors. | Source ↗ |
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| LEGO-Prover | Tsinghua University, The Chinese University of Hong Kong (2023) | Proofs · Proof-state search | GPT-3.5 / LLaMA-2 prover and lemma-evolver agents | Isabelle/HOL proof kernel and Sledgehammer ATP | Formal proof / check | Raised miniF2F-valid pass@100 to 57.0% and miniF2F-test to 50.0% in Isabelle/HOL, accumulating thousands of reusable verified lemmas. | Source ↗ |
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| VoxPoser | Stanford University (2023) | Robotics · Formalize and solve | GPT-4 3D potential-field synthesizer | Model Predictive Control (MPC) trajectory planner and IK solver | Empirical benchmark | Zero-shot execution of 25 everyday manipulation tasks across real-world and simulated robot arms with 88% success, plus online adaptation to moving obstacles. | Source ↗ |
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| Augmented Hill-Climb | University of Cambridge (2022) | Chemistry · Oracle-trained generation | SMILES RNN (and RL-stabilized transformer), updated by reinforcement learning | Task scoring functions including docking, plus diversity filters | Physics simulation | On the authors' benchmark tasks, compared with REINVENT, optimization ability improved about 1.5-fold and sample efficiency about 45-fold, and Augmented Hill-Climb outperformed the other reinforcement learning strategies tested on six tasks. | Source ↗ |
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| Lib-INVENT with docking and RFXscore | Sanofi (2022) | Chemistry · Oracle-trained generation | Lib-INVENT RNN prior and agent (scaffold decoration) | Glide XP docking, RFXscore rescoring, MM/GBSA post-check | Physics simulation | In a factor Xa case study, docking followed by RFXscore gave the best results, especially when diverse structures fitting a binding site were wanted; RFXscore plus the factor Xa model left the most compounds after MM/GBSA and other filters. RFXscore had a test r2 of 0.494 and MAE of 1.086. | Source ↗ |
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