Task taxonomy¶

The catalog ships 2,401 task cards, of which 2,396 are runnable. This page organizes every card into a three-tier click-to-expand tree — domain → sub-domain → individual task — grouped purely by what the problem is, independent of where it came from.

How to read the tree

Click a domain to reveal its sub-domains; click a sub-domain to reveal every individual task in it. Counts are shown at each level.

import galapagos as gx
gx.available_tasks()          # all 2,401 task-card names (including five spec cards)

The 1,120 individually registered ARC-AGI-2 tasks are summarized by public split below rather than expanded into a thousand-line ID list.

Visual map¶

Galapagos task taxonomy Domain → sub-domain → individual task

2,401 task cards

1 Abstract Reasoning1 sub-domain 1,120

Visual grid reasoning1,120

2 Kernel Engineering2 sub-domains 317

GPU kernel optimization316

Compiler optimization1

3 Symbolic Regression6 sub-domains 248

Physical laws111

Nonlinear oscillator dynamics44

Chemical reaction kinetics36

Materials laws25

Population dynamics24

Scaling laws8

4 Mathematical Discovery8 sub-domains 259

Shape packing184

Analytic inequalities27

Extremal combinatorics23

Point configuration geometry15

Black-box optimization5

Discrete geometry2

Number theory2

Best known linear codes1

5 Competitive Programming6 sub-domains 233

Heuristic optimization87

Interactive query problems65

Constructive algorithm problems56

Constraint satisfaction20

Applied coding4

Maximum satisfiability1

6 High-Performance Algorithms13 sub-domains 157

Mathematical optimization33

Linear algebra29

Discrete optimization19

Numerical methods19

Graph algorithms16

Signal processing15

Statistical estimation9

Cryptography5

Computational geometry4

Control4

Data compression2

Iterative solvers1

Lattice challenges1

7 Quantum Computing2 sub-domains 2

QEC decoder design1

Quantum circuit optimization1

8 Single-cell Genomics4 sub-domains 21

Biological inference6

Preprocessing6

OpenProblems BioML-Bench5

Spatial transcriptomics4

9 Computational Biology3 sub-domains 8

ProteinGym DMS6

ProteinGym Kermut1

Multiple sequence alignment1

10 Biomedical Imaging1 sub-domain 4

Kaggle BioML-Bench4

11 Drug Discovery1 sub-domain 9

Molecular property prediction9

12 Systems Design8 sub-domains 15

Distributed systems5

Vector search3

Chip placement2

Diffusion sampling speedup1

LLM serving1

Query optimization1

VLSI placement1

World models1

13 Generative AI Optimization4 sub-domains 8

Prompt optimization4

Generative modeling2

Game-playing agents1

Generative outputs1

Detailed tree¶

1 · Abstract Reasoning — 1,120 tasks

Discover general rules over symbolic grids and synthesize transformations that transfer from demonstrations to held-out inputs.

1.1 · Visual grid reasoning — 1,120

ARC-AGI-2 Public Train — 1,000 individually registered tasks (arc_agi_2_public_train_<task-id>)
ARC-AGI-2 Public Eval — 120 individually registered tasks (arc_agi_2_public_eval_<task-id>)

2 · Kernel Engineering — 317 tasks

Low-level performance engineering for GPU kernels and compiler-level transformations.

2.1 · GPU kernel optimization — 316

GPU MODE: Ag Gemm (amd_distributed)
GPU MODE: All2All (amd_distributed)
GPU MODE: Causal Conv1D (helion)
GPU MODE: Conv2D (pmpp)
GPU MODE: Conv2D (pmpp_v2)
GPU MODE: Cross Entropy (princeton)
GPU MODE: Eigh (linalg)
GPU MODE: Float16 Vector Addition (Triton)
GPU MODE: Fp8 Mm (amd)
GPU MODE: Fp8 Quant (helion)
GPU MODE: Gated Deltanet Chunk Fwd H (helion)
GPU MODE: Gated Deltanet Chunk Fwd O (helion)
GPU MODE: Gated Deltanet Recompute W U (helion)
GPU MODE: Gemm Rs (amd_distributed)
GPU MODE: Grayscale (pmpp)
GPU MODE: Grayscale (pmpp_v2)
GPU MODE: Histogram (pmpp)
GPU MODE: Histogram (pmpp_v2)
GPU MODE: Identity (amd)
GPU MODE: Matmul (pmpp)
GPU MODE: Matmul (pmpp_v2)
GPU MODE: Mixed Mla (amd_202602)
GPU MODE: Mla Decode (amd)
GPU MODE: MLA Decode (Triton)
GPU MODE: Modal Nvfp4 Dual Gemm (nvidia)
GPU MODE: Moe (amd)
GPU MODE: Moe Mxfp4 (amd_202602)
GPU MODE: Mxfp4 Mm (amd_202602)
GPU MODE: Nvfp4 Dual Gemm (nvidia)
GPU MODE: Nvfp4 Gemm (nvidia)
GPU MODE: Nvfp4 Gemv (nvidia)
GPU MODE: Nvfp4 Group Gemm (nvidia)
GPU MODE: Prefixsum (pmpp)
GPU MODE: Prefixsum (pmpp_v2)
GPU MODE: Qr (linalg)
GPU MODE: Qr V2 (linalg)
GPU MODE: RGB to Grayscale (Triton)
GPU MODE: Sort (pmpp)
GPU MODE: Sort (pmpp_v2)
GPU MODE: Triangle Multiplicative Update (Triton)
GPU MODE: Trimul (bioml)
GPU MODE: Vectoradd (pmpp)
GPU MODE: Vectoradd (pmpp_v2)
GPU MODE: Vectorsum (pmpp)
GPU MODE: Vectorsum (pmpp_v2)
KernelBench L1 P100: HingeLoss
KernelBench L1 P10: 3D tensor matrix multiplication
KernelBench L1 P11: 4D tensor matrix multiplication
KernelBench L1 P12: Matmul with diagonal matrices
KernelBench L1 P13: Matmul for symmetric matrices
KernelBench L1 P14: Matmul for upper triangular matrices
KernelBench L1 P15: Matmul for lower triangular matrices
KernelBench L1 P16: Matmul with transposed A
KernelBench L1 P17: Matmul with transposed B
KernelBench L1 P18: Matmul with transposed both
KernelBench L1 P19: ReLU
KernelBench L1 P1: Square matrix multiplication
KernelBench L1 P20: LeakyReLU
KernelBench L1 P21: Sigmoid
KernelBench L1 P22: Tanh
KernelBench L1 P23: Softmax
KernelBench L1 P24: LogSoftmax
KernelBench L1 P25: Swish
KernelBench L1 P26: GELU
KernelBench L1 P27: SELU
KernelBench L1 P28: HardSigmoid
KernelBench L1 P29: Softplus
KernelBench L1 P2: Standard matrix multiplication
KernelBench L1 P30: Softsign
KernelBench L1 P31: ELU
KernelBench L1 P32: HardTanh
KernelBench L1 P33: BatchNorm
KernelBench L1 P34: InstanceNorm
KernelBench L1 P35: GroupNorm
KernelBench L1 P36: RMSNorm
KernelBench L1 P37: FrobeniusNorm
KernelBench L1 P38: L1Norm
KernelBench L1 P39: L2Norm
KernelBench L1 P3: Batched matrix multiplication
KernelBench L1 P40: LayerNorm
KernelBench L1 P41: Max Pooling 1D
KernelBench L1 P42: Max Pooling 2D
KernelBench L1 P43: Max Pooling 3D
KernelBench L1 P44: Average Pooling 1D
KernelBench L1 P45: Average Pooling 2D
KernelBench L1 P46: Average Pooling 3D
KernelBench L1 P47: Sum reduction over a dimension
KernelBench L1 P48: Mean reduction over a dimension
KernelBench L1 P49: Max reduction over a dimension
KernelBench L1 P4: Matrix vector multiplication
KernelBench L1 P50: conv standard 2D square input square kernel
KernelBench L1 P51: Argmax over a dimension
KernelBench L1 P52: Argmin over a dimension
KernelBench L1 P53: Min reduction over a dimension
KernelBench L1 P54: conv standard 3D square input square kernel
KernelBench L1 P55: conv standard 2D asymmetric input square kernel
KernelBench L1 P56: conv standard 2D asymmetric input asymmetric kernel
KernelBench L1 P57: conv transposed 2D square input square kernel
KernelBench L1 P58: conv transposed 3D asymmetric input asymmetric kernel
KernelBench L1 P59: conv standard 3D asymmetric input square kernel
KernelBench L1 P5: Matrix scalar multiplication
KernelBench L1 P60: conv standard 3D square input asymmetric kernel
KernelBench L1 P61: conv transposed 3D square input square kernel
KernelBench L1 P62: conv standard 2D square input asymmetric kernel
KernelBench L1 P63: conv standard 2D square input square kernel
KernelBench L1 P64: conv transposed 1D
KernelBench L1 P65: conv transposed 2D square input asymmetric kernel
KernelBench L1 P66: conv standard 3D asymmetric input asymmetric kernel
KernelBench L1 P67: conv standard 1D
KernelBench L1 P68: conv transposed 3D square input asymmetric kernel
KernelBench L1 P69: conv transposed 2D asymmetric input asymmetric kernel
KernelBench L1 P6: Matmul with large K dimension
KernelBench L1 P70: conv transposed 3D asymmetric input square kernel
KernelBench L1 P71: conv transposed 2D asymmetric input square kernel
KernelBench L1 P72: conv transposed 3D asymmetric input asymmetric kernel strided padded grouped
KernelBench L1 P73: conv transposed 3D asymmetric input square kernel strided padded grouped
KernelBench L1 P74: conv transposed 1D dilated
KernelBench L1 P75: conv transposed 2D asymmetric input asymmetric kernel strided grouped padded dilated
KernelBench L1 P76: conv standard 1D dilated strided
KernelBench L1 P77: conv transposed 3D square input square kernel padded dilated strided
KernelBench L1 P78: conv transposed 2D asymmetric input asymmetric kernel padded
KernelBench L1 P79: conv transposed 1D asymmetric input square kernel padded strided dilated
KernelBench L1 P7: Matmul with small K dimension
KernelBench L1 P80: conv standard 2D square input asymmetric kernel dilated padded
KernelBench L1 P81: conv transposed 2D asymmetric input square kernel dilated padded strided
KernelBench L1 P82: conv depthwise 2D square input square kernel
KernelBench L1 P83: conv depthwise 2D square input asymmetric kernel
KernelBench L1 P84: conv depthwise 2D asymmetric input square kernel
KernelBench L1 P85: conv depthwise 2D asymmetric input asymmetric kernel
KernelBench L1 P86: conv depthwise separable 2D
KernelBench L1 P87: conv pointwise 2D
KernelBench L1 P88: MinGPTNewGelu
KernelBench L1 P89: cumsum
KernelBench L1 P8: Matmul with irregular shapes
KernelBench L1 P90: cumprod
KernelBench L1 P91: cumsum reverse
KernelBench L1 P92: cumsum exclusive
KernelBench L1 P93: masked cumsum
KernelBench L1 P94: MSELoss
KernelBench L1 P95: CrossEntropyLoss
KernelBench L1 P96: HuberLoss
KernelBench L1 P97: ScaledDotProductAttention
KernelBench L1 P98: KLDivLoss
KernelBench L1 P99: TripletMarginLoss
KernelBench L1 P9: Tall skinny matrix multiplication
KernelBench L2 P100: ConvTranspose3d Clamp Min Divide
KernelBench L2 P10: ConvTranspose2d MaxPool Hardtanh Mean Tanh
KernelBench L2 P11: ConvTranspose2d BatchNorm Tanh MaxPool GroupNorm
KernelBench L2 P12: Gemm Multiply LeakyReLU
KernelBench L2 P13: ConvTranspose3d Mean Add Softmax Tanh Scaling
KernelBench L2 P14: Gemm Divide Sum Scaling
KernelBench L2 P15: ConvTranspose3d BatchNorm Subtract
KernelBench L2 P16: ConvTranspose2d Mish Add Hardtanh Scaling
KernelBench L2 P17: Conv2d InstanceNorm Divide
KernelBench L2 P18: Matmul Sum Max AvgPool LogSumExp LogSumExp
KernelBench L2 P19: ConvTranspose2d GELU GroupNorm
KernelBench L2 P1: Conv2D ReLU BiasAdd
KernelBench L2 P20: ConvTranspose3d Sum ResidualAdd Multiply ResidualAdd
KernelBench L2 P21: Conv2d Add Scale Sigmoid GroupNorm
KernelBench L2 P22: Matmul Scale ResidualAdd Clamp LogSumExp Mish
KernelBench L2 P23: Conv3d GroupNorm Mean
KernelBench L2 P24: Conv3d Min Softmax
KernelBench L2 P25: Conv2d Min Tanh Tanh
KernelBench L2 P26: ConvTranspose3d Add HardSwish
KernelBench L2 P27: Conv3d HardSwish GroupNorm Mean
KernelBench L2 P28: BMM InstanceNorm Sum ResidualAdd Multiply
KernelBench L2 P29: Matmul Mish Mish
KernelBench L2 P2: ConvTranspose2d BiasAdd Clamp Scaling Clamp Divide
KernelBench L2 P30: Gemm GroupNorm Hardtanh
KernelBench L2 P31: Conv2d Min Add Multiply
KernelBench L2 P32: Conv2d Scaling Min
KernelBench L2 P33: Gemm Scale BatchNorm
KernelBench L2 P34: ConvTranspose3d LayerNorm GELU Scaling
KernelBench L2 P35: Conv2d Subtract HardSwish MaxPool Mish
KernelBench L2 P36: ConvTranspose2d Min Sum GELU Add
KernelBench L2 P37: Matmul Swish Sum GroupNorm
KernelBench L2 P38: ConvTranspose3d AvgPool Clamp Softmax Multiply
KernelBench L2 P39: Gemm Scale BatchNorm
KernelBench L2 P3: ConvTranspose3d Sum LayerNorm AvgPool GELU
KernelBench L2 P40: Matmul Scaling ResidualAdd
KernelBench L2 P41: Gemm BatchNorm GELU ReLU
KernelBench L2 P42: ConvTranspose2d GlobalAvgPool BiasAdd LogSumExp Sum Multiply
KernelBench L2 P43: Conv3d Max LogSumExp ReLU
KernelBench L2 P44: ConvTranspose2d Multiply GlobalAvgPool GlobalAvgPool Mean
KernelBench L2 P45: Gemm Sigmoid LogSumExp
KernelBench L2 P46: Conv2d Subtract Tanh Subtract AvgPool
KernelBench L2 P47: Conv3d Mish Tanh
KernelBench L2 P48: Conv3d Scaling Tanh Multiply Sigmoid
KernelBench L2 P49: ConvTranspose3d Softmax Sigmoid
KernelBench L2 P4: Conv2d Mish Mish
KernelBench L2 P50: ConvTranspose3d Scaling AvgPool BiasAdd Scaling
KernelBench L2 P51: Gemm Subtract GlobalAvgPool LogSumExp GELU ResidualAdd
KernelBench L2 P52: Conv2d Activation BatchNorm
KernelBench L2 P53: Gemm Scaling Hardtanh GELU
KernelBench L2 P54: Conv2d Multiply LeakyReLU GELU
KernelBench L2 P55: Matmul MaxPool Sum Scale
KernelBench L2 P56: Matmul Sigmoid Sum
KernelBench L2 P57: Conv2d ReLU HardSwish
KernelBench L2 P58: ConvTranspose3d LogSumExp HardSwish Subtract Clamp
KernelBench L2 P59: Matmul Swish Scaling
KernelBench L2 P5: ConvTranspose2d Subtract Tanh
KernelBench L2 P60: ConvTranspose3d Swish GroupNorm HardSwish
KernelBench L2 P61: ConvTranspose3d ReLU GroupNorm
KernelBench L2 P62: Matmul GroupNorm LeakyReLU Sum
KernelBench L2 P63: Gemm ReLU Divide
KernelBench L2 P64: Gemm LogSumExp LeakyReLU LeakyReLU GELU GELU
KernelBench L2 P65: Conv2d AvgPool Sigmoid Sum
KernelBench L2 P66: Matmul Dropout Softmax
KernelBench L2 P67: Conv2d GELU GlobalAvgPool
KernelBench L2 P68: Matmul Min Subtract
KernelBench L2 P69: Conv2d HardSwish ReLU
KernelBench L2 P6: Conv3d Softmax MaxPool MaxPool
KernelBench L2 P70: Gemm Sigmoid Scaling ResidualAdd
KernelBench L2 P71: Conv2d Divide LeakyReLU
KernelBench L2 P72: ConvTranspose3d BatchNorm AvgPool AvgPool
KernelBench L2 P73: Conv2d BatchNorm Scaling
KernelBench L2 P74: ConvTranspose3d LeakyReLU Multiply LeakyReLU Max
KernelBench L2 P75: Gemm GroupNorm Min BiasAdd
KernelBench L2 P76: Gemm Add ReLU
KernelBench L2 P77: ConvTranspose3d Scale BatchNorm GlobalAvgPool
KernelBench L2 P78: ConvTranspose3d Max Max Sum
KernelBench L2 P79: Conv3d Multiply InstanceNorm Clamp Multiply Max
KernelBench L2 P7: Conv3d ReLU LeakyReLU GELU Sigmoid BiasAdd
KernelBench L2 P80: Gemm Max Subtract GELU
KernelBench L2 P81: Gemm Swish Divide Clamp Tanh Clamp
KernelBench L2 P82: Conv2d Tanh Scaling BiasAdd Max
KernelBench L2 P83: Conv3d GroupNorm Min Clamp Dropout
KernelBench L2 P84: Gemm BatchNorm Scaling Softmax
KernelBench L2 P85: Conv2d GroupNorm Scale MaxPool Clamp
KernelBench L2 P86: Matmul Divide GELU
KernelBench L2 P87: Conv2d Subtract Subtract Mish
KernelBench L2 P88: Gemm GroupNorm Swish Multiply Swish
KernelBench L2 P89: ConvTranspose3d MaxPool Softmax Subtract Swish Max
KernelBench L2 P8: Conv3d Divide Max GlobalAvgPool BiasAdd Sum
KernelBench L2 P90: Conv3d LeakyReLU Sum Clamp GELU
KernelBench L2 P91: ConvTranspose2d Softmax BiasAdd Scaling Sigmoid
KernelBench L2 P92: Conv2d GroupNorm Tanh HardSwish ResidualAdd LogSumExp
KernelBench L2 P93: ConvTranspose2d Add Min GELU Multiply
KernelBench L2 P94: Gemm BiasAdd Hardtanh Mish GroupNorm
KernelBench L2 P95: Matmul Add Swish Tanh GELU Hardtanh
KernelBench L2 P96: ConvTranspose3d Multiply Max GlobalAvgPool Clamp
KernelBench L2 P97: Matmul BatchNorm BiasAdd Divide Swish
KernelBench L2 P98: Matmul AvgPool GELU Scale Max
KernelBench L2 P99: Matmul GELU Softmax
KernelBench L2 P9: Matmul Subtract Multiply ReLU
KernelBench L3 P10: ResNet101
KernelBench L3 P11: VGG16
KernelBench L3 P12: VGG19
KernelBench L3 P13: DenseNet121TransitionLayer
KernelBench L3 P14: DenseNet121DenseBlock
KernelBench L3 P15: DenseNet121
KernelBench L3 P16: DenseNet201
KernelBench L3 P17: SqueezeNetFireModule
KernelBench L3 P18: SqueezeNet
KernelBench L3 P19: MobileNetV1
KernelBench L3 P1: MLP
KernelBench L3 P20: MobileNetV2
KernelBench L3 P21: EfficientNetMBConv
KernelBench L3 P22: EfficientNetB0
KernelBench L3 P23: EfficientNetB1
KernelBench L3 P24: EfficientNetB2
KernelBench L3 P25: ShuffleNetUnit
KernelBench L3 P26: ShuffleNet
KernelBench L3 P27: RegNet
KernelBench L3 P28: VisionTransformer
KernelBench L3 P29: SwinMLP
KernelBench L3 P2: ShallowWideMLP
KernelBench L3 P30: SwinTransformerV2
KernelBench L3 P31: VisionAttention
KernelBench L3 P32: ConvolutionalVisionTransformer
KernelBench L3 P33: VanillaRNN
KernelBench L3 P34: VanillaRNNHidden
KernelBench L3 P35: LSTM
KernelBench L3 P36: LSTMHn
KernelBench L3 P37: LSTMCn
KernelBench L3 P38: LSTMBidirectional
KernelBench L3 P39: GRU
KernelBench L3 P3: DeepNarrowMLP
KernelBench L3 P40: GRUHidden
KernelBench L3 P41: GRUBidirectional
KernelBench L3 P42: GRUBidirectionalHidden
KernelBench L3 P43: MinGPTCausalAttention
KernelBench L3 P44: MiniGPTBlock
KernelBench L3 P45: UNetSoftmax
KernelBench L3 P46: NetVladWithGhostClusters
KernelBench L3 P47: NetVladNoGhostClusters
KernelBench L3 P48: Mamba2ReturnY
KernelBench L3 P49: Mamba2ReturnFinalState
KernelBench L3 P4: LeNet5
KernelBench L3 P50: ReLUSelfAttention
KernelBench L3 P5: AlexNet
KernelBench L3 P6: GoogleNetInceptionModule
KernelBench L3 P7: GoogleNetInceptionV1
KernelBench L3 P8: ResNetBasicBlock
KernelBench L3 P9: ResNet18
KernelBench L4 P10: google-bigbird-roberta-base bs1024 seq32
KernelBench L4 P11: google-electra-small-discriminator bs1 seq511
KernelBench L4 P12: google-electra-small-discriminator bs1024 seq32
KernelBench L4 P13: google-reformer-enwik8 bs32 seq256
KernelBench L4 P14: google-electra-small-discriminator bs32 seq256
KernelBench L4 P15: google-reformer-enwik8 bs1024 seq32
KernelBench L4 P16: gpt2 bs1 seq1023
KernelBench L4 P17: facebook-bart-large bs1024 seq32
KernelBench L4 P18: EleutherAI-gpt-neo-2p7B bs512 seq32
KernelBench L4 P19: gpt2 bs1024 seq32
KernelBench L4 P1: EleutherAI-gpt-neo-2p7B bs32 seq256
KernelBench L4 P20: facebook-bart-large bs32 seq256
KernelBench L4 P2: facebook-opt-1p3b bs1 seq2047
KernelBench L4 P3: EleutherAI-gpt-neo-2p7B bs1 seq2047
KernelBench L4 P4: facebook-opt-1p3b bs32 seq256
KernelBench L4 P5: google-bigbird-roberta-base bs1 seq4095
KernelBench L4 P6: facebook-bart-large bs1 seq1023
KernelBench L4 P7: gpt2 bs32 seq256
KernelBench L4 P8: facebook-opt-1p3b bs512 seq32
KernelBench L4 P9: google-bigbird-roberta-base bs32 seq256
Metal Kernel Optimization

2.2 · Compiler optimization — 1

Attention Kernel Optimization

3 · Symbolic Regression — 248 tasks

Recover a closed-form equation that fits observed data.

3.1 · Physical laws — 111

LSR-Transform I.10.7_1_0
LSR-Transform I.11.19_0_0
LSR-Transform I.11.19_1_0
LSR-Transform I.11.19_2_0
LSR-Transform I.11.19_3_0
LSR-Transform I.11.19_4_0
LSR-Transform I.11.19_5_0
LSR-Transform I.12.2_3_0
LSR-Transform I.12.4_2_0
LSR-Transform I.13.12_3_0
LSR-Transform I.15.1_1_0
LSR-Transform I.15.3t_0_0
LSR-Transform I.24.6_0_0
LSR-Transform I.24.6_1_1
LSR-Transform I.24.6_2_1
LSR-Transform I.24.6_3_1
LSR-Transform I.27.6_2_0
LSR-Transform I.29.16_0_0
LSR-Transform I.29.16_1_0
LSR-Transform I.30.3_0_0
LSR-Transform I.32.17_2_0
LSR-Transform I.32.17_3_0
LSR-Transform I.32.17_4_3
LSR-Transform I.32.17_5_3
LSR-Transform I.32.5_0_1
LSR-Transform I.32.5_1_1
LSR-Transform I.34.14_2_0
LSR-Transform I.34.1_2_0
LSR-Transform I.37.4_0_1
LSR-Transform I.37.4_1_1
LSR-Transform I.40.1_4_0
LSR-Transform I.43.43_0_0
LSR-Transform I.43.43_3_0
LSR-Transform I.44.4_2_0
LSR-Transform I.44.4_4_0
LSR-Transform I.48.2_1_0
LSR-Transform I.50.26_0_0
LSR-Transform I.50.26_3_0
LSR-Transform II.11.17_0_0
LSR-Transform II.11.17_2_0
LSR-Transform II.11.17_4_0
LSR-Transform II.11.17_5_0
LSR-Transform II.11.20_1_1
LSR-Transform II.11.27_0_0
LSR-Transform II.11.27_1_0
LSR-Transform II.11.27_3_0
LSR-Transform II.11.28_0_0
LSR-Transform II.11.3_0_0
LSR-Transform II.11.3_2_0
LSR-Transform II.11.3_3_1
LSR-Transform II.11.3_4_1
LSR-Transform II.13.23_1_0
LSR-Transform II.13.34_1_0
LSR-Transform II.15.4_1_0
LSR-Transform II.15.5_0_0
LSR-Transform II.15.5_1_0
LSR-Transform II.21.32_2_0
LSR-Transform II.21.32_3_0
LSR-Transform II.24.17_0_1
LSR-Transform II.24.17_1_1
LSR-Transform II.24.17_2_1
LSR-Transform II.27.16_2_0
LSR-Transform II.27.18_1_0
LSR-Transform II.3.24_1_0
LSR-Transform II.34.29a_2_0
LSR-Transform II.34.29b_0_0
LSR-Transform II.34.29b_2_0
LSR-Transform II.34.29b_3_0
LSR-Transform II.34.29b_4_0
LSR-Transform II.34.2_1_0
LSR-Transform II.35.18_0_0
LSR-Transform II.35.18_2_1
LSR-Transform II.35.18_3_1
LSR-Transform II.35.18_4_1
LSR-Transform II.35.21_2_1
LSR-Transform II.36.38_0_0
LSR-Transform II.36.38_1_0
LSR-Transform II.36.38_3_0
LSR-Transform II.36.38_4_0
LSR-Transform II.36.38_5_0
LSR-Transform II.36.38_7_0
LSR-Transform II.37.1_0_0
LSR-Transform II.37.1_1_0
LSR-Transform II.37.1_2_0
LSR-Transform II.6.15a_1_0
LSR-Transform II.6.15a_2_0
LSR-Transform II.6.15a_3_1
LSR-Transform II.6.15a_4_1
LSR-Transform II.6.15a_5_0
LSR-Transform II.6.15b_1_0
LSR-Transform II.6.15b_3_0
LSR-Transform II.8.31_1_0
LSR-Transform III.10.19_1_1
LSR-Transform III.10.19_2_1
LSR-Transform III.10.19_3_1
LSR-Transform III.12.43_0_0
LSR-Transform III.13.18_0_0
LSR-Transform III.13.18_1_1
LSR-Transform III.15.12_0_0
LSR-Transform III.15.14_1_0
LSR-Transform III.15.27_1_0
LSR-Transform III.15.27_2_0
LSR-Transform III.17.37_0_0
LSR-Transform III.17.37_1_0
LSR-Transform III.19.51_1_0
LSR-Transform III.19.51_3_0
LSR-Transform III.21.20_2_0
LSR-Transform III.21.20_3_0
LSR-Transform III.4.33_3_0
LSR-Transform III.9.52_0_0
LSR-Transform III.9.52_1_0

3.2 · Nonlinear oscillator dynamics — 44

LSR-Synth Phys Oscillator PO0
LSR-Synth Phys Oscillator PO1
LSR-Synth Phys Oscillator PO10
LSR-Synth Phys Oscillator PO11
LSR-Synth Phys Oscillator PO12
LSR-Synth Phys Oscillator PO13
LSR-Synth Phys Oscillator PO14
LSR-Synth Phys Oscillator PO15
LSR-Synth Phys Oscillator PO16
LSR-Synth Phys Oscillator PO17
LSR-Synth Phys Oscillator PO18
LSR-Synth Phys Oscillator PO19
LSR-Synth Phys Oscillator PO2
LSR-Synth Phys Oscillator PO20
LSR-Synth Phys Oscillator PO21
LSR-Synth Phys Oscillator PO22
LSR-Synth Phys Oscillator PO23
LSR-Synth Phys Oscillator PO24
LSR-Synth Phys Oscillator PO25
LSR-Synth Phys Oscillator PO26
LSR-Synth Phys Oscillator PO27
LSR-Synth Phys Oscillator PO28
LSR-Synth Phys Oscillator PO29
LSR-Synth Phys Oscillator PO3
LSR-Synth Phys Oscillator PO30
LSR-Synth Phys Oscillator PO31
LSR-Synth Phys Oscillator PO32
LSR-Synth Phys Oscillator PO33
LSR-Synth Phys Oscillator PO34
LSR-Synth Phys Oscillator PO35
LSR-Synth Phys Oscillator PO36
LSR-Synth Phys Oscillator PO37
LSR-Synth Phys Oscillator PO38
LSR-Synth Phys Oscillator PO39
LSR-Synth Phys Oscillator PO4
LSR-Synth Phys Oscillator PO40
LSR-Synth Phys Oscillator PO41
LSR-Synth Phys Oscillator PO42
LSR-Synth Phys Oscillator PO43
LSR-Synth Phys Oscillator PO5
LSR-Synth Phys Oscillator PO6
LSR-Synth Phys Oscillator PO7
LSR-Synth Phys Oscillator PO8
LSR-Synth Phys Oscillator PO9

3.3 · Chemical reaction kinetics — 36

LSR-Synth Chem ReactKinetics CRK0
LSR-Synth Chem ReactKinetics CRK1
LSR-Synth Chem ReactKinetics CRK10
LSR-Synth Chem ReactKinetics CRK11
LSR-Synth Chem ReactKinetics CRK12
LSR-Synth Chem ReactKinetics CRK13
LSR-Synth Chem ReactKinetics CRK14
LSR-Synth Chem ReactKinetics CRK15
LSR-Synth Chem ReactKinetics CRK16
LSR-Synth Chem ReactKinetics CRK17
LSR-Synth Chem ReactKinetics CRK18
LSR-Synth Chem ReactKinetics CRK19
LSR-Synth Chem ReactKinetics CRK2
LSR-Synth Chem ReactKinetics CRK20
LSR-Synth Chem ReactKinetics CRK21
LSR-Synth Chem ReactKinetics CRK22
LSR-Synth Chem ReactKinetics CRK23
LSR-Synth Chem ReactKinetics CRK24
LSR-Synth Chem ReactKinetics CRK25
LSR-Synth Chem ReactKinetics CRK26
LSR-Synth Chem ReactKinetics CRK27
LSR-Synth Chem ReactKinetics CRK28
LSR-Synth Chem ReactKinetics CRK29
LSR-Synth Chem ReactKinetics CRK3
LSR-Synth Chem ReactKinetics CRK30
LSR-Synth Chem ReactKinetics CRK31
LSR-Synth Chem ReactKinetics CRK32
LSR-Synth Chem ReactKinetics CRK33
LSR-Synth Chem ReactKinetics CRK34
LSR-Synth Chem ReactKinetics CRK35
LSR-Synth Chem ReactKinetics CRK4
LSR-Synth Chem ReactKinetics CRK5
LSR-Synth Chem ReactKinetics CRK6
LSR-Synth Chem ReactKinetics CRK7
LSR-Synth Chem ReactKinetics CRK8
LSR-Synth Chem ReactKinetics CRK9

3.4 · Materials laws — 25

LSR-Synth MatSci MatSci0
LSR-Synth MatSci MatSci1
LSR-Synth MatSci MatSci10
LSR-Synth MatSci MatSci11
LSR-Synth MatSci MatSci12
LSR-Synth MatSci MatSci13
LSR-Synth MatSci MatSci14
LSR-Synth MatSci MatSci16
LSR-Synth MatSci MatSci18
LSR-Synth MatSci MatSci19
LSR-Synth MatSci MatSci2
LSR-Synth MatSci MatSci20
LSR-Synth MatSci MatSci21
LSR-Synth MatSci MatSci22
LSR-Synth MatSci MatSci23
LSR-Synth MatSci MatSci24
LSR-Synth MatSci MatSci25
LSR-Synth MatSci MatSci28
LSR-Synth MatSci MatSci3
LSR-Synth MatSci MatSci4
LSR-Synth MatSci MatSci5
LSR-Synth MatSci MatSci6
LSR-Synth MatSci MatSci7
LSR-Synth MatSci MatSci8
LSR-Synth MatSci MatSci9

3.5 · Population dynamics — 24

LSR-Synth Bio PopGrowth BPG0
LSR-Synth Bio PopGrowth BPG1
LSR-Synth Bio PopGrowth BPG10
LSR-Synth Bio PopGrowth BPG11
LSR-Synth Bio PopGrowth BPG12
LSR-Synth Bio PopGrowth BPG13
LSR-Synth Bio PopGrowth BPG14
LSR-Synth Bio PopGrowth BPG15
LSR-Synth Bio PopGrowth BPG16
LSR-Synth Bio PopGrowth BPG17
LSR-Synth Bio PopGrowth BPG18
LSR-Synth Bio PopGrowth BPG19
LSR-Synth Bio PopGrowth BPG2
LSR-Synth Bio PopGrowth BPG20
LSR-Synth Bio PopGrowth BPG21
LSR-Synth Bio PopGrowth BPG22
LSR-Synth Bio PopGrowth BPG23
LSR-Synth Bio PopGrowth BPG3
LSR-Synth Bio PopGrowth BPG4
LSR-Synth Bio PopGrowth BPG5
LSR-Synth Bio PopGrowth BPG6
LSR-Synth Bio PopGrowth BPG7
LSR-Synth Bio PopGrowth BPG8
LSR-Synth Bio PopGrowth BPG9

3.6 · Scaling laws — 8

Data-Constrained Scaling Law
Domain Mixture Scaling Law
Learning Rate & Batch Size Scaling Law
Mixture-of-Experts Scaling Law
Parallel Scaling Law
Supervised Finetuning Scaling Law
U-Shaped Scaling Law
Vocabulary Scaling Law

4 · Mathematical Discovery — 259 tasks

Open mathematical problems whose deliverable is a better construction, configuration, set, sequence, or bound.

4.1 · Shape packing — 184

AlphaEvolve: Packing Circles, Max Sum of Radii (n=26)
Circle Packing (n=26)
Circle Packing in a Rectangle
Circle Packing with Artifacts
Circles in a Circle (n=11)
Circles in a Circle (n=12)
Circles in a Circle (n=14)
Circles in a Circle (n=16)
Circles in a Circle (n=17)
Circles in a Circle (n=20)
Circles in a Circle (n=5)
Circles in a Hexagon (n=15)
Circles in a Hexagon (n=22)
Circles in a Hexagon (n=24)
Circles in a Hexagon (n=8)
Circles in a Pentagon (n=13)
Circles in a Pentagon (n=23)
Circles in a Pentagon (n=7)
Circles in a Square (n=10)
Circles in a Square (n=13)
Circles in a Square (n=17)
Circles in a Square (n=19)
Circles in a Triangle (n=11)
Circles in a Triangle (n=13)
Circles in a Triangle (n=8)
Dominoes in a Circle (n=17)
Dominoes in a Circle (n=4)
Dominoes in a Circle (n=9)
Dominoes in a Hexagon (n=16)
Dominoes in a Hexagon (n=3)
Dominoes in a Hexagon (n=9)
Dominoes in a Octagon (n=10)
Dominoes in a Octagon (n=17)
Dominoes in a Octagon (n=5)
Dominoes in a Pentagon (n=11)
Dominoes in a Pentagon (n=19)
Dominoes in a Pentagon (n=5)
Dominoes in a Square (n=13)
Dominoes in a Square (n=19)
Dominoes in a Square (n=5)
Dominoes in a Triangle (n=14)
Dominoes in a Triangle (n=26)
Dominoes in a Triangle (n=7)
Hexagon Packing (n=11)
Hexagon Packing (n=12)
Hexagons in a Circle (n=13)
Hexagons in a Circle (n=17)
Hexagons in a Circle (n=22)
Hexagons in a Circle (n=4)
Hexagons in a Circle (n=5)
Hexagons in a Circle (n=8)
Hexagons in a Octagon (n=12)
Hexagons in a Octagon (n=21)
Hexagons in a Octagon (n=5)
Hexagons in a Pentagon (n=17)
Hexagons in a Pentagon (n=3)
Hexagons in a Pentagon (n=9)
Hexagons in a Square (n=13)
Hexagons in a Square (n=26)
Hexagons in a Square (n=5)
Hexagons in a Triangle (n=13)
Hexagons in a Triangle (n=23)
Hexagons in a Triangle (n=6)
Kissing Cylinders (N=7)
Octagons in a Circle (n=11)
Octagons in a Circle (n=16)
Octagons in a Circle (n=20)
Octagons in a Circle (n=3)
Octagons in a Circle (n=5)
Octagons in a Circle (n=7)
Octagons in a Hexagon (n=17)
Octagons in a Hexagon (n=3)
Octagons in a Hexagon (n=9)
Octagons in a Octagon (n=14)
Octagons in a Octagon (n=28)
Octagons in a Octagon (n=6)
Octagons in a Pentagon (n=13)
Octagons in a Pentagon (n=3)
Octagons in a Pentagon (n=7)
Octagons in a Square (n=13)
Octagons in a Square (n=19)
Octagons in a Square (n=6)
Octagons in a Triangle (n=11)
Octagons in a Triangle (n=16)
Octagons in a Triangle (n=2)
Octagons in a Triangle (n=22)
Packing Unit Cubes (n=11)
Packing Circles, Max Sum of Radii (n=32)
Pentagons in a Circle (n=12)
Pentagons in a Circle (n=16)
Pentagons in a Circle (n=20)
Pentagons in a Circle (n=4)
Pentagons in a Circle (n=7)
Pentagons in a Circle (n=9)
Pentagons in a Hexagon (n=12)
Pentagons in a Hexagon (n=20)
Pentagons in a Hexagon (n=5)
Pentagons in a Octagon (n=11)
Pentagons in a Octagon (n=23)
Pentagons in a Octagon (n=5)
Pentagons in a Pentagon (n=17)
Pentagons in a Pentagon (n=25)
Pentagons in a Pentagon (n=7)
Pentagons in a Square (n=12)
Pentagons in a Square (n=19)
Pentagons in a Square (n=5)
Pentagons in a Triangle (n=14)
Pentagons in a Triangle (n=27)
Pentagons in a Triangle (n=5)
Squares in a Circle (n=11)
Squares in a Circle (n=13)
Squares in a Circle (n=18)
Squares in a Circle (n=19)
Squares in a Circle (n=25)
Squares in a Circle (n=3)
Squares in a Circle (n=33)
Squares in a Circle (n=6)
Squares in a Circle (n=8)
Squares in a Hexagon (n=21)
Squares in a Hexagon (n=27)
Squares in a Hexagon (n=38)
Squares in a Hexagon (n=9)
Squares in a Octagon (n=19)
Squares in a Octagon (n=29)
Squares in a Octagon (n=8)
Squares in a Pentagon (n=16)
Squares in a Pentagon (n=24)
Squares in a Pentagon (n=3)
Squares in a Square (n=10)
Squares in a Square (n=11)
Squares in a Square (n=17)
Squares in a Square (n=19)
Squares in a Triangle (n=22)
Squares in a Triangle (n=38)
Squares in a Triangle (n=8)
Tans in a Circle (n=11)
Tans in a Circle (n=15)
Tans in a Circle (n=18)
Tans in a Circle (n=20)
Tans in a Circle (n=5)
Tans in a Circle (n=7)
Tans in a Hexagon (n=11)
Tans in a Hexagon (n=18)
Tans in a Hexagon (n=5)
Tans in a Octagon (n=11)
Tans in a Octagon (n=19)
Tans in a Octagon (n=5)
Tans in a Pentagon (n=11)
Tans in a Pentagon (n=19)
Tans in a Pentagon (n=5)
Tans in a Square (n=13)
Tans in a Square (n=17)
Tans in a Square (n=24)
Tans in a Square (n=5)
Tans in a Triangle (n=10)
Tans in a Triangle (n=16)
Tans in a Triangle (n=22)
Tans in a Triangle (n=4)
Triangles in a Circle (n=11)
Triangles in a Circle (n=13)
Triangles in a Circle (n=16)
Triangles in a Circle (n=19)
Triangles in a Circle (n=21)
Triangles in a Circle (n=27)
Triangles in a Circle (n=4)
Triangles in a Circle (n=7)
Triangles in a Hexagon (n=13)
Triangles in a Hexagon (n=25)
Triangles in a Hexagon (n=47)
Triangles in a Hexagon (n=7)
Triangles in a Octagon (n=11)
Triangles in a Octagon (n=24)
Triangles in a Octagon (n=5)
Triangles in a Pentagon (n=28)
Triangles in a Pentagon (n=5)
Triangles in a Pentagon (n=9)
Triangles in a Square (n=11)
Triangles in a Square (n=17)
Triangles in a Square (n=26)
Triangles in a Square (n=36)
Triangles in a Triangle (n=17)
Triangles in a Triangle (n=38)
Triangles in a Triangle (n=50)
Triangles in a Triangle (n=6)

4.2 · Analytic inequalities — 27

3D Moving Sofa
Ambidextrous Moving Sofa (2D)
Beat the Average Game
Block Stacking Overhang
Borcea's Conjecture (p=1, n=5)
Classical Inequalities (Hausdorff-Young)
Crouzeix's Conjecture (extremal ratio)
de Bruin-Sharma Inequality (n=5)
Erdos Minimum Overlap
Fast Matrix Multiplication
First Autocorrelation Inequality
First Autocorrelation Inequality (upper bound C_1)
Flat Polynomials / Golay's Conjecture (n=26)
Gagliardo-Nirenberg Inequality (p=4)
Matrix Multiplications & AM-GM (Duchi ratio)
Moving Sofa 2D (single turn)
Ovals Problem (Benguria-Loss curvature eigenvalue)
Rudin Problem for Polynomials (L4/L2, degree 10)
Schmeisser's Conjecture (n=5)
Second Autocorrelation Inequality
Sendov's Conjecture (n=8)
Smale's Mean Value Problem (n=12)
Sphere Packing LP Bound (Laguerre, m=6, n=25)
Third Autocorrelation Inequality
Uncertainty Inequality
Uncertainty Principle (Laguerre double roots, m=7)
Young's Convolution Inequality

4.3 · Extremal combinatorics — 23

Arithmetic Kakeya (entropy ratio)
Autocorrelation & Difference Bases (n=20)
Difference Bases (minimize |B|^2/k)
Edges vs Triangles (AlphaEvolve)
Erdos Discrepancy (discrepancy <= 2)
Erdős Squarefree Problem (N=500)
Erdős–Gyárfás Conjecture (min-degree-3 graph, no power-of-2 cycle)
Finite Field Kakeya (F_p^3)
Finite Field Kakeya (F_p^4)
Finite Field Kakeya (F_p^5)
Finite Field Nikodym (F_p^3)
Finite-Field Nikodym Set (F_q^2, q=p^2)
Finite-Field Sum-Product Problem
Furstenberg-Sárközy Set (Z/205Z, squares)
IMO 2025 Problem 6 -- Grid Tiling (n=2025)
Kakeya Needle (2D triangle union)
Kakeya Needle Set (3-D, N=8)
Ring Loading Problem (m=15)
Sidorenko's Conjecture (K_{5,5} minus a matching)
Sum-Difference Problem II (dilatation ratio)
Sums and Differences (Ruzsa MSTD set)
Sums and Differences of Finite Sets
Tetrahedron Hypergraph Turan Density

4.4 · Point configuration geometry — 15

Equidistant Points in Convex Polygons (n=20)
Erdos-Szekeres Happy Ending (k=7)
Fejes-Toth: Points on a Sphere (n=6)
Heilbronn Convex Region (n=13)
Heilbronn Convex Region (n=14)
Heilbronn Triangle (n=11)
Isosceles-Free Grid Subset (n=64)
Kissing Number (d=11)
Min Max-Min Distance Ratio (d=2)
Min Max-Min Distance Ratio (d=3)
No 5 on a Sphere (n=8)
Spherical t-Design (d=2, t=15, N=120)
Szemerédi–Trotter Incidences (n=128 points, m=64 lines)
Tammes Problem (n=32)
Thomson Problem (n=32)

4.5 · Black-box optimization — 5

Adaptive Signal Processing
BBOPlace ISPD2005 (MGO macro placement, 6 benchmarks)
Function Minimization
K-Module Pipeline Configuration
TSP Tour-Length Minimization

4.6 · Discrete geometry — 2

Erdos Unit Distance (demo, n=10)
Erdos Unit Distance (n=65536)

4.7 · Number theory — 2

Factoring N! into N factors (N=100)
Prime Number Theorem (partial function)

4.8 · Best known linear codes — 1

Best Known Linear Code — binary [40, 20]

5 · Competitive Programming — 233 tasks

Problems whose deliverable is a program solving a contest-style task, grouped by the kind of algorithmic challenge.

5.1 · Heuristic optimization — 87

ahc001
ahc002
ahc003
ahc004
ahc005
ahc006
ahc007
ahc008
ahc009
ahc010
ahc011
ahc012
ahc014
ahc015
ahc016
ahc017
ahc019
ahc020
ahc021
ahc024
ahc025
ahc026
ahc027
ahc028
ahc031
ahc032
ahc033
ahc034
ahc035
ahc038
ahc039
ahc040
ahc041
ahc042
ahc044
ahc045
ahc046
future-contest-2022-qual
problem_0
problem_111
problem_112
problem_149
problem_15
problem_150
problem_151
problem_152
problem_153
problem_154
problem_155
problem_156
problem_157
problem_158
problem_159
problem_160
problem_161
problem_162
problem_163
problem_164
problem_165
problem_166
problem_167
problem_168
problem_169
problem_170
problem_171
problem_188
problem_189
problem_210
problem_225
problem_227
problem_228
problem_229
problem_24
problem_241
problem_301
problem_302
problem_303
problem_304
problem_44
problem_45
problem_46
problem_48
problem_50
problem_72
problem_81
problem_83
toyota2023summer-final

5.2 · Interactive query problems — 65

ahc030
problem_10
problem_101
problem_104
problem_106
problem_107
problem_108
problem_109
problem_110
problem_113
problem_120
problem_122
problem_123
problem_124
problem_125
problem_127
problem_13
problem_132
problem_133
problem_134
problem_135
problem_14
problem_140
problem_141
problem_143
problem_144
problem_147
problem_148
problem_16
problem_17
problem_203
problem_209
problem_217
problem_222
problem_231
problem_233
problem_245
problem_249
problem_252
problem_253
problem_254
problem_255
problem_256
problem_257
problem_258
problem_28
problem_3
problem_30
problem_36
problem_4
problem_40
problem_52
problem_53
problem_54
problem_59
problem_63
problem_64
problem_68
problem_70
problem_73
problem_79
problem_80
problem_86
problem_89
problem_93

5.3 · Constructive algorithm problems — 56

problem_1
problem_11
problem_117
problem_119
problem_121
problem_137
problem_138
problem_142
problem_145
problem_2
problem_205
problem_207
problem_211
problem_212
problem_213
problem_214
problem_22
problem_220
problem_23
problem_239
problem_248
problem_26
problem_263
problem_27
problem_305
problem_306
problem_307
problem_308
problem_309
problem_310
problem_311
problem_312
problem_313
problem_314
problem_315
problem_33
problem_35
problem_41
problem_42
problem_43
problem_47
problem_5
problem_57
problem_58
problem_6
problem_60
problem_61
problem_62
problem_69
problem_7
problem_75
problem_77
problem_8
problem_82
problem_85
problem_9

5.4 · Constraint satisfaction — 20

problem_174
problem_175
problem_176
problem_177
problem_178
problem_179
problem_180
problem_181
problem_182
problem_183
problem_184
problem_185
problem_186
problem_187
problem_192
problem_193
problem_243
problem_247
problem_25
problem_87

5.5 · Applied coding — 4

Adaptive Sort (Rust)
Online Judge Programming
Robust Regression (R)
Web Scraper Prompt

5.6 · Maximum satisfiability — 1

MAX-3SAT on SATLIB uuf250-1065 (10 instances)

6 · High-Performance Algorithms — 157 tasks

Take a correct reference implementation and make it faster while preserving its output.

6.1 · Mathematical optimization — 33

Aircraft Wing Design
Battery Scheduling
Channel Capacity
Chebyshev Center
CVAR Projection
Earth Movers Distance
Group Lasso
Kalman Filter
Kmeans
L0 Pruning
L1 Pruning
LP Box
LP Centering
LP MDP
Markowitz
Matrix Completion
Minimum Volume Ellipsoid
NMF
Optimal Advertising
Power Control
QP
Queuing
Robust Kalman Filter
Robust Linear Program
Rocket Landing Optimization
Sinkhorn
Sparse PCA
SVM
Tensor Completion 3D
Unit Simplex Projection
Vector Quantization
Wasserstein Dist
Water Filling

6.2 · Linear algebra — 29

Cholesky Factorization
Complex Eigenvectors
Eigenvalues Complex
Eigenvalues Real
Eigenvectors Real
Generalized Eigenvalues Complex
Generalized Eigenvalues Real
Generalized Eigenvectors Complex
Generalized Eigenvectors Real
Linear System Solver
LU Factorization
Matrix Exponential
Matrix Exponential Sparse
Matrix Multiplication
Matrix Sqrt
Outer Product
Procrustes
PSD Cone Projection
QR Factorization
QZ Factorization
Randomized SVD
RBF Interpolation
Sparse Eigenvectors Complex
Sparse Lowest Eigenvalues Posdef
Sparse Lowest Eigenvectors Posdef
SVD
Sylvester Solver
Toeplitz Solver
Two Eigenvalues Around 0

6.3 · Discrete optimization — 19

BTSP
Capacitated Facility Location
Dynamic Assortment Planning
Graph Coloring Assign
Job Shop Scheduling
Kcenters
Max Weighted Independent Set
Maximum Clique
Maximum Independent Set
Min Dominating Set
Multi Dim Knapsack
Queens With Obstacles
Rectanglepacking
Set Cover
Set Cover Conflicts
Stable Matching
TSP
Vehicle Routing
Vertex Cover

6.4 · Numerical methods — 19

Count Riemann Zeta Zeros
Cumulative Simpson 1D
Cumulative Simpson Multid
Elementwise Integration
ODE Brusselator
ODE Fitzhughnagumo
ODE Hires
ODE Hodgkinhuxley
ODE Lorenz96 Nonchaotic
ODE Lotkavolterra
ODE Nbodyproblem
ODE Seirs
ODE Stiff Robertson
ODE Stiff Vanderpol
PDE Burgers1d
PDE Heat1d
Polynomial Mixed
Real Polynomial Roots
Vectorized Newton

6.5 · Graph algorithms — 16

Articulation Points
Communicability
Count Connected Components
Cyclic Independent Set
Dijkstra From Indices
Edge Expansion
Graph Global Efficiency
Graph Isomorphism
Graph Laplacian
Max Common Subgraph
Max Flow Min Cost
Min Weight Assignment
Minimum Spanning Tree
Pagerank
Shortest Path Dijkstra
Spectral Clustering

6.6 · Signal processing — 15

2D Affine Transform
2D Convolution (full)
Complex N-D FFT
Convolve 1D
Correlate 1D
Correlate2d Full Fill
DCT Type I
DST Type II
FFT Convolution
Firls
Real FFT
Rotate 2D
Shift 2D
Upfirdn1d
Zoom 2D

6.7 · Statistical estimation — 9

Clustering Outliers
Kernel Density Estimation
KS Test 2samp
Lasso
Least Squares
ODR
PCA
Quantile Regression
Frontier-Bench — Lake Temperature GLM

6.8 · Cryptography — 5

AES GCM Encryption
Chacha Encryption
Discrete Log
Integer Factorization
Sha256 Hashing

6.9 · Computational geometry — 4

Convex Hull
Delaunay
KD Tree
Voronoi Diagram

6.10 · Control — 4

Feedback Controller Design
LQR
LTI Simulation
Lyapunov Stability

6.11 · Data compression — 2

Base64 Encoding
Gzip Compression

6.12 · Iterative solvers — 1

Sparse Approximate-Inverse Preconditioner for CG (SuiteSparse SPD systems)

6.13 · Lattice challenges — 1

TU Darmstadt SVP Challenge — dimension 40, seed 0

7 · Quantum Computing — 2 tasks

Improve quantum circuits and error-correction decoders under exact physical or logical checks.

7.1 · QEC decoder design — 1

Surface-Code Decoder Design (distance 5, circuit-level noise)

7.2 · Quantum circuit optimization — 1

Two-Qubit Gate Count Reduction under Strict Unitary Equivalence

8 · Single-cell Genomics — 21 tasks

Single-cell analysis methods, one task per analysis problem or benchmark protocol.

8.1 · Biological inference — 6

Open Problems: Cell-Cell Communication
Open Problems: Differential expression
Open Problems: GRN Inference
Open Problems: Label projection
Open Problems: Perturbation Prediction
Open Problems: Predict Modality

8.2 · Preprocessing — 6

Open Problems: Batch Integration
Open Problems: Cyto Batch Integration
Open Problems: Denoising
Open Problems: Dimensionality Reduction for Visualization
Open Problems: Foundation models
Open Problems: iST Preprocessing

8.3 · OpenProblems BioML-Bench — 5

BioML-Bench: Cell-Cell Communication (OpenProblems)
BioML-Bench: Label Projection (OpenProblems)
BioML-Bench: Predict Modality (OpenProblems)
BioML-Bench: Single-Cell Perturbations (OpenProblems)
BioML-Bench: Spatially Variable Genes (OpenProblems)

8.4 · Spatial transcriptomics — 4

Open Problems: Spatial Decomposition
Open Problems: Spatial Segmentation
Open Problems: Spatial Simulators
Open Problems: Spatially Variable Genes

9 · Computational Biology — 8 tasks

Predict protein fitness from sequence and construct biologically faithful sequence alignments.

9.1 · ProteinGym DMS — 6

BioML-Bench: CBX4 Stability (ProteinGym)
BioML-Bench: CSN4 Indels (ProteinGym)
BioML-Bench: PSAE Stability (ProteinGym)
BioML-Bench: MtrA Indels (ProteinGym)
BioML-Bench: Sbi Stability (ProteinGym)
BioML-Bench: Spike RBD ACE2 Binding (ProteinGym)

9.2 · ProteinGym Kermut — 1

AutoScientists: ProteinGym Spike (Kermut evolution)

9.3 · Multiple sequence alignment — 1

Multiple Sequence Alignment — BAliBASE 3.0 RV11 (10 instances)

10 · Biomedical Imaging — 4 tasks

Predict clinically relevant outcomes and segment anatomy from histology, CT, and MRI data.

10.1 · Kaggle BioML-Bench — 4

BioML-Bench: Histopathologic Cancer Detection (Kaggle)
BioML-Bench: OSIC Pulmonary Fibrosis Progression (Kaggle)
BioML-Bench: RSNA-MICCAI Brain Tumor MGMT (Kaggle)
BioML-Bench: UW-Madison GI Tract Segmentation (Kaggle)

11 · Drug Discovery — 9 tasks

Predict molecular properties from chemical structure representations.

11.1 · Molecular property prediction — 9

BioML-Bench: Aqueous Solubility (Polaris/ADME-Fang)
BioML-Bench: Blood-Brain Barrier (TDCommons/Martins)
BioML-Bench: Caco-2 Permeability (TDCommons)
BioML-Bench: CYP2D6 Substrate (TDCommons)
BioML-Bench: EGFR WT Kinase Inhibition (Polaris/PKIS2)
BioML-Bench: hERG Inhibition (TDCommons)
BioML-Bench: HLM Intrinsic Clearance (Polaris/ADME-Fang)
BioML-Bench: Human Plasma-Protein Binding (Polaris/ADME-Fang)
BioML-Bench: Lipophilicity (TDCommons/AstraZeneca)

12 · Systems Design — 15 tasks

Design decisions for real computing systems — cloud networking, GPU placement, database scheduling, vector search, LLM serving, and chip placement.

12.1 · Distributed systems — 5

Cloudcast Multi-Cloud Broadcast
Expert Parallelism Load Balancer (EPLB)
LLM-SQL Prefix-Cache Column Reordering
Prism GPU Model Placement
Transaction Scheduling

12.2 · Vector search — 3

Vector DB ANN (SIFT1M-scale)
Vector DB ANN Disk (SIFT100M throughput)
Vector DB ANN Relaxed (SIFT1M-scale ANN service, recall@10 >= 0.95)

12.3 · Chip placement — 2

BBOPlace Direct — ICCAD2015 superblue1 (macro placement)
BBOPlace Direct — ISPD2005 adaptec1 (macro placement)

12.4 · Diffusion sampling speedup — 1

NanoWM Rollout Speedup (fast diffusion sampling for a frozen video world model)

12.5 · LLM serving — 1

vLLM LLM-Serving Latency Optimization

12.6 · Query optimization — 1

DuckDB E2E Query Optimization (TPC-H speedup)

12.7 · VLSI placement — 1

BBOPlace Macro Placement (ICCAD2015, MGO MP-HPWL)

12.8 · World models — 1

NanoWM Rollout Stability (minimize long-horizon drift at fixed compute)

13 · Generative AI Optimization — 8 tasks

Optimizing prompts, generative outputs, and generative models of AI systems.

13.1 · Prompt optimization — 4

GSM8K Adapter
HotpotQA RAG Prompt Optimization
LLM Prompt Optimization
LLM Agents: Logic-Puzzle Prompt

13.2 · Generative modeling — 2

Crystal Structure Prediction (MP-20 polymorph split, METRe)
Crystal Structure Prediction — MaskGXT algorithm seed (MP-20-PS, METRe)

13.3 · Game-playing agents — 1

Generals.io Bot Arena

13.4 · Generative outputs — 1

Floating Sky Festival (Image Generation)

Browse the live catalog

Every task is browsable on the Hub — open a task card to see its metric, seed program, and evaluator.