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Three taxonomies across the corpus: what an idea solves, where it lands in ML, and which math it uses.

Solves

Stability 2538 Accuracy 2136 Generalization 1253 Sample efficiency 740 Speedup 689 Scalability 655 Memory 493 Inference speedup 44 Speed 26 Regularization 3 Training 2 Initialization 1 Sampling 1 Training dynamics 1

ML areas

Training dynamics 1326 Regularization 1021 Optimizer 797 Ssm 735 Rnn 638 Graph nn 567 World model 552 Transformer 509 Mlp 441 Attention 406 Embedding 397 Loss 374 Inference speedup 364 Training 351 Moe routing 299 Rl 222 Cnn 185 Scheduler 169 Memory 165 Initialization 161 Fine tuning 136 Diffusion 121 Architecture 115 Diffusion sampling 107 Vae 99 Data augmentation 87 Quantization 73 Pruning 60 Geometry 37 Kv cache 35 Retrieval 32 Federated 28 Sampling 28 Curriculum 21 Distillation 20 Batching 19 Gan 15 Rlhf 13 Dynamics 9 Neural operator 8 Tokenizer 8 Normalization 5 Representation 5 Pde 4 Distributed 3 Resnet 3 Sample efficiency 3 Scalability 3 Autoencoder 2 Compression 2 Contrastive learning 2 Pooling 2 Sparsity 2 Uncertainty 2 Active learning 1 Conditioning 1 Convolution 1 Distributional rl 1 Few shot 1 Generalization 1

Math fields

Dynamical systems 1490 Linear algebra 1271 Optimization 979 Probability 752 Control theory 699 Geometry 682 Spectral theory 522 Numerical analysis 460 Statistics 408 Stochastic processes 407 Graph theory 366 Combinatorics 360 Convex analysis 359 Functional analysis 292 Approximation theory 276 Harmonic analysis 216 Information theory 205 Pde 203 Statistical mechanics 169 Algebra 162 Differential geometry 153 Bifurcations 142 Measure theory 130 Representation theory 97 Optimal transport 95 Metric geometry 88 Random matrix 72 Topology 72 Tensor decomposition 64 Lie groups 53 Inequalities 25 Renormalization 25 Stability 25 Symplectic 21 Computation 19 Number theory 19 Algebraic topology 17 Complex analysis 16 Group theory 14 Game theory 13 Analysis 12 Logic 9 Hamiltonian 8 Category theory 7 Operator theory 7 Matrix analysis 6 Symmetry 6 Calculus of variations 4 Fractional analysis 4 Scaling 4 Asymptotic analysis 3 Dynamic programming 3 Dynamic systems 3 Dynamics 3 Generating functions 3 Polynomial 3 Regularization 3 Robust statistics 3 Singular perturbation 3 Special functions 3

SynthCore

An autonomous research pipeline: reads recent arXiv mathematics papers, extracts concrete machine-learning ideas, and tests them empirically — a mechanism check first, then a benchmark against a tuned baseline. Verdicts are computed by deterministic test code.

AI-generated research hypotheses, automatically tested. Not peer-reviewed.

Contact: contact@synthcore.org

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All ideas Beat the baseline Mechanism confirmed Analyzed papers

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SynthCore — autonomous math → ML research. Built by Maxim Zhivotok. 2026. Every idea is available as structured JSON via /api/idea/{id}.json.