Exhaustive enumeration of functions up to complexity k across operator bases shows the integrability fraction declines with k but rises sharply with logarithms, and the method discovers three integrals that resist SymPy, Mathematica, RUBI, FriCAS, Maxima, and Giac.
Deep learning for symbolic mathematics.arXiv preprint arXiv:1912.01412, 2019
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GPT-f, a transformer-based prover for Metamath, generated new short proofs that were accepted into the main library—the first such contribution from a deep-learning system.
LEE performs iterative amortized inference in a functionally grounded latent space to produce 2-10x simpler symbolic expressions than strong baselines on SRBench.
FISolver trains a compact LLM on backward-generated (differential equation, first integral) pairs and uses guided reinforcement learning to outperform larger models and Mathematica on first-integral benchmarks at lower cost.
Latent Grammar Flow discovers ODEs by placing grammar-based equation representations in a discrete latent space, using a behavioral loss to cluster similar equations, and sampling via a discrete flow model guided by data fit and constraints.
k-server-bench formulates potential-function discovery for the k-server conjecture as a code-based inequality-satisfaction task; current agents fully solve the resolved k=3 case and reduce violations on the open k=4 case.
A permutation-equivariant transformer trained on self-supervised oracle trajectories from scrambled expressions achieves near-perfect simplification rates for dilogarithms and 100% success on 5-point gluon scattering amplitudes with over 200 terms.
Massive activations are constant large values in LLMs that function as indispensable bias terms and concentrate attention probabilities on specific tokens.
SIGS is a neuro-symbolic framework that discovers analytical solutions to PDEs by generating grammar-constrained expressions, embedding them in a topology-regularised latent manifold, and refining structure and coefficients against the PDE residual and boundary/initial conditions.
Physics equation corpora exhibit exponential decay in mathematical operator frequencies, proposed as a meta-law that narrows the space of plausible expressions for symbolic regression.
Introduces GSM8K dataset and demonstrates that verifier-based selection of solutions from multiple candidates outperforms fine-tuning baselines on math word problems.
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Neuro-Symbolic ODE Discovery with Latent Grammar Flow
Latent Grammar Flow discovers ODEs by placing grammar-based equation representations in a discrete latent space, using a behavioral loss to cluster similar equations, and sampling via a discrete flow model guided by data fit and constraints.