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.
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author Charton, F
11 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
The grokking delay in encoder-decoder models on one-step Collatz prediction stems from decoder inability to use early-learned encoder representations of parity and residue structure, with numeral base acting as a strong inductive bias that can raise accuracy from failure to 99.8%.
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.
citing papers explorer
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Exhaustive Symbolic Integration: Integration by Differentiation and the Landscape of Symbolic Integrability
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.
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Generative Language Modeling for Automated Theorem Proving
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.
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Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learning
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.
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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.
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$k$-server-bench: Automating Potential Discovery for the $k$-Server Conjecture
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.
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The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior
The grokking delay in encoder-decoder models on one-step Collatz prediction stems from decoder inability to use early-learned encoder representations of parity and residue structure, with numeral base acting as a strong inductive bias that can raise accuracy from failure to 99.8%.
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Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories
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.
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Massive Activations in Large Language Models
Massive activations are constant large values in LLMs that function as indispensable bias terms and concentrate attention probabilities on specific tokens.
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Neuro-Symbolic AI for Analytical Solutions of Differential Equations
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.
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Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature
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.
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Training Verifiers to Solve Math Word Problems
Introduces GSM8K dataset and demonstrates that verifier-based selection of solutions from multiple candidates outperforms fine-tuning baselines on math word problems.