An LLM-based agent with Lean verification autonomously solved multiple open Erdős problems and OEIS conjectures in the first large-scale test.
Point convergence of nesterov’s accelerated gradient method: An ai-assisted proof
11 Pith papers cite this work. Polarity classification is still indexing.
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There exists a differentiable convex potential in R^2 such that the Nesterov ODE converges to the minimizer along a trajectory of infinite path length.
Accelerated augmented Lagrangian schemes for convex linearly constrained problems achieve o(1/k^2) rates on feasibility violation and objective residual plus iterate convergence under critical parameters.
An AI model produced a new formula for a central element of U_q(so_12) at the quality level of advanced undergraduate research, along with faster computation via SageMath, prompting changes in mentorship practices.
APAPC integrates Nesterov acceleration into primal-dual forward-backward schemes by exploiting dual strong convexity to achieve optimal sublinear and accelerated linear convergence rates.
Proves convergence to saddle points and o(1/t²) gap rates for continuous-time dynamics with α/t damping (α≥3) and for a structure-preserving discretization under a t_k sequence condition with ρ≤1.
AI scientific discovery needs a middle layer of model formation—recognizing structural inadequacy and importing missing concepts from neighboring fields—beyond search and execution.
The accelerated backward-forward method achieves O(1/k²) convergence on convex composite problems and accelerated linear convergence when the smooth component is strongly convex.
AI agents exploring Platonic mathematical structures via proof hypergraphs may reveal the overall architecture of formal mathematics and what makes parts of it human-accessible.
AI for math combines task-specific architectures and general foundation models to support research and advance AI reasoning capabilities.
AI models discovered the worst-case complexity of the Kaczmarz algorithm for solving linear systems.
citing papers explorer
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Advancing Mathematics Research with AI-Driven Formal Proof Search
An LLM-based agent with Lean verification autonomously solved multiple open Erdős problems and OEIS conjectures in the first large-scale test.
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Nesterov Flow May Travel Infinitely Long to Converge to a Minimizer
There exists a differentiable convex potential in R^2 such that the Nesterov ODE converges to the minimizer along a trajectory of infinite path length.
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Convergence of iterates and improved rates for accelerated augmented Lagrangian methods for linearly constrained convex optimization
Accelerated augmented Lagrangian schemes for convex linearly constrained problems achieve o(1/k^2) rates on feasibility violation and objective residual plus iterate convergence under critical parameters.
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Using Large Language Models as a Co-Author in Undergraduate Quantum Group Research
An AI model produced a new formula for a central element of U_q(so_12) at the quality level of advanced undergraduate research, along with faster computation via SageMath, prompting changes in mentorship practices.
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A Nesterov-Accelerated Primal-Dual Splitting Algorithm for Convex Nonsmooth Optimization
APAPC integrates Nesterov acceleration into primal-dual forward-backward schemes by exploiting dual strong convexity to achieve optimal sublinear and accelerated linear convergence rates.
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Fast primal-dual methods for convex-concave bilinear saddle point problems: continuous-time dynamics and discrete algorithms
Proves convergence to saddle points and o(1/t²) gap rates for continuous-time dynamics with α/t damping (α≥3) and for a structure-preserving discretization under a t_k sequence condition with ρ≤1.
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A Three-Layer Framework for AI in Scientific Discovery
AI scientific discovery needs a middle layer of model formation—recognizing structural inadequacy and importing missing concepts from neighboring fields—beyond search and execution.
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Accelerated Backward Forward Method for Convex Optimization
The accelerated backward-forward method achieves O(1/k²) convergence on convex composite problems and accelerated linear convergence when the smooth component is strongly convex.
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Artificial Intelligence and the Structure of Mathematics
AI agents exploring Platonic mathematical structures via proof hypergraphs may reveal the overall architecture of formal mathematics and what makes parts of it human-accessible.
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AI for Mathematics: Progress, Challenges, and Prospects
AI for math combines task-specific architectures and general foundation models to support research and advance AI reasoning capabilities.
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How AI settled the complexity of the oldest SGD algorithm
AI models discovered the worst-case complexity of the Kaczmarz algorithm for solving linear systems.