convergence

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#convergence

Emergence via Phase Transitions: Mechanism Landscapes and Universal Convergence Across Complex Systems

arXiv cs.LG · 5d ago Cached

This paper introduces the Hierarchical Emergence Framework (HEF), which explains how diverse systems such as neural networks and biological evolution converge to similar internal representations through phase transitions in mechanism landscapes under physical and informational constraints. The framework is validated empirically with 111 grokking experiments that confirm universal convergence and identify a critical energy threshold.

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#convergence

Towards Serverless Semi-Decentralized Federated Learning with Heterogeneous Optimizers

arXiv cs.LG · 6d ago Cached

Proposes SSD-FL, a serverless semi-decentralized federated learning methodology that optimizes cluster formation in heterogeneous environments using effective loss functions and Cheeger inequality-based iterative clustering, improving convergence and communication efficiency.

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#convergence

Convergence of Steepest Descent and Adam under Non-Uniform Smoothness

arXiv cs.LG · 2026-06-01 Cached

This paper generalizes non-uniform smoothness assumptions to objectives whose curvature is affine in the objective value, proving convergence rates for steepest descent and diagonal variants of RMSProp and Adam, with applications to logistic regression and neural networks.

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#convergence

A Unified Framework for Gradient Aggregation in Multi-Objective Optimization

arXiv cs.LG · 2026-06-01 Cached

This paper presents a unified theoretical framework for gradient aggregation in multi-objective optimization, establishing convergence rates to Pareto stationarity. The authors introduce a sufficient alignment condition and demonstrate its application to existing and new algorithms, such as capped MGDA.

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#convergence

Agentic Patterns

Hacker News Top · 2026-05-25 Cached

A comprehensive research guide from Veso detailing the universal architecture patterns that have converged across major AI agent systems (Claude Code, OpenAI Codex, Gemini CLI, etc.), presenting 8 postulates for building production-grade agentic systems.

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#convergence

DynMuon: A Dynamic Spectral Shaping View of Muon

Hugging Face Daily Papers · 2026-05-16 Cached

This paper introduces DynMuon, a dynamic spectral shaping optimizer that schedules the update parameter p from positive to mildly negative during training, consistently achieving lower validation loss and requiring 10.6-26.5% fewer steps than the standard Muon optimizer.

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