Using physics-inspired Singular Learning Theory to understand grokking & other phase transitions in modern neural networks

arXiv — stat.MLTuesday, December 2, 2025 at 5:00:00 AM
  • A recent study has applied Singular Learning Theory (SLT), a physics-inspired framework, to explore the complexities of modern neural networks, particularly focusing on phenomena like grokking and phase transitions. The research empirically investigates SLT's free energy and local learning coefficients using various neural network models, aiming to bridge the gap between theoretical understanding and practical application in machine learning.
  • This development is significant as it enhances the understanding of how neural networks operate under different conditions, particularly in terms of their learning dynamics and interpretability. By addressing the limitations of classical statistical inference, the findings could lead to improved methodologies for training neural networks, ultimately benefiting various applications in artificial intelligence.
  • The exploration of grokking as a computational phenomenon highlights ongoing discussions in the field regarding the nature of learning in neural networks. This research aligns with broader trends in integrating physics-based approaches into machine learning, emphasizing the importance of understanding underlying mechanisms that govern model behavior, which is crucial for advancing AI technologies.
— via World Pulse Now AI Editorial System

Was this article worth reading? Share it

Recommended apps based on your readingExplore all apps
Continue Readings
Leaked "Soul Doc" reveals how Anthropic programs Claude’s character
PositiveArtificial Intelligence
A recently leaked internal document, referred to as the "Soul Doc," has revealed how Anthropic programs the personality and ethical guidelines of its AI model, Claude 4.5 Opus. The authenticity of this document has been confirmed by Anthropic, indicating a unique approach to AI character development in the industry.
Mistral launches Mistral 3, a family of open models designed to run on laptops, drones, and edge devices
PositiveArtificial Intelligence
Mistral AI has launched the Mistral 3 family, a suite of 10 open-source models designed for diverse applications, including smartphones, drones, and enterprise systems. This release represents a significant advancement in Mistral's efforts to compete with major tech players like OpenAI and Google, as well as emerging competitors from China.
A Claude user gets Claude 4.5 Opus to generate a 14,000-token document that Claude calls its "Soul overview"; an Anthropic staffer confirms its authenticity (Simon Willison/Simon Willison's Weblog)
PositiveArtificial Intelligence
A user of Claude has successfully utilized the Claude 4.5 Opus model to generate a comprehensive 14,000-token document, referred to as its 'Soul overview.' This document is believed to have been instrumental in shaping the model's personality during its training phase, as confirmed by an Anthropic staff member.
‘The biggest decision yet’: Jared Kaplan on allowing AI to train itself
NeutralArtificial Intelligence
Jared Kaplan, chief scientist at Anthropic, has highlighted a critical decision facing humanity by 2030 regarding the autonomy of artificial intelligence systems, which could lead to an 'intelligence explosion' or a loss of human control. This pivotal moment raises questions about the extent to which AI should be allowed to train itself and evolve independently.
Study: using the SCONE-bench benchmark of 405 smart contracts, Claude Opus 4.5, Sonnet 4.5, and GPT-5 found and developed exploits collectively worth $4.6M (Anthropic)
NeutralArtificial Intelligence
A recent study utilizing the SCONE-bench benchmark of 405 smart contracts revealed that AI models Claude Opus 4.5, Sonnet 4.5, and GPT-5 collectively identified and developed exploits valued at $4.6 million. This highlights the growing capabilities of AI in cybersecurity tasks, showcasing their potential economic impact.
Flow Equivariant Recurrent Neural Networks
PositiveArtificial Intelligence
A new study has introduced Flow Equivariant Recurrent Neural Networks (RNNs), extending equivariant network theory to dynamic transformations over time, which are crucial for processing continuous data streams. This advancement addresses the limitations of traditional RNNs that have primarily focused on static transformations, enhancing their applicability in various sequence modeling tasks.
Superposition Yields Robust Neural Scaling
NeutralArtificial Intelligence
Recent research highlights the significance of representation superposition in large language models (LLMs), suggesting that these models can represent more features than their dimensions allow, which may explain the observed neural scaling law where loss decreases as model size increases. This study utilizes weight decay to analyze how loss scales with model size under varying degrees of superposition.
Emergent Riemannian geometry over learning discrete computations on continuous manifolds
NeutralArtificial Intelligence
A recent study has revealed insights into how neural networks learn to perform discrete computations on continuous data manifolds, specifically through the lens of Riemannian geometry. The research indicates that as neural networks learn, they develop a representational geometry that allows for the discretization of continuous input features and the execution of logical operations on these features.