Singular Learning Theory and Transformer Dynamics

The field of neural networks is moving towards a deeper understanding of phase transitions and dynamic behavior, with a focus on physics-inspired frameworks such as Singular Learning Theory. This approach has been shown to provide valuable insights into the success of modern neural networks, which often defy explanation by classical statistical inference and learning theory. Recent research has also highlighted the importance of understanding the dynamical properties of tokens in self-attention and the effects of positional encoding on Transformer models. Furthermore, new architectures such as the Phase-Resonant Intelligent Spectral Model (PRISM) have been proposed, which encode semantic identity as resonant frequencies in the complex domain and replace quadratic self-attention with linearithmic Gated Harmonic Convolutions. Noteworthy papers include: the work on Singular Learning Theory, which empirically studies the framework in toy settings relevant to interpretability and phase transitions. The paper on PRISM, which introduces a diagnostic protocol revealing the limitations of standard Transformers and demonstrates Lossless Plasticity in real-time knowledge adaptation.

Sources

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

Pay Attention Later: From Vector Space Diffusion to Linearithmic Spectral Phase-Locking

The Mean-Field Dynamics of Transformers

Dynamical Properties of Tokens in Self-Attention and Effects of Positional Encoding

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