Authors - Sai Sundarakrishna, Vedant Maheshwari Abstract - Recent literature has posed LLMs as nonlinear dynamical systems. LLM safety, in these modern LLMs is about the systematic and critical monitoring of logit based oscillations, hidden state rotations and entropy fluctuations. Many of these important factors are spectral proxies for the generation of imaginary eigenvalues. These imaginary eigenvalues are, in a way, determinants of the latent oscillation energy. Though the system in its original state space is inherently nonlinear, through the Koopman operator, we can linearize the evolution in the lifted space of observables. We design a spectral jailbreak detector that has a Sparsely regularized koopman autoencoder as its backbone. We obtain the koopman operator through this SR-KAE, and also obtain the imaginary component of the eigenvalues of that spectral operator, A new risk score metric is proposed that is used to classify prompts as either jailbreak or safe. This becomes a physics-style stability classifier on prompts. We present several test cases, while we discuss the strengths and limitations of this new system.
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