Preventing Model Collapse with Resonant Geodesic Dynamics

Exploring the issue of model collapse in synthetic data recursion, a speculative framework suggests using scale-invariant resonant geodesic dynamics in latent spaces. Inspired by concepts from cosmology and wave turbulence, the framework proposes that current latent spaces lack intrinsic structure, leading to degeneration when models are trained recursively on their outputs. By introducing a resonant Riemannian metric and gated geodesic flow, the framework aims to preserve harmonic structures and prevent collapse by anchoring geodesics to a resonant skeleton. Additionally, a scale-invariant coherence score is proposed to predict model stability, offering a geometric interpretation of latent space dynamics and a potential path to more stable recursive training. This matters because it provides a novel approach to enhancing the robustness and reliability of machine learning models trained on synthetic data.

The exploration of scale-invariant resonant geodesic dynamics in latent spaces presents an intriguing approach to addressing the problem of model collapse in synthetic data loops. The issue arises when models recursively train on their own outputs, leading to a gradual erosion of distribution tails and a drift towards high-probability blobs, resulting in a loss of diversity and meaningfulness in the generated data. By drawing inspiration from cosmology, wave turbulence, and geometric deep learning, the proposed framework suggests treating latent manifolds as possessing an intrinsic scale-invariant resonant structure. This approach aims to preserve harmonic ratios across scales and anchor geodesics with irreducible structural points, potentially maintaining the integrity of the latent space over recursive training cycles.

The introduction of a resonant Riemannian metric is a key component of this framework. By adding a resonance bonus for directions that phase-align under a multiscale frequency operator, the metric aims to ensure that geodesics preserve harmonic structures across scales. This preservation is crucial because it allows interpolations within the latent space to remain meaningful for longer periods, resisting the typical tail erosion seen in unconstrained probabilistic models. The concept of a gated geodesic flow further enhances this stability by introducing a velocity-dependent gating term that binds geodesics to a resonant skeleton, potentially preventing the exponential collapse often observed in synthetic loops.

A scale-invariant coherence score is proposed as a predictor of impending model collapse. This score measures the volume change in the latent space, penalized by the loss of resonance power across scales. The idea is that standard training methods lead to an exponential drop in this score, signaling a loss of multiscale structure. In contrast, resonant-gated training aims to maintain a stable coherence score, akin to how cosmic or turbulent systems resist dissipation. This approach offers a geometric interpretation of why unconstrained probabilistic latents collapse and suggests a pathway to achieving more stable recursive training without the constant need for real-data refreshes.

The speculative nature of this framework invites further exploration and experimentation. While the ideas presented are innovative, they require validation through empirical studies, potentially using Riemannian optimizers and wavelet-based regularization. The discussion around resonance and phase-alignment regularizers in latent spaces, as well as the use of “prime” or quasicrystal anchors for manifold stabilization, opens up new avenues for research. By addressing the fundamental issue of model collapse, this framework could significantly impact the development of more robust and reliable generative models, ultimately leading to better performance and more meaningful outputs in various applications.

Read the original article here