Relative Geometry of Neural Forecasters: Linking Accuracy and Alignment in Learned Latent Geometry
This work addresses the challenge of interpreting neural network representations for researchers in machine learning and dynamical systems, though it is incremental in linking geometry to performance.
The study tackled the problem of understanding how neural networks internally represent the latent geometry of dynamical systems by introducing relative embeddings to remove ambiguities. It found that alignment between models correlates with forecasting accuracy across seven systems, but high accuracy can occur with low alignment.
Neural networks can accurately forecast complex dynamical systems, yet how they internally represent underlying latent geometry remains poorly understood. We study neural forecasters through the lens of representational alignment, introducing anchor-based, geometry-agnostic relative embeddings that remove rotational and scaling ambiguities in latent spaces. Applying this framework across seven canonical dynamical systems - ranging from periodic to chaotic - we reveal reproducible family-level structure: multilayer perceptrons align with other MLPs, recurrent networks with RNNs, while transformers and echo-state networks achieve strong forecasts despite weaker alignment. Alignment generally correlates with forecasting accuracy, yet high accuracy can coexist with low alignment. Relative geometry thus provides a simple, reproducible foundation for comparing how model families internalize and represent dynamical structure.