UnHiPPO: Uncertainty-aware Initialization for State Space Models
This work addresses a specific bottleneck in state space models for sequence problems, offering an incremental improvement by making initialization more robust to noise.
The paper tackles the problem that HiPPO initialization for state space models assumes noise-free data, which is often unrealistic, by extending the theory to include measurement noise and deriving an uncertainty-aware initialization. The result shows improved resistance to noise during training and inference, though no concrete numbers are provided in the abstract.
State space models are emerging as a dominant model class for sequence problems with many relying on the HiPPO framework to initialize their dynamics. However, HiPPO fundamentally assumes data to be noise-free; an assumption often violated in practice. We extend the HiPPO theory with measurement noise and derive an uncertainty-aware initialization for state space model dynamics. In our analysis, we interpret HiPPO as a linear stochastic control problem where the data enters as a noise-free control signal. We then reformulate the problem so that the data become noisy outputs of a latent system and arrive at an alternative dynamics initialization that infers the posterior of this latent system from the data without increasing runtime. Our experiments show that our initialization improves the resistance of state-space models to noise both at training and inference time. Find our implementation at https://cs.cit.tum.de/daml/unhippo.