  Reasoning from sequences of raw sensory data is a ubiquitous problem across
fields ranging from medical devices to robotics. These problems often involve
using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to
predict sequences of desirable physical quantities (e.g. force, inertial
measurements). While classical approaches are powerful for locally-linear
prediction problems, they often fall short when using real-world sensors. These
sensors are typically non-linear, are affected by extraneous variables (e.g.
vibration), and exhibit data-dependent drift. For many problems, the prediction
task is exacerbated by small labeled datasets since obtaining ground-truth
labels requires expensive equipment. In this work, we present Hierarchical
State-Space Models (HiSS), a conceptually simple, new technique for continuous
sequential prediction. HiSS stacks structured state-space models on top of each
other to create a temporal hierarchy. Across six real-world sensor datasets,
from tactile-based state prediction to accelerometer-based inertial
measurement, HiSS outperforms state-of-the-art sequence models such as causal
Transformers, LSTMs, S4, and Mamba by at least 23% on MSE. Our experiments
further indicate that HiSS demonstrates efficient scaling to smaller datasets
and is compatible with existing data-filtering techniques. Code, datasets and
videos can be found on https://hiss-csp.github.io.
