Hierarchical State Space Models for Continuous Sequence-to-Sequence Modeling (2402.10211v3)

Abstract: 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.

• The paper introduces a hierarchical approach that reduces MSE by at least 23% compared to causal Transformers and other models on sensor datasets.
• The model employs a dual temporal resolution architecture to effectively capture complex, non-linear dynamics in continuous sequence data.
• Its application on the CSP-Bench benchmark establishes a new standard for scalable and robust sequence prediction in real-world sensor scenarios.

Improving Continuous Sequence Prediction with Hierarchical State Space Models

Introduction to Continuous Sequence Prediction with HiSS

In the arena of processing and analyzing sequential sensory data, recent advancements have been heralded by the introduction of Hierarchical State Space Models (HiSS). This novel approach, tailored for continuous sequence-to-sequence prediction, capitalizes on the inherent temporal structure in sensor data to deliver improved prediction accuracy. By benchmarking against an extensive dataset comprising six real-world sensor applications, HiSS has demonstrated a significant outperformance of contemporary sequence models, namely causal Transformers, LSTMs, S4, and Mamba, by at least 23% in Mean Squared Error (MSE).

The Challenge of Continuous Sequence Prediction

Continuous sequence-to-sequence prediction necessitates the transformation of long sequences of raw sensor data into sequences representing desired physical quantities. Traditional models often falter in adequately capturing the complex, non-linear dynamics present in real-world sensor data. Furthermore, the limited availability of labeled datasets for such tasks posits additional hurdles, underscoring the need for a robust and scalable solution.

CSP-Bench: A Novel Benchmark in CSP

A critical step forward in this research was the establishment of CSP-Bench, a comprehensive benchmark explicitly curated for continuous sequence prediction tasks. Comprising six diverse real-world labeled datasets, CSP-Bench facilitates a standardized evaluation platform, unveiling the superior performance of State Space Models (SSMs) over conventional models like LSTMs and Transformers.

Delving into Hierarchical State-Space Models

The crux of HiSS lies in its hierarchical modeling architecture, stacking structured state-space models to formulate a temporal hierarchy. This design encapsulates the temporal redundancies in sensor data, enabling a distilled rendition of the input data through dual temporal resolutions. The architecture comprises a lower-level SSM that processes the data into chunks, subsequently synthesized by a higher-level SSM for global sequence prediction. This hierarchical division aligns with natural physical processes, which often exhibit behaviors across different frequency scales, thus rendering HiSS potent in disentangling and accurately predicting underlying physical quantities from noisy, high-dimensional sensor data.

Empirical Validation and Insights

Empirical scrutiny across six sensor datasets validates the prowess of HiSS, showcasing an unequivocal enhancement in prediction accuracy. Moreover, the research explores the model's compatibility with existing data-filtering techniques and its scalability to smaller datasets, affirming its adaptability and efficiency.

Theoretical and Practical Implications

The HiSS model introduces a paradigm shift in approach towards continuous sequence prediction tasks, emphasizing the utility of hierarchical temporal processing. Theoretically, it underscores the potential of tailored architectures in managing the complexities of sequential sensor data. Practically, its efficacy in dealing with data-dependant drift, noise, and other sensor-specific challenges holds promising implications for domains requiring real-time analysis of sensory data, such as robotics, medical diagnostics, and environmental monitoring.

Future Directions and Conclusion

Despite its notable achievements, HiSS, as a harbinger in the domain of continuous sequence prediction, opens avenues for further exploration. Determining optimal chunk sizes and extending the model to encompass a broader range of sensors are potential directions for future research. By pushing the boundaries of what's achievable in continuous sequence prediction, HiSS not only sets a new benchmark but also paves the way for more nuanced and sophisticated approaches to understanding and predicting the physical world through sensor data.