Self-supervised contrastive learning performs non-linear system identification (2410.14673v2)

Abstract: Self-supervised learning (SSL) approaches have brought tremendous success across many tasks and domains. It has been argued that these successes can be attributed to a link between SSL and identifiable representation learning: Temporal structure and auxiliary variables ensure that latent representations are related to the true underlying generative factors of the data. Here, we deepen this connection and show that SSL can perform system identification in latent space. We propose dynamics contrastive learning, a framework to uncover linear, switching linear and non-linear dynamics under a non-linear observation model, give theoretical guarantees and validate them empirically.

• The paper presents DynCL, which leverages self-supervised contrastive learning to achieve identifiability of latent spaces and non-linear dynamics.
• The methodology integrates temporal structures and auxiliary variables to improve predictive accuracy, especially in noisy environments.
• Empirical results demonstrate that DynCL effectively distinguishes between switching linear and non-linear dynamics, offering robust system identification.

Analyzing "Self-supervised contrastive learning performs non-linear system identification"

Self-supervised learning (SSL) has demonstrated substantial efficacy across various domains, achieving noteworthy success in connecting latent representations to true generative data factors. The paper discusses the development and theoretical underpinnings of DynCL, a novel SSL framework for system identification in latent space. This work primarily focuses on identifying linear, switching linear, and non-linear dynamics, offering both theoretical assurances and empirical validations of its approach.

Framework and Theoretical Insights

The identification of dynamics from observational data remains a challenging task in machine learning, and the paper proposes addressing this through self-supervised contrastive learning (CL). DynCL leverages temporal structure and auxiliary variables to refine latent representations, thus improving system identification capabilities. The dynamical systems are formulated using latent and observable variables, control signals, and external noise within a discrete-time framework, and the objective is to infer non-linear functions driving system evolution.

In theoretical contributions, the paper extends existing results on identifiability in non-linear ICA, establishing that SSL can indeed identify system dynamics in a latent space. By leveraging symmetry-breaking via distinct encoders and dynamics models, DynCL achieves identifiability of latent spaces and dynamics. Additionally, the framework includes parameterization techniques such as $\nabla$-SLDS for piecewise linear approximation, offering practical methods to capture complex non-linear dynamics.

Empirical Validation and Results

Empirical evaluations were conducted against benchmark datasets simulating different dynamical systems. DynCL is demonstrated to accurately identify dynamics and latent structures of systems with varying linearity and noise. Compared to baselines, DynCL shows superior predictive accuracy, particularly in cases with substantial system noise where other models falter. In switching linear dynamics, DynCL notably achieves almost perfect latent and dynamics identification, showcasing the robustness and applicability of the proposed methods.

Discussion and Implications

The paper significantly advances the understanding of SSL in system identification. By combining contrastive learning with explicit modeling of dynamics, it provides a more interpretable approach compared to other non-generative inference algorithms. This work means SSL can now be applied to more complex systems, bridging the gap between theory and real-world applications, such as neuroscience and engineering.

Moreover, the study highlights the importance of carefully designed dynamics models within SSL frameworks, showcasing their central role in accurate system identification. However, there remains room for exploration, particularly in applying such frameworks to real-world datasets where dynamics are inherently more complex and multi-faceted.

Future Directions

Potential future work could explore extending the DynCL framework's capabilities to broader classes of non-linear systems or improving the efficiency of approximations used for dynamics modeling. Integration with other innovative architectures such as neural ODEs or S4 models may enhance its efficacy further. Moreover, the scalability of DynCL on real-world large-scale datasets would be an important area for empirical evaluation and further optimization.

In conclusion, this paper provides valuable theoretical insights and practical solutions in using SSL for non-linear system identification. DynCL represents an important step forward, with significant implications for advancing machine learning approaches in contexts where understanding and modeling underlying dynamics is crucial.