InputDSA : Demixing then comparing recurrent and externally driven dynamics

Area of Science:

• Dynamical systems analysis
• Computational neuroscience
• Machine learning

Background:

• Comparing dynamical systems is crucial for understanding emergent computations in neural systems and deep learning.
• Existing methods like Dynamical Similarity Analysis (DSA) focus on recurrent dynamics but neglect input effects.
• Real-world systems are rarely autonomous, necessitating methods that account for input-driven dynamics.

Purpose of the Study:

• To introduce InputDSA (iDSA), a novel metric for comparing intrinsic and input-driven dynamics of dynamical systems.
• To extend the DSA framework to incorporate the influence of external inputs on system dynamics.
• To provide a robust method for comparing partially observed, input-driven systems from noisy data.

Main Methods:

• InputDSA (iDSA) extends Dynamical Similarity Analysis (DSA) by estimating and comparing input and intrinsic dynamic operators.
• A variant of Dynamic Mode Decomposition with control (DMDc) based on subspace identification is employed.
• The method demonstrates robustness with surrogate inputs when true inputs are unknown.

Main Results:

• InputDSA successfully compares partially observed, input-driven systems using noisy data.
• High-performing Recurrent Neural Networks (RNNs) trained with Deep Reinforcement Learning show dynamic similarity.
• Neural data from rats performing a cognitive task revealed a transition from input-driven to intrinsically-driven decision-making.

Conclusions:

• InputDSA (iDSA) is a robust and efficient method for comparing dynamical systems, considering both internal dynamics and external input effects.
• The findings highlight the utility of iDSA in analyzing complex systems like artificial neural networks and biological neural data.
• iDSA offers a powerful tool for understanding how external factors shape system behavior in neuroscience and control theory.