Learning neural evolution operators: from decoding to identifiable causal state-space models

Neural encoding, decoding, and representation-learning approaches have substantially advanced our ability to predict sensory, behavioral, and cognitive variables from neural population activity. At the same time, dynamical systems approaches increasingly model neural computation as the evolution of latent population states governed by recurrent interactions and structured state transitions. Although these frameworks are often presented as competing paradigms, both can successfully reproduce neural observations while still failing to uniquely identify the computational mechanisms implemented by biological circuits. This perspective argues that this reflects a central unresolved challenge in systems neuroscience: observational recordings alone often provide insufficient constraints for distinguishing mechanistically valid neural dynamics from observationally equivalent alternatives. Accordingly, this perspective proposes a unifying framework integrating representational models, latent neural dynamics, identifiability analysis, and perturbation-based validation within a common mechanistic perspective. First, neural representations are discussed as potentially emerging from temporally localized projections of underlying latent dynamical processes evolving on low-dimensional manifolds. Second, recent advances in learning neural evolution operators using recurrent neural networks, latent state-space models, and dynamical system reconstruction methods are reviewed. Third, it is argued that latent trajectories and predictive performance alone do not guarantee mechanistic validity because multiple latent organizations and evolution operators may remain observationally equivalent despite implying distinct causal mechanisms. Finally, perturbation, intervention, and closed-loop neural interfaces are discussed as additional causal constraints capable of falsifying candidate dynamical explanations under targeted manipulation. Across these four principles, the central challenge in modern neuroscience is framed not simply as decoding neural activity or reconstructing latent trajectories, but as determining which inferred dynamical operators remain predictive under intervention and how perturbation can reduce the admissible class of observationally equivalent candidate mechanisms. From this perspective, evolution operators become experimentally testable hypotheses rather than purely descriptive latent models. Integrating latent dynamical modeling with perturbation-based validation may therefore support a transition from prediction-oriented neuroscience toward perturbation-constrained mechanistic dynamical neuroscience.