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The advent of large-scale neural recordings has enabled new methods todiscover the computational mechanisms of neural circuits by understanding therules that govern how their state evolves over time. While these \textit{neuraldynamics} cannot be directly measured, they can typically be approximated bylow-dimensional models in a latent space. How these models represent themapping from latent space to neural space can affect the interpretability ofthe latent representation. We show that typical choices for this mapping (e.g.,linear or MLP) often lack the property of injectivity, meaning that changes inlatent state are not obligated to affect activity in the neural space. Duringtraining, non-injective readouts incentivize the invention of dynamics thatmisrepresent the underlying system and the computation it performs. Combiningour injective Flow readout with prior work on interpretable latent dynamicsmodels, we created the Ordinary Differential equations autoencoder withInjective Nonlinear readout (ODIN), which captures latent dynamical systemsthat are nonlinearly embedded into observed neural activity via anapproximately injective nonlinear mapping. We show that ODIN can recovernonlinearly embedded systems from simulated neural activity, even when thenature of the system and embedding are unknown. Additionally, ODIN enables theunsupervised recovery of underlying dynamical features (e.g., fixed points) andembedding geometry. When applied to biological neural recordings, ODIN canreconstruct neural activity with comparable accuracy to previousstate-of-the-art methods while using substantially fewer latent dimensions.Overall, ODIN's accuracy in recovering ground-truth latent features and abilityto accurately reconstruct neural activity with low dimensionality make it apromising method for distilling interpretable dynamics that can help explainneural computation.

Expressive dynamics models with nonlinear injective readouts enable reliable recovery of latent features from neural activity