The architecture of LFADS is described in more detail in the original publication [1]. We used a dimension of 64 for the initial condition (IC) encoder, controller input (CI) encoder, initial condition, and controller. The controller output dimension was 2 and the generator dimension was 100. The latent factor dimensionality was 40 for the maze dataset and 100 for both calcium datasets. LFADS models benefit from appropriate hyperparameter (HP) tuning, as optimal HP combinations can vary from dataset to dataset [2, 3]. As mentioned in the main text, we use AutoLFADS [3] to ensure appropriate HP tuning. The framework combines a regularization strategy (coordinated dropout; CD [2]) with a largescale framework for optimizing model hyperparameters (population-based training; PBT [4]).

Autoregressive (AR) models remain widely used in time series analysis due to their interpretability, but convencional parameter estimation methods can be computationally expensive and prone to convergence issues. This paper proposes a Neural Network (NN) formulation of AR estimation by embedding the autoregressive structure directly into a feedforward NN, enabling coefficient estimation through backpropagation while preserving interpretability. Simulation experiments on 125,000 synthetic AR(p) time series with short-term dependence (1 <= p <= 5) show that the proposed NN-based method consistently recovers model coefficients for all series, while Conditional Maximum Likelihood (CML) fails to converge in approximately 55% of cases. When both methods converge, estimation accuracy is comparable with negligible differences in relative error, R2 and, perplexity/likelihood. However, when CML fails, the NN-based approach still provides reliable estimates. In all cases, the NN estimator achieves substantial computational gains, reaching a median speedup of 12.6x and up to 34.2x for higher model orders. Overall, results demonstrate that gradient-descent NN optimization can provide a fast and efficient alternative for interpretable AR parameter estimation.

Recent insights have revealed that rate-coding is a primary form of information representation captured by surrogate-gradient-based Backpropagation Through Time (BPTT) in training deep Spiking Neural Networks (SNNs).

Both of the techniques assume bitwise access to the oracle as a classical function.

Computing gradients through backpropagation is crucial to the success of modern deep neural networks.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/