Despite their success, traditional V AEs rely on continuous latent variables, which deviates sharply from the discrete nature of biological neurons.

However, since this decoder effectively approximates thenth derivative of the input vector, it is very sensitive to noise. In our framework, the input is often very noisy, since it corresponds to the converging points of different learning traces. In this section we describe two linear decoders that differ from that in [35] and are more noise-resilient. A.9 and A.10 is crucial for long temporal horizons, since regularization causes the overall magnitude of the recoveredτ-space to decrease asτ increases3. Normalization amends thedecreasing magnitude problem bymaking theτ-space to sum to 1 for everyτ.

The encoder contains three linear layers with output size [d,k,k], each but the last layer is followed by batch normalization, witheps = 0.00005 and momentum=0.1,andtheReLU Thedecoder contains threelinear layers withoutput size [k,k,d] where each but the last layer contains a Batch normlization and the ReLu activation similar asabove. Following the standard linear evaluation procedure inself-supervised learning works (32;34),we used an one linear layer network as the linear decoder for the decoding accuracy. We used the neural activity dataset that is collected from two rhesus macaque monkeys (Chewie and Mihi). They were trained to move the computer cursor to reach a target on a screen.

However, existing linear techniques for neural decoding may not fully reveal or exploit the fidelity of the neural signal.

Charge carrier dynamics critically affect the efficiency and stability of organic photovoltaic devices, but they are challenging to model with traditional analytical methods. We introduce β - Linearly Decoded Latent Ordinary Differential Equations ( β - LLODE), a machine learning framework that disentangles and reconstructs extraction dynamics from time - resolved charge extraction measurements of P3HT:PCBM cells. This model enables the isolated analysis of the underlying charge carrier behaviour, which was found to be well described by a compressed exponential decay. Furthermore, the learnt interpretable latent space enables simulation, including both interpolation and extrapolation of experimental measurement conditions, offering a predictive tool for solar cell research to support device study and optimisation. Introduction A detailed understanding of charge carrier dynamics in organic photovoltaic (OPV) devices is critical to optimising for power conversion efficiency and long - term stability, but remains difficult to model due to complex, incompletely understood processes [1 ].

NER learns to regress continuous representations of neural dynamics (i.e., embeddings) on continuous movements.

Evaluation of deep Gaussian V AEs (averaged over 5 trials) on real-valued MNIST. All results in the paper are now consistent with this. We are grateful for your comments and suggestions. We agree that the experiments and theory could have been better aligned. However, the non-linear model has some unexplained behaviours -- e.g. the best model has some posterior collapse.