Extended Data Fig. 5: Latent stability and neural decoding.

It has previously been reported that stable neural activity can be identified in a common latent space even when there is a turnover of recorded neurons⁴³. As we show in Fig. 2e, this can be consistent with either stable or drifting single unit activity. While we have already shown a high degree of similarity for single neurons, here we investigate whether ‘aligning’ the neural activity between sessions can identify a common subspace with even higher similarity. These analyses require simultaneous recording of a large population of neurons, which in general was not the case in our dataset (c.f. Fig. 3c). Instead, we considered a single week of recording in a single animal with recordings from DLS (day 8-14 in Fig. 3c), where we simultaneously recorded 16 neurons firing at least 10 spikes during the task on each day. (a) We first computed the similarity as a function of time difference as the correlation between single neuron PETHs, averaged across neurons (black line). We then proceeded to align the neural activity on each pair of days using CCA and computed the similarity in the resulting aligned space as the average correlation across all dimensions. This CCA-aligned similarity was generally lower than the similarity averaged over individual neurons, suggesting that the neuron-aligned coordinate system is more stable than the CCA-aligned alternative (note that CCA performs a greedy alignment rather than finding the optimal alignment, which would provide an upper bound on the single neuron similarity). Shadings indicate standard error across all pairs of days with a given time difference. (b) We proceeded to consider population decoding of behavior from neural activity, using the same data as in a. We fitted a linear model to predict the trajectories of the left and right forelimbs from neural activity on each day using crossvalidated ridge regression, and we tested the models on data from all other days. Here, we plot the performance as a function of time difference, averaged across the vertical and horizontal dimensions and both forelimbs. Line and shading indicate mean and standard error across pairs of days with a given time difference. (c) We proceeded to compute stability indices for the data in b to see whether there was a significant negative trend. We bootstrapped the individual datapoints (before taking the mean) 10,000 times and estimated stability indices from each surrogate dataset. The distribution over the resulting stability indices was not significantly smaller than 0 (one-sided p = 0.48). (d) While the analysis in a suggests that the single neurons provide a good coordinate system for stable representations, it does not address the question of whether an aligned low-dimensional manifold can provide better decoding⁴³. We therefore proceeded to train a population decoding model as in b, but where the decoder was trained on the top 10 PCs from a single day and tested on the top 10 PCs from every other day after alignment via CCA⁴³ (blue dashed line). We found that decoding performance from this aligned latent space was almost identical to the decoding performance from raw neural activity (black line). This provides further evidence that the stable aligned dynamics identified in previous work are the result of stable single unit tuning curves. Shading indicates standard error across pairs of days with a given time difference. (e) Finally, we considered how the relationship between kinematics and neural activity changed over time at a single neuron level. We used the GLM discussed in Fig. 5e to predict neural activity from behavior. This GLM was trained on the first day of recording for each neuron and tested on each subsequent day. The figure shows the correlation between the predicted firing rate and true spike count as a function of time difference, averaged across all neurons which were recorded for at least a week and had a training correlation of at least 0.1. Blue indicates neurons recorded from DLS (n = 58 units), red from MC (n = 61 units), and shadings indicate standard errors across neurons. Dashed lines indicate the average correlation across neurons from hold-one-out crossvalidation on all trials from the first day of recording.