The geometry of representational drift in natural and artificial neural networks
Fig 3
Passive data: Drift geometry and classifier persistence.
[a-c] How various drift metrics depend on PC dimension of the earlier session’s variational space. Metrics are plotted as a function of PCi’s ratio of variance explained, vi, across all stimulus groups. Colored curves are linear regression fits and shaded regions (often too small to see) are all fits within the 95% confidence intervals of slope and intercept. (a) Magnitude of drift along PCi direction relative to full (L2) magnitude of drift. (b) Angle of drift with respect to PCi direction. (c) Post-drift variance explained along PCi direction, black dotted line is equality. Linear regression fit to log(var. exp.). [d-f] Various metrics and how they change between sessions. The darker dots/lines always show mean value with error bars of ± s.e. The lighter color dots show data from individual mice. (d) The variational space overlap between earlier and later stimulus groups, 0 ≤ Γ ≤ 1. The “–” marker indicates the average value of Γ for randomly oriented variational spaces of the same dimensions. (e) Angle between linear support vector classifiers (normal vector) trained on distinct sessions. The purple dotted line is the average angle between different sessions. (f) Cross classification accuracy as a function of trained data session (Class.) and tested data session (Data). The “–” marker shows average classification accuracy when SVCs are randomly rotated by same angle that separates respective sessions’ classifiers. (g) The relative cross accuracy, see Eq (14), as a function of the angle of a random SVC rotation. The purple dotted line is again the average angle found between drift sessions, also shown in (e).