Fig. 5.

Dendritic balance prevents learning of redundant representations for inhibitory transmission delays. (A) Decoder loss of networks of 200 neurons coding for natural scenes for different inhibitory transmission delays δ. For transmission delays longer than 0.3 ms, Hebbian-like learning in SB networks leads to highly inefficient representations and large decoder loss. In contrast, for networks learning with DB, the decoder loss increases only moderately even for long transmission delays. The results are robust with respect to the stochasticity of firing $\mathrm{\Delta }u$ and the firing rate ρ (SI Appendix, Fig. S8). (B) Selection of learned weights for a transmission delay of 1 ms. DB learns similar weights as before (Fig. 4D), while SB leads to a collapse of representations. (C–E) To illustrate the effect of feedforward plasticity, we repeated the MNIST experiment in Fig. 3 with long transmission delays of 3 ms (before, 0.1 ms in Fig. 3). (C) First, only recurrent connections were learned (1); later, feedforward weights were learned (2). As before, recurrent plasticity decorrelates responses and decreases the decoder loss. When feedforward plasticity was turned on, Hebbian-like plasticity (SB) learned worse representations than random feedforward weights, which is indicated by the increase in decoder loss. In contrast, our model with DB learned improved representations with substantially reduced decoder loss. (D) The poor performance of the SB model is a consequence of highly synchronous spiking responses to the inputs, whereas neurons fire asynchronously in the model with DB. (E) Neurons in the SB model learn overly similar feedforward weights, whereas neurons with dendritic balance learn feedforward weights that capture the input space well. (F–H) This effect is still present when input signals show fast changes in time. Here, 100 coding neurons firing at 5 Hz encode a speech signal. (F) Spectrogram of the signal presented in 25 frequency channels. (G) As can be seen in the reconstructed signal (Top), SB finds a good encoding for instant inhibition ($\text{loss}=0.06$), but even for extremely small delays of 0.05 ms the learned representations collapse, leading to pathological network behavior and bad encoding performance ($\text{loss}=0.23$). (H) In contrast, DB finds a similar encoding for both instant inhibition ($\text{loss}=0.057$) and inhibitory delays of 0.05 ms ($\text{loss}=0.06$).