Extended Data Fig. 1: Related to Fig. 2.

A Teacher as in Fig. 2. The students are trained on a varying number of recorded neurons M. B Average error in the recorded and unrecorded activity between teacher and students. C Left: Error in the network activity for a given student network in a given trial, when M = 20 neurons are recorded. Right: Error in the task-related readout signal. While the recorded neurons have low error, the unrecorded neurons in the student display large deviations. D Analogous to C, when more neurons are recorded, M = 60. In this case, the activity of unrecorded neurons and the readout are well predicted. E Teacher network from panel A receives a strong external two-dimensional time-varying input, fed to a subset of 100 excitatory neurons. Middle: The dimensionality of the activity, measured by the participation ratio, increases with the input. F Error in unrecorded neuronal activity after training student networks to match the input-driven teacher (color dots), compared to the non-driven teacher (grey dots). Fewer recorded neurons are required to predict activity of unrecorded neurons in this example input-driven network. G Input-driven teacher network with different levels of connectivity sparsity and gain heterogeneity. Teachers have E-I random connectivity, and are initialized at the fixed point. A positive input of unit strength is delivered to 5 excitatory neurons. Recorded neurons correspond to excitatory neurons, while unrecorded neurons can be both excitatory or inhibitory. Teacher networks are generated with different fractions f of non-zero weights, and different ranges for the uniformly distributed gains. Both gains and biases are trained in the students. H Error in unrecorded activity after training vs number of recorded neurons, for different level of sparsity f and gain distributions. While the overall magnitude of the error changes for different gain strengths, the decay of the error as a function of M does not change.