Comparison of FORCE trained spiking and rate neural networks shows spiking networks learn slowly with noisy, cross-trial firing rates
Fig 3
FORCE can train both spiking LIF and LIF-matched rate networks.
Spiking LIF and parameter matched LIF-matched rate networks are trained on different tasks. The network outputs and sample neuron firing rates are overlaid. Spiking LIF values are plotted with a solid line, LIF-matched rate values are plotted with a dotted line, and supervisors with a thick grey line. A FORCE training can be broken down into three phases: pre-learning, learning, and post-learning. Before learning, the network dynamics are spontaneously chaotic. During learning, the network output is forced to match the target output, and the network dynamics are stabilized accordingly. After learning, if the training is successful, the network output and dynamics will continue to reproduce those stabilized during learning without any further weight updates. The green line indicates the change in the Euclidean norm of the decoder. Across all three stages of learning, the neural dynamics and network outputs of the spiking and rate networks are highly correlated. B Networks of 2000 neurons were trained to reproduce the random kick pitchfork system using 120s of training, with 27s of testing displayed. C Networks of 2000 neurons were chaotically initialized, then trained to reproduce the product of a 1Hz and 2Hz sine wave using 5s of training, with 5s of testing displayed. D–E Networks of 2000 neurons were chaotically initialized, then trained to reproduce the first bar of the song “Ode to Joy" by Beethoven. Each of the 5 notes in the first bar was converted to a component of a 5-dimensional target signal. Quarter notes were represented by the positive portion of a 2Hz sine wave, and half notes by the positive portion of a 1Hz sine wave. Training consisted of 80s or 20 bar repetitions, while the testing displayed consists of 4s or 1 repetition. F–G Networks of 5000 neurons were randomly initialized into chaos, then trained to reproduce the global dynamics of the Lorenz system with parameters ,
, and
. To train the networks, 200s of Lorenz target trajectory was used, and then 200s of testing output is displayed. Each of the 3 components of the Lorenz system was used to train a component of the 3-dimensional network output.